howard b. - petroleum engineers handbook, part 3

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Chapter 21

Crude Oil Properties and Condensate Properties and Correlations Paul Buthod, U. of Tulsa*

Introduction

All crude oils are composed primarily of hydrocarbons, which are made by the combination of the elements carbon and hydrogen. In addition, most crudes contain sulfur compounds and trace quantities of oxygen, nitrogen, and heavy metals. The difference in crude oils is caused by the amount of sulfur compounds and by the types and molecular weights of the hydrocarbons making up the oil.

The hydrocarbons found in crude oil range in size from the smallest molecule, methane, which contains 1 atom of carbon, to the largest ones, which contain nearly 100 atoms of carbon. The types of hydrocarbon compounds are paraffin, naphthene, and aromatic, found in raw crude, and olefin and diolefin, which are sometimes found in refined products after thermal treatment. Since any crude oil will have several thousand different compounds in it, it has been impossible so far to develop exact analyses of the actual compounds present. Three methods of reporting analyses are available-ultimate analysis, chemical analysis, and evaluation analysis.

Ultimate analysis lists the composition in percentages of the elements carbon, hydrogen, nitrogen, oxygen, and sulfur. This tells very little about the type of compounds present or the physical characteristics of the oil. It is useful, however, in determining the amount of sulfur that must be removed. Table 21.1 shows the ultimate analysis of several crude oils.

Chemical analysis gives composition in percentage of paraffin, naphthene, and aromatic-type compounds present in the crude. This type of analysis can be determined with fair accuracy by means of chemical reaction and solvency tests. An analysis of this sort gives an idea of the usefulness of refined products but does not give any

‘This author also wrote the tiginal chapter on this topic in the 1962 edation.

means of predicting the amount of various refined products. Table 2 1.2 gives the chemical analysis of several fractions of four crude oils.

The crude-oil evaluation consists primarily of a fractional distillation of the oil followed by physical- property tests (for parameters such as gravity, viscosity, and pour point) on the distillation products. Since the primary means of separating products in the refinery is fractionation, this analysis makes it possible to predict yields of refined products and physical properties studied in the evaluation. The evaluation curves shown in Fig. 2 1.1 make it possible to predict the physical properties of the refined products. As an example of the use of evaluation curves, Table 2 1.3 shows product yields and properties when a refinery is operated for maximum gasoline yield, and Table 2 1.4 shows product yields and properties when the objective is to produce lubricating oils and diesel fuel.

Since the early 1970’s, much research has-been performed on the use of the gas chromatograph to generate simulated distillations. This has the advantage of producing crude-oil evaluation curves with very small samples of crude and in a period of about an hour, compared with about a gallon of crude for a fractional distillation column and about 2 days for the analysis. The simulated distillation is called ASTM Test Method D2887. I

Base of Crude Oil

Since the beginning of the oil industry in the U.S., it has been convenient to separate crude oils into three broad classifications or bases. These three, paraffin, intermediate, and naphthene, are useful as general classifications but lead to ambiguity in many instances. Because a crude may exhibit one set of characteristics for

21-2 PETROLEUM ENGINEERING HANDBOOK

TABLE Pl.l-ULTIMATE CHEMICAL ANALYSES OF PETROLEUM

Specific Component

Gravity Temperature WI Petroleum -r PC) C H N 0 S - - -- -

Pennsylvania pipeline 0.862 15 85.5 14.2 Mecook, WV 0.897 0 83.6 12.9 3.6 Humbolt, KS 0.912 85.6 12.4 0.37 Healdton, OK 85.0 12.9 0.76 Coalinga, CA 0.951 15 86.4 11.7 1.14 0.60 Beaumont, TX 0.91 85.7 11.0 2.61 l 0.70 Mexico 0.97 15 83.0 11 .o 1.7* 4.30 Baku, USSR 0.897 66.5 12.0 1.5 Colombia, South America 0.948 20 65.62 11.91 0.54

‘Combined mtrogen and oxygen.

TABLE 21.2-CHEMICAL ANALYSES OF PETROLEUM, %

Grozny Grozny (“Paraffin- Oklahoma California (“High Paraffin”) Free Upper Level”), (Davenport), (Huntmgton Beach),

Fraction 45.3% at 572OF

(“0 Aromatic Naphthene Paraffin

140 to 203 3 25 72 203 to 252 z 30 65 252 to 302 35 56 302 to 392 14 29 57 392 to 482 18 23 59 482 to 572 17 22 61

40.9% at 572OF

Aromatic Naphthene Paraffin

4 31 65 8 40 52

13 52 35 21 55 24 26 63 11 35 57 8

64% at 572OF

Aromatlc Naphthene Paraffin

5 21 73 7 28 65

12 33 55 16 29 55 17 31 52 17 32 51

Base

paraffin paraffin mixed mixed

naphthene naphthene naphthene

34.2% at 57Z°F

Aromatic Naohthene Paraffin -A

i 31 46 65 46 11 64 25 17 61 22 25 45 30 29 40 31

TABLE 21.3-EVALUATION WHEN OPERATING PRIMARILY FOR GASOLINE’

Material

Gas loss Straight-run gasoline (untreated) Catalytic charge

V&breaker charge or asphalt Crude oil

Percent Distilled Gravity Basis Range Midpoint Yield (OAPI) Other Properties ~-

0 to 1.3 1.3 54.5 octane number 1.3 to 32 16.6 30.7 56” 390DF ASTM endpoint7

900°F cut 32 to 80.5 56.2 48.5 28.8 165OF aniline point or 47.5 diesel index

remainder 80.5 to 100 19.5 6.4$ 110 penetration 100.0 32.0 11.65 characterization factor

‘Topping follwed by YaWUrn flashing to produce a gas 011 for catalflic cracking. The Cycle stcck IrOm catalytic cracking is thermally cracked along wtth the asphalt or vis- breaker chargestock.

“Average gravity from instantaneous curve of API gravity. ?At about 400aF endpoint the truebOiling.pCint cut point is about 2PF higher than the ASTM end point *By a material balance.

TABLE 21.4-EVALUATION WHEN OPERATING PRIMARILY FOR LUBRICATING-OIL STOCK0

Percent Distilled API Material

Viscosity, Basis Range Midpoint Yield Gravity SU’S Other Properties

Gas loss 0 to 1.3 -13 Light gasoline (untreated) 300 EPb 1.3 lo 21.0 10.5 19.7 61.2C 63.8 octane numberd Reforming naphtha 445 EPb 21 .O to 38.5 29.7 17.5 41.3e 0.16% sulfur Diesel fuel 156 aniline point 38.5 to 56.5 47.5 18.0 32.1 Light lube or cracking stock

41 (estimated) 50 diesel Index; 0.82% sulfur remainder 56.5 to 74.9 65.7 18.4 25.9 145 at 100°F 1.49% sulfur’

Lube stock (untreated) 100 W’s viscosity at 2lOOF 74.9 to 80.9 77.9 6.0 19.1 100 at 210°F Asphalt 100 penetration 80.9 to 100.0 19.1 100 penetration at 77OFg Crude oil 100.0 32.0

CRUDE-OIL & CONDENSATE PROPERTIES & CORRELATIONS 21-3

TABLE 21.5-BASES OF CRUDE OILS’

API Gravity Approximate UOP* * at 60°F Characterization Factor

Low-Boiling High-Boiling Key Fraction Key Fraction Low- High- Part Part 1 2 Boiling Boiling

paraffin paraffin 40+ 30+ 12.2+ 12.2+ baraff in intermediate paraffin naphthene

intermediate paraffin intermediate intermediate intermediate naphthene naphthene intermediate naphthene paraffin naphthene naphthene

‘USBM, Repon 3279 (Sept. 1935). “Universal Oil Products Co.. Chicago

40+ 40+

33 to 40 33 to 40 33 to 40

33- 33- 33-

its light materials and another set for the heavy-lube fractions, the USBM has developed a more useful method of classifying oils.

Two fractions (called “key fractions”) are obtained in the standard Hempel distillation procedure. Key Fraction 1 is the material that boils between 482 and 527°F at atmospheric pressure. Key Fraction 2 is the material that boils between 527 and 572°F at 40 mm absolute pressure. Both fractions are tested for API gravity, and Key Fraction 2 is tested for cloud point. In naming the type of oil, the base of light material (Key Fraction 1) is named first, and the base of the heavy material (Key Fraction 2) is named second. If the cloud point of Key Fraction 2 is above 5”F, the term “wax-bearing” is added. If the pour point is below 5”F, it is termed “wax- free.”

Thus, “paraffin-intermediate-wax-free” would mean a crude that has paraffinic characteristics in the gasoline portion and intermediate characteristics in the lube portion and has very little wax. Table 21.5 shows the criteria used in establishing bases of oil by the USBM method.

Several attempts have been made to establish an index to give a numerical correlation for the base of a crude oil. The most useful of these is the characterization factor K developed in Ref. 2,

3% K=- Y ’

in which TB is the molal average boiling point (degrees Rankine) and y is the specific gravity at 60°F. This has been used successfully in correlating not only crude oils, but refinery products both cracked and straight-run. Typical numerical values for characterization factors are listed in Table 2 1.6.

In addition to the relationship between the characterization factor and the specific gravity and boiling point defined above, a number of other physical properties have been shown to be related to the chamcterization factor. Among these properties are viscosity, molecular weight, critical temperature and pressure, specific heats, and percent hydrogen.

Table 21.7 shows characterization factors for a

20 to 30 20- 30+

20 to 30 20-

20 to 30 30+ 20-

12.2+ 11.4 to 12.0 12.2 + 11.4-

11.5 12.0 to 12.2+ 11.4 12.1 to 11.4 to 12.1 11.4 12.1 to 11.4-

11.5- 11.4 to 12.1 11.5- 12.2+ 11.4- 11.4-

TABLE 21.6-TYPICAL CHARACTERIZATION FACTOR VALUES

Product Characterization

Factor

Pennsylvania stocks (paraffin base) 12.1 to 12.5 Mid-Continent stocks (intermediate) 11.8 to 12.0 Gulf Coast stocks (naphthene base) Cracked gasoline Cracking-plant combined feeds Recycle stocks Cracked residuum

11 .o to 11.6 11.5 to 11.8 10.5 to 11.5 10.0 to 11.0 9.8 to 11 .O

number of worldwide crudes and products and typical hydrocarbon compounds that have the same characterization factor as the oil in question.

Physical Properties Fig. 21.2 shows the relationship of carbon-to-

hydrogen ratio, average molecular weight, and mean average boiling point as a function of API gravity and characterization factor. The API Technical Data Book3 has published a number of correlations for physical properties of petroleum. For the most accurate data, this reference should be consulted.

When oil is heated or cooled in a processing operation, the amount of heat required is best obtained by the use of the specific heat. Fig. 21.3 shows the specific heat of liquid petroleum oils as a function of API gravity and temperature. This chart is based on a characterization factor of 11.8, and if the oil being studied is other than that, there is a correction shown at the lower right side of the chart. The number obtained for the specific heat should be multiplied by this correction factor. Certain paraffin hydrocarbons are also shown on the chart. No correction need be applied to these.

If vaporization or condensation occurs in a processing operation, the heat requirements are most easily handled by the use of total heats. Fig. 2 1.4 gives total heats of petroleum liquid and vapor, with liquid at 0°F as a reference or zero point. This eliminates the necessity of selecting a latent heat, specific heats of both vapor and liquid, and deciding at what temperature to apply the latent heat. Certain corrections must be applied for characterization factor and for pressure.


TABLE 21.7-CHARACTERIZATION FACTORS OF A FEW HYDROCARBONS, PETROLEUMS, AND TYPICAL STOCKS

Characterization Factor Hydrocarbons Typical Crude Oils Miscellaneous Products

14.7 14.2

13.85 13.5 to 13.6 13.0 to 13.2

12.8 12.7 12.6 12.55 12.5

12.1 to 12.5 12.2 to 12.44 12.0 to 12.2 11.9 to 12.2

propane propylene isobutane butane butane-l and isopentane hexane and tetradecened P-methylheptane and tetradecane pentene-1, hexene-1, and cetene 2,2,4-trimethylpentane hexene-2 and 1.3-butadiene 2,2,3,3tetramethyl butane 2,l l-dimethyl dodecadiene

11.9 11.8 to 12.1

11.85 11.7 to 12

11.75 11.7 11.6

11.5 to 11.8 11.5

hexylcyclohexane

butylcyclohexane octyl or diamyl benzene

11.45 ethylcyclohexane and 9-hexyl-l l-methylheptadiene 11.4 methylcyctohexane

11.3to 11.6 11.3 cyclobutane and 2,6,10,14tetramethyl hexadiene

Cotton Valley (LA) lubes

Pennsylvania-Rodessa (LA) Big Lake (TX) Lance Creek (WY) Mid-Continent (MC.) Oklahoma City (OK)

Fullerton (W. TX) Illinois; Midway (AR) W. TX; Jusepin (Venezuela) Cowden (W TX) Santa Fe Springs (CA) Slaughter (W. TX); Hobbs (NM) Colombian Hendrick and Yates (W. TX)

Elk Basin, heavy (WY) Kettleman Hills (CA) Smackover (AR)

Lagunillas (Venezuela) Gulf Coast light distillates

‘12.66 (range 12.1 to 13.65) calculated lrom factors of raw and dewaxed lube stocks

‘\ / (YIELD1

94.5 API adsorption gasoline Four Venezuelan paraffin waxes paraffin wax*: MC. 82.2 API natural gasoline CA 81.9 API natural gasoline

debutanized E. TX natural gasoline San Joaquin (Venezuela) wax distillate Panhandle (TX) lubes Six Venezuelan wax distillates paraffin-base gasolines Middle East light products cracked gasoline from paraffinic feeds E. TX gas oil and lubes light cycloversion gasoline from M.C. feeds Middle East gas oil and lubes cracked gasoline from intermediate feeds E. TX and IA white products cracked gas oil from paraffinic feeds catalytic cycle stocks from paraffinic feeds cracked gasoline from naphthene feeds Tia Juana (Venezuela) gas oil and lubes naphthenic gasoline: catalytic (cracked)

gasoline catalytic cycle stocks from MC. feeds cracked gasoline from hrghly naphthenrc feeds high-conversion catalytic cycle stocks from

parafbnic feeds typical catalytic cycle stocks liaht-ail coil thermal feeds catalytic cycle stocks from

11.7~characterization-factor feeds gasoline from catalytic re-forming

*.- , , 1 I I I I ,

IO 20 30 40 50 60 i-0 80 90 100” +

PERCENTAGE DISTILLED I I

Ftg. 21 .l-Evaluation curves of a 32.0°API intermediate-base crude oil of characterization factor 11.65.

CRUDE-OIL 8 CONDENSATE PROPERTIES & CORRELATIONS

1100

1000

900

800

700

600

500

400

300

200

100

21-5

9.0

8.0

7-o

6.0

IO 20 30 40 50

Fig. 21.2-Petroleum properties as a function of API gravity and characterization factor. Note: the parameters in the curves refer to the characterization factor.


m

7

/

L

o-

o-

o-

o-

9

3-

34 0

I i I I I I I I I I I I I I I I I I I III I

0 200 400 600 000 TEMPERATURE,“F

Fig. 21.3-Specific heats of Mid-Continent liquid oils with a correction factor for other bases of oils.

1,.,!,,,,,,., K =CHARACTEklZATION FACTOR = 3MOLAL AVG. BOILING POINT,“R

- / SPEClF(C G.,ilTYf~

/ I I I I I 000 900 , OF

1,000 1,100 1,200

Fig. 21.4-Heat content of petroleum fractions including the effect of pressure.


Gravity, API Sulfur, % Viscosity, SUS at lOOoF Date Characterization factor

At 25O“F At 450°F At 550°F At 750DF Average

Base Loss, % Gasoline

% at 300°F Octane number, clear Octane number, 3 cc TEL % to 400°F Octane number, clear Octane number, 3 cc TEL % to 450°F Quality

Jet stock % to 550°F API gravity Qualitv

TABLE 21.8-TRUE-BOILING-POINT CRUDE OIL ANALYSES

Location

Kerosene distillate %, 375 to 500°F API gravity Smoke point Sulfur, % Quality

Distillate or diesel fuel %, 400 to 700°F Diesel index Pour point Sulfur, O/O

Quality Cracking stock (distilled)

%, 400 to 900°F Octane number (thermal) API gravity Quality

Cracking stock (residual) % above 550°F API gravity API cracked fuel % gasoline (on stock) % gasoline (on crude oil)

Lube distillate (undewaxed) % 700 to 900°Fc Pour point Viscosity index Sulfur, % Quality

Residue, % over 900°F Asphalt quality

Atlanta, Smackover, AR

AR

20.5 2.30 270

413139

11.62 11.82 11.48 12.05 11.47 12.08 11.55 12.25 11.53 12.05

I IP 0 1.5

6.0 73.2a a9.0a 11 .o 66.0b

25.2d

14.4 good b

39.2d

48.5b

45.3d

24.1 41.9 good

56.3d 6.1 d 57.4 29.5b

9.5 38.0 16.0b 0.29b

15.0d 46.0 27.0b 0.06b

excellent

29.2 35.0d 19.7d 23.8 38.4d 28.0d 43.0b 76.0d mob 33.0 33.0b 48.5”

Ob high - 30.0b - 3.0 -25.ob 20.0b 0.82 b 0.15b 0.8b 2.56 0.35b 0.W’

48.2 51.4d 71.4b 64.5 b 25.7 35.5

75.9 42.2d 14.7 27.1 4.8 9.6

35.5 54.9 27.0 23.2

19.0 16.4d 22.2d

37.0b 2.45 b

40.8 good

113.0b 0.8b

excellent 7.9d

1.5b

57.0d excellent

(limestone)

44.5 0.48c

35

Kern River,

CA

10.7 1.23

6,000 +

11.13 11.15 11.15

N 0

0

1.2d

2.P

2.7d 32.5d 13.0b 0.38b

41.8d 7.5.6b 20.0 good

93.9d 9.1

a Simply aviation gasoline, not always 300-F cut point ’ Esbmated from general cotrelat~ons. ‘Sour oils (1.e.. oils containing more than 0.5 cu ft hydrogen sulfide per 100 gal before stabilization.) dApproximat.+d from data on other fractions of same oil. ‘Research method Octane number

Santa Maria,

CA

15.4 4.63 368

812154

Coalinga (East),

CA

20.7 0.51 178

Coalinga, CA

31.1 0.31 40

11.90 11.42 11.29 11.11 11.48

IN 0

11.28 11.20 11.23

N 3.0

11.5 11.53 11.59 11.72 11.58

I 1.1

7.0 1.2d 21 .6d 72.ob

13.2 59.8e 70.30 17.0

9.6d 31 .6d 67.0 b 66.7b

15.6d 35.6d good b excellent b

25.0 43.0 good

8.5 34.5

1.8d

29.3d 36.9

46.2d 46.0d good

16.0d Il.Od 34.0d 37.0 14.5b 17.0b o.ub 0.06b

39.8 75.6d 22.8

59.46

22.3 excellent

45.6d 70.4b 28.0 good

75.0

i:: 15.0 11.0

16.0

67.7d 52.P 11 .o 18.2 4.2 5.0

27.5 42.2 18.6 22.2

13.06 17.6d

0.67b 56.0b 0.43b

47.0 28.0d 21.7d excellent excellent good


Sampling pressure Sampling temperature Total fluid mol wt Liquid/gas ratio,

bbl per million scf Gas mol WI Gas analysis, mol%

Carbon dioxide Nitrogen Methane Ethane Propane i-butane n-Butane i-pentane n-Pentane Hexanes Heptane plus

Liquid gravity, OAPI Llquld mol wt

Liquid analysts

Light gasoline Naphtha Kerosene dtstlllate Gas oil Nonviscous lube Residuum and loss

TABLE 21.9-ANALYSIS OF CONDENSATE LIQUID AND GAS FROM SELECTED TEXAS ZONES

Chapel Hill Palusy Zone

645

Carthage Upper Carthage Old Ocean Old Ocean Pettite Lower Pettile Chenault Larson Seellgson Seeligson Zone Zone Zone Zone 21 D Zone 21 A Zone Saxet

607 632- 752 702 810 410 1087 82 70 67 85 85 80 85 25.03 19.62 20.19 20.76 20.51 20 64 20.63

88 21.34

88.74 16.23 29.28 29.33 28.71 29.88 24.48 41.33 20.18 18.25 18.25 18.70 18.17 18.42 18.69 18.89

0.794 0.695 0.646 0.448 0.468 0.130 0.200 0.299 1.375 1.480 1.967 0.370 0.414 0 075 0.253 0.281

76.432 89.045 88.799 87.584 90.162 89.498 88.731 86.733 7.923 4.691 3.363 5.312 4.067 4 555 5.224 4.816 4.301 1.393 1.536 2.302 1.616 1 909 1.795 2.873 1.198 0.401 0.335 0.584 0.464 0 465 0.488 0.836 1.862 0.394 0.583 0.630 0.390 0 493 0.452 0.788 0.937 0.283 0.302 0.416 0.274 0.286 0.172 0.583 0.781 0.191 0.254 0.207 0.123 0209 0.241 0.256 1.415 0.379 0.574 0.505 0.418 0 385 0.414 0.633 2.992 1.098 1.641 1.642 1.604 2015 2.032 2.102

Total 100.00 100.00 100.00 100.00 100 00 100.00 100.00 10000 71.8 61.0 64.8 54 0 47.6 52.7 52.1 60.0 68.64 91.51 81.55 85.93 110.07 94.49 103.22 68.73

Vol % OAPI Vol % OAPI ---__ 55.1 82.9 29.1 74.8 37.2 60.5 48.4 59 2 21.1 50.8 18.2 48.1

5.6 4.3 4.4

Vol % “API

40.7 76.6 47.0 59.3

7 9 47.6

Fig. 21.5-Approximate relation between viscosity, temperature, and characterization factor.

Vol % ‘=APl Vol % “API Vol % OAPI Vol % ‘API Vol % OAPI --- 21.2 71.2 14.7 70.9 22.6 70.1 20.7 68.4 35.7 73.6 55.3 52.9 36.9 52.2 47.7 53.4 49.5 53.1 47.6 55.9 15.0 42.6 17.4 42.1 15.9 43.8 16.1 43.0 10.0 44.9 3.8 37.8 21.3 36.6 7.3 37.4 7.2 37.0 2.4 38.2

7 4 29.8 4.7 2.3 6.5 6.5 4.3

An important physical property of petroleum necessary in studying flow characteristics is viscosity. Viscosity of petroleum is often reported in Saybolt Universal Seconds (SUS), derived from one of the common routine tests for oils. For engineering calculation, however, the viscosity should be obtained in centipoise. The relation between these two systems, according to the U . S Bureau of Standards, is

149.7 5 =0.219ts” --, Yo tsu

where FL0 = viscosity, cp

Yo = specific gravity of oil at measured temperature, and

tSU = Universal Saybolt viscosity, seconds.

An accurate correlation for viscosity is difficult, especially for viscous oils, but an estimate of viscosity may be obtained from Fig. 21.5. Four characterization factors are given, and interpolation must be made for other factors.

True-Boiling-Point Crude-Oil Analyses A number of true-boiling-point crude-oil analyses are included in Table 21.8. In addition to the gravity, viscosity, sulfur content, and characterization factor, there is a breakdown of typical products made from each crude. This table may be used either to estimate the value of the products listed or to plot and evaluate any set of products obtained (see Fig. 21.1). The table is separated first according to state, and within each group according to gravity.


When the quality of a product is indicated as good or excellent, it means not only that the quality is good but that it is present in normal amounts and that a salable product can be made without excessive treatment.

Table 21.9 shows the analysis of the gas and liquid phases after a stage separation of several condensates.

Nelson4 gives a compilation of 164 crudes and lists the gravity, characterization factor, sulfur content, and viscosity of each. Those tables include yields of typical refined products, along with their physical properties and an indication of their quality. A true-boiling-point curve can be generated by plotting the end points of these products against the cumulative volume percent yield. If the characterization factor is plotted on the same graph, the characterization factor at any instantaneous boiling point can be calculated. When instantaneous temperatures and characterization factors at different percents are known, specific gravity, API gravity, and viscosity curves may be estimated. Thus, evaluation curves such as those in Fig. 21 .l may be produced for any of the 164 crudes listed. A typical page of these data is shown in Table 21.8.

More recently, a series on evaluations of non-U.S. crude oils was published. 5 The format is similar to those in Nelson’s compilation, 4 but the physical properties are usually more complete. An example of an analysis from this series is shown in Table 21.10.

The USBM in Bartlesville, OK, began making distillation analyses before 1920. This laboratory [U.S. DOE Bartlesville Energy Technology Center (BETC)] has continued to evaluate crude oil up to the present time and has two publications6,7 that show the distillation data along with gravity and viscosity of the distilled fractions. They also show the percentage composition of the fractions in terms of paraffins, naphthenes, and aromatics. This set of tables uses the correlation index rather than characterization factor as a correlating number. In general, low correlation index (1,) numbers indicate highly paraffinic (pure paraffin hydrocarbons, I, =O). High numbers indicate a high degree of aromaticity (benzene, I,. = 100). The correlation index is defined as follows.

1,=413.7 y-456.8+87552/T~,

where y is the specific gravity of the fraction at 60°F and T, is the average normal boiling point in degrees Rankine .

All U.S. DOE analysis data have been built into the BETC Crude Oil Analysis Data Bank.8 The data retrieval system, Crude Oil Analysis System (COASYS),

is available by telephone hookup, and customers may search, sort, and retrieve analyses from the file. More than 30 keywords are available for searching; for example, YEAR, APIG, LOC, GEOL and SULF, allow a search on year analyzed, API gravity, location by state and coun- try, geological formation, and percent sulfur in the oil, respectively. Table 21.11 shows the type of information obtained in a typical analysis retrieved from a computer search by COASYS.

Bubblepoint Pressure Correlations* In the study of reservoir flow properties, it is important to know whether the fluid in the reservoir is in the liquid, ‘The rematnder of this chapter was written by M.0 Standing in the 1962 editon.

TABLE Pl.lO-TYPICAL CRUDE OIL EVALUATION, EKOFISK, NORWAY

Crude

Gravity, “API Basic sediment and water, vol% Sulfur, wt% Pour test, OC Viscosity, SUS at lOOoF Reid vapor pressure, psi at 1 OO°F Salt, lbm/l,OOO bbl Nitrogen compounds and lighter, ~01%

Gasoline

Range, OF Yield, VOWI Gravity, OAPI Sulfur, wt% Research octane number, clear Research octane number, - 3 mL tetraethyl

lead per gallon

Gasoline

Range, OF Yield, ~01% Gravity, OAPI Paraffins, ~01% Naphthenes. vol% Aromatics, ~01% (0 + A) Sulfur, wt% Research octane number, clear Research octane number, + 3 mL tetraethyl

lead per gallon

60 to 400 31.0 60.1

56.52 29.52 13.96

0.0024 52.0

76.0

Kerosene

Range, OF 400 to 500 Yield, ~01% 13.5 Gravity, OAPI 40.2 Viscosity, SUS at lOOoF 32.33 Freezing point, OF -38 Aromatics, VOW (0 + A) 13.1 Sulfur, wt% <0.05 Aniline point, OF 146.2 Smoke point, mm 21

Liaht Gas Oil

Range, OF 500 to 650 Yield, ~01% 15.7 Gravity, OAPI 33.7 Viscosity, SUS at lOOoF 43.83 Pour point, OF -25 Sulfur, wt% 0.11 Aniline point, OF 164.3 Carbon residue, Ramsbottom, wt% 0.08 Cetane index 56.5

TopPed Crude

Range, OF Yield, ~01% Gravity, OAPI Viscosity, SUS at 122OF Pour point, OF Sulfur, wt% Carbon residue, Ramsbottom, wt% Nickel, vanadium, ppm

650 + 38.8 21.5

80.25 -85 0.39

4.0 5.04, 1.95

36.3 1 .o

0.21 +20

42.40 5.1

14.5 1.0

60 to 200 10.7 77.2

0.003 74.4

90.0


TABLE 21.11-ADAPTATION OF BETC COMPUTER SEARCH PRINTOUT

Crude Petroleum Analysis: BETC Sample-B75008

lndentification

Webb W Field, Grant County, OK Red Fork, Des Moines, Middle Pennsylvanian-4,464 to 4,482 ft

General Characteristics

Gravity, specific [OAPI] Sulfur, wt% Viscosity, SUS

at 77OF at 1 OO°F

Pour point, OF Nitrogen, wt% Color

0.820[41.1] 0.24

42 39

<5 0.054

brownish-black

Distillation. USBM Method (First droo at 79OF)

Stage l-Distillation at Atmospheric Pressure 746 mm Hg

Gravity at

Fraction Cut Cumulative 6OOF Refraction Viscosity Cloud

Correlation Index Specific at lOOoF point wwo

Number (OF) Vol% VOW0 Specific API Index at 20°C Dispersion (SW (OF) Residuum Crude

-122 -1.5 ~~-

1 1.5 0.639 89.9 79.7 7 1.38560 126.3 67.2 17 1.39755 131.1 60.2 21 1.41082 133.0 55.4 22 1.42186 134.0 51.6 23 1.43039 134.7 48.8 22 1.43770 135.2 45.8 23 1.44415 135.5 42.8 24 1.45102 137.6 40.4 25 1.45771 138.0

2 167 2.2 3.7 0.670 3 212 5.5 9.2 0.712 4 257 7.4 16.6 0.738 5 302 5.8 22.4 0.757 6 347 6.7 29.1 0.773 7 392 6.0 35.1 0.785 8 437 59 41.0 0 798 9 482 6.8 47.8 0.812

10 527 5.1 52.9 0.823

Stage 2-Distillation continued at 40 mm Hg

11 392 7.2 12 437 6.2 13 482 5.6 14 527 4.8 15 572 5.1

Restduum Carbon Sulfur Nitrogen

17.0

Approximate Summary

Light gas 9.2 Gas+ Naoh 35.1 Kerosend Gas oil Non viscous lub Med viscous lub Viscous lub Restdue Loss

17.8 11.6

10.3

6.0 1.3

17.0 1.0

60.1 0.842 38.6 66.3 0.851 34.8 72.1 0.863 32.5 76.9 0.874 30.4 82.0 0.887 28.0

99.0 0.934 20.0

0.690 73.6 0.743 58.9 0.311 43.1 0.845 35.9

0.854 to 0.875 34.3 to 30.3

0.875 to 0.890 30.3 to 27.4 0.890 to 0.894 27.4 to 26.8

0.934 20.0

vapor, or two-phase state. With crude oils, the fluid may be subcooled liquid, but with some dissolved gas. Upon reduction in reservoir pressure, a point where the gas starts to come out of solution, called “bubblepoint pressure,” is reached. At this point the flow characteristics change. Some of the earliest work in this field was done by Lacey , Sage, and Kircher. 9

Several empirical correlations have been developed to predict the bubblepoint pressure, and some of these arc presented later.

Dewpoint-Pressure Correlations The dewpoint, like the bubblepoint, is characterized by a substantial amount of one phase in equilibrium with an infinitesimal amount of the other phase. At the dew-

30 1.46481 30 1.47017 33 1.47736 35 38

141.2 40 14

145.6 148.4 i: ii 96 76

179 98

7.1 1.4 0.67 0.235

5oto 100

loot0 200 >200

point, the liquid phase is at its minimum. In general, petroleum-reservoir systems that involve dewpoint behavior at reservoir conditions are characterized by (1) surface gas/oil ratios (GOR’s) greater than 6,000 cu ft/bbl in most instances; (2) lightly colored tank oils, usually straw-colored to light orange for reservoir systems at 3,000 to 5,000 psi but grading to brown for systems at 7,C00 psi and greater; (3) tank oil gravity usually greater than 45”API; and (4) methane content usually greater than 65 mol% .

Few dewpoint-pressure correlations of reservoir systems have been published. Sage and Olds” published a very general correlation of the behavior of several San Joaquin Valley, CA, systems. A correlation developed by Organick and Golding I1 is discussed in


TABLE 21.11-ADAPTATION OF BETC COMPUTER SEARCH PRINTOUT (continued)

Hvdrocarbon-tvpe Analvsis for Crude Petroleum Analvsis 875008

Fraction Number

1 2 3 4 5 a 7 a 9

10 11 12

vow0 of Specific Crude Gravity

1.5 0.639 2.2 0.670 5.5 0.712 7.4 0.738 5.8 0.757 6.7 0.773 6.0 0.785 5.9 0.798 6.8 0.812 5.1 0.823 72 0.842 6.2 0.851

Analvsis of Naotha Fractions

Fraction Vol% of P-N

Number Naphtha Paraffin A 2 7.1 92.9 3 23.7 76.3 4 38.6 61.4 5 44.0 56.0 6 43.6 56.4 7 43.6 56.4

Summarv Data for Blends

Correlation Index

- 7

17 21 22 23 22 23 24 25 30 30

Aromatics P-N * (VOW0 of (vol% of Fraction) Fraction)

0.0 100.0 2.4 97.6 5.9 94.1 7.5 92.5 9.1 90.9

10.2 89.8 10.6 89.4 10.7 89.3 11.5 88.5 10.4 89.6 13.0 87.0 16.2 83.8

Correlation Gravity index of P-N of P-N

- 0.639 5 0.665

13 0.702 16 0.727 17 0.746 17 0.761 16 0.772 16 0.784 17 0.796 18 0.809 22 0.825 21 0.831

Vol% of Fraction Fraction Number Aromatic Naphthenes Naphtha Paraffin Number of Total Rings per mol

6.9 90.7 12 1.4 0.3 1.1 22.3 71.8 14 1.7 0.6 1.1 35.7 56.8 40.0 50.9 39.2 50.7 39.0 50.4

Naphtha Blend Gas/oil Blend (Fractions 1 (Fractions 8 through 7) through 12)

VOW of Crude in Blend Aromatic, VOW of Blend Paraffin-Naphthene, vol% of Blend Naphthene, ~01% of Blend Paraffin, ~01% of Blend Naphthene, ~01% of P-N in Blend Paraffin, vol% of P-N in Blend Naphthene Ring, wt% of P-N in Blend Paraffin + Side Chains, ~1% of P-N in Blend

35.1 31.2 7.9 12.5

92.1 07.5 32.6 59.5 35.3 64.7 20.0 28.3 80.0 71.7

‘Parafbn-Naphtha

detail. Calculation of the dewpoint pressure by means of the composition and equilibrium ratios is discussed in Chap. 23.

Sage and Olds’ Correlation Laboratory studies on five San Joaquin Valley systems resulted in the correlation shown in Table 21.12. The basis for the 160°F data presented in this table is shown in Fig. 21.6. Although the five systems correlate within themselves, it is not known how representative the correlation is of systems from other fields. The data are reproduced here more as a guide to dewpoint-pressure behavior than as a means of estimating precise values of dewpoints.

primarily conditions that pertain to dewpoints, and it is

in this capacity that they will be discussed. The reader should be aware, however, that the charts also may be used to estimate critical pressure and temperature of the more volatile systems. The correlation has limited usefulness as a bubblepoint-pressure correlation because it covers primarily high-volatility systems. system. The short-cut method suffices for most calculations.

Calculation of Ts. The molal average boiling point of the system is defined as

Organick and Golding’s Correlation

TB=CyxTa, . . . . . . . . . . . . . . . . . . . . . . . . . . ...(l)

where y is the mole fraction and T, the atmospheric boiling point.

This correlation relates saturation pressure of a system Boiling points of the pure compounds (methane, directly to its chemical composition by geans of two ethane, nitrogen, carbon dioxide, etc.) are listed in generalized composition characteristics TB, the molal Chap. 20. The boiling point of the CT + fraction is taken average boiling point, and W,, a modified weight as the Smith and Watson I2 mean average boiling point average equivalent molecular weight. The saturation (MABP). The MABP can be calculated from the ASTM pressure may be either bubble-point pressure, dewpoint distillation curve, the procedure being first to calculate pressure, or the very special case of critical pressure. the ASTM volumetric average boiling point (VABP, “F) The 15 working charts (Figs. 21.7 through 21.21) cover and then to apply a correction factor to obtain the


TABLE Pl.lZ--RELATION OF DEWPOINT PRESSURE OF CALIFORNIA CONDENSATE SYSTEMS

Tank-Oil Gravity (“API)

lOOoF

52 54 56 58 60 62 64

16OOF

52 54 56 58 60 62 64

220°F

GOR (cu ft/bbl)

15,000 20,000 25,000 30,000

4,440 4,140 3,000 3,680 4,190 3,920 3,710 3,540 3,970 3,730 3,540 3,390 3,720 3,540 3,380 3.250 3,460 3,340 3,220 3,100 3,290 3,190 3,070 2,970 3,080 3,010 2,920 2,840

4,760 4,530 4,270 4,060 3,890 3,650 4,400 4,170 3,950 3,760 3,610 3,490 4,090 3,890 3,690 3,520 3,380 3,270 3,840 3,650 3,470 3,320 3,200 3,110 3,610 3,430 3,280 3,150 3,040 2,960 3,390 3,240 3,100 2,990 2,090 2,810 3,190 3,060 2,930 2,820 2,740 2,670

54 4,410 4,230 4,050 3,890 3,750 3,620 56 3,990 3,780 3,600 3,440 3,300 3,180 58 3,700 3,480 3,280 3,110 2,970 2,850 60 3,430 3,210 3,030 2,880 2,760 2,660 62 3,150 2,970 2,800 2,670 2,570 2,480 64 2,900 2,740 2,590 2,470 2,380 2,300

35,000 40,000 -~

3,530 3,420 3,410 3,310 3.280 3,180 3,140 3,060 3,010 2,930 2,880 2,800 2,770 2,700

TABLE 21.14-VALUES OF EQUIVALENT MOLECULAR

WEIGHTS FOR NATURAL- GAS CONSTITUENTS

Methane 16.0 Ethane 30.1 Propane 44.1 i-butane 54.5 n-Butane 58.1 i-pentane 69.0 n-Pentane 72.2 Hexanes 85 Ethylene 26.2 Nitrogen 28.0 Carbon dioxide 44.0 Hydrogen sulfide 34.1

MABP. The VABP is the average of the temperatures at which the distillate plus loss equals 10, 30, 50, 70, and 90% by volume of the ASTM charge, that is,

y, = TlOW + T30% + Tsox + T70% + T90%

5 ) . . . . (2)

where TI/ is the ASTM volumetric average boiling point. The correction to add to TV to obtain the mean average

boiling point is given in Table 2 1.13 as a function of TV and the slope of the ASTM curve between the 10 and 90% distilled points. In the correlation, r, is in degrees Rankine (i.e., “F+460).

Calculation of W,. The modified weight average equivalent molecular weight, W,, is a more complex function to evaluate. It is defined as the equivalent molecular weight multiplied by the summation of the weight fractions. The equivalent molecular weight of a paraffin hydrocarbon compound is its true molecular

9 2 hi 4500 5 z 4000

E

; 3500

z

x 3000

i

x

GAS-OIL RATIO, CU FT/EEiL

Fig. 21.6-Influence of gas/oil ratio and tank-oil gravity on retrograde dewpoint pressure at 1 60°F.

TABLE 21.13-CORRECTION TO ADD TO ASTM VOLUMETRIC AVERAGE BOILING POINT TO OB-

TAIN MEAN AVERAGE BOILING POINT

Slope of ASTM Curve (OF/%) ASTM VABP (OF)

10 to 90% points 200 300 400 500

2.0 -13- -11.5 - 10.5 -9.5 _._ 2.5 -17 - 15.5 - 14 -13 3.0 -22 -20 - 18.5 -17 3.5 -27 -25 -23 -21.5 4.0 -33 - 30.5 - 28.5 -26.5 4.5 - - - 34.5 -32.5

TABLE 21.15-CORRECTION TO ADD TO ASTM VOLUMETRIC AVERAGE BOILING

POINT TO OBTAIN CUBIC AVERAGE BOILING POINT

Slope of ASTM Curve (oF/%)

ASTM VABP (OF)

10 to 906/o points 200 400 600

2.0 - 5.0 -4.0 -3.5 2.5 - 6.5 - 5.5 -4.5 3.0 -8.0 -7.0 - 5.5 3.5 - 10.0 -8.5 - 7.0 4.0 - 12.5 -10.0 - 8.5 4.5 - 15.0 -12.5 - 10.0

weight. For other than straight-chain paraffin compounds (isoparaffns and olefins), the equivalent molecular weight is defined as the molecular weight that an n-paraffin would have if it boiled at the same temperature as the isopamftin or olefin in question. Values of the equivalent molecular weights for natural- gas constituents are given in Table 21.14.

The equivalent molecular weight of the C 7 + fraction is determined by calculating the Watson characterization factor, Kw , and using Fig. 21.7. Use of the characterization factor permits some account to be taken of the paraffinicity of the heavy-end material.

Kw= . . . . . . . . . . . . . . . . . . . . . . . . (3)

where Tc is the cubic average boiling point, “R. The cubic average boiling point (Fc) is obtained by adding the corrections in Table 21.15 to the ASTM TV, “F.


SLOPE OF ASTM DISTILLATION CURVE lo%-90%, OF/% TEMPERATURE.“F

Fig. 21.7-Equivalent molecular weight of C, + fraction. Organick and Golding dewpointlpressure correlation.

Fig. 21.10-Saturation pressure vs. temperature at W, =80. Parameter T,

POOC

TEMPERATURE.‘F

Fig. 21.8-Saturation pressure vs. temperature at W, = 100. Parameter Ta.

TEMPERATURE, “F

Fig. 21.9-Saturation pressure vs. temperature at W, = 90. Parameter Ta

TEMPERATURE, “F

Fig. 21 .ll-Saturation pressure vs. temperature at W, = 70. Parameter T,.

Fig. 21

v “““” 3

E 5000-

a \ 6 4000-

-

;: 3000-

2 2 2000-

TEMPERATURE,“F

.12-Saturation pressure vs. temperature Parameter Ts.

at W, =60.


8000

$ 7000

g 6000

4 g 5000 a

5 4000 F

i 3 3000

&

m 2000

0 100 200 300

TEMPERATURE.‘F TEMPERATURE.‘F

Fig. 21.13-Saturation pressure vs. temperature at W, = 55. Fig. 21.16-Saturation pressure vs. temperature

Parameter T, Parameter T,

TEMPERATURE.“F

Fig. 21.14-Saturation pressure vs. temperature at W, = 50 Fig. 21.17-Saturation pressure vs. temperature at W, =35.

Parameter T,. Parameter T,.

TEMPERATURE.“F

I I O-50 0 100 200

TEMPERATURE,“F

C

Fig. 21.15-Saturation pressure vs. temperature at W, = 45. Parameter i;,

Fig. 21.18-Saturation pIessure vs. temperature at W, =X.5. Parameter T,.

at W, =40.

L I O-50 0

I I I” I I I 100 200 300

TEMPERATURE, OF

10


TEMPERATURE, OF TEMPERATURE, “F

Fig. 21.19-Saturation pressure vs. temperature at W, =30. Parameter T,.

Fig. 21.20-Saturation pressure vs. temperature at W, = 27.5. Parameter 1,.

Example Problem 1. The dewpoint pressure at 200°F for a well effluent having the composition shown in Table 21.16 is predicted as follows.

1. Calculating first the properties of the separator liquid CT+, we have

TV= 232+260+313+383+497

=337”F 5

and

497 -232 lo-90% slope= =3.31.

80

From Table 21.13, MABP is 337-22.5=315”F or 775”R. From Table 21.15, CABP is 337-8.3=329”F or 789”R, giving

3vTiG Kw= = 12.3.

0.7535

From Fig. 21.7 the W, for the CT + material from the separator liquid is estimated to be 142.

Properties of the C 7 + material from the separator gas are assumed to be equal to those of n-octane (i.e., Tg=718’R, W, = 114).

2. Calculating values of TB and W, for the well effluent, we obtain the results shown in Table 2 I. 17.

3. Having calculated Ts and I@, for the well effluent, we can now determine the desired dewpoint pressure at 200°F by interpolation between Figs. 21.14 and 21.15. At TB =240”F, the dewpoint pressure is

w, =50 w, =45

nw 2 4000

9

g 3000

6 c 2000

2

2 1000 :: 0 130 200 300

TEMPERATURE,OF

Fig. 21.21-Saturation pressure vs. temperature at W, =25. Parameter Ts

Accuracy of Organick-Golding Correlation. About 50% of the 2 14 points that form the basis for the correlation were in error less than 5 % and 82 % were in error less than 10%. Standard deviation of all points is about 7.0%.

Total Formation Volume Correlations The total formation volume factor (FVF) defines the total volume of a system regardless of the number of phases present. Vink et al. I3 have shown that it is possible to have more than two hydrocarbon phases in equilibrium when the system contains an excessively large amount of one component. Naturally occurring systems usually exist in either one or two phases. For this reason, the term “two-phase formation volume” has become synonymous with total formation volume.

The relationship of specific volume and density to the total formation volume is the same as indicated in the preceding section for the oil-formation volume.

4,850 4,ooO ’ Total Formation Volume Factors

and the calculated dew point (at W, =49) is 4,680 psia. of Gas-Condensate Systems

It will be noticed that at 4,680 psia and 200°F the Total formation volume factors, specific volumes, and material is about 200°F and 900 psi above the critical densities of gas-condensate systems may be calculated temperature and pressure of the system. (From Figs. by use of the ideal gas-law equation with the proper com- 21.14 and 2 1.15, the locus of critical states line gives pressibility factor applied provided that the liquid phase Tc=O”F and pc=3,800 psia.) present does not amount to an appreciable fraction of the


TABLE 21.16-WELL EFFLUENT COMPOSITION

Separator Component Gas

co* 0.0060 N2 0.0217

c: 3

0.8986

0.0461 0.0131 i-C, 0.0043 n-C 4 0.0043 i-C 5 0.0019 n-C 5 0.0017 C6 0.0019 c,+ l 0.0004 c,+ l *

-

1 .oooo

Mole Fraction

Separator Liquid Effluent”

- -

0.0988 0.0350 0.0381 0.0201 0.0382 0.0495 0.0313 0.1284

-

0.5606

1 .oOOo

Properties of C, + *separator gas C, + mOfec”lar we,gtlt= 114

“Separator liquid C, + Molecular weight = 139 Density= 0.7535 g/cc=56.3°API ASTM distillation

BP (%) 21WF

10 232 20 245

0.0056 0.0204 0.8498 0.0454 0.0146 0.0053 0.0064 0.0048 0.0035 0.0096 0.0004 0.0342

Example Problem 2. The specific volume of a gas- condensate system at reservoir conditions given the system molal analysis shown in Table 21.18 is calculated as follows, assuming 1 pound mole of system.

460 + 199 Tpr =

370.7 =1.78,

2,500 -=3.75,

Ppr= 666.0

1 .oooo z=O.885 (from Fig. 20.2)

30 260 40 269 50 313 60 349 70 363 60 416 90 497 95

Endpoint tEffluen1 composition calculated on the basis of separator liquid/gas

ratio 3.0 gal/lo3 cu H.

system volume. Usually, at reservoir pressures and temperatures and for systems whose composition can be expressed as having a surface GOR greater than 10,000 cu ft/bbl, the presence of 10 ~01% liquid phase will not cause errors greater than 2 or 3% when the two-phase mixture density is calculated as though the mixture existed in only a single phase. This comes about because the partial volumes of components in the liquid phase are substantially the same as the partial volumes of the same components in the vapor phase.

Calculations from Composition of the Condensate System. As outlined previously, the formation volume (total or single phase) can be calculated from the relation

Mm vro B=- L M,,v,, .,,.,..................~ . . .

where Example Problem 3. The total formation volume of a gas-condensate system at reservoir conditions given the parameters in Table 21.19 is calculated as follows, assuming 1 bbl of stock-tank condensate.

M, = molecular weight of reservoir system,

“RJ = specific volume of reservoir system, M,, = molecular weight of stock-tank oil,

VSI = specific volume of stock-tank oil, and L = moles of stock-tank oil per 1 mole of

3,700x0.65+170x1.20 Yg’ =0.675

reservoir system. 3,700+170

L can be calculated by use of equilibrium ratios and and 1 bbl condensate per million cubic feet is the methods outlined in Chap. 23.

To use the pseudoreduced-temperatuatureipseudoreduce- d-pressure/compressibility chart in the calculation of vrO, it is necessary to determine suitable pseudocritical temperature and pressure values for the heptanes and

325

3.70+0.17 =84,

where yp is the gravity of total surface gas.

heavier components. These values can be obtained by the chart shown in Fig. 21.22. The following example illustrates the calculation of M, and v, .

and at 2,500 psia and 199°F

vro _ zRT 0.885 x 10.73~659 -

MP 19.39x2,500 =O. 129,

where Tpr is the pseudoreduced temperature, ppr the pseudoreduced pressure, z the compressibility factor,

and v, the specific volume (cu ftilbm) at reservoir conditions.

In the above solution, two phases ale present at 2,500 psia, as the dewpoint pressure calculated by the method of Organick and Golding is 2,690 psia at 199°F. Pro- bably no correlation will indicate directly the amount of liquid present at pressures less than the dewpoint pressure, although it can be calculated by use of suitable equilibrium-ratio and density data.

Calculations from GOR and Produced Fluid Proper- ties. A second method of calculating specific volume or formation volume on the basis of the gas-law equation was developed by Standing. I4 This method uses a correlation (Fig. 21.23) to obtain the gravity of the well effluent (or reservoir system) from the condensate liquid/gas ratio, gas gravity, and the stock-tank-oil gravity of the surface products. The effluent gravity is then used to obtain values of pseudocritical temperatures and pressures and, by means of these, to evaluate compressibility factors for the entire effluent. The condensate curve of Fig. 2 1.24 should be used when employing this method.


TABLE 21 .17-CALCULATED VALUES OF 7, and W,

Fig.

Component

co2

F2

c:

C3 i-C 4 n-C, i-C 5 n-C,

c6 C, + separator gas C, + separator liquid

Fraction

0.0056 0.0204 0.8498 0.0454 0.0146 0.0053 0.0084 0.0048 0.0035 0.0096 0.0004 0.0342

Boiling Point

(W 350 139 201 332 416 471 491 542 557 600 718

1 .oooo

Fraction Times Boiling

Point

(W 2.0 2.8

170.8 15.1 6.1 2.5 3.1 2.6 1.9 5.8 0.3

26.9

7s = 239.9

Fraction

0.0107 0.0244 0.5831 0.0586 0.0274 0.0133 0.0158 0.0150 0.0107 0.0356 0.0019 0.2035

1.0009

Weight Fraction Times

Equivalent Equivalent Molecular Molecular

Weight Weight

44 0.47 28 0.68 16.0 9.33 30.1 1.76 44.1 1.21 54.5 0.72 58.1 0.92 69.0 1.03 72.2 0.77 85 3.03

114 0.22 142 28.90

w, = 49.04

TABLE 21.18-CALCULATION OF SPECIFIC VOLUME OF GAS-CONDENSATE SYSTEM’

Critical Critical Temperature of Pressure of

Mole Molecular Weight, ybf Components, 7, yT, Components, pc Component Fraction, y Weight, M Ubm) vu (OR) (wia) YPC

co2 N2 Cl c, C, i-Cd n-C‘, i-C 5 n-C,

C6 c,+

0.0059 44.0 0.26 548 3.2 1,072 6.3 0.0218 28.0 0.61 227 4.9 492 10.7 0.8860 16.0 14.18 344 304.8 673 596.3 0.0460 30.1 1.39 550 25.3 709 32.8 0.0134 44.1 0.59 666 8.9 618 8.3 0.0045 58.1 0.26 733 3.3 530 2.4 0.0048 58.1 0.28 766 3.7 551 2.6 0.0026 72.1 0.19 830 2.2 482 1.3 0.0021 72.1 0.15 847 1.8 485 1 .o 0.0037 86.2 0.32 915 3.4 434 1.6 0.0084 138 1.16 1,090’. 9.2 343” 2.9

Reservoir iemperature = 19&F Molecular weight of C, b = 138. Specific gravity of C, f = D 7535.

‘*Pseudocrttical values from Fig 21.22

ri ’ $ Id0 120 140 160 180 200 220 240

F MOLECULAR WEIGHT 1

d BOOM.&+--+ SPkIFIC:GRAVliY 60&O -j

hw’ ’ ’ ’ ’ ’ ’ J 1 lo3 120 140 I60 180 hxl 220 240

iz MOLECULAR WEIGHT

k

19.39

21 .Z?-Pseudocritical temperatures and pressures heptanes and heavier.

for

370.7 666.0

1.5 060

GAS GR

1.4 0.70 GAS GR.

CFB

20 40 60 El0 ICC

Sbl Condensate per IO’ C” ft

Fig. 21.23-Effect of condensate volume on the ratio of surface-gas gravity to well-fluid gravity.


TABLE 21 .l g--DATA FOR CALCULATING TOTAL FORMATION VOLUME OF A GAS-CONDENSATE

SYSTEM’

Reservoir pressure, psia 3,000 Reservoir temperature, OF 250 Stock-tank-condensate production, B/D 325 Stock-tank condensate gravity, OAPl 45 Tank vapor rate, IO3 cu ft/D 170 Tank vapor gravity (air = 1) 1.20 Trap gas rate, lo3 cu ft/D 3,700 Trap gas gravity, (air = 1 .O) 0.65

‘0as1s 1 bbl of stock-tank condensate

TABLE 21.20-DATA FOR CORRELATION FOR OBTAINING TOTAL FORMATION VOLUME FACTORS OF

DISSOLVED GAS AND GAS-CONDENSATE SYSTEMS SHOWN IN FIG. 21.25

Pressure, psia 400 to 5,000 GOR, cu ft/bbl 75 to 37,000 Temperature, OF 100 to 258 Gas gravity 0.59 to 0.95 Tank-oil gravity, OAPI 16.5 to 63.8

From Fig. 21.23, at 45”API

~&~~=1.367

and

yl,,=1.367x0.675=0.923,

where

Ylw = well fluid gravity, ysr = trap gas gravity,

and

Ylwr = well fluid reservoir gravity.

From Fig. 21.24,

Tpc =432

and

ppc =647.

At reservoir conditions of 3,000 psia and 250”F,

460+250 Tpr =

432 =1.64,

3,000 PPr =------4.64,

647

and from Fig. 20.2

z=O.845.

By using 350 lbm/bbl for water, the weight of stock- tank condensate per barrel is

350x 141.5 =281.

131.5+“API

TABLE 21.21-DATA FOR CALCULATING TOTAL FORMATION VOLUME OF THE GAS-CONDENSATE

SYSTEM DESCRIBED IN EXAMPLE PROBLEM 4

Reservoir pressure, psia 3,000 Reservoir temperature, OF 250 GOR (condensate total), cu ft/bbl 11,900 Gas gravity (total) 0.675 Tank-oil gravity, OAPI 45

TABLE 21.22-DATA USED TO CALCULATE TOTAL FORMATION VOLUME FACTOR IN EXAMPLE

PROBLEM 5

Reservoir pressure, psia Reservoir temperature, OF GOR, cu ftlbbl

Separator Tank Total

Gas gravity Tank-oil gravity, OAPI

1,329 145

566 37

603 0.674

36.4

From Fig. 21.23 the molecular weight of stock-tank condensate, M, , is 140, moles of stock-tank condensate per barrel is 281/140=2.00, moles of surface gas per barrel of stock-tank condensate is l/325 x (3,870x 103) x l/379=31.4, and total moles per barrel of stock-tank condensate is 2.00+31.4=33.4.

From gas law,

n*T 33.4~0.845~ 10.73~710 y=-= =71.7

P 3,000

and

71.7 V=-=

5.615 12.8,

where the first value of V is in cubic feet and the second in barrels, giving a formation volume B, of 12.8 bbllbbl of stock-tank condensate.

Total Formation Volume Factors of Dissolved Gas Systems

A suitable correlation for obtaining total formation volume factors of both dissolved gas and gas-condensate systems was developed by Standing. t5 This correlation is shown in Fig. 21.25, and the graphical chart for simplified use of the correlation is given by Fig. 2 1.26. The correlation contains 387 experimental points, 92% of which are within 5% of the correlation. Range of the data comprising the correlation is given in Table 2 1.20.

Example Problem 4. The total formation volume of the gas-condensate system described in Example Problem 3 is calculated as follows, given the data in Table 2 1.2 1.


675

a 4 650

aw 2 2 625

i 600

2 u 575 t

5 g 550 3

; 525

4 a 500

F. 475 E : 450

2 f 425

:

- 2

400

z 375

8 2 350

I a 325 I I I I I I I

I 3oo ~ ~ j / 1 / 1 I I

060 080 100 120 140 160 160

Fig. 21.24-Pseudocritical properties of gases and condensate well fluids.

Fig. 21.25-Formation volume of gas plus liquid phases from GOR, total gas gravity, tank-oil gravity, temperature, and pressure.

Fig. 21.26-Chart for calculating total formation volume by Standing’s correlation.

PETROLEUM ENGINEERING HANDBOOK 21-20

141.5 Yo= =0.802

131.5+45

and

=11,90() (250)o’5 x~~~~~~~~.~X’~-“~ooo27x”~wo

(0.675) o.3

15.8 =11,900 -

0.877 x(O.802)‘.O

=1.72x105

where y0 is the tank-oil specific gravity. From Fig. 21.25, B,=13+bbl/bbl oftank oil. From Fig. 21.26, B, = 13.7 bbl/bbl of tank oil.

Example Problem 5. The total formation volume of well production at reservoir conditions given the data in Table 21.22 is calculated as follows.

From Fig. 21.26, B,= 1.72 bblibbl of tank oil. Ex- perimental value calculated from PVT test results is 1.745 bbl/bbl of tank oil.

Nomenclature B=

I, = K=

L, = L, =

M=

Mm = Mst = n=

PC =

Ppr = R=

tsu = T=

T, =

Tpr =

Ta = TB =

formation volume, m3 (bbl) correlation index characterization factor moles of stock-tank condensate per barrel moles of stock-tank oil per 1 mole of reser-

voir system, kmol/m3 (lbm moligal) molecular weight molecular weight of reservoir system molecular weight of stock-tank oil total moles critical pressure, psia (lbflsq in.) pseudoreduced pressure universal gas constant Universal Saybolt viscosity, seconds temperature, “F critical temperature, “C (“F) pseudoreduced temperature

atmospheric boiling point, K (“R) molal average boiling point, K (“R)

Tc = cubic average boiling point, K (“R)

Tm = mean average boiling point, K (“R)

Tm = mean average boiling point, K (“R) TV = volumetric average boiling point, “F

vro = specific volume of reservoir system

-vst = specific volume of stock-tank oil w, = modified weight average equivalent

Y=

molecular weight mole fraction

z = compressibility factor

Ye = gas specific gravity ygt = trap gas gravity

Ylw = well fluid gravity

Y lwr = well fluid reservoir gravity

Yo = tank-oil specific gravity p = viscosity, Pa. s (cp)

References 1.

2.

3.

4.

5. 6.

7.

8.

9.

10.

11.

12.

13.

ASTM Standards on Petroleum Products and Lubricants, Part 24, ASTM, Philadelphia (1975) 796. Watson, K.M., Nelson, E.F., and Murphy, G.B.: “Charactetiza- tion of Petroleum Factions,” Ind. and Eng. Chem. (Dec. 1935) 1460-64. Technical Data Book-Petroleum Refining, API, Washington, D.C. (1970) 2-11. Nelson, W.L.: Petroleum Refinery Engineering, fourth edition, McGraw-Hill Book Co. Inc., New York City (19X3), 910-37. “A Guide to World Export Crudes,” Oil and Gas J, (1976). Ferrem, E.P. and Nichols, D.T.: “Analyses of 169 Crude Oils fmm 122 Foreign Oil Fields,” U.S. Dept. of the Interior, Bureau of Mines, Bartlesville, OK (1972). Coleman, H.J. et a[.: “Analyses of 800 Crude Oils from United States Oil Fields,” U.S. DOE, Bartlesville, OK (1978). Woodward, P.J.: Crude Oil Analysis Data Bank, Bartlesville Energy Technology Center, U.S. DOE, Bartlesville, OK (Oct. 1980) 1-29. Lacey, W.N., Sage, B.H., and Kircher, C.E. Jr.: “Phase Equilibrja in Hydrocarbon Systems III, Solubility of a Dry Natural Gas in Crude Oil,” Ind. and Eng. Chem. (June 1934) 652-54. Sage, B.H. andOlds, R.H.: “VolumetricBehaviorofOiland Gas from Several San Joaquin Valley Fields,” Trans., AIME (1947) 170, 156-62. Organick, E.I. and Golding, B.H.: “Prediction of Saturation Pressures for Condensate-gas and Volatile-oil Mixtures,” Trans., AIME (1952), 195, 135-48. Smith, R.L. and Watson, K.M.: “Boiling Points and Critical Pmperties of Hydrocarbon Mixtures.” Ind. and Enn. Chem. (19j7) 1408. Vink, D.J. er al.: “Multiple-phase Hydrocarbon Systems,” Oil and Gas J. (Nov. 1940) 34-38.

14. Standing, M.B.: Volumetric and Phase Behavior of Oil Field Hydrocarbon Systems, Reinhold Publishing Corp., New York Ci- ty (1952).

15. Standing, M.B.: “A Pressure-Volume-Temperature Correlation for Mixtures of California Oils and Gases,” Drill. and Prod. Prac., API (1947), 275.

Chapter 22

Oil System Correlations H. Dale Beggs. Petroleum Consukant*

Introduction Knowledge of petroleum fluids’ physical properties is required by petroleum engineers for both reservoir and production system calculations. These properties must be evaluated at reservoir temperature and various pressures for reservoir performance studies, and at conditions of both changing pressure and temperature for wellbore hydraulics calculations.

If reservoir fluid samples are available, the fluid properties of interest can be measured with a pressure-volume- temperature (PVT) analysis. However, these analyses usually are conducted at reservoir temperature only and the variation of the properties with temperature is not available for production system calculations. Also, in many cases a PVT analysis may not be available early in the life of the reservoir or may never be available because of economic reasons. To overcome these obstacles, empirical correlations have been developed for predicting various fluid physical properties from limited data. The development and application of several of these empirical correlations are presented in this chapter. Methods for estimating physical properties for both saturated and undersaturated oils as functions of pressure, temperature, stock-tank oil gravity, and separator gas gravity are given.

Fluid properties are calculated here only for oil systems with and without fluid composition known. Methods for calculating physical properties of gas-condensate systems are presented in Chaps. 2 I, 23, and 30. Therefore, no correlations for dewpoint pressure are presented, as the dewpoint pressure can be calculated with the procedures outlined in Chap. 2 1 if the composition of the fluid is known.

Many of the older correlations were presented in graphical form only and are therefore not suitable for use in computers or programmable calculators. These graphs are converted to equation form where possible.

The generally accepted definitions of the fluid properties correlated in this chapter are as follows.*

Oil density, p,, , is the ratio of the mass of the oil plus its dissolved or solution gas per unit volume, which varies with temperature and pressure.

Bubblepointpressure, P/), is the pressure at which the first bubble of gas evolves as the pressure on the oil is decreased. It also is frequently called “saturation pressure, ” as the oil will absorb no more gas below that pressure. The bubblepoint pressure varies with temperature for a particular oil system.

Solution gas/oil ratio (GOR), R,, , is the amount of gas that will evolve from the oil as the pressure is reduced to atmospheric from some higher pressure. It is usually expressed in units of scf/STB. The gas is frequently referred to as “dissolved gas.”

Oilformation volume factor (FVF), B,, , is the volume occupied by 1 STB oil plus its solution gas at some elevated pressure and temperature. It is usually expressed as bbl/STB. It is a measure of the shrinkage of the oil as it is brought to stock-tank conditions.

Total FW, B,, means the volume occupied at some elevated pressure and temperature by 1 STB oil, its remaining solution gas, and the free gas (R,i -R,) that has evolved from the oil. It is also expressed as bbl/STB.

Oil viscosi@, po. measures the oil’s resistance to flow, defined as the ratio of the shearing stress to the rate of shear induced in the oil by the stress. It is usually measured in centipoise and is required for both reservoir and piping system calculations.

Inferfacial tension (IFT), co, is the force per unit length existing at the interface between two immiscible fluids. This property is not required in most reservoir calculations but is a parameter in some correlations for piping system calculations. It is usually expressed in units of dyne/cm.

‘General terms are deftned I” the Glossary at the end of this chapter

Fig. 22.1-Pseudoliquid density of systems containing methane and ethane.

Oil Density Determination Oil density is required at various pressures and at reservoir temperature for reservoir engineering calculations. The variation with temperature must be calculated for production system design calculations. An equation for oil density is

PO = 350y,+O.O7647,R,

, I.. . . . . . 5.6158,

where

PO = oil density, lbmicu ft,

Yo = oil specific gravity,

YK = gas specific gravity, R,y = solution or dissolved gas, scf/STB, B, = oil FVF, bbl/STB,

3.50 = density of water at standard conditions, lbm/STB,

0.0764 = density of air at standard conditions, lbmlscf, and

5.615 = conversion factor, cu ft/bbl.

If the pressure and temperature conditions are such that all of the available gas is in solution-i.e., the pressure is above the bubblepoint at the temperature of interest-

PETROLEUM ENGINEERING HANDBOOK

increased pressure will merely compress the liquid and increase its density. For the case of p> p,, . the oil density is calculated from

p. =poh exp[c,(p--ph)], . . . .(2)

where

PO = oil density at p, T, poh = oil density at ph, T,

p = pressure, psia, pb = bubblepoint pressure at T, psia, and

co = oil isothermal compressibility at T, psi - ’ .

Correlations for calculating R,T, B,, c, and ~b at various conditions are presented later.

In the petroleum industry, it is common to express gravity in terms of the API gravity of the oil, or:

141.5 Yo = 131,5+YAP,, . . . . .

where y. is oil specific gravity, and YAPI is oil gravity, “API.

Density From Ideal Solution Principles- Composition Known

The principle of ideal solutions states that the volume of the total solution is the sum of the individual component volumes. The principle applies at atmospheric pressure for fluids in which the components are closely related chemically, such as petroleum. If the composition of the fluid is known, the density at standard conditions (14.7 psia and 60°F) may be calculated from

c - & mi Cm I

Psc = - Cmilpi ) . .

5 vi i=l

(4)

where m; = mass of the ith component, Vi = volume of the ith component,

PI = density of the ith component at standard conditions, and

C = number of components.

Once the density at standard conditions is calculated, it must be corrected for compressibility and thermal expansion if the density at other conditions is required. This can be accomplished by use of charts presented by Standing. ’

When the ideal solution principle is applied to reservoir ,oils that contain large amounts of dissolved gas, it is obvious that the fluid cannot be brought to standard or stock-tank conditions and still remain in the liquid phase. This limitation is overcome by calculating a pseudoliquid density, the value of which depends on the mass or weight fractions of methane and ethane in the fluid. The pseudoliquid density correlation was presented by Standing ’ and is illustrated in Fig. 22. I,

OIL SYSTEM CORRELATIONS 22-3

DENSITY AT 6O”F, 1 ATM, LBKU FT

Fig. 22.2-Density correction for compressibility of hydrocar- Fig. 22.3-Density correction for thermal expansion of bon liquids. hydrocarbon liquids.

The procedure for calculating oil density at any pressure and temperature when the composition is known is as follows.

1. Calculate the mass or weight of the ethane and heavier components in the mixture.

2. Calculate the density of the propane and heavier components with Eq. 4.

3. Calculate the weight or mass percent of ethane in the ethane and heavier mixture.

4. Calculate the weight percent methane in the total mixture.

5. Determine the pseudoliquid density from Fig. 22.1. 6. Correct for compressibility with Fig. 22.2 7. Correct for thermal expansion with Fig. 22.3.

Example Problem 1. Using the known composition of a reservoir fluid as given in Table 22.1, calculate the den-

Component

Cl C* C3 C4 C5 C6 C T&l

Mole Fraction.

Y, 0.4404 0.0432 0.0405 0.0284 0.0174 0.0290 0.4011 1 .oooo

10

b- 9

: G

B

E5 a 7

F 6

4I b3 5 mu =\

0-J WC0 4 IL

$ 3

G 2

z P 1

i? ‘25 30 35 40 45 50 55 60 65

DENSITY AT 60°F

sity at the bubblepoint pressure of 3,280 psi and temperature of 218°F.

Solution.

1. Weight of ethane plus=130.69-7.046=123.46 lbm.

2. Density of propane plus equals (weight of propane plus) divided by (volume of propane plus):

130.69-7.046-1.296 =54.94 lbm/cu ft.

2.227

3. Weight percent ethane in ethane plus:

1.296(100) = 1.05.

123.46

TABLE 22.1- EXAMPLE PROBLEM 1 SOLUTION

Mole Weight of Components,

M, 16.0 30.1 44.1 58.1 72.2 86.2

297

Weight of Components Liquid Density of

mi =Y,M, Components,’ (Ibm) PI 7.046 1.296 1.766 31.66 1.650 35.77’ l

1.256 39.16’* 2.500 41.43

115.1 56.6 130.69

Liquid Volume of Components,’

V, =m,lp, fcu ft\

0.0564 0.0461 0.0321 0.0603 2.032 2.227

‘at 60°F and 14.7 ps,a. “Arithmetic average of is.0 and normal values

22-4

GAS GRAVITY, AIR q 1

Fig. 22.4-Apparent liquid density of natural gases.

4. Weight percent methane in methane plus:

7.046(100) =5.39.

130.69

5. From Fig. 22.1, psr=50.8 lbm/cu ft at 60°F and 14.7 psia.

6. From Fig. 22.2, the correction for pressure is 0.89 lbmicu ft.

Therefore, the density at 3,280 psia and 60°F is 50.8+0.89=51.7 lbmicu ft. 7. From Fig. 22.3, the correction for temperature is

-3.57 Ibm/cu ft. Therefore, the density at 3,280 psia and 218°F is

51.7-3.57=48.1 Ibm/cu ft.

Density From Ideal Solution Principles- Composition Unknown

The procedure for estimating oil density outlined in the preceding section used charts for determing the apparent gas density, which required knowledge of the total fluid composition. Katz* extended the apparent density concept to apply to natural gases in general. This results in a method that can be used when solution GOR stock-tank- oil gravity, and gas gravity are known. The fluid composition is not required. The correlation for the apparent density of the dissolved gas as a function of oil and gas gravity is shown in Fig. 22.4. The gravity of the produced gas is calculated as a volume-weighted average of the gas evolved at the separator and the stock tank.

Application of Fig. 22.4 in estimating the oil density from limited data is illustrated in Example Problem 2. In this example, the fluid passed through two separators between the wellhead and the stock tank.

Example Problem 2. Calculate the density and specific volume of the oil system at the bubblepoint conditions of pb =3,280 psia at T=218”F. The stock-tank oil gravity


is 27.4”API and the quantities and gravities of the produced gas are given in Table 22.2.

Solution.

1. Average gas gravity, yr. =CI?iy,~iICRj,

r, = (414)(0.640)+90(0.897)+25(1.540) =. 726

. . 414+90+25

and

141.5

I”‘= 131.5+27.4 =0.89.

2. Molecular weight of produced gas, M,, =y,(M,i,);

M,Y =0.726(28.97)=21.03 Ibmimol.

3. Mass of dissolved gas, m,, is given by

529 scf/STB 379,5 scf,mol (21.03 lbm/mol)=29.32 lbm/STB.

4. Mass of stock-tank oil, m,,, is given by

350 lbm/STB(O. 89) = 3 11.50 lbm/STB.

Fig. 22.4 shows that the apparent liquid density of the dissolved gas is about 24.9 lbmicu ft at 60°F and 14.7 psia. This is used to calculate the volume of the dissolved gas.

5. Volume of dissolved gas, I’,, is given by

mR 29.32 lbm/STB -= = 1.178 cu ft/STB. PK 24.9 lbmicu ft

6. Volume of stock-tank

5.615 cu ft/STB.

7. Pseudoliquid density, PAL

m, fm, zz-

04 V,, is given by

“0 - “,

311.50 lbm/STB+29 32 1bmiSTB - - 5.615 cu ft/STB+1.178 cu ft/STB

=50.17 Ibm/cu ft.

TABLE 22.2-PRODUCED GAS CHARACTERISTICS

R (scf/STB) y9

First-stage separator 414 0.640 Second-stage separator 90 0.897 Stock tank 25 1.540

Total 529


Correction of the density for compression and thermal expansion is accomplished with Figs. 22.2 and 22.3.

Fig. 22.2 shows that the pressure correction to 3,280 psia is 0.90 lbmicu ft. Therefore,

p3Z80, 60=50.17+0.90=51.07 lbmicu ft.

Fig, 22.3 shows that the temperature correction to 218°F is -3.63 Ibm/cu ft. Therefore,

~32~0, 218=51.07-3.63=47.44 lbmicu ft

The specific volume of the oil is defined as the reciprocal of the density. Therefore,

v,, = i = I

-----0.021 cu ft/lbm. P 0 47.44

Bubblepoint-Pressure Correlations Reservoir performance calculations require that the reservoir bubblepoint pressure be known. This is determined from a PVT analysis of a reservoir fluid sample or calculated by flash calculation procedures if the composition of the reservoir fluid is known. However, since this information is frequently unavailable. empirical correlations for estimating P/, from limited data were developed. These correlations may be used to estimate bubblepoint or saturation pressure as a function of reservoir temperature, stock-tank oil gravity. dissolved-gas gravity, and solution GOR at initial reservoir pressure. That is,

A value for R.,h = R,,i can be obtained from the initial solution GOR (produced) if the reservoir pressure is above !I/>, where R,,b is the solution GOR at bubblepoint pressure and R,, is the solution GOR at initial reservoir pressure.

Three methods for estimating bubblepoint pressure are presented. The correlations were developed by use of experimentally measured bubblepoint pressures obtained from PVT analyses on reservoir fluid samples. Other correlations were developed for application in specific reservoirs, but the methods presented here gave good results over a wide range of oil systems.

Standing Correlations

Standing’ presented an equation and nomograph to estimate bubblepoint pressures greater than 1,000 psia. The correlation was based on 105 experimentally determined bubblepoint pressures of California oil systems. The average error of the correlation when applied to the data used to develop the method was 4.8% and 106 psi. The ranges of data used to develop the method are given in Table 22.3

The gases evolved from the systems used to develop the correlation contained essentially no nitrogen or hydrogen sulfide. Some of the gases contained CO,. but in quantities less than 1 mol%. No attempt was made to

characterize the tank oils other than by the API gravity. The value for gas gravity to be used is apparently the volume-weighted average of the gas from all stages of separation. The correlation should apply to other oil systems as long as the compositional makeup of the gases and crudes is similar to those used in developing the method.

The equation for estimating bubblepoint pressure is

0.83

x IO!‘v , (5)

where

Y<? = mole fraction gas, = 0.00091(TR)-0.0125yA~I,

PJ, = bubblepoint pressure, psia, R ,,b = solution GOR at PLP~, scf/STB,

7,s = gas gravity (air= 1 .O), TR = reservoir temperature, “F, and

YAPI = stock-tank oil gravity, “API.

A nomograph developed from Eq. 5 is shown in Fig. 22.5. The example bubblepoint determination shown in the nomograph is calculated with Eq. 5 in the following example.

Example Problem 3. Estimate pl, where R ,,, = 350 scfi STB. TR =200”F, -yX =0.75, and ?,+#I =30”APl.

Solution.

y!: =0.0009i(200)-0.0125(30)= -0.193.

0.83 x 10 -0.1Y3

,LJ~ = 1,895 psia.

Lasater Correlation

A correlation by Lasater4 was developed in 1958 from 158 experimental data points, which included the ranges of variables shown in Table 22.4.

The correlation was presented graphically in the form of two charts. Equations were fitted to these graphical correlations to enhance the use of this method with computers or calculators. The graphical correlations are shown in Figs. 22.6 and 22.7.

The following procedure is used to estimate ph using Figs. 22.6 and 22.7.

TABLE 22.3~DATA PARAMETERS AND RANGES

prb. via 130 to 7,000

R, “F 100 to 258 R sb, scf/STB

YAPI~ ‘ApI yQ (air = 1 .O)

20 to 1,425 16 5 to 63.8 0.59 to 0.95


. BUBBLE-POINT PRESSURE,

Fig. 22.5-Chart for calculating bubblepotnt pressure by Standing’s correlation.

1. Find the effective molecular weight of the stock-tank oil from the API gravity using Fig. 22.6.

2. Calculate the mol fraction of gas in the system from

R,yh1379.3 ?I: =

R,h1379.3+350y,,lM, ' '.""""..' (6)

3. Find the bubblepoint pressure factor, phyRITR, from Fig. 22.7

4. Calculate the bubblepoint pressure ph = [(ph~~)lT] TR/~,~ where TR is in “R. The following equations can be used to replace Figs.

22.6 and 22.7.

Equations for Fig. 22.6

For API I 40:

M,,=630-lOyAp,. . . . . . . . . . . . . . . . . . . . . . ...(7)

For API > 40:

hi’,, =73,1 10 (-yAPI) -‘.56’. .(8)

Equations for Fig. 22.7

For ys 5 0.60:

P b Y ,q -=0.679 ex~(2.786y,~)-0.323. .(9)

TR

TABLE 22.4-VARIABLE RANGES

Tb- Asia ‘I= R, 48 82 to to 5,780 272 YAPI> oAPl 17.9 to 51.1

yg 0.574 to 1.223 R scf/STB sb, 3 to 2,905

For Y,~ > 0.60:

PhYg -=8.26y;.56+1.95.

TR

. . . .(lO)

A nomograph that combines Figs. 22.6 and 22.7 is presented in Fig. 22.8. The example given in Fig. 22.8 is worked with the equations in the following example.

Example Problem 4. Given the following data, use the

Lasater method to estimate P,,

Rch =500 scf/STB, TR=200”F=660”R, yI: =0.80, YAP[ =30, and yg =0.876.

Solution.

M,,=630-10(30)=330.


EFFECTIVE MOLECULAR WEIGHT OF TANK OIL

Fig. 22.6-Effective molecular weight related to tank-oil gravity.

5001379.3

” = 500/379.3+350(0.876)1330 =0.587

PhYg - =0.679 exp[2.786(0.587)] -0.323:

TR

Phh -=3.161. TR

3.161(660) Ph=

0.80 =2,608 psia.

Vasquez and Beggs Correlation

Vasquez and Beggs’ used results from more than 600 oil systems to develop empirical correlations for several oil properties including bubblepoint pressure. The data en- compassed very wide ranges of pressure, temperature, oil gravity, and gas gravity and inciuded approximately 6,000 measured data points for R,, , B, and pLo at various pressures and temperatures. The ranges of the pertinent parameters are given in Table 22.5.

It was found that the gas gravity was a strong correlating parameter and, unfortunately, usually is one of the variables of most questionable accuracy. The gravity of the evolved gas depends on the pressure and temperature of the separators, which may not be known in many cases.

The gas gravity used to develop all the correlations reported by Vasquez and Beggs was that which would result from a two-stage separation. The first-stage pressure was chosen as 100 psig and the second stage was the stock tank. If the known gas gravity resulted from a first-stage separation at a pressure other than 100 psig, the corrected gas gravity to be used in the correlations can be obtained from Eq. 11. If separator conditions are unknown,

5.2 I I I II II

4.8

3.6

3.2

2.8

2.0

1.6

1.2

1~~~~ 0 0.2 0.4 0.6 0.8 1.0

GAS MOLE FRACTION

Fig. 22.7-Lasater’s correlation of bubblepoint-pressure factor with gas-mole fraction.

the uncorrected gas gravity may be used in the correlations for ph, R,v, B,, and c,.

y,,.=y,[1.0+5.912x 10P5yAP,Ts log(p,Y/l 14.7)]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . (11)

where ync = corrected gas gravity,

7,: = gas gravity resulting from a separation at

P .5 7 Ts T,, = separator temperature, “F, p,, = separator pressure, psia, and

-yAPI = oil gravity, “API.


Fig. 22.8-Chart for calculating bubblepoint pressure by Lasater’s correlation

The correlations are presented in equation form only. The bubblepoint pressure is calculated from

. . . . . . . . . . . . . . . . . . . . . . . . . . . (12)

where pb = bubblepoint pressure, psia,

R sb = solution GOR at pb, scf/STB, = gas gravity,

-,,‘,: = oil gravity, “API, and TR = temperature, “F.

The accuracy of the correlation was greater if the samples were divided into ranges of oil API gravity. A dividing point of 30”API was chosen. The values of the constants in Eq. 12 depend on API gravity of the stock- tank oil and are given in Table 22.6.

TABLE 22.5-VARIABLE RANGES

prb’ psia ‘I= 50 to 5,250 R, 70 to 295

R scflSTB sb, 20 to 2,070 ~npl> ‘ApI 16 to 58 YQ 0.56 to 1.18

Example Problem 5. Calculate the bubblepoint pressure for the oil system given in Example Problem 4 using the Vasquez and Beggs correlation and the following data. Use the uncorrected gas gravity. R.rb =500 scf/STB, TR = 220”F, yfi =0.80, and YAPI =30”API.

Solution. Eq. 12 and the correct C values from Table 22.1 give:

I

500 Ph= l- I.0937

0.0362(0.80) exp[25.724(30)/680] ’

pb =2,562 psia.

This compares well with the value of 2,608 obtained in Example Problem 4 with Lasater’s correlation. With Standing’s Eq. 5, a value of 2,415 psia is obtained.

Accuracy of Bubblepoint Correlations

Comparison of the accuracy with which the measured bubblepoint pressures used in each correlation agreed with

TABLE 22.8-CONSTANTS FOR BUBBLEPOINT EQUATION

OAPI I 30 OAPI > 30

C, 0.0362 0.0178 C2 1.0937 1.1870 C3 25.7240 23.9310


TABLE 22.7-COMPARISON OF ACCURACY OF BUBBLEPOINT-PRESSURE CORRELATIONS

Number of points in correlations Standing Lasater Vasquez-Beggs

105 158 5.008 Data points’wlthin 10% of correlation, % 87 87 85 Data points more than 200 PSI in error, % 27 Mean.error, % 4.0 3.8 - 0.7

values determined from the final correlation shows that the Vasquez and Beggs correlation is the most accurate,

For 7 < 3.29:

followed by Lasater’s and then by Standing’s This is shown in Table 22.7. ys =0.359 In

1.473py, +0.476

T (15)

Solution GOR for Saturated Oils For &?3 29: Both reservoir engineering and production engineering T ’

calculations require estimates of the amount of dissolved gas remaining in solution at oil system pressures below bubblcpoint pressure. The amount of free gas--that is,

ys = (

O.l21py, -0.236

T >

0.!81

,

the gas that has evolved from 1 STB oil as the pressure is reduced below p(,-IS R,,, -R,,, where R,, is the gas where T is in “R. remaining in solution at the pressure of interest. In effect. any pressure below the original bubblepoint pressure is also a bubblepoint pressure, since the oil is Vasquez and Beggs Correlation

saturated with gas at this pressure. Therefore, the correlations presented in the previous section can be solved for solution GOR and a value of R, can be obtained at any R,~=CI~,P~~ exp pressure less than the reservoir ph. That is, R, =f(p,T, T+460 ’ “““’

. (16)

(17)

YAP[-Y#). The nomographs presented in Figs. 22.5 and 22.8 can where

be used to determine R, by entering the bubblepoint axis R,, = gas in solution at p and T, scf/STB.

at the pressure of interest and proceeding “backward” through the graph to determine R,.

yh’ = gas gravity, p = pressure of interest, psia,

YAP] = stock-tank oi] gravity, “API

Standing Correlation

R,=y, ( ],x~o~~) ‘.?04 1

T = temperature of interest. “F, and Cl, Cl. C3 = are obtained from Table 22.6.

(13) Example Problem 6. Estimate the solution GOR of the following oil system using the correlations of Standing, Lasater, and Vasquez and Beges and the data: n=765

where psia, T= 137”F, +A~1 =22”AF[ and ys ~0.65.’ Jr = 0,00091(T)-0.0125(yAP,), R’; = solution GOR. scf/STB,

p = pressure, psia.

ys = gas gravity, -yAPI = oil gravity. “API. and

T = temperature of interest, “F

Standing

765 1 I 204

R,, =0.6.5 18x 1o-O,‘j

= 90 scf/STB.

Lasater Correlation

Lasater

R,= 132755y,,.vy M,,(, -r,s) ( (14)

ms 765(0.65)

T- =0.833.

137+460

where M,, is obtained from Eq. 7 or 8 and ys is calculated by either Eq. 9 or IO, depending on whether the value of the pressure factor is less than or greater than 3.29.

.~=0.359 ln[1.473(0.833)+0.476]=0.191 (Eq. IS).

M,,=630- 10(22)=410 (Eq. 7).


141.5 Y/J = =0.922

131.5+22

R = 132755(0.922)(0.191) \

410(1-0.191) =70 scf/STB (Eq. 14).

If yh’ is read from Fig. 22.7 rather than calculated from Eq. IS, a value of approximately 0.25 is obtained. This gives a value of R,, = 100 scf/STB. In this example, the graphical value is closer to those calculated from the other two correlations. The accuracy of the Lasater equation is much better at higher R,, values.

Vasquez and Beggs

R, =0.0362(0.65)(765)‘~“““’ exp[ 2~3~4@~] ;

Standing Correlation. Standing’ used the same oil systems described in the bubblepoint correlation section to develop a correlation for B,, at pressures less than ph. The method was presented in both equation and nomograph form. In equation form,

B~,=0.972+0.000147F’~““, . . . (18)

where F is a correlating function and is determined from the equation

F = R,y(y,ly,j)o.5 + 1.25T, B, = oil FVF, bbl/STB, R,, = solution GOR, scf/STB,

Yn = gas gravity,

YO = oil specific gravity= 141.5/(131.5 +yAPt), and

T = temperature of interest, “F.

R,, = 87 scf/STB. A nomograph that solves Eq. 18 graphically is presented

in Fig. 22.9.

Oil FVF Correlations The oil FVF is required for both reservoir and production system calculations. The reservoir engineer must be able to relate stock-tank volumes to reservoir volumes at various pressures and a constant reservoir temperature. Production engineering involves converting surface- measured volumetric flow rates to in-situ flow rates at various pressures and changing temperatures as the fluid is produced to the surface.

As defined previously, the oil FVF is the volume that would be occupied at some pressure and temperature by 1 STB oil plus any gas dissolved in the oil at these pressure and temperature conditions. It is a function of the composition of the system and the conditions under which the gas and liquid are separated.

Values of oil FVF at reservoir temperature and various pressures can be obtained from a standard PVT analysis of a reservoir fluid sample. However, this type of analysis is often unavailable and the engineer must then resort to empirical correlations that require only limited data. Two empirical correlations for saturated oil systems will be presented in this section. Both require values for solution GOR, R,, which can be obtained by the methods presented in the previous section.

At pressures above the bubblepoint, the oil is undersaturated and the liquid expands as pressure is reduced. Calculation of oil FVF thus requires a value for oil compressibility. Two correlations for estimating the compressibility of an undersaturated oil system will be prcscnted.

Saturated Systems

If an oil system is saturated with gas at given conditions of pressure and temperature, a reduction in pressure will allow solution gas to evzolve, thus causing the oil to shrink. The Ilquid volume is also affected by temperature. Solu- tion gas increases as temperature is decreased, but the liquid volume decreases as the oil is cooled. The correlations presented in this section can be expressed as

Example Problem 7. Use both Standing’s equation and nomograph to estimate the oil FVF for the oil system described by the data T=2009F, R,v =350 scf/STB, Y,~ = 0.75, and YAP] =30”API.

Solution.

Yo = 141.5/(131.5+30)=0.876. F = 350(0.75/0.876)“.5 + 1.25(200) =574.

B,, = 0.972+0.000147(574)‘~‘75; B,, = 1.228 bbl/STB.

A value of 1.22 bbl/STB is obtained from the nomograph, Fig. 22.9.

Vasquez and Beggs Correlation. In conjunction with development of the bubblepoint and solution GOR correlations, Vasquez and Beggs’ also presented an equation for oil FVF for saturated oils. To improve the accuracy of the correlation. the 600 oil systems were divided into two groups, those having API gravities 5 30 and those having gravities > 30. The gas gravity used in the equation should be the corrected gravity calculated by Eq. 11 if the separator pressure is known. If separator conditions are unknown, the uncorrected gas gravity may be used. The equation is

+CjR,(T-660)(yAP,/y~:c), . . . . . . . (19)

where B,, = oil FVF at p and T, bbl/STB R, = solution GOR at p, T, scf/STB

T = temperature of interest, “F p = pressure of interest, psia

-)‘,&P[ = stock-tank oil gravity, “API. and

-Yv = gas gravity, corrected, air= I

B,, =f(R,. YAPI. Ys. T). The constants are determined from Table 22.8.

OIL SYSTEM CORRELATIONS Z-11

EXAMPLE

FORMATION VOLUME OF BUBBLE-POINT LIQUID, -

Fig. 22.9-Chart for calculating oil-formation volume by Standing’s correlation.

Example Problem 8. Use the Vasquez and Beggs equation to determine the oil FVF at bubblepoint pressure for the oil system described by ph ~2,652 psia, Rsb =500

scf/STB. y,,-=O.SO. YAP] =30”API, and 7’=220”F.

Solution.

B ,,h = 1+4.677x1O-4(5OO)+1.751x1O-5(16O) ~(3010.80)-1.811x10-s(500)(160) .(30/0.80).

B,,, = 1.285 bbl/STB.

Undersaturated Systems

The oil FVF decreases with pressure increase at pressures above the bubblepoint. In this case, B, is calculated from

B, =Boh exp[c,,(ph -p)], . (20)

where B nh = oil FVF at pb, ph = bubblepoint pressure, psia,

p = pressure of interest, psia, and

cc1 = oil isothermal compressibility, psi - ’ .

Values for B,,h can be calculated with the Standing or

Vasquez and Beggs correlation. The oil compressibility can be determined from a PVT analysis or estimated from empirical correlations. Two correlations for c,, will be

presented.

TABLE 22.8-CONSTANTS FOR OIL FVF

OAPI 530 “API>30

Cl 4.677 x 10 -4 4.670~10-~

c2 1.751x10-5 1.100x10-~

c3 -1.811x10-8 1.337x1o-g

Oil Isothermal Compressibility-Trube Method. The Trube method6 makes use of the following relationships.

and

where cpr- = pseudoreduced compressibility.

CO = oil isothermal compressibility.

P,x = pseudocritical pressure, T,,, = pseudocritical temperature,

,.,.. \ .i

Fig. 22.10-Variation of pseudocritical temperature 01 reservoir Fig. 22.11-Pseudocritical pressure variation with pseudo- oils with 60DF bubblepoint pressure; Trube’s correlation.

critical temperature and 60°F specific gravity of reservoir oil; Trube’s correlation.

PP = pseudoreduced pressure, when used to predict the 2,000 measured values of c, T,,,. = pseudoreduced temperature, from which the correlation was developed. No compari-

p = pressure of interest, and son of the two methods is available using independent T = temperature of interest. data. The equation for c, is

The pseudoreduced compressibility is a function ofp,, and T,,,. Once cpr is obtained, c,) is calculated from

c,=cp’/pP’. . . . I. . . . . . . . (21)

Three graphs are required to obtain the necessary parameters to calculate cO. The pseudocritical temperature Tp,. is obtained from Fig. 22.10 as a function of the spe- c~fic gravity of the undersaturated liquid at the bubblepoint pressure and 60°F. It also depends on the bubblepoint pressure of the oil at 60°F. Values for these parameters may be estimated using the correlations for density and bubblepoint pressure presented previously.

A value for ppc. is obtained from Fig. 22.11 using the liquid specific gravity at 60°F and the value of T,, obtained from Fig. 22.10. Once ppi. and T,,< are known, p,,,. and T,,, at the pressure and temperature of interest can be calculated. A value of c,,,. is obtained from Fig. 22.12 using ppr and T,,,. Then c, is calculated by Eq. 2 1.

Application of the Trube method using a computer or calculator would require digitization of Figs. 22.10, 22.11, and 22.12.

Because of its complexity, no example will be given illustrating the application of this method. An example problem may be found in Ref. 6.

Oil Isothermal Compressibility-Vasquez and Beggs Method. Vasquez and Beggs5 used approximately 2,000 experimentally measured values of c,, from more than 600 oil systems to develop a correlation for c, as a function of R ,h. T, ys, y,4pI, and p. This method is much simpler to use than the Trube method and is more accurate

a C-J CL


2ooo\ I.84

SPECIFIC GRAVITY OF UNDERSATURATED RESERVOIR LIQUID AT 60°F

co - 5R,b+17.2T-1,180y,+12.61yAP,-1,433

pxlo”

. . . . . . . . . . . . . . . . . . . . . . . . . . . (22)

where

co = oil isothermal compressibility, psi -’ Rvb = solution GOR, scf/STB

T = temperature of interest, “F p = pressure of interest, psia

TX = gas gravity, and TAP[ = stock-tank oil gravity, “API.

Example Problem 9. Calculate the oil FVF for the oil system described in Example Problem 8 at a pressure of 3,000 psia. Use Eq. 22 to determine a value for c, where pb =2,652 psia, Rsb =500 scf/STB, y,? =0.80, YApI = 30”API, T=220”F, and Bob = 1.285 bbl/STB.

Solution.

co =

5(500)+17.2(200)-1,180(0.80)+12.61(30)-1,433

3.000x 105

c,,=1.43X10-5 psi-‘.

OIL SYSTEM CORRELATIONS

With Eq. 20,

B,=l.285 exp[l.43x10~5(2,652-3,000)];

B, = 1.285(0.995)= 1.279 bbl/STB

Total FVF’s When material-balance calculations are made for reservoir engineering, it is often convenient to calculate the volume at reservoir conditions that is occupied by all the material associated with a stock-tank barrel of oil-i.e., the volume of the saturated oil and the volume of the evolved or liberated gas. This can be expressed as a total FVF, B,.

The total FVF can be calculated if B, and the amount of liberated gas is known. That is, B, equals volume of oil plus dissolved gas/STB plus volume of liberated gas/STB.

In equation form,

B, =B, +B,(R,Th -R,y), . . (23)

where B, =

B, =

Rsh =

Rs =

total FVF, bbl/STB, oil FVF, bbl/STB, solution GOR at Ph. scf/STB, solution GOR at pressure of interest,

scf/STB, and

B, = gas FVF at pressure and temperature of interest, bbl/scf.

The gas FVF requires a value for the gas compressibility or zR factor that may be obtained from Chap. 17.

B,= 0.005042, T

) .,.,,.,................. 0

P

where B, = gas FVF, bbllscf,

ZK = gas compressibility factor at p, T, p = pressure of interest, psia, and T = temperature of interest, “R.

A nomogra by Standing. P

h for estimating total FVF was presented The correlation was developed from 387

experimental data points that included the ranges given in Table 22.9.

The nomograph, on which an example calculation is worked, is shown in Fig. 22.13.

Oil Viscosity Correlations The absolute viscosity of a fluid is a measure of the fluid’s resistance to flow. The resistance to flow is caused by internal friction generated when the fluid molecules are sheared. The viscosity can be quantified as the ratio of the shearing stress required to induce a particular rate of shear in the fluid at specific conditions of pressure and temperature. The absolute viscosity of a Newtonian fluid is independent of the rate of shear. Only Newtonian fluids are considered in this section.

22-13

1 2 5 10 20 50 100

PSEUDOREDUCED PRESSURE. p,

Fig. 22.12-Variation of pseudoreduced compressibility with pseudoreduced pressure and temperature.

Values of oil viscosity are required at various pressures and temperatures for both reservoir and production engineering calculations. If a PVT analysis is available, measured values of oil viscosity will be reported at reservoir temperature and at various pressures. However, as the fluid flows through the production system, the temperature also changes. This necessitates correcting the viscosity for temperature changes, which is usually accomplished by empirical correlations.

The absolute viscosity, which is usually referred to merely as the viscosity, can be expressed in various units. The so-called “oilfield unit” is the centipoise or poise. A relationship among various systems of units is given as 1 cp = 0.01 poise = 0.001 Pa*s = 6.72~ 10m4 lbm/(ft-set).

The kinematic viscosity of a fluid is the absolute viscosity divided by the density, or

CL Y=-.

P The most commonly used unit of kinematic viscosity

is the centistoke (cSt), where the conversion to SI units is 1 cSt=10-6 m*/s.

In addition to absolute and kinematic viscosity units, the units of Saybolt seconds universal (SSU) and Saybolt

TABLE 22.9-DATA RANGES FOR STANDING CORRELATION

Pressure, psia GOR, scf/STB Temperature, OF Gas gravity Oil gravity, OAPl

400 to 5,000 75 to 37,000

100 to 258 0.59 to 0.95 16.5 to 63.6


Fig. 22.13-Chart for calculating total formation volume by Standing’s correlation.

seconds furol (SSF) are commonly used. An approximate rect this value for dissolved gas. The dead-oil viscosity conversion between centistokes and the time units can be depends on API gravity of the stock-tank oil and the tem- made with the following equations. perature of interest.

The dead-oil viscosity can be obtained from empirical v=0.220tsu- 180/rsU, correlations or, if measured values are available at two

temperatures, the viscosity at any other temperature can and be calculated from the equation

v=2.12tsF-- 139/tp, . . . . . (25) log[log(v+0.8)]=A+B log 7-, . . .(26)

where v = kinematic viscosity in cSt,

tsu = Saybolt seconds universal, and tSF = Saybolt seconds furol.

Factors Affecting Oil Viscosity

The principal factors of interest to the petroleum engineer that affect viscosity are composition, temperature, dissolved gas, and pressure. Oil viscosity increases with a decrease in API gravity and also increases with a decrease in temperature.

The effect of dissolved gas is to lighten the oil and thus decrease its viscosity, while an increase in pressure on an undersaturated oil compresses the oil and causes the viscosity to increase.

where v = kinematic viscosity at T, T = temperature of interest, and

A,B = constants for a particular oil that can be determined if two measured values of u and T are available.

Beal’s Correlation for Dead Oils. Beal’ presented a graphical correlation showing the effects of both oil gravity and temperature on dead-oil viscosity. The correlation was developed from measurements made on 6.55 oil samples. The relationship among viscosity, API gravity, and temperature is shown in Fig. 22.14.

Oil Viscosity Correlations-Saturated Systems Effect of Dissolved Gas-Chew and Connally Method. The decrease in the dead-oil viscosity as gas goes into so-

The most common method for obtaining the viscosity of lution can be estimated with Fig. 22.15, which was pub- a crude oil that contains dissolved gas is first to estimate lished by Chew and Connally 8 in 1959. The procedure the viscosity of the gas-free or dead oil and then to cor- for using the chart and an example problem are shown


0.4 - -_ \

0.3 1.

0.2

I 90

/ I 20 ;0 40 50 60

Crude-oil grwity *API at 60*F ond atmospheric pressure

Fig. 22.14-Gas-free crude viscosity as a function of reservoir temperature and stock-tank crude gravity.

in the figure. They also proposed an equation for correcting for the dissolved gas:

h /.lr,,,=upo(j ,...............,..........,.. (27)

where

PO = saturated oil viscosity, p,,d = gas-free or dead-oil viscosity, and a,h = functions of R,, , shown in Fig. 22.16.

Beggs and Robinson Correlation. A method for calculating both dead-oil and saturated-oil viscosity was presented by Beggs and Robinson’ in 1975. The correlation was developed from more than 2,000 measured data points using 600 oil systems. The range of variables of the data is given in Table 22.10.

The equation developed reproduced the measured data with an average error of - 1.83% and a standard deviation of 27%.

The equation for dead-oil viscosity is

j~~>~=lO-~-l.O. . . . . . . . . . . (28)

where x = T-‘.16’ exp(6.9824-0.04658TpiI),

pod = dead-oil viscosity, cp, T = temperature of interest, “F, and

YAPI = stock-tank oil gravity, “API.

To correct for the effect of dissolved gas, an equation similar to Eq. 27 was developed.

CL 0, =Ap<,f, . . . . . . . . . . . . . . . . . . . . . . . . . . . ..(29)

i II I Ill

I O’o304 I 06 08, 2 3 456 810 20 30 40 60 ml00 1

Fig. 22.15-Viscosity and gas-saturated crude oils at reservoir temperature and pressure; Chew and Connally’s correlation.

where pLos = saturated-oil viscosity P,~~, = dead-oil viscosity, A,B = functions of R,,,

A = 10.715(R. + 100~“~“‘s, ., (30)

B = 5.44(R,+l50)p"8. . . . . . . . . . . . . ..(31)

where R,v is the solution GOR in scf/STB. No graphs are required to apply this method.

Example Problem 10. Calculate the viscosity of the saturated oil system described next using the Beal and Chew and Connally correlations and the Beggs and Robinson correlation where T= 137”F, -yApI =22”API, and R,, =90

scf/STB. Solution-Beal with Chew and Connally. From Fig.

22.14, p,d=20 cp. From Fig. 22.16, a=0.82 and h= 0.9. po,s=0.82(20)09=12.15 cp.

Interpolation was necessary on both Figs. 22.14 and 22.16 to obtain values for pl,d. a, and b. Use of Fig. 22.15 to correct for R,y gives a value of approximately 12 cp for p,,.

Solution-Beggs and Robinson. x = (137) -1.‘63 exp [6.9824-0.04658(22)]: x = 1.2658.

P Od = 10’.*6’* - l.O= 17.44 cp. A = 10.715(90+ 100) -o.s’5 =0.719. B = 5.44(90+ 150) -o.338 =0.853.

p,,,? = 0.719(17.44)".8"3 =8.24 cp.


Fig. 22.16-a and b factors for use in Chew and Connally’s viscosity correlation.

TABLE 22.10-BEGGS AND ROBINSON CORRELATION DATA

R,) SCflSTB 20 to 2,070 YAW 3 ,‘API 16 to 58

7: rg 0 70 to to 5,250 295

>E VISCOSITY OF GAS-SATURATED CRUDE OIL AT BUBBLE-POINT PRESSURE, CP

Fig. 22.17-Effect of pressure on viscosity of gas-saturated crude oils; Eeal’s correlation.

Oil Viscosity Correlations-Undersaturated Systems Solution.

The effect of increasing the pressure on an oil system From Eq. 12:

above the bubblepoint is to compress the liquid and to increase the viscosity. This effect was measured by Beal

Ph=

and presented graphically in Fig. 22.17. The graph gives

L

532 the viscosity increase in cpi 1 ,OOO-psi increase in pressure above pb as a function of the saturated or bubblepoint vis- 0.0178(0.745) exp 23.931(31)/(240+460) 1

111.187

cosity, pLob. Vasquez and Beggs5 extended the Beggs and Robin- ph =3,093 psia.

son correlation for undersaturated oils with the equation From Eq. 28:

p. =/.~,(p/p~)‘~, . . . . . . . . . . . . (32)

where

PO = viscosity at p >ph,

@ob = viscosity at pb, p = pressure of interest, and

pb = bubblepoint pressure.

The exponent m is pressure dependent and is calculated from

m=Clpc2 exp(Cj +Cdp), . . . .(33)

where p = pressure of interest, psia,

C, = 2.6, C2 = 1.187, C3 = -11.513, and C4 = -8.98~10-~.

Example Problem 11. Calculate the viscosity of the oil system described at a pressure of 4,750 psia, with T=240”F, YApI =31”API, yR =0.745, and Rsb =532

scf/STB.

n = (240)-I.163 exp[6.9824-0.04658(31)]; x = 0.4336,

pod = 10°‘4336-1.0=1.71 Cp.

From Eqs. 29, 30, and 31:

A = 10.715(532+100-“~5’5=0.387, B = 5.44(532+ 150) -“.338 =0.599,

and

/lob = 0.387(1.71)0.599=0.53 cp.

From Eqs. 32 and 33:

m = 2.6(4,750)‘,‘87

~exp[-11.513-4,750(8.98x10-5];

m = 0.393, and

PO = 0.53(4,750/3,093)“.393 =0.63 cp.

Gas/Oil IFT The interfacial or surface tension existing between a liquid and gas is required for estimating capillary-pressure


forces in reservoir engineering and is a parameter in some correlations used in wellbore hydraulics calculations. The surface tension between natural gas and crude oil ranges from zero to about 35 dyne/cm. It is a function of pressure, temperature, and compositions of the phases.

The surface tension of a hydrocarbon mixture can be calculated if the composition of the mixture at the pressure and temperature of interest is known. The parachor of each component must also be known. The parachor is the molecular weight of a liquid times the fourth root of its surface tension, divided by the difference between the density of the liquid and the density of the vapor in equilibrium with it. It is essentially constant over wide ranges of temperature. An equation for estimating surface tension is

oo.25= (34)

where u = surface tension, dyne/cm.

Pchi = parachor of ith component, xi = mole fraction of ith component in the liq-

uid phase, v; = mole fraction of ith component in the

vapor phase, pi = density of the liquid phase, g/cm”,

P,, = density of the vapor phase, g/cm 3, ML = molecular weight of liquid phase, M,. = molecular weight of vapor phase, and

C = number of components.

Parachors for some hydrocarbons, nitrogen, and carbon dioxide are given in Table 22.11. A correlation of the parachor with molecular weight was presented by Katz” and is shown in Fig. 22.18.

Empirical correlations in the form of graphs were presented by Baker and Swerdloff” where surface tension is correlated with temperature, API gravity, and pressure. The correlations are shown in Figs. 22.19 and 22.20. Equations that approximate Figs. 22.19 and 22.20 are:

aes=39-0.2571yAP1, . . . . . . . . (35)

and

u,oo=37.5-0.2571y/,~1, . . . . . _. . .(36)

where

068 = IFT at 68”F, dyne/cm, alOO = IFT at lOO”F, dyne/cm, and yAPI = gravity of stock-tank oil, “API.

It has been suggested that if the temperature is greater than lOO”F, the value at 100°F should be used. Also, if T<68”F, use the value calculated at T=68”F. For intermediate temperatures, use linear interpolation between the values obtained at 68 and 100°F. That is:

(T-68"F)(u68-LJloo) 07=fl68 - , ,..........

32 (37)

where or=IFT at 68”F< T< 100°F.

9oc

80C

7oc

600

‘0 500 Jz u 0

i 400

300

200

fO0

i 0 400 200 300 400

Molecular weight

Flg. 22.18-Parachors for hydrocarbons. 0, n-paraffins; 0, heptanes plus; A, gasolines; A, crude oil.

TABLE 22.11 -PARACHORS FOR PURE SUBSTANCES

Methane 77.0 Ethane 108.0 Propane 150.3 lsobutane 181.5 n-Butane 190.0

lsopentane 225 n-Pentane 232 n-Hexane 271 n-Heptane 311 n-Octane 352 Nitrogen (in n-heptane) 41.0 Carbon dioxide 78.0

The effect of gas going into solution as pressure is increased on the gas/oil mixture is to reduce the IFT. The dead-end oil IFT can be corrected by multiplying it by the following correction factor.

F,.= 1.0-0.024p”~45, . . . . . . . . . (38)

where p is in psia


The IFT at any pressure is then obtained from

u,,=F,.a7.. (39)

The IFT becomes zero at miscibility pressure, and for most systems, this will be at any pressure greater than about 5,000 psia.

P Oil = dead oil viscosity

PLO\ = saturated oil viscosity

Y= kinematic viscosity

P= fluid density CJ= surface tension, interfacial

Key Equations in SI Metric Units Most of the correlations presented in this chapter are

included in a calculator program for the HP-41C. The program is available from Hewlett-Packard. ” PO =

lOOOy, + 1.224y,R, . . . B, (1)

Nomenclature CI = function of R,, in Eq. 27 A = constant in Eq. 26 h = function of R,, in Eq. 27 B = constant in Eq. 26

B,? = gas formation volume factor B,, = oil formation volume factor C(, = I’,” =

c= c, .C?.

Cj.Cd = F=

F, =

where Y,~ =mole fraction gas,

=l.225+0.00164TR-1.769/y<,.

oil isothermal compressibility pseudo-reduced compressibility number of components

O.O148R,/, )I# =

O.O148R,,,, +35Oy,/M,, (6)

various constants correlating function in Eq. 18 correcting factor for dead oil interfacial

For y. ~0.825:

M,,=l945-1415/y,,. .

For y. >0.825: m =

tn ; =

M,, =

P=

PI, =

I),” =

I),“. =

Pch, =

RI; =

R, =

R $12 =

fsu = fSF =

T=

T /” =

T,,r = TR =

,’ =

v; =

x =

?‘,y =

7 G ,y =

Y=

YAPI =

Y,w =

Y,l =

cI=

CL,,/, =

tension. Eq. 38 pressure-dependent exponent in Eq. 32 mass of ith component molecular weight of stock-tank oil pressure of interest bubblepoint pressure pseudo-critical pressure pseudo-reduced pressure parachor of ith component free gas/oil ratio solution gas/oil ratio

solution gas/oil ratio at the bubblepoint pressure

Saybolt seconds universal Saybolt seconds furol temperature of interest pseudo-critical temperature pseudo-reduced temperature reservoir temperature specific volume volume of ith component symbol for various groups of terms,

Eq. 28 symbol for various groups of terms, Eqs.

5, 6, 9. IO, and 13-16 gas compressibility factor fluid specific gravity oil API gravity corrected gas gravity oil specific gravity fluid viscosity

oil viscosity at bubblepoint pressure

( 0.109

>

~ I.562 MO = ~-0.101

Y/l

For ys 50.60:

PhY,g - =8.427 exp(2.78~,Y)-4.01. TR

For ,vY > 0.60:

I’ b Y R -= 102.51~ “.“6+24.20. TR

-R

O.O15lT, 3.848 Y,p “Yg

YO Yn

-0.OlJT,,3.576) log (G)

where the following constants apply.

(8)


42 1 40.

38. SURFACE TENSION OF CRUDE OILS

AT ATMOSPHERIC PRESSURE $J 36.

5 34. E u 32. z ; 30.

; x8-

5 26.

24.

Fig. 22.19-Surface tension of crude oils at atmospheric Fig. 22.20-Effect of solution gas on surface tension of crude pressure. oils.

y. <0.876 y. 2 0.876

Cl 3.204 x 10 -4 7.803~10-~ c2 0.8425 0.9143 C3 1881.24 2022.19 c4 1748.29 1879.28

P >

1.204

R,, =yg 3 .““‘...“.” (13) 519.7x10?‘F

where

yR = 1.225 +O.O0164T- 1.769/r,.

R,= 23 643y,y, M,(l -y,) . . .

For a<40 7. . . T

ys =0.359 In +0.476 >

. . .

For 3 ~40.7: 1784 T 28.1RS+30.6T-1180r,+- - 10 910

(14)

O.O098py,

>

0.281

?',q = -0.236 . T

R.S=ClYg c, exp($-+), . . . . . .

where the following constants apply

(17)

y. <0.876 y. > 0.876

Cl 3.204x10-” 7.803x10-” C? 1.1870 1.0937 c3 1881.24 2022.19 c4 1748.29 1879.28

SURFACE TENSION OF CRUDE OILS EFFECT OF DISSOLVED GAS IN SOLUTION AT VARIOUS SATURATION PRESSURES ANO

ATMOSPHERIC TEMPERATURE

B 0 =0.972 -0.000147F’~‘75, . . . . (18)

where

+2.25T-5.75.

B,=1+C,R,+F(C2+CJR,), . . . . . . . . . . . (19)

where

254.7T 73 580 FZ-....-- -236.7T-- +68 380

Yo Yo

and the following constants apply.

y0 <0.876 y<, I 0.876

Cl 2.622 x 10 -3 2.626~10-~ C2 1.100x10-5 1.751 x 10-5 c3 1.337 x 10 -9 -1.811~10-~

co = Yo

px105

. . . . . . . . . . . . . . . . . . . . . . . . . . . . (22)

,A,, = lO’x-3’ -0.001, . . . . . (28)

where

~=(1.8T-460)-‘.‘~~ exp(l3.108-6.591/y.).

A=10.715(5.615R.+100)-0~“‘5. A . (30)

B=5.44(5.615Rs+150) -“.338. . . . . (31)


wjhere B,, is in m3/m3, C,, is in kPa - ’ , M,, is in kg/kg-mole,

p is in kPa, R, is in m’/m’,

Tis in K, p,, is in kg/m 3 , and pc, is in Pa.s.

Glossary These are generally accepted definitions, peculiar to reservoir engineering phase-behavior work.

Apparent liquid density is the ratio of mass to volume of a gas when dissolved m a liquid. It normally is calculated for conditions of 14.7 psia and 60°F by correcting the observed density of the system to that state and subtracting the mass and volume of the liquid component of the system.

Bubblepoint of a system is the state characterized by the coexistence of a substantial amount of liquid phase and an infinitesimal amount of gas phase in equilibrium.

Compressibility factor (gas-deviation factor, supercompressibility factor) is a multiplying factor introduced into the ideal-gas law to account for the departure of true gases from ideal behavior (pV=&T: z is the compressibility factor).

Condensate (distillate) liquids are liquids formed by condensation of a vapor or gas. The term usually identifies a light-colored liquid, usually ofSO”API gravity or higher, obtained from systems that exist in the gaseous phase in the reservoir.

Critical state is the term used to identify the unique condition of pressure. temperature, and composition wherein all properties of coexisting vapor and liquid become identical.

Critical temperature T, and/or pressure pC is the tenperature or pressure at the critical state.

Dewpoint of a system is analogous to the bubblepoint in that a large volume of gas and an infinitesimal amount of liquid coexist in equilibrium.

Dewpoint pressure p(, is the gas pressure in a system at its dewpoint.

Differential-gas liberation indicates removal of a gas phase from the system as the gas forms at bubblepoint conditions. It is generally believed that the differential- gas-liberation process is the one that predominates in solution-gas-drive reservoirs during the greater part of their producing life.

Differential process is a term used primarily in PVT work to indicate that, as a system is caused to move through a bubblepoint or dewpoint and as a result forms two phases, the minor phase is removed from further contact with the major phase. Thus, during a differential process, the “system” is continuously changing in quantity and composition.

Dissolved gas (solution gas) identifies tnaterial ordinarily gaseous at atmospheric conditions but which is part of a liquid phase at elevated pressure and temperature.

Dissolved-gas drive (solution-gas drive) is a primary recovery process whereby liquid (oil) is displaced from the reservoir rock by energy of expansion of gas components originally dissolved in the liquid.

Flash gas liberation means that a gas forms from a liquid (usually on reduction of pressure) under conditions wherein the total composition of the system remains the same in time. An example of flash gas liberation occurs during the steady-state flow of oil and gas through a gas-oil separator.

Flash process is one in which the composition of the system remains constant but the proportion of gas and liquid phases that comprise the system changes as pressure or some other independent variable is changed. For example. the determination of the PV relations of a reservoir fluid sample involves a flash process.

Formation volume factor (FVF) is a means of expressing a volumetric relation of a system. The volume of fluid, at formation pressure and temperature. that results in 1 bbl stock-tank oil is, by definition, the formation volutne B. If the system is in a single condensed state in the formation, the term oil-FVF B,, is used. If two phases exist, the term used is total-FVF B, or two-phase formation volume. Oil-formation volumes normally are between 1.1 and 2.0. Total formation volumes may be as great as 200. depending on the system composition and the pressure involved. Gas-formation volume B,q refers to the volume in the reservoir (usually expressed as barrels) per 1,000 std surface cu ft of the gas. Water-formation volume B,,. designates the volume in the fortnation occupied by I surface bbl water and its attendant gases. Water-formation volumes are usually in the range of 0.99 to 1.07. In all instances, the reference state is standard surface conditions of 14.7 psia and 60°F unless specified otherwise.

Gas gravity is a simple means of expressing the molecular weight of a gas. The unit of gas gravity is dry air of molecular weight 28.97. Thus, methane (molecular weight= 16.04) has a gas gravity of 16.04/28.97=0.55.

Gas-oil ratio (GOR) is a loose expression of system composition. Normally, the units involved are cubic feet of gas per I bbl liquid. both measured at 14.7 psia and 60°F. However. in some instances. local usage calls for tneas- uring the gas at some pressure other than 14.7 psia. Further, the barrel of liquid may refer to some pressure other than the usual stock-tank oil. The units of reservoir oil and residual oil are encountered quite often in PVT work. Lastly. several kinds of GOR are used in rescr-


voir engineering, such as solution (pas solubility in oil) R, producing R, and cumulative R,, Pressure and tcm- perature of separation and the number of stages used affect the GOR number obtained for a given system.

Mole is one molecular weight unit of any substance. For example. 16.04 Ibm methane is a lbm-mol. Likewise. 16.04 p methane constitute a gmol. The Ibm-mole is used for petroleum engineering work. A Ibm-mol of gas (perfect) occupies 370.4 cu ft at 14.7 psia and 60°F.

Phase is a portion of a system that differs in its intensive properties from adjacent portions of the system. An interface exists between phases because of this difference in properties. Systems involved in petroleum production normally occur in not more than two phases. gas and liquid. On occasion and for hydrocarbon systems of unusual composition. two liquid phases or a solid phase may occur.

Properties, Extensive and Intensive. Properties dircct- Iy proportional to the amount of material making up the system are termed extensive properties. Examples arc area, mass, inertia. and volume. An intensive property is one that is independent of the amount of material. Den- sity. pressure. temperature, viscosity, and surface tension are intensive properties. Energy is the product of an intensive property and an extensive property: for example. pressure times volume is mechanical energy.

Pseudocritical and Pseudoreduced Properties (Tem- perature, Pressure). Properties of pure hydrocarbons are often the same when expressed in terms of their reduced properties. The same reduced-state relationships often apply to multicomponent systems if “pseudo” critical tcm- peratures and pressures are used rather than the true criticals of the systems. Calculation of the pseudocritical values from the composition of the system varies depending on the correlation being used. The ratio of the properly to the pseudocritical property is called the pseudoreduced property, e.g., pseudoreduced pressure

Ppr =Ph,x

Reduced properties (temperature, pressure, volume) are the ratio of the property to the critical property: for example, the reduced pressure p I =p/~),. .

Relative oil volume is analogous to formation volume except that the reference state is other than at standard surface conditions and the oil is other than stock-tank oil. For example, the term is used often on the basis of I bhl bubblepoint oil, or saturated oil, as the reference volume. Relative oil volumes must specify pressure, tcmpcraturc. and some composition parameter, e.g., relative oil volume =0.7 (2.520 psia, 185°F. bubblepoint oil = 1 .O).

the liquid remaining in a PVT cell at the completion of a differential process carried out at or near the reservoir

Residual oil is a term common in PVT work to identify

temperature. By analogy. it refers also to the liquid that remains in an oil reservoir at depletion. General usage is that residual oil volumes and gravities are reported in PVT work at 60°F and 14.7 psia. Residual OII is to a dif- u/id Pm/. Pmr . API (1942).

ttirential gas-removal process as stock-tank oil is to a flash- gas process-the end liquid product.

Saturated liquid is a liquid in equilibrium with vapor at the saturation pressure. Likewise, saturated vapor dcnotcs equilibrium with liquid. These terms are often used ayn- onymously with the term “bubblepoint liquid” (dewpoint vapor) at the bubblepoint (dewpoint) pressure. Note that the terms “bubblepoint” and “dewpoint” identify, the spc- cial case where the minor phase is present only III an in- finitcsimal amount. whereas the term “saturated liquid” dots not involve the relative amounts of phases present.

Shrinkage refers to the decrease in volume of a liquid phase caused by release of solution gas and/or by the thermal contraction of the liquid. Shrinkage may be expressed (1) as a percentage of the final resulting stock- tank oil or (2) as a percentage of the original volume of the liquid. Shrinkage factor is the reciprocal of FVF expressed as barrels of stock-tank oil per barrel of rcscr- voir oil. A reservoir oil that rcsultcd in 0.75 bbl of stock-tank oil per I bbl of reservoir oil would have a shrinkage of 0.25/0.75=33%~ under Definition I. a shrinkage of 0.25/1.00=25% under Definition 2, a shrinkage factor of0.75. and an FVF of I .00/0.75= 1.33.

Solution gas-oil ratio, R,, . expresses the amount of gas in solution. or dissolved, in a liquid. The reference oil may be stock-tank oil or residual oil. On occasion. reservoir saturated oil is used as the rcferencc.

Standard conditions (surface) arc 14.7 psia and 60°F. Gas volumes may be specified on occasion at prcssurcs slightly removed from 14.7 psia.

Stock-tank oil is the liquid that results from production of reservoir material through surface equipment that separates normally gaseous components. Stock-tank oil may be caused to vary in composition and properties by varying the conditions of gas/liquid separation. Stock-tank oil is normally reported at 60°F and 14.7 psia but may be measured under other conditions and corrected to the standard condition.

System refers to a body or to a composition of matter that represents the material under consideration. The term “system” may be defined further as a homogeneous system or a heterogeneous system. In a homogeneous sys- tern, the intensive propertles vary only in a continuous manner with respect to the extent of the system. A hctcr- ogeneous system is made up of a number of homopcne- ous parts, and abrupt changes in the intensive proportics occur at the interface between the homogeneous parts.

Undersaturated fluid (liquid or vapor) is material capa- blc of holding additional gaseous or liquid components in solution at the specified state.


4. Lahater, J.A : “Bubble Point Prcwrc Correlation.” Twf\.. AIME (1958) 213. 379-81.

5. Vasquer. M. and Beep\, H.D.: “Correlat~on$ for Fluid Phy\al Property Prediction,” J. PH. Twh. (June 1980) 96X-70.

6. Trube. -A.S.: “Compresaihility of Undersaturated Hydrocarbon Reservoir Fluids.” Trw~s.. AIME (1957) 210. X-57

7. Beal. C.: “The Viscosity of Air. Water. Natural Gas. Crude Oil and Its Associated Gases at 011 Field Temperatures and Pre\wre~.” T/-w.\. , AIME (1946) 165. 94- Il5.

X. Chew. J. and Connally, C.A : “A Viscwity Correlation for (;a\- Saturated Crude Oils.” Trcmx.. AIME (1959) 216. 23-25

9. Beg”, H.D. and Robinson. J.R.: “Estimating the Viwwty of Crude Oil Sysrems.” J. Pe. Twh. (Sept. 19751 1140-41.

IO. Katz. D.L . Monroe, R R.. and Tramer. R.R : “Surface Tension (11 Crude Oils Contaimng Dioolved Case\,” PH. KY/I. (Sept. 19431 I-IO.

Lacey. W N.. Sage. B.H.. and Kircher. C.E. Jr.: “Phnsc Equllihrla in Hydrocarbon System\,. 111 ~ Solubility of a Dry Natural Ciao 111 Crude Oil.” /!I(/. N)/(l Orx. Clwrr. (IY3.l) 26. hS?.

Lcwts. W.K. and Squires, L.: “Mechanism ofOil Viwo~ity.” Oi/tr,~t/ Cm J. (1934) 33, No. 26. 92.

Nelson. W.L.: “How to Handle Viscous Crude Oil.” U/i and Co.\ ./. (1954) 53. No. 28. 269.

Norton. A.E.: L~thn’ccoirv~. McGmwHill Book Co. Inc.. New York Cay (1942).

Perry. J .H.: Chrrnic~trl Eqitwer’s Htrwliwok. McGraw-Hil I Bwh Co. Inc.. New York City (19.50).

I I. Baher. 0. and Swerdloff. W.. “Findmg Surface Tcnswn of. Hydrocarbon Liquids.” Uii oni/ Gay J. (Jan. 2. 1956).

Schilthuis. R.I.: “Active Oil and Reservoir Enerpy.” ~rwn.\. . AIME

IZ. HP-41C Petroleum Fluid!, Pac. Hewlett-Packard. 1000 N.E. Clr- (1936) 118. 33-52.

cle Blvd.. Corvalhs. OR 97330. Standing. M.B. and Katz. D.L.: “Densq ofCrude 011s Saturated With

General References Ndtural Gas.” Twms., AIME (1941) 136, ISYQS

Borden. G. Jr. and Raw, M.J.: “Correlation of Bottom Hole Sample

Data.” ~wrcr,~.s.. AlME (1950) 189. 345-48. van Wijk. W R., devries. D.A., and Thijscn. H.A.C.: “Study nf PVT

Relations of Reservoir Flui&.” Pro<,. , Fourth World Petroleum Con-

Dodson. C.R., Goodwill. D.. and Mayer. E.H.: “Application of Lah- gress. II, 313.

oratory PVT Data to Reservoir Engineerins Problems.” ‘frrras.. AIME (19.53) 198. 287-98. Vink. D.J. c’f a/.: “Multiple-Phase Hydrocarbon System\.” Ofi cr,rd

Cm J. (1940) 39. No. 28. 34.

Gosline. J.E. and Dodson. C.R.: “Solubility Relations and Volumet- ric Behavior of Three Gravitler of Crudes and Associated Gases.” Drill. crml Pd. Prtrc. . API (1942) 137.

W+@ns. W.R.: “Viscosity-Temperature Characteri\ticsof Petroleum Products.” Scwr7cv of Prrr0/cur,1, 2. 107 I.

Chapter 23

Phase Diagrams F.M. OTK Jr., New Mexico Inst. of Mining and Technology

J.J. Taber, New Mexico Inst. of Mining and Technology*

Introduction Petroleum reservoir fluids are complex mixtures containing many hydrocarbon components that range in size from light gases such as methane, ethane, and so on to very large hydrocarbon molecules containing 40 or more carbon atoms. Nonhydrocarbon components such as nitrogen, hydrogen sulfide (HzS), or CO2 also may be present. Water, of course, is usually present in large quantities in all reservoirs. At a given temperature and pressure, the components distribute between whatever solid, liquid, and vapor phases are present. A phase may be defined as that portion of a system that is homogeneous, bounded by a surface, and physically separable from other phases present. Equilibrium phase diagrams offer convenient representations of the ranges of temperature, pressure, and composition within which various combinations of phases coexist. Phase behavior plays an important role in a variety of reservoir engineering applications ranging from pressure maintenance to separator design to enhanced oil recovery (EOR) processes. This chapter reviews the fundamentals of phase diagrams used in such applications.

Single-Component Phase Diagrams Fig. 23.1 summarizes the phase behavior of a single component. The saturation curves shown in Fig. 23.1 indicate the temperatures and pressures at which phase changes occur. At temperatures below the triple point, the component forms a vapor if the pressure is below that indicated by the sublimation cuwe, and forms a solid at pressures above the curve. At pressures and temperatures lying on the sublimation curve, solid and vapor can coexist, and on the melting curve, solid and liquid are in equilibrium. At higher temperatures, liquid and vapor can coexist along the vaporization or vapor-pressure curve. If the pressure is greater than the vapor pressure, a liquid forms, if lower, a vapor. The vapor-pressure curve

terminates at the critical point. At temperatures above the critical temperature, T,, a single phase forms over the entire range of pressures. Thus, for a single component, the critical temperature is the maximum temperature at which two phases can exist. Critical temperatures of hydrocarbons vary widely. Small hydrocarbon molecules have low critical temperatures, while those of large ones are much higher. Critical pressures generally decline as the molecular size increases. For instance, the critical temperature and pressure of methane are - 117°F and 668 psia. For decane, the values are 652°F and 304 psia. (Fig. 23.9 shows additional vapor pressure curves and critical points for several other light hydrocarbon molecules.)

For many reservoir engineering applications liquid/vapor equilibrium is of greatest interest, though liquid/liquid equilibria are important in some EOR processes. Solid/liquid phase changes, such as asphaltene or paraffin precipitation, occasionally occur in petroleum production operations. Fig. 23.2 shows typical volumetric behavior of a single component in the range of temperatures and pressures near the vapor-pressure curve in Fig. 23.1. If the substance under consideration is placed in a pressure cell at constant temperature T1 below T, and at a low pressure (Point A, for instance), it forms a vapor phase of high volume (low density). If the volume of the sample is decreased with the temperature held constant, the pressure rises. When the pressure reaches p,, (T1 ), the sample begins to condense. The pressure remains constant at the vapor pressure until the sample volume is reduced from the saturated vapor volume (V,.) to that of the saturated liquid (V,). With further reductions in volume, the pressure rises again as the liquid phase is compressed. Note that small decreases in volume give rise to large pressure increases in the liquid phase because of the low compressibility of liquids. At a temperature Tz above the critical temperature, no phase change is observed. Instead, the sample can be

SOLID

I’

i:

MELTING CURVE

CRITICAL POINT

VAPORIZATION

SUBLIMATION VAPOR

CJRVE

T

TC

MPERATURE

Fig. 2X1-Phase behavior of a pure component.

’ Tc

TC

Tc

I I I 1

“L Vc Vv

VOLUME

Fig. 23.2-Volumetric behavior of a pure component in the liqutd/vapor region.

compressed from high volume (low density) and low pressure to low volume (high density) and high pressure with only one phase present.

Phase Rule The maximum number of phases that can coexist at fixed temperature and pressure is determined by the number of components present. The phase rule states that

F=2+C-P-n,, . . . . . . . . . . . . . . . . . . . . (1)

where F is the number of degrees of freedom, C is the number of components, P is the number of phases, and n c is the number of constraints. For a single-component system, the maximum number of phases occurs when there are no constraints (n c =0) and there are no degrees

3

z Pb

k a

Pd

PV2


’ ‘A ‘B ’ XE 1.0

MOLE FRACTION COMPONENT I

Fig. 23.3-Pressure-composition phase diagram for a binary mixture at a temperature below the critical temperature of both components.

of freedom (F=O). Thus, the maximum number of phases possible is three. Therefore, if three phases coexist in equilibrium (possible only at the triple point), the pressure and temperature are fixed. If only two phases are present for a pure component, then either the temperature or the pressure can be chosen. Once one is chosen, the other is determined. If the two phases are vapor and liquid, for example, choice of the temperature determines the pressure to be the vapor pressure at that temperature. These permitted pressure-temperature values lie on the vapor pressure curve of Fig. 23.1.

In a binary system, two phases can exist over a range of temperatures and pressures. The number of degrees of freedom is

F=2-nc, . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...(2)

and hence both the temperature and pressure can be chosen, though there is no guarantee that two phases will occur at a specific choice of T and p. For multicomponent systems, the phase rule provides little guidance, since the number of phases is always far less than the maximum number that can occur. Hence, as the number of components increases, more component concentrations must be known to determine the system.

Types of Diagrams Binary Phase Diagrams

Fig. 23.3 shows typical vapor/liquid phase behavior for a binary system at a fixed temperature below the critical temperature of both components. Such a diagram is known as a pressure-composition phase diagram. At pressures below the vapor pressure of Component 2, ~“2, any mixture of the two components forms a single vapor phase. At pressures between p “1 and p,,~ , two phases can coexist for some compositions. For instance, at pressure pb two phases will occur if the mole fraction of Component 1 lies between xE and xE. If the mixture

PHASE DIAGRAMS 23-3

:i

v

PUMP Pep,, P’Pd Pr,<P<Pb P’Pb P’Pb

Fig. 23.4-Volumetric behavior of a binary mixture at constant temperature

Pd2

Pdl

PVZ

VAPOR

xI K2 MOLE FRACTION COMPONENT I

Fig. 23.5-Pressure-composition phase diagram for a binary mixture at a temperature above the critical temperature of Component 1.

composition is xB, it will be all liquid, if it is xE, all vapor. For 1 mol of mixture of overall composition, z, between -xE and xE, the number of moles of liquid phase is

XE --z L=-. . . . . . . . . . . . . . . . . . . . . . . . . . . ...(3)

XE -xB

Eq. 3 is known as an inverse lever rule because it is

equivalent to a statement concerning the distances along a tie line from the overall composition to the liquid and vapor compositions; L=ZE/BE, where ZE and BE are lengths on the tie line shown in Fig. 23.3. Thus, the amount of liquid is proportional to the distance from the overall composition to the vapor composition divided by the length of the tie line. The line connecting the compositions of phases in equilibrium is known as a tie line. In binary phase diagrams such as Fig. 23.3, the tie lines are always horizontal.

?2!!!%? --- --- --- MERCURY PUhlP

p’pdl pi ‘pd PZ’Pl P3’P2 P’Pd2

Fig. 23.6-Volumetric behavior of a binary mixture at a constant temperature showing retrograde vaporization.

TEMPERATURE -

Fig. 23.7--Regions of temperature, pressure, and composition for which two phases occur in a binary liquid/vapor system.

Phase diagrams such as Fig. 23.3 can be determined experimentally by placing a mixture of fixed overall composition in a high-pressure cell and measuring the pressures at which phases appear and disappear. For example, a mixture of composition xa would show the behavior indicated qualitatively in Fig. 23.4. At a pressure less thanpd (Fig. 23.3), the mixture is a vapor. If the mixture is compressed by injecting mercury into the cell, the first liquid, which has composition xA, appears at the dewpoint pressure, pd. As the pressure is further increased, the volume of liquid grows as more and more of the vapor phase condenses. The last vapor, of composition X,R, disappears at the bubblepoint pRssut& pb.

If the system temperature is above the critical temperature of one of the components, the phase diagram is similar to that shown in Fig. 23.5. (See Fig. 23.13 for additional examples of this type of phase diagram.) At the higher temperature, the two-phase region no longer extends to the pure Component 1 side of


CRITICAL

< LOCUS

TEMPERATURE

Fig. 23.8-Projection of the vapor pressure (p,, and pa) curves and locus of critical points for binary mixtures. Points C, and C2 are the critical points of the pure components.

Fig. 23.9-Vapor pressure curves for light hydrocarbons and critical loci for selected hydrocarbon pairs.

Fig. 23.10-Properties of ternary diagrams

the diagram. Instead, there is a critical point, C, at which liquid and vapor phases are identical. The critical point occurs at the maximum pressure of the two-phase region. The volumetric behavior of mixtures containing less Component 1 than the critical mixture is like that shown in Fig. 23.4. Fig. 23.6 shows the volumetric behavior of mixtures containing more Component 1. Compression of mixture of composition x2 (in Fig. 23.5) leads to the appearance of liquid phase of composition xt when pressure pDl is reached. The volume of liquid first grows and then declines with increasing pressure. The liquid phase disappears again when pressure pm is reached. Such behavior is called “retrograde vaporization” (or “retrograde condensation” if the pressure is decreasing).

If the system temperature is exactly equal to the critical temperature of Component 1, the critical point on the binary pressure-composition phase diagram is located at a Component 1 mole fraction of 1 .O. Fig. 23.7 shows the behavior of the two-phase regions as the temperature rises. As the temperature increases, the critical point moves to lower concentrations of Compo- nent 1. As the critical temperature of Component 2 is approached, the two-phase region shrinks, disappearing altogether when the critical temperature is reached. A typical locus of critical temperatures and pressures for a pair of hydrocarbons is shown in Fig. 23.8. The critical locus shown in Fig. 23.8 is the projection of the critical curve in Fig. 23.7 onto the p-T plane. Thus, each point on the critical locus represents a critical mixture of different composition, though composition information is not shown on this diagram. For temperatures between the critical temperature of Component 1 and Component 2, the critical pressure of the mixtures can be much

PHASE DIAGRAMS 23-5

5 L

Fig. 23.11-Ternary phase diagram at a constant temperature and pressure for a system that forms a liquid and a vapor.

higher than the critical pressure of either component. Thus, two phases can coexist at pressures much greater than the critical pressure of either component. If the difference in molecular weight of the two components is large, the critical locus may reach very high pressures. Fig. 23.9 gives critical loci for some hydrocarbon pairs. ’

The binary phase diagrams reviewed here are those most commonly encountered. More complex phase diagrams involving liquid/liquid and liquid/liquid/vapor equilibria do occur, however, in hydrocarbon systems at very low temperatures (well outside the range of conditions encountered in reservoirs or surface separators) and in COz/crude oil systems at temperatures below about 50°C. For reviews of such phase behavior see Refs. 2 and 3.

Ternary Phase Diagrams

Phase behavior of mixtures containing three components is conveniently represented on a triangular diagram such as that shown in Fig. 23.10a. Such diagrams are based on the property of equilateral triangles that the sum of the perpendicular distances from any point to each side of the diagram is a constant equal to length of any of the sides. Thus, the composition of a point in the interior of the triangle is

Ll L2 L3 x, =-) x2 =-) x3 =-)

LT LT LT

where

LT=LI +L2 +L3. . . . . . . . . . . . . . . . . . . . (4)

Several other useful propetties of triangular diagrams are also a consequence of this fact. For mixtures along any line parallel to a side of the diagram, the fraction of the

component of the comer opposite to that side is constant

Fig. 23.12-Ternary phase diagram for the methane/ butane/decane system at 160DF 171 “Cl.

(Fig. 23.10b). In addition, mixtures lying on any line connecting a comer with the opposite side contain a constant ratio of the components at the ends of the side (Fig. 23.1Oc). Finally, mixtures of any two compositions, such as A and B in Fig. 23. lOd, lie on a straight line connecting the two points on the ternary diagram. Composi- tions represented on a ternary diagram can be expressed in volume, mass, or mole fractions. For vapor/liquid equilibrium diagrams, mole fractions are most commonly used.

Typical features of a ternary phase diagram for a system that forms a liquid and a vapor at fixed temperature and pressure are shown in Fig. 23.11. Mix- tures with overall compositions that lie inside the binodal curve will split into liquid and vapor. Tie lines connect compositions of liquid and vapor phases in equilibrium. Any mixture on one tie line gives the same liquid and vapor compositions. Only the amounts of liquid and vapor change as the overall composition changes from the liquid side of the binodal curve to the vapor side. If the mole fractions of component i in the liquid, vapor, and overall mixture are xi, yi, and zi, the fraction of the total moles in the mixture in the liquid phase is given by

L= Yi -zi yi-xi’ . . . . . . . . . . . . . . . ...“...” . . (5)

Fq. 5 is another lever rule similar to that described for binary diagrams. The liquid and vapor portions of the binodal curve meet at the plait point, a critical point where the liquid and vapor phases are identical. Thus, the plait point mixture has a critical temperature and pressure equal to the conditions for which the diagram is plotted. Depending on the pressure and temperature and components, a plait point may or may not be present.

Any one tematy diagram is given for fixed temperature and pressure. As either the temperature or pressure is varied, the location of the binodal curve and


1000 -

0 0.2 0.4 0.6 0.S

MOLE FRACTION METHANE

I 1

: I 0

Fig. 23.13-Pressure-composition phase diagrams for methane/butane and methaneldecane binary systems at 160°F [71°C].

slopes of the tie lines may change. Fig. 23.12 shows the effect of increasing pressure on ternary phase diagrams for mixtures of methane (C 1 ), butane (C,), and decane (COO) at 160°F. 4J The sides of the ternary diagram represent a binary system, so the ternary diagram includes whatever binary tie lines exist at the temperature and pressure of the diagram. Fig. 23.13 shows the corresponding binary phase diagrams for the C l-C4 and C 1 -C 1o pairs. The Cd-C 10 pair is not shown because it forms two phases only below the vapor pressure of C4, about 120 psia at 160°F (see Fig. 23.9).

As shown in Fig. 23.12, at 1,000 psia the two-phase region is a hand that stretches from the C 1 -C 10 side of the diagram to the tie line on the C I -Cd side. If the pressure is increased above 1,000 psia, the liquid composition line shifts to higher methane concentrations; methane is more soluble in both C4 and Cl0 at the higher pressure (see Fig. 23.13). The two-phase region detaches from the C ,-C4 side of the diagram at the critical pressure of the C I -C4 pair (about 1,800 psia). As the pressure increases above that critical pressure, the plait point moves into the interior of the diagram (Fig. 23.12, lower diagrams). With further increases in pressure, the two-phase region continues to shrink. It would disappear completely from the diagram if the pressure reached the critical pressure of the Cl-C 10 system at 160°F (nearly 5,200 psia).

Reservoir Fluid Systems

Real reservoir fluids contain many more than the two or three components, so phase composition data can no longer be represented with two or three coordinates. In-

P A

,” 3

z

i;’ 1

‘A

TEMPERATURE

Fig. 23.14-Pressure-temperature phase diagram for a mixture of fixed composition.

stead, phase diagrams, which give more limited information, are used. Fig. 23.14 shows one such diagram for a multicomponent mixture. Fig. 23.14 gives the region of temperatures and pressures at which the mixture forms two phases. The analog of Fig. 23.14 for a binary system can be obtained by taking a slice at constant mole fraction of Component 1 through the diagram in Fig. 23.7. Also given arc contours of liquid volume fractions, which indicate the fraction of total sample volume occupied by the liquid phase. Fig. 23.14 does not give any compositional information, however. In general, the compositions of coexisting liquid and vapor will be different at each temperature and pressure.

At temperatures below the critical temperature (Point C), a sample of the mixture described in Fig. 23.14 splits into two phases at the bubblepoint pressure (Fig. 23.4) when the pressure is reduced from a high level. At temperatures above the critical temperature, dewpoints are observed (Fig. 23.6). In this multicomponent system, the critical temperature is no longer the maximum temperature at which two phases can exist. In- stead, the critical point is the temperature and pressure at which the phase compositions and all phase properties are identical.

The bubblepoint, dewpoint, and single-phase regions shown in Fig. 23.14 are sometimes used to classify reservoirs. At temperatures above the cricondentherm, the maximum temperature for the formation of two phases, only one phase occurs at any pressure. For instance, if the hydrocarbon mixture of Fig. 23.14 were to occur in a reservoir at temperature TA and pressure PA (Point A), a decline in pressure at approximately constant temperature caused by removal of fluid from the reservoir would not cause the formation of a second phase. While the fluid in the reservoir remains a single phase, the produced gas splits into two phases as it cools and expands to surface temperature and pressure at Point A’. Thus, some condensate would be collected at the

PHASE DIAGRAMS

surface even though only one phase is present in the formation. The amount of condensate collected depends on the operating conditions of the separator (or separators). The lower the temperature at a given pressure, the larger the volume of condensate collected (Fig. 23.14).

Dewpoint reservoirs are those for which the reservoir temperature lies between the critical temperature and the cricondentherm for the reservoir fluid. Production of fluid from a reservoir starting at Point B in Fig. 23.14 causes liquid to appear in the reservoir when the dewpoint pressure is reached, and as the pressure declines further, the saturation of liquid increases because of retrograde condensation. Because the saturation of liquid is low, only the vapor phase flows to producing wells. Thus, the overall composition of the fluid remaining in the reservoir changes continuously. However, the phase diagram shown in Fig. 23.14 is for the original composition only. The preferential removal of light hydrocarbon components in the vapor phase generates new hydrocarbon mixtures which have a greater fraction of the heavier hydrocarbons. Differential liberation experiments, in which a sample of the reservoir fluid initially at high pressure is expanded through a sequence of pressures, can be used to investigate the magnitude of the effect of pressure reduction on the vapor composition. At each pressure, a portion of the vapor is removed and analyzed. Such an experiment simulates what happens when condensate is left behind in the reservoir as the pressure declines. As the reservoir fluid becomes heavier, the boundary of the two-phase region in a diagram like Fig. 23.14 shifts to higher temperatures. Thus, the composition change also acts to drive the system toward higher liquid condensation. Such reservoirs are candidates for pressure maintenance by lean gas injection to limit the retrograde loss of condensate or for gas cycling to vaporize and recover some of the liquid hydrocarbons.

Bubblepoint reservoirs are those in which the temperature is less than the critical temperature of the reservoir fluid (Point D in Fig. 23.14). These reservoirs are sometimes called “undersaturated” because there is insufficient gas for a gas phase at that temperature and pressure. Isothermal pressure reduction causes the appearance of a vapor phase at the bubblepoint pressure. Because the compressibility of the liquid phase is much lower than that of a vapor, the pressure in the reservoir declines rapidly during production in the single-phase region. The appearance of the much more compressible vapor phase reduces the rate of pressure decline. The volume of vapor present in the reservoir grows rapidly with reduction of reservoir pressure below the bubblepoint. Because the vapor viscosity is much lower than the liquid viscosity, and the gas relative permeability goes up markedly with increasing gas saturation, the vapor phase flows more easily. Hence, the produced GOR climbs rapidly. Again, pressure maintenance by water drive, water injection, or gas injection can substantially improve oil recovery over the 10 to 20% recovery typical of pressure depletion in these solution- gas-drive reservoirs. As in dewpoint reservoirs, the composition of the reservoir fluid changes continuously once the two-phase region is reached.

There is, of course, no reason why initial reservoir temperatures and pressures cannot lie within the two- phase region. Oil reservoirs with gas caps and gas reser-

r------ 23-7

Fig. 23.15~Increase in OAPI gravity with depth: (a) Ordovician Ellenberger reservoirs in Delaware Val Verde basin; (b) Pennsylvanian Tensleep reservoirs in Wyoming.

voirs with some liquids present are common. There also can be considerable variation in the initial composition of the reservoir fluid. The discussion of single-phase, dewpoint, and bubblepoint reservoirs was based on a phase diagram for one fluid composition. Even for one fluid, all the types of behavior occur over a range of temperatures. In actual reservoir settings, the composition of the reservoir fluid correlates with depth and temperature. Deeper reservoirs usually contain lighter oils.‘j Fig. 23.15 shows the relationships between oil gravity and depth for two basins. The higher temperatures of deeper reservoirs alter the original hydrocarbon mixtures to produce lighter hydrocarbons over geologic time. 6 Low oil gravity, low temperature, and relatively small amounts of dissolved gas all combine to produce bubblepoint reservoirs. High oil gravity, high temperatures, and high GOR’s produce dewpoint or condensate systems.

Phase Diagrams for EOR Processes

Phase behavior plays an important role in a variety of EOR processes. Such processes are designed to overcome, in one way or another, the capillary forces that act to trap oil during waterflooding. In surfactant/polymer processes, the effects of capillary forces are reduced by injection of surfactant solutions that contain molecules with oil- and water-soluble portions. Such molecules migrate to the oil/water interface and reduce the interfacial tension, thereby reducing the magnitude of the capillary forces that resist movement of trapped oil. Miscible displacement processes are designed to eliminate interfaces between the oil and the displacing phase, thereby removing the effects of capillary forces between the injected fluid and the oil. Unfortunately, fluids that are strictly miscible with oil are too expensive for general use. Instead, fluids such as methane or methane enriched with intermediate hydrocarbons, CO*, or nitrogen are injected, and the required miscible displacing fluid is generated by mixing of the injected fluid with oil in the reservoir.

23-8

b1a.b

O-0-b SURfACTANl

TYPE II( )

b. TYPE III

SURfACTANl

A c. TYPE II( + )

/ \

&

BllHE OIL


DEW POINTS -

75% 50% 2 5 % 5% I VOLUME PERCENT LIQUID PHASE

Fig. 23.16-Ternary representation of phase diagrams MOLE PERCENT CO2

Phase diagrams typical of those used to explain the behavior of surfactant systems are shown in Fig. 23.16. ’ In those ternary diagrams, the components shown are no longer true thermodynamic components since they are mixtures. A crude oil contains hundreds of components, and the brine and surfactant pseudocomponents may also be complex mixtures. The simplified representation, however, has obvious advantages for describing phase behavior, and it is reasonably accurate as long as each pseudocomponent has approximately the same composition in each phase. In Fig. 23.16a for instance, the “oil” pseudocomponent can appear in an oil-rich phase or in a phase containing mostly surfactant and brine. If the oil solubilized into the surfactantlbrine phase is nearly the same mixture of hydrocarbons as the original “oil,” then the representation in terms of pseudocomponents is reasonable. The compositions shown in Fig. 23.16 are in volume fractions. An inverse lever rule similar to Eqs. 3 or 5 gives the relationship between the volumes of the two phases for a given overall composition, as illustrated in Fig. 23.16.

Fig. 23.16a is a phase diagram for the liquid/liquid equilibrium behavior typical of mixtures of brines of low salinity with oil. If there is no surfactant present, the oil and brine are immiscible; mixture compositions on the base of the diagram split into essentially “pure” brine in equilibrium with “pure” oil. Addition of surfactant causes some oil to be solubilized into a microemulsion rich in brine. That phase is in equilibrium with a phase containing nearly pure oil. Thus in the low-salinity brine, the surfactant partitions into the brine phase,

Fig. 23.17-Typical pressure-composition phase diagram for a binary mixture of CO, with a crude oil at temperatures above 120°F [49%].

solubilizing some oil. The plait point in Fig. 23.16a lies close to the oil comer of the diagram. Because only two phases occur and the tie lines all have negative slope, such phase is often called “Type II( -).”

Phase diagrams for high-salinity brines are often similar to Fig. 23.16~. In the high-salinity systems the surfactant partitions into the oil phase and solubilizes water into an oil-external microemulsion. In this case the plait point is close to the brine apex on the ternary diagram. For intermediate salinities, the phase behavior can be more complex, as shown in Fig. 23.16b. Accord- ing to the phase rule, if the temperature and pressure are set, then up to three phases can coexist for a three component system. If three phases do occur, then the compositions of the phases are fixed at a given temperature and pressure. The three-phase region on a ternary diagram is represented as a triangle (Fig. 23.16b). Any overall composition lying within the three-phase region splits into the same three phases. Only the amounts of each phase change as the overall composition varies in the three-phase region. The edges of the three-phase region are tie lines for the associated two-phase regions. Thus, there is a two-phase region adjacent to each of the sides of the three-phase triangle. In Fig. 23.16b, the two-phase region at low surfac.tant concentrations is too small to show on the diagram. It must be present, however, since oil and brine form only two phases in the absence of surfactant.

PHASE DIAGRAMS 23-9

Fig. 23.18-Pressure composition diagram-Gas 1 system for Rangely oil: 95% CO, and 5% methane gas system at 160aF 171 “Cl.

Phase behavior of COzlcrude oil systems is often summarized in pressure-composition (p-x) diagrams such as those shown in Fig. 23.17. Fig. 23.18 is an example of a p-x diagram for mixtures of CO1 (containing a small amount of methane contamination) with crude oil from the Rangely field. 8 In such diagrams, the behavior of binary mixtures of COZ with a particular oil is reported for a fixed temperature. Thus, the oil is represented as a single pseudocomponent on such a diagram. Such diagrams indicate bubble- and dewpoint pressures, the regions of pressure and composition for which two or more phases exist, and information about the volume fractions of the phases. However, they provide no information about the compositions of the phases in equilibrium. The reason for the absence of composition data is illustrated in Fig. 23. 19,3 which gives data reported by Metcalfe and Yarborough9 for a ternary system of CO*, Cd, and C 10. Binary phase data for the CO*-Cd (Ref. 10) and COz-C tc (Ref. 11) systems also are included. Fig. 23.19 shows a triangular solid within which all possible compositions (mole fractions) of COz-Cd-C to mixtures for pressures between 400 and 2,000 psia are contained. The two-phase region is bounded by a surface that connects the binary phase envelope for the COz-C ra binary pair to that on the CO+4 side ofthe diagram. That surface is divided into two parts-liquid compositions and vapor compositions. Tie lines (heavy dashed lines in Fig. 23.19) connect the compositions of liquid and vapor phases in equilibrium at a fixed pressure. Thus, the ternary phase diagram for CO2-C4-C tc mixtures at any pressure is just a constant

Fig. 23.19-Phase behavior of CO,-C,-C,, mixtures at 16OOF [71 “Cl.

pressure (horizontal) slice through the triangular prism. Several such slices at different pressures are shown in Fig. 23.19. At pressures below the critical pressure of CO 2 -C 4 mixtures ( 1,184 psia) , both CO 2 -C , c mixtures and CO2-C4 mixtures form two phases for some range of COz concentrations. At 400 and 800 psia, the two- phase region is a band across the diagram. Above the critical pressure of COz-Cd mixtures, CO2 is miscible with Cd. and ternary slices at higher pressures show a continuous binodal curve on which the locus of liquid compositions meets that of vapor compositions at a plait point. The locus of plait points (labeled “P” in Fig. 23.19) connects the critical points of the two binary pairs.

To see the effect of representing the phase behavior of a ternary system on a pseudobinary diagram, consider a p-x diagram for an “oil” composed of 70 mol% C ,c and 30 mol% CJ. At any fixed pressure, the mixtures of CO2 and oil which would be investigated in an experiment to determine ap-x diagram lie on a straight line (the dilution line), which connects the original oil composition with the CO2 apex. Thus, a P-X diagram for this


LIQUID LIQUID L

J I

-,I /

/” /

Fig. 23.20-p-x diagrams for mixtures of CO, with Wasson oil, where L, is Liquid Phase 1 (oil-rich phase), L, is Liquid Phase 2 (COP-rich phase), and V is the vapor phase. Dashed lines indicate constant volume fraction of L, phase.

system is a vertical slice through the triangular prism shown in Fig. 23.19. The saturation pressures on a p-x diagram are those at which the dilution plane intersects the surface which bounds the two-phase region. Bubble- point pressures (B) occur where the dilution plane intersects the liquid composition side of the two-phase surface, while dewpoint pressures (D) occur at the intersection with vapor compositions. Comparison of the phase envelope on the resulting p-x diagram with binary phase diagrams yields the following observations.

1. Tie lines do not, in general, lie in the dilution plane. Instead, they pierce that plane. This means that the composition of vapor in equilibrium with a bubblepoint mixture on the p-x diagram is not the same as that of the dewpoint mixture at the same pressure.

2. The critical point on the p-x diagram occurs where the locus of plait points pierces the dilution plane. It is not, in general, at the maximum saturation pressure on the p-x diagram. The maximum pressure occurs where the binodal curve is tangent to the dilution plane. The critical point on the p-x diagram can lie on either side of the maximum pressure, depending on the position of locus of plait points on the two-phase surface.

It is apparent from Fig. 23.19 that the composition of the original oil has a strong influence on the shape of the saturation pressure curve, and on the location of the critical point on the p-x diagram. If the oil had been richer in C4, the critical pressure and maximum pressure both would have been lower. Thus, it should be anticipated that the appearance of p-x diagrams for C02icrude oil systems should depend on the composition of the oil.

Figs. 23.18 and 23.20 illustrate the complexity of

phase behavior observed for COz/crude oil systems. Fig. 23.18 gives the behavior of mixtures of CO2 (with about 5 % methane as a contaminant) with Rangely crude oil at 16O“F. The oil itself has a bubblepoint pressure of about 350 psia. Mixtures containing up to about 80 mol% CO;? (+C 1) show bubblepoints, while those containing more CO2 show dewpoints. At the relatively high temperature of the Rangely field, only two phases, a liquid and a vapor, form. At lower temperatures, more complex phase behavior can occur. Figs. 23.20a, b and c show the behavior of mixtures of a dead oil from the Wasson field3 with CO2. At 90°F and 105”F, the mixtures form a liquid and a vapor at low pressures and two liquid phases at high pressures and high CO2 concentm- tions. They form three phases, two liquids and a vapor, for a small range of pressures at high CO* concentrations. The liquid/liquid and liquid/liquid/vapor behavior disappears if the temperature is high enough. At 120°F (Fig. 23.2Oc), the three-phase region had disappeared. For the systems studied to date, 120°F appears to be a reasonable estimate of the maximum temperature for liquid/liquid/vapor separations. For detailed discussions of such phase behavior, see Refs. 2 and 3.

Calculation of Phase Compositions

Calculations of the compositions of phases that occur for multicomponent mixtures are important for the design of surface separators and for the design of EOR processes such as high-pressure and condensing-gas drives and CO1 floods. There are two widely used methods for such calculations-K-value correlations and equations of state (EOS’s).

PHASE DIAGRAMS 23-l 1

The use of K-values, also called “equilibrium ratios” or “equilibrium constants,” is based on the behavior of mixtures of gases at relatively low pressures and temperatures. According to Raoult’s law, the partial vapor pressure phi of component i in a liquid mixture is equal to the product of the mole fraction of component i in the liquid and its pure component vapor pressure

p~i=Xjpvj. . . . . . f.. . . . . . . . . . . . . (6)

In addition, Dalton’s law states that the partial pressure of component i in the vapor is

p;j =yjpr, . . . . . . . . . . . . . . . . . . . . . . * . . . . (7)

where yi is the mole fraction of component i in the vapor andp, is the total pressure. Rearrangement of Eqs. 6 and 7 gives the definition of K-value for an ideal (low pressure) system:

PRESSURE,PSIA

Fig. 23.21-Typical equilibrium ratios at 22CPF [104%] (dashed lines are the ideal ratios).

K.-Y; I

-pvi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (8) xi Pr

Thus, for a multicomponent mixture at low pressure, the equilibrium value can be estimated from the vapor pressure, which is a function of temperature only, and the total pressure. The assumption of an ideal gas in Raoult’s and Dalton’s laws is reasonable only if the pressure is below about 50 to 100 psia. ‘* At higher pressures, equilibrium ratios are functions of pressure, temperature, and composition. Fig. 23.21 shows a typical set of equilibrium ratios for a hydrocarbon system containing some CO2 at 220°F. I3 Also shown (as dashed lines) are the ideal equilibrium ratios. At high pressures, the K-values for ethane and heavier hydrocarbons pass through a minimum and appear to converge to a value of one, in this case at 4,200 psia. This observation is the basis for a widely used empirical correlation for K-values. K-value charts for a variety of convergence pressures and a recommended technique for estimating the convergence pressure are given in GPSA’s Engineer- ing Data Book. ’

If K-values ate known or can be estimated, then amounts of liquid and vapor and phase compositions can be calculated easily. Consider 1 mol of a mixture in which the overall mole fraction of the ith component is zi . If the mole fractions of component i in the liquid and vapor are Xi and yi , and the fraction of the mole of mixture that is liquid is L, then a material balance gives

Zi=Xil+y~(l-L). . . . . . . . . . . . . . . . . . (9)

By definition, cXi=Eyi=l, SO cXi-Cyi=O which gives the nonlinear function f(L):

f(L)= T Ky;;;;)L =o. . . . . . . . . . . (12) 1 1

Eq. 12 can be solved for L by application of a Newton- Raphson iteration. If Lk is the kth estimate of the solution, an improved estimate is given by

Lk+l=Lk- pi’ ) .....,,,...,........(13)

z Lk

where

The iterative calculation is complete when AL) as given by Eq. 12 and AL=Lk+l -Lk are both smaller than some preset tolerances. Once the liquid mole fraction has been determined, the Xi and yi are obtained from Eqs. 10 and 11.

If the mixture is at its bubblepoint pressure, then L= 1 and Czi=l, and Eq. 12 reduces to

Substitution of the definition of Ki=yilXi into Eq. 9 C(ziKi)=l. ...........,.......... . . . . . ..(15)

and rearrangement gives Thus, if Ki’s are known as a function of pressure, then

Zi xj = Ki +(l-Ki)L. . . . . . . . . . . . . . . . . . . . . . (10)

the bubblepoint pressure can be obtained as the pressure at which Eq. 15 is satisfied. Bubblepoint pressures are generally most sensitive to the K-values of the lightest

Similarly, Eq. 9 can be solved for yi, giving components, which axe the largest. If the mixture is at its dewpoint pressure, then L=O, CZi = 1, and

KiZi Yi= Kj +(l-Ki)L. . . . . , . . . . . . . . . . . . -(II) c =l. . . . . . . . . . . . . . . . . . . . . . . . . (16)


Fig. X3.22-Comparison of calculated and measured phase compositions for ternary mixtures of CO,. methane (C,), and decane (C,,), at 160°F [71”C] and 1,250 psia.

Dewpoint pressures are most sensitive to the smallest K- values, those of the heavy components, which often are least accurately known. Thus, there is often more uncertainty in calculated values of dewpoint pressure. The sums of Eqs. 15 and 16 also are useful for determining whether the mixture forms one or two phases. If C(K;z;) < 1, the mixture is all liquid. If C(ziIKi) < 1, the mixture is all vapor. If both C(K,zi)> 1 and C(K;Iz,) > 1, the mixture forms two phases.

In recent years, EOS’s also have been used extensively for phase equilibrium calculations. Most of the widely used EOS’s are refinements of the equation proposed by van der Waals:

RT a --- p= “-b v2, ,,........................ (17)

volume is small enough to be close to the constant h, then the pressure increases rapidly as the volume is reduced. Thus, the EOS is qualitatively consistent with liquid behavior when the pressure is high.

The calculation of phase compositions is based on the fact that, at thermodynamic equilibrium, the fugacity of each component must be the same in each phase. The fugacity of a component in a phase can be calculated if the volumetric behavior of the phase is known. It can be shown I4 that the fugacity of component i, fi , in a phase is given by

RTlnfi=Sm[ (2) TV

Vt t 3 l’“, -$]dV,

t

-RTln vt

- ) . . . . . . . . . . . . . niRT

where T is the temperature, p the pressure, V, the total volume, ni the number of moles of component i, and R the gas constant. If the relationship between pressure, composition, and total volume is known from an EOS, then taPlaniJT,V ,n can be obtained and the integral evaluated. A var!e<y of EOS’s have been suggested for hydrocarbon mixtures. For example, the original Redlich-Kwong equation has the form

n,RT 2 ntam

P= V,-0, - t t ,,,

T” v (v +nb ) ’ ‘. . . . . (20)

where n, =Cni is the total number of moles and a,,, and b, depend on the mixture composition and the critical properties of the components as follows.

(EyiA; 1/2)2R2T5’2 am= ) . . . . . . . . . . . . . . . (21) p

where

where p is the pressure, R the gas constant, T the temperature, and V the molar volume. The constants a

A, = Qa(PIpci) , (T,T,i)5,2 . . . . . . . . . . . . . . . . . (22)

and b can be determined for a particular component from thermodynamic constraints at the critical point, which requires that

and

(ap/w)~, =(ap%v*)T, =o, 1

a,= EO.4275. . . . . . . . . . . . . . . . . . . 9(2” -1)

which gives

21 R2Tc2 a=- -

64 PC

b = @Y;BiPT m , . . . . . . . . . . . . . . . . . . . . . . . (24)

P

where and

b=F, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . c

B, = nb(P/Pci)

(18) ’ . . . . . . . . . . . . . . (T,T,i) (25)

where T, is the critical temperature and pc is the critical pressure.

and

van der Waals’ equation reduces to the ideal gas law if 2’* -1

~0.08664. . . . . . . . . (26) the molar volume is large (low pressure). If the molar

fib=- 3

PHASE DIAGRAMS

In Eqs. 21 through 26, y, is the mole fraction of component i in the mixture, and pci and T,; are the critical pressure and temperature of component i. The constants Q, and fib arise from the thermodynamic constraints, cwa v) Tr =(a2piavl)T, =0, at the critical point. From Eqs. 19 through 26, an expression for the fugacity of each component in a phase can be obtained. To calculate phase compositions, the following procedure is used.

1. Estimate compositions of liquid and vapor. 2. Calculate fugacities of each component in each

phase. 3. Iff,,, =fiL stop. Otherwise, obtain improved phase

compositions and return to Step 2. Similar calculations can be performed for liquid/liquid

and even liquid/liquid/vapor systems. Because the equations for fugacities are complex and nonlinear, computer implementation of this iterative scheme to find phase compositions is required.

The Redlich-Kwong EOS given as an example here is by no means the only equation available. Many modifications to the Redlich-Kwong equation have been proposed to improve the accuracy of the predictions of phase compositions, and equations with different analytical forms are also in use. The Soave modification of the Redlich-Kwong equation and the Peng-Robinson equation are among the most widely used. Ref. 14 gives details of a variety of EOS’s, and Ref. 15 is a useful collection of papers relevant to phase equilibrium calculations for hydrocarbon systems. Computer programs for such calculations are available. *

EOS’s currently in use are quite accurate for mixtures of light hydrocarbons for which critical properties are known and extensive phase behavior data are available. For instance, Fig. 23.22 shows a comparison of phase compositions calculated with the Peng-Robinson EOS with measured values for mixtures of CO*, C 1, and C 10 at 1,250 psia and 160°F. For this well-characterized system, the calculated values agreed well with the measured compositions. For crude oil systems, phase behavior predictions are less reliable because the chamcterization of heavy components is less certain. For such systems some experimental data are required to tune the EOS to represent the particular hydrocarbon system. Improvement of the predictive power of EOS’s for complex hydrocarbon systems is an area of active current research.

Nomenclature a, = defined by Eq. 21 Ai = defined by Eq. 22

6, = defined by Eq. 24 Bi = defined by Eq. 25 C = critical point when liquid and vapor phases

are identical fir. = liquid fugacity of Component i fiV = vapor fugacity of Component i Ki = K-value of Component i

L = total moles of liquid-phase in mixture Lk = kth estimate of L by Newton-Raphson

iteration no = number of constraints

‘Gas Processors Suppliers Assn Tulsa, OK

23-13

p = pressure PJ,, = bubblepoint pressure pd = dewpoint pressure pt = total pressure

PV = vapor pressure pVi = vapor pressure of Component i in liquid

mixture p:i = partial vapor pressure of Component i in li-

quid mixture

PVZ = any mixture of two components which form a single vapor phase

pyl = pressure below vapor pressure of Compo- nent z which may form a single vapor phase

pv2 = pressure above vapor pressure of Compo- nent z which may form a single vapor phase

T,. = critical temperature T, = constant temperature below T, T2 = constant temperature above T,. VL = saturated liquid volume V, = saturated vapor volume Zi = overall mole fraction of the ith component

Q, = defined in Eq. 23 Qb = defined in Eq. 26

Subscripts

C = number of components F = number of degrees of freedom P = number of phases

References 1.

2.

3.

4.

5.

6.

7.

8.

9.

Engineering Data Book, Gas Processors Suppliers Assn., ninth edition, Tulsa (1972). Stalkup, F.I. Jr.: Miscible Displacement, Monograph Series, SPE, Dallas (1983) 8. Orr, F.M. Jr. and Jensen, C.M.: “Interpretation of Pressure- Composition Phase Diagrams for CO*-Cmde Oil Systems,” Sot. Pet. Eng. J. (Oct. 1984) 485-97. Reamer, H.H., Fiskin, J.M., and Sage, B.H.: “Phase Equilibria in Hydrocarbon Systems,” Ind. Eng. Chem. 41 (Dec. 1949) 2871. Sage, B.H. and Lacey, W.N.: Thermodynamic Properties of the Lighter Parafin Hydrocarbons and Nitrogen, Monograph on API Research Project 37, American Petmleum Inst., New York City (1950). Hunt, J.M.: Petroleum Geochemistry and Geology, W.H. Freeman and Co., San Francisco (1979). Nelson, R.C. and Pope, GA.: “Phase Relationships in Chemical Flooding,” Sot. Pet. Enr. 1. (Oct. 1978) 325-38. Graue, D.J. and Zana, E.T.: “Study of a Possible CO, Flood in the Rangely Field, Colorado,” J. Per. Tech. (July 1981) 1312-18. Metcalfe, R.S. and Yarbomugh, L.: “The Effect of Phase Equilibria on the CO* Displacement Mechanism,” Sot. Pet. Eng. J. (Aug. 1979) 242-52; Trans., AIME, 267.

10. Olds, R.H. el al.: “Phase Equilibria in Hydmcarbon Systems,” Ind. Eng. Chem. 41 (March 1949) 475-82.

11. Reamer, H.H. and Sage, B.H.: “Phase Equilibria in Hydrocarbon Systems. Volumetric and Phase Behavior of the n-Decane-CO2 System,” J. Chem. Eng. Data 8, No. 4 (1963) 508-13.

12. Standing, M.B.: Volumetric and Phase Behavior of Oil Field Hydrocarbon Sysrems, SPE, Dallas (1977). .

13. Allen, F.H. and Roe, R.P.: “Performance Characteristics of a Volumetric Condensate Reservoir,” Trans., AIME (1950) 189, 83-90.

14. Reid, R.C., Prausnitz, J.M., and Sherwood, T.K.: The Properties of Gases and Liquids, third edition, McGraw-Hill Book Co. Inc., New York City (1977).

15. Phase Behavior. Reprint Series, SPE, Dallas (1981) 15.

Chapter 24

Properties of Produced Waters A. Gene Collins,* U S. DOE Bartlesville Energy Technology Center**

Introduction and History Early U.S. settlements commonly were located close to

salt licks that supplied salt to the population. Often these

salt springs were contaminated with petroleum. and

many of the early efforts to acquire salt by digging wells

were rewarded by finding unwanted increased amounts

of oil and gas associated with the saline waters. In the

Appalachian Mts.. many saline water springs occurred

along the crests of anticlines. ’

In 1855 it was found that distillation of petroleum pro-

duced a light oil that was similar to coal oil and better

than whale oil as an illuminant.’ This knowledge

spurred the search for saline waters that contained oil.

Using the methods of the salt producers, Col. Edward Drake drilled a well on Oil Creek, near Titusville. PA. in

1859, He struck oil at a depth of 70 ft, and this first oil

well produced about 3.5 B/D.’

The early oil producers did not realize the significance

of the oil and saline waters occurring together. In fact, it

was not until 1938 that the existence of interstitial water

in oil reservoirs was generally recognized. 4 Torrey ’ was

convinced as early as 1928 that dispersed interstitial

water existed in oil reservoirs, but his belief was rejected

by his colleagues because most of the producing wells

did not produce any water upon completion. Occur-

rences of mixtures of oil and gas with water were

recognized by Griswold and Munn,6 but they believed

that there was a definite separation of the oil and water,

and that oil, gas, and water mixtures did not occur in the

sand before a well tapped the reservoir.

It was not until 1928 that the first commercial

laboratory for the analysis of rock cores was established,

and the first core tested was from the Bradford third sand

(from the Bradford field. McKcan County. PA). The

‘Now with the Natl Ins1 of Petroleum and Energy Research Eartlesv~lle OK

“The author of the or!gmal chapter on this topic I” the 1962 edlllon was J Wade W2fk,“<

percent saturation and percent porosity of this core were

plotted vs. depth to construct a graphic representation of

the oil and water saturation. The soluble mineral salts

that were extracted from the core led Torrey to suspect

that water was indigenous to the oil-productive sand.

Shortly thereafter a test well was drilled near Custer Ci-

ty, PA, that encountered higher than average oil satura-

tion in the lower part of the Bradford sand. This high oil

saturation resulted from the action of an unsuspected flood. the existence of which was not known when the

location for the test well had been selected. The upper

part of the sand was not cored. Toward the end of the

cutting of the first core with a cable tool core barrel. oil

began to come into the hole so fast that it was not

necessary to add water for the cutting of the second sec-

tion of the sand. Therefore, the lower 3 ft of the Bradford

sand was cut with oil in a hole free from water. Two

samples from this section were preserved in sealed con-

tainers for saturation tests, and both of them, when

analyzed, had a water content of about 2O%PV. This

well made about IO BOPD and no water after being shot

with nitroglycerine. Thus, the evidence developed by the

core analysis and the productivity test after completion

provided a satisfactory indication of the existence of im-

mobile water, indigenous to the Bradford sand oil reser-

voir, which was held in its pore system and could not be

produced by conventional pumping methods.’

Fettke’ was the first to report the presence of water in

an oil-producing sand. However, he thought that it might

have been introduced by the drilling process.

Munn* recognized that moving underground water might be the primary cause of migration and accumula-

tion of oil and gas. However, this theory had little ex-

perimental data to back it until Mills” conducted several

laboratory experiments on the effect of moving water

and gas on water/oil/gas/sand and water/oil/sand

systems. Mills concluded that “the up-dip migration of


oil and gas under the propulsive force of their buoyancy

in water, as well as the migration of oil, either up or

down dip, caused by hydraulic currents, are among the

primary factors influencing both the accumulation and

the recovery of oil and gas.” This theory was seriously

questioned and completely rejected by many of his

contemporaries.

Rich “I assumed that “hydraulic currents, rather than

buoyancy, are effective in causing accumulation of oil or

its retention. ” He did not believe that the hydraulic ac-

cumulation and flushing of oil required a rapid move-

ment of water but rather that the oil was an integral con-

stituent of the rock fluids and that it could be carried

along with them whether the movement was very slow or

relatively rapid.

The effect of water displacing oil during production

was not recognized in the early days of the petroleum in

dustty in Pennsylvania. Laws were passed, however, to

prevent operators from injecting water into the oil reser-

voir sands through unplugged wells. In spite of these

laws, some operators at Bradford secretly opened the

well casing opposite shallow groundwater sands to start a

watertlood in the oil sands. Effect of artificial

watertloods were noted in the Bradford field in 1907,

and became evident about 5 years later in the nearby oil

fields of New York. ” Volumetric calculations of the

oil-reservoir volume that were made for engineering

studies of these waterflood operations proved that in-

terstitial water was generally present in the oil sands.

Garrison ” and Schilthuis’ gave detailed information

concerning the distribution of water and oil in porous

rocks, and of the origin and occurrence of “connate”

water with information concerning the relationship of

water saturation to formation permeability.

The word “connate” was first used by Lane and Gor-

don ” to mean interstitial water that was deposited with

the sediments. The processes of rock compaction and

mineral diagenesis result in the expulsion of large

amounts of water from sediments and movement out of

the deposit through the more permeable rocks. It is

therefore highly unlikely that the water now in any pore

is the same as that which was there when the particles

that surround it were deposited. White ” redefined con-

nate water as “fossil” water because it has been out of

contact with the atmosphere for an appreciable part of a

gcnlogic time period. Thus. connate water is distin-

cruished from “meteoric” 2 water, which has entered the

rocks in geologically recent times, and from “juvenile”

water. which has come from deep in the earth’s crust and

has never been in contact with the atmosphere.

Meanwhile. petroleum engineers and geologists had

learned that waters associated with petroleum could be

identified with regard to the reservoir in which they oc-

curred by a knowledge of their chemical characteristics.

Commonlv, the waters from different strata differ con-

siderably In their dissolved chemical constituents. mak-

ing the identification of a water from a particular stratutn

easy. Howjcvcr. in some areas the concentrations of

dissolved constituents in waters from different strata do

not dit’fcr significantly, and the identification of such

waters is difficult or impossible.

The amount of water produced with the oil often in-

creases as the amount of oil produced decreases. lfthis is

edge water. nothing can be done about it. If it is botton-

water, the well can be plugged back. However, it often is

intrusive water from a shallow sand gaining access to the

well from a leaky casing or faulty completion and this

can be repaired.

Enormous quantities of water are produced with the oil

in some fields, and it is necessary to separate the oil from

the water. Most of the oil can be removed by settling.

Often, however, an oil-in-water emulsion forms, which

is very difficult to break. In such cases, the oil is heated

and various surface-active chemicals are added to induce

separation.

In the early days, the water was dumped on the

ground, where it seeped below the land surface. Until

about 1930, the oilfield waters were disposed into local

drainage, frequently killing fish and even surface vegeta-

tion. After 1930, it became common practice to

evaporate the water in earthen pits or inject it into the

producing sand or another deep aquifer. The primary

concern in such disposal practice is to remove all oil and

basic sediment from the waters before pumping them in-

to injection wells to prevent clogging of the pore spaces

in the formation receiving the waste water. Chemical

compatibility of waste water and host aquifer water also

must be ensured.

Waters produced with petroleum are growing in im-

portance. In years past, these waters were considered

waste and had to be disposed of in some manner. Injec-

tion of these waters into the petroleum reservoir rock

serves three purposes: it produces additional petroleum

(secondary recovery), it utilizes a potential pollutant.

and in some areas it controls land subsidence.

The volume of water produced with petroleum in the

U.S. is large. In 1981 domestic oil production was about

8.6~ IO’ B/D and the amount of water produced with

the oil ranges from 4 to 5 times the oil production.

Therefore, the water production, assuming a factor of

4.5, would be about 38.7~ IO’ BID.

Secondary and tertiary oil recovery processes that use

water injection usually result in the production of even

more water along with the oil. To inject these waters into

reservoir rocks, suspended solids and oil must be re-

moved from the waters to prevent plugging of the porous

formations. Water injection systems require xepardtors,

filters, and, in some areas, deoxygenating and bacteria

control equipment with chemical and physical methods

to minimize corrosion and plugging in the injection

system.

In waterflooding most petroleum reservoirs, the

volume of produced water is not sufficient to rccovcr the

additional petroleum efficiently. Therefore, supplemen-

tal water must be added to the petroleum reservoir. The

use of waters from the other sources requires that the

blending of produced water with supplemental water

must yield a chemically stable mixture so that plugging

solids will not be formed. For example, a produced

water containing considerable calcium should not be

mixed with a water containing considerable carbonate

because calcium carbonate may precipitate and prevent

injection of the tloodwater. The design and successful

operation of a secondary or tertiary recovery operation

requires a thorough knowledge of the composition of the

waters used.

Chemical analyses of waters produced with oil are

useful in oil production problems. such as identifying the

PROPERTIES OF PRODUCED WATERS 24.3

source of Intrusive water, planning watcrfood and

saltwater disposal projects. and treating to prevent corro-

sion problems in primary, secondary, and tertiary

recovery. Electrical well-lo g interpretation rcquircs a

knowlc$Fc of the dissolved solids concentration and

composltton of the interstitial water. Such information

also is useful in correlation of stratigraphic units and of

the aquifers within these units. and in studies of the

movcmcnt of xubsurfacc waters. It is impossible to

understand the processes that accumulate petroleum or

other minerals without insight into the nature of these

waters.

Sampling The composition of subsurface water commonly changes

with depth and also laterally in the same aquifer.

Changes may be brought about by the intrusion of other

waters. and by discharge from and recharge to the

aquifer. It is thus difficult to obtain a representative sari--

pie of a given subsurface body of water. Any one sample

is a very small part of the total mass. which may vary

MJidely in composition. Therefore. it is generally

necessary to obtain and analyze many samples. Also. the

samples may change with time as gases come out of

solution and supersaturated solutions approach

saturation.

The sampling sites should be selected, if possible, to

fit into a comprehensive network to cover an oil-

productive geologic basin.

There is a tendency for some oilfield waters to become

more diluted as the oil reservoir is produced. Such dilu-

tion may result from the movement of dilute water from

adjacent compacting clay beds into the petroleum rescr-

voir as pressure declines with the continued removal of

oil and brine. ”

The composition of oilfield water varies with the posi-

tion within the geologic structure from which it is ob-

tained. In some cases the salinity will increase upstruc-

ture to a maximum at the point of oil/water contact.

Few of the samples collected by drillstem test (DST)

arc truly representative formation-water samples. During

drilling. the pressure in the wellbore is intentionally maintained higher than that in the formations. Filtrate

from the drilling mud seeps into the permeable strata.

and this filtrate is the first liquid to enter the test tool.

The most truly representative formation-water sample

usually is obtained after the oil well has produced for a

period of time and all extraneous fluids adjacent to the

wellhore have been flushed out. Samples taken im-

mediately after the well is completed may be con-

taminated with drilling fluids and/or with well complc-

tion fluids. such as filtrate from cement, tracing fluids,

and acids. which contain many different chemicals.

Sampling methods are discussed in publications of the

American Petroleum Inst. (API), ” American Sot. for

Testing and Materials (ASTM), ” and the Natl. Assn. of

Corrosion Engineers (NACE). I8

Drillstem Test

The DST, if properly made, can provide a reliable for-

mation water sample. it is best to sample the water after

each stand of pipe is removed. Normally, the total

dissolved solids (TDS) content will increase downward

and become constant when pure formation water is ob-

tained. A test that ilows water will give even higher

assurance of an uncontaminated sample. If only one DST

water sample is taken for analysis. it should bc taken just

above the tool. since this is the last water to enter the tool

and is least likely to show contamination.

Analyses of water obtained from a DST of Smackovcr

limestone water in Rains County. TX. show how errors

can be caused by improper sampling of DST water.

Analyses of top, middle. and bottom samples taken from

a SO-ft fluid recovery show an increase in salinity with

depth in the drillpipe. indicating that the first water wa\

contaminated by mud filtrate. I’) Thus. the bottom sam-

ple was the most representative of Smackovcr water.

Sample Procedure

No single procedure is universally applicable for obtain-

ing a sample of oilfield water. For cxamplc. inthrmation

may bc desired concerning the dissolved gas or

hydrocarbons in the water or the reduced species present.

such as ferrous or manganous compounds. Sampling

procedures applicable to the desired infomlation must be

used.

Some of the special information and sample location

cases, with appropriate procedures or references cited for

proper sampling. follow.

Sample Containing Dissolved Gas. Knowlcdgc of ccr-

tain dissolved hydrocarbon gases is used in

exploration. ‘OZ’

Sampling at the Flowline. Another method of obtaining

a sample for analysis of dissolved gases is to place a

sampling device in a flowline. Fig. 24. I illustrates such

a device. The device is connected to the flowline. and

water is allowed to flow into and through the container.

which is held above the flowlinc. until 10 or more

volumes of water have flowed through. The lower valve

on the sample container is closed and the container

removed. If any bubbles are present in the sample, the

sample is discarded and a new one is obtained.

Sampling at the Wellhead. It is common practice in the

oil industry to obtain a sample of formation water from a

sampling valve at the wellhead. A plastic or rubber tube

can be used to transfer the sample from the sample valve

into the container (usually plastic). The source and sam-

ple container should be flushed to remove any foreign

material before a sample is taken. After flushing the

system. the end of the tube is placed in the bottom of the

container, and several volumes of fluid are displaced

bcforc the tube is removed slowly from the container and

the container is sealed. Fig. 24.2 illustrates a method of

obtalnmg a sample at the wellhead. An extension of this

method is to place the sample container in a larger con-

tainer. insert the tube to the bottom of the sample con-

tainer. allow the brine to overflow both containers. and

withdraw the tube and cap the sample under the fluid.

At pumping wellheads the brine will surge out in heads

and be mixed with oil. In such situations a larger con-

tainer equipped with a valve at the bottom can be used as

a surge tank or an oil-water separator or both. To use this

device, place the sample tube in the bottom of the large

container, open the wcllhead valve, rinse the large con-

tainer with the well fluid, allow the large container to


Valve

74

Sample

I-+

container

Fig. 24-l-Flowline sampler.

fill, and withdraw a sample through the valve at the bot-

tom of the large container. This method will serve to ob-

tain samples that are relatively oil-free.

Field Filtered Sample. In some studies it is necessary to

obtain a field filtered sample. The filtering system shown

in Fig. 24.3 was designed and has proved successful for

various applications.

Fig. 24.2-Example of the method used for obtaining a sample at the wellhead.

This filtering system is simple and economical. It con-

sists of a SO-mL disposable syringe, two check valves.

and an inline-disk-filter holder. The filter holder takes

size 47-mm diameter, 0.45pm pore size filters, with the

option of a prefilter and depth prefilter.

After the oilfield brine is separated from the oil, the

brine is drawn from the separator into the syringe. With

the syringe, it is forced through the filter into the collec-

tion bottle. The check valves allow the syringe to be used

as a pump for filling the collection bottle. If the filter

becomes clogged, it can be replaced in a few minutes.

About 2 minutes are required to collect 250 mL of sam-

ple. Usually two samples are taken, with the one being

acidified to pH 3 or less with concentrated HCI or

HN03. The system can be cleaned easily or flushed with

brine to prevent contamination.

Sample for Stable-Isotope Analysis. Stable isotopes

have been used in several research studies to determine

the origin of oilfield brines. 22-24

Sample for Determining Unstable Properties or Species. A mobile analyzer was designed to measure

pH, Eh (redox potential), Oz, resistivity, S=, HCOT,

CO,, and CO2 in oilfield water at the wellhead. When

oilfield brine samples are collected in the field and

transported to the laboratory for analysis, many of the

unstable constituents change in concentration. The

amount of change depends on the sampling method,

sample storage, ambient conditions, and the amounts of

the constituents in the original sample. Therefore an

analysis of the brine at the wellhead is necessary to ob-

tain reliable data.”

Sample Containers. Containers that are used include

polyethylene, other plastics, hard rubber, metal cans,

and borosilicate glass. Glass will adsorb various ions

such as iron and manganese, and may contribute boron

or silica to the aqueous sample. Plastic and hard rubber

containers are not suitable if the sample is to be analyzed

to determine its organic content. A metal container is

used by some laboratories if the sample is to be analyzed

for dissolved hydrocarbons such as benzene.

The type of container selected depends on the planned

use of the analytical data. Probably the more satisfactory

container, if the sample is to be stored for some time

Fig. 24.3-Example of field filtering equipment.

PROPERTIES OF PRODUCED WATERS 24-5

TABLE 24.1-DESCRIPTION NEEDED FOR EACH OILFIELD WATER SAMPLE

Sample Number Field Farm or lease ~ Well No. ~ in the of Section Townshlp Range County State Operator Operator’s address (main office) Sample obtained by Date Address Representing Sample obtained from (lead line, separatory flow tank, etc.)

Completion date of well Name of productive zone from which sample is produced Sand Shale Lime Other Name of productive Names of formations formation well passes through Depths: Top of formation Bottom of formation

Top of producing zone Bottom of producing zone Top of depth drilled Present depth

Bottomhole pressure and date of pressure Bottomhole temperature Date of last workover Are any chemicals added to treat well If yes, what? Well production Initial Present Casing service record, Oil, BID Water, B/D Gas, cu ft/D

Method of production (primary, secondary, or tertiary)

Remarks: (such as casing leaks, communication or other pay in same well, lease or field)

before analysis. is the polyethylene bottle. Not all

polyethylenes are satisfactory because some contain

relatively high amounts of metal contributed by catalysts

in their manufacture. The approximate metal content of

the plastic can bc determined by a qualitative emission

spectrographic technique. If the sample is transported

during freezing temperatures, the plastic container is less

likely to break than is glass.

Tabulation of Sample Description. Information such as that in Table 24.1 should be obtained for each sample of

oilfield water.

Analysis Methods for Oilfield Waters Analytical methods for analyzing oilfield waters are im-

proving with respect to precision, accuracy, and speed.

There have been at least two groups trying to standardize

methods of oilfield water analysis during the past 20

years. They are the API and ASTM. The API published

Recommended Practice 45 for Analysis of Oilfield

Waters. ”

The ASTM’s Committee D-19 standardizes methods

of analyzing oilficld brines. Methods standardized by

rigorous round-robin testing by several laboratories and

subsequent ASTM committee balloting procedures are

found in Ref. 17.

Table 24.2 illustrates the analyses for various proper-

ties or constituents of oilfield water. Methods to deter-

mine most of these properties or constltucnts can bc

found in Refs. 16, 17, and 25 through 30.

Chemical Properties of Oilfield Waters Oilfield waters are analyzed for various chemical and

physical properties. Most oilfield waters contain a varie-

ty of dissolved inorganic and organic compounds.

TABLE 24.2-GEOCHEMICAL WATER ANALYSES*

Steam Produced Injection Generation Disposal Water Water Water Water

PH Eh Speciilc resistwty

Speciitc gravity Bacteria

Barium Bicarbonate Boron

Bromide Calcium Carbonate

Carbon dioxide Chlonde

Hydrogen sulfide Iodine IlOll

Magnesium Manganese

Oxygen Potassium

Residual hydrocarbons Sodium Silica Strontium Sulfate Suspended solIds Total dissolved solids

‘X = usually requesm O=somellmes requested

X

0 X X

0

X

:: 0 X

:: X

0 0 X

::

0 0

X

0 0 X

X

X

X

X

X

; X

X

:: 0

X

:: X 0


TABLE 24.3-CHARACTERISTICS OF SOME WATERS PRODUCED FROM APPALACHIAN FIELDS

Number of Analyses* System

KentuckyZ3,24

4 Devonian-Silurian

8 Mississippian

5 -

Ohi0 35.36

8 Mississippian

7 Ordovician

8 Mississrppian

10 Upper Devonian

12 Mississippian

Pennsylvania3’ 38

IO Devonian

7 Devono- Mississippian

12 Devontan

West Virginia39

29 Mtssisstppian

6 Mississippian

21 Mississippian

44 Pennsylvanian

43 Devonian

Formation

Subsurface Depth

(fl)

Corniferous 400 to 1,506

McClosky 1,390 to 2,618

Jett 939 to 1,534

Blue Lick

Sub Trenton

Second Water Big Lime First Water Big Lime Berea

1,843 to 3,263

3,820 to 5,815

2,175 to 3,270

5,175 to 5,300

401 to 1,592

Bradford

Venango

Bradford III

-

-

-

Big lnjun 1,390 to 3,215

Squaw 1,908 to 2,019

Maxton 1,287 to 3,259

Salt Sand 450 to 1,960

Oriskany 3,036 to 8,089

Constituents (mg/L)

Ca Mg Na

1,520 670 9,520 12,160 3,350 44,740

1,700 990 15,700 3,400 2,180 33,600

370 130 1,860 830 320 15,500

1,390 650 10,500 9,230 2,900 33,600

11,000 2,700 39,500 44,000 6,600 58,600 32,300 5,180 36,000 51,200 10,200 60,700 25,900 4.100 21.600 29,600 1O;OOO 861400 4,600 1,500 25,000

11,900 3,000 43,900

40 30 1,600 - 32,400 1,940 39,500 -

7,000 70 3,600 - 82,000 2,020 16,000 -

420 40 300 - 16,900 2,530 39,200 -

30 300 50 1,730 3,910 52,200

630 200 6,300 8,920 2,250 38,100

100 40 3,800 15,300 2,740 35,100

400 340 2,500 20,600 2,650 50,900 2,500 480 34,000

33,600 3,800 98,300

K

120 1,290 ND*’

ND ND ND

150 1,510

0 2,890 1,950 2,330

270 2,370

120 220

IO 750 290 340

30 660

3,6:: 200

6,900

However. oil producers usually are interested in only a

few of the macro properties. This is understandable

because oil producers wish to spend the least amount of money possible. Therefore, they will look at only the

properties that are necessary to evaluate any treatment

for rcinjection to recover more oil or to dispose of the

oilfield waters.

Composition of Oilfield Waters , ,,

The composition ot otltteld waters varies from relatively

dilute waters to heavy brines. Several thousand oilfield

water analyses are available on computerized files.”

Tables 24.3 through 24. I4 show characteristics of pro

duced waters. and much of the text was taken from the

1962 edition of this book.”

The tabulated data on water analyses following arc

lihted alphabetically in order of general oil-productive

areas of the U.S.. Canada. and Venezuela. rather than by

the smaller subdivisions of basins. geologic provinces.

or gcosynclines. An exception to this is the Illinois

basin, a large area not generally otherwise identifiable.

This division has been made arbitrarily for convenience

and because of the lack of a uniform system and is not in-

tended as a precedent for any system of classification.

The states or provinces from which reliable analyses

were available are listed alphabetically in the tables

under each area.

The reader is referred to the original indicated sources

of analytical data for more complete information.

Appalachian Area. The Appalachian area was the first

in the U.S. in which petroleum was produced commer-

cially and is one of the best known and studied geologic

features of North America. Table 24.3 gives the

characteristics of some waters produced from Ap-

palachian fields. F--~‘,

Petroleum and associated water are produced from

more than 50 strata in systems from the Cambrian to the

Permian. Most of the productive strata are sandstones,

although some limestones are productive. Many of the

PROPERTIESOF PRODUCED WATERS 24-7

TABLE24.3-CHARACTERISTICSOF SOMEWATERSPRODUCEDFROMAPPALACHIANFIELDS (continued)

Ba Sr

Constituents (mg/L)

HCO, SO, Cl

Specific Gravity

I Br 60°/600 TDS

O-ML)

- 0 - 630 - ND - ND

ND ND

628: 10 19,600 Trace 120

690 93,900 10 820 60 910 31,700 ND ND

230 3,320 61,000 ND ND 120 50 14,000 ND ND 250 3.200 26.000 ND ND

1.022 1.120 1.036 1.070 1.020 1.039

31,600 158,330 51,060

103,730 16,530 46,100

Trace 110 30 18,200 0 0 1.025 31,030 - 315 380 380 77,600 IO 570 1.089 125,180 - 0 20 150 113,500 10 150 1.150 167,030 - 900 510 490 189,400 30 600 1.224 304,020 - 0 60 30 113,000 ND 580 1.151 189,100

1,240 140 100 216,300 ND 1,900 1.240 344,110 - Trace 30 210 114,200 ND 1,230 1.125 167,540

Trace 230 550 193.100 ND 2,100 1.211 324,350 - 0 20 0 52,700 ND 320 1.063 84,260 - 1,800 20 60 93,400 ND 520 1.115 154,820

- -

- -

- - -

30 30 1,100 - - - 560 1,080 83,200 - - -

0 260 30,900 - 0 1,270 75,300 - - - 0 0 490 - - -

40 1.080 97.600

2,790 158,680 41,830

176,590 1,260

157,350

Trace 10 IO 5 70 Trace Trace 1.001 300 830 70 320 121,000 20 1,750 1.149

0 0 0 0 11,330 2 80 1.010 540 70 40 10 81,130 10 700 1.101

IO 5 10 20 5.830 Trace Trace 1.007 1,500 220 1,680 530 89,900 10 500 1.115

10 2::

10 5 2,500 Trace 5 1.004 870 1,330 400 125.000 10 780 1.159

20 Trace Trace 10 44,300 2 40 1.059 760 1.570 270 900 170,000 30 2,500 1.219

475 191,580

18,832 132,110

9,825 148,090

5,810 206,430

51,552 318,630

sandstones are nonuniform and discontinuous. although

the Big In.jun and Berea sands have been traced across

wide areas. The oil-producing states included in the Ap-

palachian area from which analyses were available arc

Kentucky, Ohio. Pennsylvania. and West Virginia. The

concentrations ofdissolved salts in waters produced Gth

petroleum range from a few hundred to more than

300,000 IllgiL.

California. In different fields of California. oil is pro-

duced from many reservoirs, ranging in age from

Cretaceous to Pleistocene. Sandstones and sands are the

principal productive rocks. Many of the formations arc

of massive thickness. and much folding and faulting are

evident. In general. mineralized water produced with

petroleum from California reservoirs is by no means as

concentrated as that from reservoirs in many other areas.

especially the midcontincnt. Table 24.4 gives the

characteristics of some water produced from California fields, JO.41

U.S. Gulf Coast. For many years since the Spindletop

dome was discovered in 1901, copious quantities of oil

have been produced from Tertiary and Quaternary for-

mations on the flanks, in the caprock, and in structures

abovle the capmck of massive salt domes. usually con-

sidered intrusive in nature. During recent years. offshore

drilling has focused attention on drilling oft the coasts of

Louisiana and Texas. Some waters produced from gulf

coast fields are quite fresh; others have concentrations of

dissolved salts as high as 170.000 nngit, (Table

24.5). 4L44

Illinois Basin. The Illinois basin. divided roughly into

halves by the LaSallc anticline. comprises much of II-

linois and southwestern Indiana. Oil is produced here

from many fields, principally from Pennsylvanian and

Mississippian sandstones and. to a smaller extent. from

limestones. TDS in the produced waters range from

about I.000 to more than 160,000 mg/L (Table 24.6).j5

24-a PETROLEUM ENGINEERING HANDBOOK

TABLE 24.4-CHARACTERISTICS OF SOME WATERS PRODUCED FROM CALIFORNIA FIELDS

Subsurface Constituents (mg/L)

Depth

(fi) Ca Mg Na a

--z- 10 HCO,

1,104 to 1,916 40 50 180 390 340 3,290 480 360

1,495 to 3,250 20 IO 910 0 180 2,890 690 13,250 360 360

2,270 to 3,550 60 20 3,650 0 50 1,280 570 11,650 90 4,270

400 to 3,000 10 10 50 0 20 20 1,550 390 7: - 200 140 4,770 150 0

220 230 7,640 460 0 - 200 10 1,300 0 4

2,900 1,300 15,015 510 1,020 10 3 2,050 0 1,700 80 140 7,090 340 3,900

so,

190

TDS Number of Analyses’

17

10

System Formation

Tertiary Coalinga

Tertiary Midway

Tertiary Sunset

Tertiary Kern River

Tertiary Lost Hills

Tertiary Maricopa

Tertiary Zone A

Cl

90 2,520 1,010

23,550 4,360

21,420 10 60

FwU 580

7.260 14,640 2,140

42,120 8,145

39,320 80

2,130 13,020 21,120

10 1,380

5 40

5

4

2

26

18

0 20 20

630 2

110

7,740 11,950

1,170 27,100

1,300 9,560

2,686 47,995

5,064 21,200 90

'Upper ligure in each column IS m~n~murn value and lower figure IS maximum value for number of analyses ndlcated '+I'

Midcontinent Area. The midcontinent oil productive

area is the largest geographically of all oil-productive

areas in the U.S. For purposes of this section, it is con-

sidered to include Arkansas, Kansas. northern Loui-

siana, Missouri, Nebraska, Oklahoma. and all of Texas

except the gulf coast fields.

Oil and associated brines are produced from many sandstones and limestones, as well as from other types of

formations, in geologic systems ranging from the Cam-

brian through the Upper Crctaceous. Waters produced

with petroleum from midcontinent fields have a wide

range of concentration of dissolved salts, from little

more than 1,000 to more than 350.000 mg/L. Tables

24.7 through 24.9 present the characteristics of some

produced waters from the midcontinent fields of Kansas,

Oklahoma, and Texas.36-“’

Rocky Mt. Area. Petroleum is produced in Colorado,

Montana. New Mexico, Utah, and Wyoming from many

fields in the Rocky Mt. area. The principal production is

from rocks of the Cretaceous system, although oil and

associated waters also are produced from Jurassic, Per-

mian, Pennsylvanian, and Mississippian rocks. Pro-

duced waters from Rocky Mt. fields have comparatively

low concentrations of dissolved salts and often are

characterized by comparatively high concentrations of

bicarbonate. Tables 24.10 and 24.11 give the

characteristics of some waters produced from Rocky Mt.

fields of Colorado, Montana, and Wyoming. 55m5y

Canada. The principal oil-productive areas in Canada

are the lower Ontario Peninsula, where oil is produced

from rocks ranging from Ordovician to Devonian age,

and the western provinces, principally Alberta, Sas-

katchewan, and the Northwest Territories. Reservoir

rocks in western Canada range in age from Devonian to

Cretaceous. Although many of the waters produced with

petroleum have quite low concentrations of dissolved

salts, others are quite concentrated. Tables 24.12 and

24. I3 present the characteristics of some waters from

Canadian fields in Alberta, Manitoba, and Saskatche- wan, hObh5

TABLE 24.5-CHARACTERISTICS OF SOME WATERS PRODUCED FROM GULF COAST FIELDS (TEXAS)

Constituents (mg/L) Subsurface

Depth

u9

2,579 to 11 400

40610 1 100

1.305 to 3.296

FormatIon or field Mg

50

Cl

TDS (m9L)

5 700 116900

353 4 500

10,860

54480

10.470

171.300 18.900

109.990

570 1.710

11.490 36400

Number of

Analyses' System

42 Terilary

5

6 Oligocene

6 Upper Eocene

5 Oligocene

Ca Na

2.240 40.600

60 1.330

3,800

18,200

3.600 61.000

6.700

40.800

340 30

4.460

12.730

HCO,

30

990

230

770

70

400

so,

0 3.180

69.100

20 2.130 6.300

33.700

6.100 105000

Fno

Norm Coastal

Goose Creek

Humble

Damon Mound

Barber HIII Dome

Powell-Mexla

1,000

10

30

110

3

160

120

210

Trace 1.750 270

3.010

16

230 10

210

775 to

250to 11 300

63400

110

610 6.700

21 600

4 Pliocene-Miocene 70

550 30

240

6


TABLE 24.6-CHARACTERISTICS OF SOME WATERS PRODUCED FROM ILLINOIS FIELDS

Number of Formatton

Subsurface

Depth

Analyses’ System of field (N

12 Misswloolan Wallersbura 1.994

2 437

18 M~ss~ss~pp~an Tar Springs 1.125

2,596 57 M~ss~ss~pp~an Cypress 1.045

2.960

17 Ordowclan Trenton 672 to 4,000

134 Mwssipplan St Geneweve 1.104 to 3.519

Ca

1.200

2.970 960

6.020 840

6.600

50

7.500

1.900 16.430

Constituents (mg/L)

MC! Na HCO_, so,

640 22.660 30 0 1.020 32.220 390 1 620

IO 240 20 0

1.730 42.810 1.050 980 510 3.970 10 10

1,660 47.900 1.660 3.840 40 340 20 30

1.830 41.830 960 1.350

910 8.740 20 30 3.460 47.660 1.470 2.990

Cl

38 300

56 700 700

76 000

25 800

83 200

200 82 400

14000 95 400

TDS

(mglL)

62.830

93 920 62 930

i 28 590 31 140

143.940

680 135870

25 600

167.940

‘Upper figure in each column IS minimum value and lower llgure IS ma~~rnum value for number of analyses Indicated ”

Venezuela. The principal productive formations in oilfield waters are sodium, calcium, and magnesium.

Venezuela are Tertiary sandstones and Cretaceous The concentrations of these ions can range from less than

limestones. In general. the various waters produced with 10.000 mg/L for sodium, and from less than I .OOO mg/L

petroleum have low concentrations of dissolved salts to more than 30,000 me/L for calcium and/or

(Table 24. 14).66m69 magnesium.

Inorganic Constituents

Petroleum companies often analyze oilfield waters to

determine their major dissolved inorganic constituents.

The major constituents usually are sodium, calcium,

magnesium, chloride, bicarbonate, and sulfate. The

analytical data are used in studies such as water iden-

tification. log evaluation, water treatment, environmen-

tal impact, geochemical exploration, and recovery of

valuable minerals. 26

Other cations that often are present in oilfield waters in

concentrations greater than 10 mg/L are potassium,

strontium, lithium, and barium. Some oilfield waters

contain concentrations in excess of IO mg/L of

aluminum, ammonium, iron, lead, manganese, silicon, and zinc, 26.70.71

Anions

Cations

The presence of various cations and anions in oilfield

waters can cause solubility, acidity, and redox (Eh)

potential changes as well as the precipitation and adsotp-

tion of some constituents. The major cations in most

The major anion in most oilfield waters is chloride. The

chloride concentration can range from less than 10,000

to more than 200,000 mg/L. There are exceptions to

this-e.g., some Venezuelan oilfield waters contain

more bicarbonate than chloride.”

Most oilfield waters contain bromide and iodide. The

concentrations of these anions range from less than 50 to

more than 6.000 mg/L for bromide and from less than IO

TABLE 24.7-CHARACTERISTICS OF SOME WATERS PRODUCED FROM MID-CONTINENT FIELDS (KANSAS)

Subsurface Constituents (nq/L)

Speclflc Number01 Depth ~ Gravely TDS Analyses’ System Formamn tft) ca blq N.3 Ba HCO, so, Cl I Br (60”160~) (mg,L)

-~ 87 Pennsylvanian Kansas C~fy Lansmg 1.228 lo 3.409 2 040 840 16940 4 5 0 34.100 2. 30 1040 53.959 16 DO0 3 950 77.000 70 450 2 160 158.800 15 400 1 159 256.830

8 Ordovlclan WllCOX 3.500 to 3 800 790 5.560 10800 0 20 80 10,870 Trace 80 1015 28.120 14400 68500 142,500 0 530 300 142600 3 x50- 1140 369.180

123 Ordowaan Arbuckle 2.750 lo 3 770 700 240 6 820 0 50 0 12.300 0 Trace ,014 20.180 19 BOO 10.900 34 450 0 640 2 700 79200 Trace 60 1 091 145.060

76 Ordoviaan VIOla 2091 lo 4 14, 620 230 5240 0 IO 20 330 0 5 1012 6,455 11 000 3.110 52000 0 650 1180 112.700 10 90 1116 160.740

27 Pennsylvania” Bartlesvllle 625 to 3 200 420 1EO 7550 0 10 1 12.600 2 20 1016 20.782 12 100 3,480 69.800 10 520 750 141 200 10 200 1 141 224.870

20 Mississippian Mississippian 1010 to 4 679 560 220 9 150 0 30 0 14.400 1 2 ,017 24.363 12 900 2.660 59300 20 670 3540 122000 60 3 1140 201.153

8 Basal Pennsylvaman Conglomerate 3320 to 3469 1 000 360 11 600 0 0 0 20.700 0 200 1023 33.850 8 480 2.000 47.000 0 180 700 58,300 Trace 400 1 105 116.660

24 PWlS”lWllX Chat 2697f0 3 365 3.120 640 24400 0 30 0 42,700 2 10 1 088 70,902 13480 1.950 66,500 0 130 2.200 137700 3 420 1143 222,383

12 SllUrlan H”“lO” 2 390 to 2 893 230 90 3610 0 70 100 5,300 0 10 1007 9.410 5 220 1.460 36600 3 480 1,230 68.400 2 70 1075 113.460

10 Basal Pennsylvanian Gorham 33ooto 3 854 920 280 6 560 0 160 40 11.300 0 5 1019 19.265 3 960 1.030 17100 10 840 3.010 36,000 0 10 ,045 58,940

9 Pennsyl”anlan PrUe 1 032 to 2.400 2.310 720 14300 0 20 0 28.000 0 0 1033 45.350 11 300 2.610 68 700 10 330 50 138.900 0 0 1 139 221.900

12 Cambraan Reagan 3175f03609 1 390 310 9 300 0 80 30 14,700 NO ND ,021 26.810 5 250 1.370 43000 0 410 2,570 76,900 ND ND 1088 126.930

‘Upper fqure I” each column IS mlnimum value and lower hgure IS maximum value for number of analyses Ind~caled %‘+’


TABLE 24.8-CHARACTERISTICS OF SOME WATERS PRODUCED FROM MID-CONTINENT FIELDS (OKLAHOMA)

Subsurlace Constituents (mg/L)

Speclflc Depth

~--~ _~ Grady TDS

ut1 -~Ca Mg Na Ba HCO, SO, Cl (60°/600) (mg/L)

4.489 to 5,524 1.900 910 12,100 0 0 0 24 100 1031

3,436 to 7.233

1,240 10 4.800

542 to 6.094

1.48070 5430

1,800 to 2,490

1,837 lo 4.872

3.927 10 5.977

1.258 to 6.025

1.213 lo 6.495

1,030 to 4.567

1.876 to 2 300

3.197 lo 5,021

2.403 to 4.650

3.458 to 5.004

2.267 to 3.587

982 to 3.163

2 417 to 3,254

790 to 5.000

1.882 to 3.218

2.173 to 7,569

83.800 730 48.300 0 80.230 130 31.300 0 79.000 380 14,000 0 63.800 110 34.600 1 51.500 20 42.500 1 57.700 200 43,600 2 72.000 30

19000 2.740 6.800 1.400 18500 3300 5.300 1,800 18900 4.300 2.200 900 18.800 2,700 4,600 1.400 11.900 4.300 5,900 2.000

13.300 2.600 6400 2000

22,400 2,500 4.600 1.100

18.400 3.200 1 700 600

15.800 3.100 5.600 1.200

17,600 3,000 6.200 1.500 18.700 3.200 6600 1,500 12700 2.500

300 80 28.900 4,300 9.700 1.700 19.600 2.600

200 60 16000 2,400 8.500 1.300 11,700 3.100

740 230 7.300 2,900

14.000 2.200 17.400 3.100 10,900 1,800

300 20

160 10 80 0

850 0

29,500 0 76.000 10 17,600 10 61.300 280

310 15

120 10 80 30

24.400 0 71,900 2 31,700 0

I390 144.000 0 91.300

720 163.000 0 34,900

510 160.000 0 33,000

1.880 127.000 0 65,000

1.130 113.500 0 81.600

200 115.000 24 84.200

430 157.000 60 55,400

1.920 156,000 0 29.800

2,750 121.000 0 50.900

440 140.000 30 64,100

450 139.000 0 90,000

110 20 90

67,400 IO 42,500 0 56,500 240 4.000 0

0 110 IO

130

75.900 170 42,800 5 71.700 220 2900 0

62,000 10 43,400 5

5 140 15

660 3

680 117,000 0 8,200

7.010 142,000 0 101.000

72,900 20 10800 0

20.000 3.500 5.500 900 13.900 2.000

700 400 22.400 3.500

27,900 50 23800 0 76400 5 43200 2 69,000 40 32.000 0 54700 10 11 500 10 80500 450

170 40

940 50

120 20

380 0

50 20 133 50 130

1 175 1 103 1170 1075 1179 1.034 1 147 1073 1 130 1.091 I 129 1095 1 173 1.066 1 173 1.039 1 134 1059 1.159 1075 1157 1.103 1.131 1012 1155 1115 1 164 1005 1137 1 110

1 158 1022 1076 1 160 1 171 1 109 1 163 1073 1 122 1024 1 183

370 149,000 0 4,400

980 122,000 30 86.300

480 142.000 2 18.600

40 63,600 130 132,800 370 156.200 15 99,300

260 149.000 40 45,500

760 108.000 0 19,500

920 167,000

39.010 251 460 147.820 266.010 73.310

263.170 50,100

214.140 105 701 182,660 132,016 189,120 136.212 254440 90,690

250,640 49.730

204.320 82.100

233.042 103,540 228.890 141.050 189.760 11.995

258.948 155.208 243.660

7.600 204.330 139.885 230,320 30.392

102,170 172.930 253,525 155,235 241.930 86.900 179,500 32,110

275,270

Number of Analyses‘ System Formaflon

Bartlesvllle

WllCOX

Layton

Atbuckle

Cromwell

Burgess

Mississippi

Mlsener

Pennsylvanian

Slmpso"

Skinner

Booth

Hunton

Red Fork

VIola

Prue

Healdion

Tonkawa

Burbank

Dutcher

Bromide

75 PennsylvanEln

94 Ordovlclan

25 Pennsyfvanlan

28 Ordovua"

I9 Pennsylvanian

12 Pennsylvanian

22 M~ss~ss~pp~an

18 Mlssisslpplan

I7 Pennsylvaman

10 Ordowan

22 Pennsylvania"

22 Pennsylvama”

22 Siluro-Devontan

27 Pennsylvania”

12 Ordowclan

20 Pennsyfvan,an

13 Pennsylvanian

15 Pennsylvanian

24 Pennsylvanian

15 Pennsylvanian

14 Ordowuan

TABLE 24.9-CHARACTERISTICS OF SOME WATERS PRODUCED FROM MID-CONTINENT FIELDS (TEXAS)

Number of Analyses’ System

Subsurface Specific Depth Constituents (mg/L) TDS _ Grawty

Formation (ft) Ca Mg Na so4 HCO, Cl (60~160~) (m9Q

North-Central Texas 50-52

33 Upper Pennsylvanian

El Upper Pennsylvaman

7 Upper Pennsylvanian

13 Upper Cretaceous

20 5 10,700 2.450

1,884 !O 2,081 14,400 2,440

16.700 2.860 2.540 to 2,668 10.200 2,030

13,800 2,440

3.844 to 4.446 3.100 370

7,900 600

530

48.200

58,300

66,800

52,500

61,000 32.100

62,900

61;

1

690

0 300

0 520 0 630

10 740 130 250

410 370

460

97,900

122,200

139,800 106,000

119,000

57.500

112,500

ND”

ND

ND

ND ND

ND

ND

ND

1,017

160,550

197,640

226.680 171,360

196,990

93,450

184.680

160 6.030 0 IO 10.000 1.015 16,700

3,000 60,400 180 400 134,000 1.157 221,080 640 15,700 10 40 31,400 1044 50,010

2,300 57,100 650 4,840 109,500 1 145 188,390

350 12,000 4 20 25,300 1.035 39,374

2,850 55.700 1,840 2.140 130,500 1 173 214,330 810 25,500 2 2 82,900 1.105 112,414

3,500 74,300 710 710 161,800 1212 262,320 310 4.400 210 350 19,000 1.033 25,010

7,900 67.000 1.840 4,900 140,500 1 154 241,940

200 210 0 160 890 ND 1,710

3,700 122,500 0 8,600 212,000 ND 356.600

Dyson

Landreth

Woodbine

North and West Texas5354

21 Pennsylvanian

35 Pennsylvanian

47 Cambro-Ordovcian

56 Pennsylvanian

50 Permian

42 Permian

Cisco

Canyon

Ellenberger

Straw

San Andres

Big Lime

700 IO 1.950 500

23,100

2.200 IO 7.000 2.200 14.000

3,800 to 8.370 1.700

22.300 1,700 to 6,900 3,200

21.300

740

19.800

- 250

9.800


TABLE 24.10-CHARACTERISTICS OF SOME WATERS PRODUCED FROM ROCKY MOUNTAIN FIELDS (COLORADO AND MONTANA)

Constrtuents (mg/L)

System

Subsurface

Depth

(ft)

Cretaceous Dakota 2.819 to 5.830

Cretaceous Frontrer 1,230 IO 3.464

Eocene Wasatch 2,230 to 5.283

Jurasw Morrtson 3,020 to 4.395

Jurassrc Sundance 4,564 lo 6,263

Ca Mg

0

NC3 co3 HCO3 so,

TDS Cl ml/L)

310 0 210 40 40 560

13,000 160 3,600 890 22,100 41,220

820 0 340 0 820 1,980

8,200 240 4.900 90 12.800 26.490

1,800 0 120 20 2,000 3.990

10,600 150 2,000 870 18,900 33,830

1,400 0 540 160 260 2.360

3,600 120 3,350 980 5,000 13,160

1,070 0 200 0 260 1,530

5,250 0 3,030 1,040 8,060 17.840

3.900 220

710

6,200

260

4.670

1.110

3,140

30

1,390

20

0 140 0 10 4,050

0 2,000 1,850 5,530 9,770

0 260 0 280 1,250

0 1,400 250 8,800 16,900

0 500 0 10 790

0 4,900 290 6.000 16.010

0 1,670 0 370 3,150

0 4,040 820 2.890 11,060

0 150 1,310 10 1.560

0 400 5.540 440 8,470

0 220 trace 10 250

Number of

Analyses’

Colorado5ss6

7

6

6

4

3

Montana5s-s7

Jurassic

Upper Cretaceous

Lower Cretaceous

Upper Jurasw

Pennsylvanian

Upper MIssIssippian

Lower Missrssippian

9

10

11

55

22

25

Montana -

Colorado -

Kootenar -

HIS

Quadrant

Tensleep

Madison

-

0 1,180

0

190

30

900

0

80

0

380

0

70

40

410

0

30

0

80

0

100

0

130

0

90 trace

90

60

680

0

0

70

0

120

0

60

0

80

trace

700

0

500 430 2,330 0 4,830 2,110 2,790 12,990

TABLE 24.11-CHARACTERISTICS OF SOME WATERS PRODUCED FROM ROCKY MT. FIELDS (WYOMING)

Constttuents (mg/L) -

CO, HCO, Na

410 trace 280

5,560 230 1,900

550 trace 1,270

20,000 1,050 7,800

200 trace 1,000

5,320 320 5.460

1,740 trace 890 7,000 590 6.950

1,040 trace 110

6,210 300 2,290

180 trace 230

13,000 280 6,900

630 trace 1.000 5.560 380 3.680

180 0 480

430 60 980

520 0 410

6,800 330 6.850

140 0 210

5,170 0 1.690

5 0 30 790 10 1,000

20 trace 20

580 20 1,080

630 0 190

1,670 0 550

Subsurface

Depth

(4

900 to 1,300

1,000 to 3.080

TDS Number of

Analvses’ System Ca Mg 10

330

so, 0

3,710

trace 240

trace

60

trace

880

0

110

20 980

trace 60

60

820

40

5,880 190

5,790

10

2,500 50

1,940 1,930

3,870

Cl @WLl

20 ~ 730

Formatron

Shannon

Frontier

First Wall Creek

Second Wall Creek

Cleverly

Dakota

Dakota

Greybull

Sundance

Embar

Tensleep

Madtson

Mmnelusa

10

250

24 Cretaceous

7,670 19.650

70 1,890 27,900 57.340

220 1,420 5,940 17.230

1,170 3,800 6,600 22.070

150 1,300

7,590 16,630

20 450

19,200 40,750

110 1,740 1,930 11.730

40 760

90 2.420

140 1.110

35 Cretaceous

45 Cretaceous

50 Cretaceous

14 Jurassrc

22 Jurasstc

24 Jurasstc

5 Jurassrc

60 Jurassic

20 Permian

50 Pennsylvaman

19 Mississippian

20 Triassic

trace trace

220 130

trace trace

30 100

trace trace 40 10

trace trace

110 20

trace trace 230 160

trace trace 60 60

irace trace

40 trace

0 0

400 60

140 30 630 220

40 10

720 250

20 trace

870 180 250 50

450 60

-

1,400 to 1.500

4,050 to 4.505

4,353 to 8.500

-

- 7,700 28,020

10 620

3,930 17,430

3 98

1,080 6,350 4 114

1,070 5.740

250 3,300

610 7,210

-

-

-


TABLE 24.12-CHARACTERISTICS OF SOME WATERS PRODUCED FROM CANADIAN FIELDS

Number of AllalySeS’ System Formalton

Subsurface Depth

ml

Specllic Constlt”enls (mJ/L, GLWy TDS

Ca Mg Na CO, HCO, SO, Cl I Br ~60°/60”l (mg/L)

215 10 1,890

1.670 10 2 072

2 706 10 2,744

10 10 660 0 320 5 50 10 3.000 80 790 600 70 20 6400 0 580 20

620 230 19.000 60 640 40 29.200 5 60 1 030 0 180 0 670

1.250 190 9.100 410 1250 2500 - -

1.570 to 3 323

2.200 to 2 942

3.000 lo 3 422

870 to 2 060

1,322 lo 2 553

2516fO4604

1.698 to 3 717

980 850 0 100 1 000 67 340 44.900 40 2.140 4,600

240 4.900 0 110 900 2.000 81.400 30 360 4.900

550 21.300 0 80 3900 1 400 72.800 80 780 4.300

200 4.500 6.400

11.000

- -

-

850 94,900

7.000 149.600

34 900 120 700

740 31 200

530 8.800 7.900

173.500 14.300

154 900

ND ND ND” 1 205 NO ND ND 9,030

10 10 1010 13.510 40 620 1 060 64.160

ND ND 1 006 2.145 ND ND 1 032 25.700

0 10 - - 20 460 - -

2 20 - - 20 220 - -

3 90 ~ - 10 110 - -

2 200 - - 20 1.500 - -

- 1010 3.940 - ,089 150 380 - 1016 14.150 - 1157 248.990 ~ 1031 62 930 - 1136 203 880 - 1 004 3 150 - 1 033 25 680 - 1 002 1 840 - 1 025 25 780 - 1 025 16.120 - 1180 290.070 ~ 1 026 26 760 - 1176 264,300

to more than 1,400 mg/L for iodide. 26 Bromide concen- Physical Properties of Oilfield Waters* tration is important in determining the origin of an

oilfield brine and is an important geochemical marker Compressibility

constituent.‘” Bicarbonate and sulfate are present in The compressibility of formation water at pressures

many oilfield waters. Their concentrations can range above the bubblepoint is defined as the change in water

from none to several thousand milligrams per liter. volume per unit water volume per psi change in pressure.

Other anions found in oilfield waters include arsenate, This is expressed mathematically as

borate, carbonate, fluoride, hydroxide, organic acid I av (',,. = --

( > -

salts, and phosphates. Boron concentrations in excess of T, _. _. (la)

100 mg/L can affect electric log deflections. 26 v ap

‘This sechon. except for the pH and Eh, was writlen by Howard B Bradley

TABLE 24.13-CHARACTERISTICS OF SOME WATERS PRODUCED FROM CANADIAN FIELDS, PROVINCE OF SASKATCHEWAN

Subsurface Number of Depth Constituents (mg/L)

Spectffc

Analyses’ System Formatron (W Ca Mg Na Gravrty TDS

CO, HCO, SO, Cl (60°/600) (ma/L)

27 Cretaceous Blafrmore 998 to 3,713 ~ ~ trace trace 2,200x---- 190 - 2.800

5

5

25

12

9

11

4

11

Shaunavon 3,205 to 3.413

Gravelbourg 3.290 to 4.175

Mfssron Canyon 3,700 to 5,785

Ntsku 4,682 to 6,927

Duperow 2,253 to 4,024

Mississippian 4,487 to 5,665

Lodgepole 2.305 to 4,470

80 1,300 - 190

- 300

- 140

- 350

- 60

- 440

- 200

- 2,350

- 100

- 860 - 120

110 850

- 480

- 600

- 70 - 2,600

- 40

- 1,580

- 290

- 1,320

1 000 6,190

8

a

Devonian

Devonian

MissIssippIan

Mississippian

Lower

Cretaceous

Devonian

Jurassic

Viking 2,395 to 3,026

Devonian 3,356 to 6,605

Jurassfc shale 3,105 to 4,325

2,300 870 20,300 170 100 8,800

1,850 230 t 2,400 470 220 11,700 620 370 t 2.900 100 130 760

7.100 3,100 73.700 740 190 1,000

14,100 7.150 73,000 680 170 940

9,000 900 17.700 trace trace 4,300 5,600 1,600 71,000 730 90 1,400

2.800 610 27,000

trace trace 1,100 190 100 9,300

0 0 0

1,100 1,200 69,100 trace trace 4,300 8,100 160 10,900

3,500 2,100

3,100

270

2,100

3,200 Trace

2,500

2,200

5,000 340

3,900

3,400

3,900

38,900 1.048 67,250 890 1.007 12.250

t 3,800 1.014 31.580 14,500 1 022 27.300 20,100 1.026 36.440

280 1.001 1.330 155,000 1 093 242.540

640 1 002 2.770

142,800 1 186 242.600 700 t ,002 4,790

31,100 1.040 64,560 5,700 1.004 10.460

123,800 1 150 206,860

580 1.004 6,680 45,700 1 061 80,610

0 2,100 1.002 3,270 790 12,700 1.014 25,680 190 4,800 1.012 5,030

2,400 111.000 1.160 185,380 0 2,800 1.002 7,390

3,600 15,400 1.029 39,480

‘Upper ftgure tn each column IS mmmum value and lower figure is maxmum value far number of analyses mdlcafed 65

PROPERTIES OF PRODUCED WATERS 24-l 3

TABLE 24.14-CHARACTERISTICS OF SOME WATERS PRODUCED FROM VENEZUELAN FIELDS

Number of

Analyses

5

7

6

7

a

8

7

8

10

11

Constituents (mg/L) TDS

System Formation or Fteld Ca Mg Na CO, HCO, SO, Cl --

~

(mglL)

Tertiary Zeta (Quiriquire) 170 100 1,750 0 3,050

330 270 5.150 0 5.400

Tertiary

Tertiary

Cretaceous

Tertiary

Tertiary

Tertiary

Cretaceous

Eta (Quiriquire)

Cabtmas field, La Rosa formation

Lagunillas field,

lceota formatlon

Bachaquero field,

Pueblo Viejo main sandstone

Mene Grande field,

Pauji and Mason-Trujillo range

La Conception field. Punta Gorda sands and deeper sands

La Paz field,

Guasare formation

70 50 400 300

60 60

10 60

40 60

2:040 0 12,360 0

1,740 0

2,000 120

4,610 0

1,800 100

4,700 1,900

3;050 7.410

2,010

5,260

6,250

30 20 3,570

50 20 30

30 20 6,000 80 1,230

Cretaceous

Tertiary

S. El Mene field,

El Salto formation

Oficma and W. Guard ftelds

OF, sand

AB, sand

D, sand Du and Eu sands

F, sand

H sand

L, sand M’ sand

P sand

S sand

U sand

30 50 2,660 0 1,130

30 40 3,000 0 1,130

150 50 9,000 0 2,440

50 20 1,260 0 2,330

40 30 1,360 0 2,780

40 30 3,080 0 1,100

40 60 4,000 0 1,430

140 70 7,900 0 3,500

70 70 8,400 0 2,050

160 100 7,300 0 4,420

110 30 7,700 0 2,100

140 80 7,800 0 970

330 80 8,600 0 1,700

940 180 11,800 0 1,100

4 1,910 7,190

10 5,420 16,260

5 710 6,900 30 11 ,170 36,500

0 1,780 5,643

0 90 5,260

5 3,700 14,657

0 690 6.210

0 6,250 12,955

0 8,550 15.911

0 3,450 7,320

0 1,260 5,460

0 9,000 20,640

140 640 4,424

60 560 4,830

130 4,230 8,520 0 5,500 11,030

150 10,500 22,260

10 12,090 22,690

trace 9,260 21,240

20 10,900 20,860

0 11,600 20,590 100 13,050 23,860

0 19,800 33,820

‘Upper tlgure I” each column 1s minimum value and lower figure IS maximum value for number ot analyses mdlcated “-”

or

1 v*--v, T,=-

( > v PI--P2

, . . . . . . . . . . . . . . . . . . . . .

01

Bw2 -B,I c,.= - B,.(p, -p2), . . . . . . . . . . . . . .

(lb)

where

CkV = water compressibility at the given pressure

and temperature, bbl/bbl-psi,

-cw = average water compressibility within the

given pressure and temperature interval,

bbl/bbl-psi,

V = water volume at the given pressure and

temperature, bbl,

V = average water volume within p and T inter-

vals, bbl,

PI and p2 = pressure at conditions 1 and 2 with p r >pz,

psi, B,,, and

B 4 = water FVF p I and ~2, bbl/bbl, and

B,. = average water FVF corresponding to V,

bbhbbl.

Eq. 2 was fit for pressures between 1,000 and 20,000

psi, salinities of 0 to 200 g NaClIL, and temperatures

from 200 to 270°F. Compressibilities were independent

of dissolved gas.

In an oil reservoir, water compressibility also depends Where conditions overlap, the agreement with the

on the salinity. In contrast to the literature, laboratory results reported by both Dorsey 75 and Dotson and Stand-

measurements by Osif 74 show that the effect of gas in ing 76 is very good. Results from the Rowe and Chou”

solution on compressibility of water with NaCl concen-

trations up to 200 g/cm3 is essentially negligible. Osif’s

results show no effect at gas/water ratios (GWR’s) of 13

scf/bbl, at GWR’s of 35 scf/bbl probably no effect, but

certainly no more than a 5% increase in the com-

pressibility of brine.

Laboratory measurements 74 of water compressibility

resulted in linear plots of the reciprocal of compressibili-

ty vs. pressure. The plots of l/c, vs. p have a slope of

m r , and intercepts linear in salinity and temperature.

Data points for the systems tested containing no gas in

solution resulted in Eq. 2.

l/c~,=m~p+m~C+m~T+m4, (2)

where

cw = water compressibility, psi -’ ,

p = pressure, psi,

C = salinity, g/L of solution,

T = temperature, “F,

ml = 7.033,

m2 = 541.5,

lfl3 = -531, and

m4 = 403.3 X 103.


Fig. 24.4-Specific gravity of salt solutrons at 60°F and 14.7 psia.

Fig. 24.5-Density of NaCl solutions at 14.7 psia vs. temperature.

equation agree well up to 5.000 psi (their upper pressure

limit) but result in larger deviations with increasing

pressure. In almost all cases, the Rowe and Chou com-

pressibilities are less than that of Eq. 2.

Density

The density of formation water is a function of pressure,

temperature. and dissolved constituents. It is determined

most accurately in the laboratory on a representative

sample of formation water. I7 The formation water den-

sity is defined as the mass of the formation water per unit

volume of the formation water. For engineering pur-

posts, density in metric units (g/cm’) is considered

equal to specific gravity. Therefore, for most engineer-

ing calculations density and specific gravity are

interchangeable. ‘e

When laboratory data are not available, the density of

fomration water at reservoir conditions can be estimated

(usually to within & 10%) from correlations (Figs. 24.4

through 24.6). The only field data necessary are the den-

sity at standard conditions, which can be obtained from

the salt content by use of Fig. 24.4. The salt content can

be estimated from the formation resistivity (obtained

from electric log measurements) by use of Fig. 49.3 (see

Chap. 49). The density of formation water at reservoir

conditions can be calculated in four steps.

I. Using the temperature and density at atmospheric

pressure, obtain the equivalent weight percent NaCl

from Fig. 24.5.

2. Assuming the equivalent weight percent NaCl re-

mains constant. extrapolate the weight percent to reser-

voir temperature and read the new density.

3. Knowing the density at atmospheric pressure and

reservoir temperature, use Fig. 24.6 to find the increase

in specific gravity (density) when compressed to reser-

voir pressure. Note that for oil reservoirs below the bub-

blepoint, the “saturated-with-gas” curves should be

used; for water considered to have no solution gas, the “no-gas-in-solution” curves should be used. These

curves were computed from data given by Ashby and

Hawkins.”

4. The density of formation water (g/cm’) at reservoir

conditions is the sum of the values read frotn Figs. 24.5

and 24.6. They can be added directly since the metric


units are referred to the common density base of water (1

g/cm3). The metric units can be changed to customary

units (1 bmicu ft) by multiplying by 62.37.

Also the specific gravity of formation water can be estimated if the dissolved solids are known. The equa-

tion is

y,*>=1+c,~xo.695x10-6, . . . . . I.. . .(3)

where Csd is the concentration of dissolved solids

(mgfL). For precise but very detailed calculations, the reader is

referred to a recent paper by Rogers and Pitzer. 79 They

tabulated a large number of values of compressibility,

expansivity and specific volume vs. molality ,

temperature, and pressure. A semiempirical equation of

the same type found to be effective in describing thermal

properties of NaCl (0.1 to 5 molality) was used to

reproduce the volumetric data from 0 to 300°C and I to

1,000 bars.

Formation Volume Factor (FVF)

The water FVF, II,., is defined as the volume at reser-

voir conditions occupied by 1 STB of formation water

plus its dissolved gas. It represents the change in volume

of the formation water as it moves from reservoir condi-

tions to surface conditions. Three effects are involved:

the liberation of gas from water as pressure is reduced,

the expansion of water as pressure is reduced. and the

shrinkage of water as temperature is reduced.

The water FVF also depends on pressure. Fig. 24.7 is

a typical plot of water FVF as a function of pressure. As

the pressure is decreased to the bubblepoint, ph. the FVF

increases as the liquid expands. At pressures below the

bubblepoint. gas is liberated, but in most cases the FVF

still will increase because the shrinkage of the water

resulting from gas liberation is insufficient to counter-

balance the expansion of the liquid. This is the effect of

the small solubility of natural gas in water.

The most accurate method of obtaining the FVF is

from laboratory data. It also can be calculated from den-

sity correlations if the effects of solution gas have been

accounted for properly. The following equation is used

to estimate B,,. if solution gas is included in the

laboratory measurement or correlation of P,.~:

H,,=L,.. VW P r“

. . (4)

where

V,. = volume occupied by a unit mass of water at

reservoir conditions (weight of gas

dissolved in water at reservoir or standard

conditions is negligible), cu ft,

V,,. = volume occupied by a unit mass of water at

standard conditions, cu ft,

p,(. = density of water at standard conditions,

lbmicu ft, and

prc. = density of water at reservoir conditions,

lbmicu ft.

Fig. 24.6--Specific gravity increase with pressure--salt water

pb PRESSURE, PSI A

Fig. 24.7-Typical plot of water FVF vs. pressure

The density correlations and the methods of estimating

P,,~ and prc. were described previously.


The FVF of water can be less than one if the increase

in volume resulting from dissolved gas is not great

enough to overcome the decrease in volume caused by

increased pressure. The value of FVF is seldom higher

than I .06.

Resistivity

The resistivity of formation water is a measure of the

resistance offered by the water to an electrical current. It

can be measured directly or calculated. ” The direct-

measurement method is essentially the electrical

resistance through a 1 -m’ cross-sectional area of I m7

of formation water, The fomlation water resistivity,

R ,, $, is expressed in units of Q-m. The resistivity of for-

mation water is used in electric log interpretation and for

such use the value is adjusted to formation

temperature. “i (See Chap. 49 for more information).

Surface (Interfacial) Tension (IFT)

Surface tension is a measure of the attractive force acting

at a boundary between two phases. If the phase boundary

separates a liquid and a gas or a liquid and a solid, the at-

tractive force at the boundary usually is called “surface

tension”; however. the attractive force at the interface

between two liquids is called “IFT.” IFT is an impor-

tant factor in enhanced recovery processes (see Chap.

47. Chemical Flooding, describing “Low-1FT Proc-

CSSCS” and “Phase Behavior and IFT” in the

Miccllar/Polymer Flooding section).

Surface tension is measured in the laboratory by a ten-

siometer. by the drop method, or by other methods.

Descriptions of these methods arc found in most physical

chemistry texts.

Viscosity

The viscosity of formation water, p,, , is a function of

pressure. temperature. and dissolved solids. In gcncral,

brine viscosity increases with increasing prcsaure, in-

creasing salinity. and decreasing tempcraturc. ”

Dissolved gas in the fomlation water at reservoir condi-

tions generally results in a negligible effect on hater

viscosity. There is little information on the actual

numerical cffcct of dissolved gas on water viscosity.

Gas in solution behaves entirely differently from gas in

hydrocarbons. * In water the presence of the gas actually

causes the water molecules to interact with each other

more strongly, thus increasing the rigidity and viscosity

of the water. However. this effect is very small and has

not been measured to date. In the physical chemistry

literature there is an enormous amount of indirect

evidence to support this concept.

For the best estimation of the viscosity of water. the

reader is referred to a paper by Kestin (11 (11. ” Their cor-

relating equations involve 32 parameters for calculating

the numerical effect of pressure, temperature. and con-

ccntration of aqueous NaCl solutions on the dynamic and

kinematic viscosity of water. Twenty-eight tables

gcncratcd from the correlating equations cover a

temperature range from 20 to 150°C. a pressure range

from 0. I to 35 mPa. and a concentration range from 0 to

6 molal.

Figs. 24.X through 24. IO may be used to approximate

water viscosity for engineering purposes. These figures

show the effects of pressure, temperature, and NaCl con-

tent on the viscosity of water. They may be used when

the primary contaminant is sodium chloride.

Some engineers assume that reservoir brine viscosity

is equal to that of distilled water at atmospheric pressure

and reservoir temperature. In this case it is assumed that

the viscosity of brine is essentially independent of

pressure (a valid premise for the pressure ranges usually

encountered).

The pH

The pH of oilfield waters usually is controlled by the

COfibicarbonate system. Because the solubility of CO?

is directly proportional to temperature and prcssurc, the

pH measurement should be made in the field if a close-

to-natural-conditions value is desired. The pH of the

water is not used for water identification or correlation

purposes. but it does indicate possible scale-forming or

corrosion tendencies of a water. The pH also may in-

dicate the presence of drilling-mud filtrate or well-

trcatmcnt chemicals.

The pH of concentrated brines usually is less than 7.0.

and the pH will rise during laboratory storage. indicating

that the pH of the water in the reservoir probably is ap-

preciably lower than many published values. Addition of

the carbonate ion to sodium chloride solutions will raise

the pH. If calcium is present, calcium carbonate

precipitates. The reason the pH of most oilficld waters

rises during storage in the laboratory is because of the

fomlation of carbonate ions as a result of bicarbonate

decomposition.

The Redox Potential (Eh)

The redox potential often is abbreviated “Eh,” and also

may be referred to as oxidation potential. oxidation-

reduction potential, or pE. It is expressed in volts. and at

equilibrium it is related to the proportions of oxidized

and reduced species present. Standard equations of

chemical thermodynamics express the relationships.

Knowledge of the redox potential is useful in studies

of how compounds such as uranium. iron. sulfur. and

other minerals are transported in aqueous systems. The

solubility of some elements and compounds depends on

the redox potential and the pH of their environment.

Some water associated with petroleum is interstitial

(“connate”) water, and has a negative Eh: this has been

proved in various field studies. Knowledge of the Eh is

useful in determining how to treat a water before it is

rein.jected into a subsurface formation. For example. the

Eh of the water will be oxidizing if the water is open to

the atmosphere, but if it is kept in a closed system in an

oil-production operation the Eh should not change ap-

preciably as it is brought to the surface and then rein-

jetted. In such a situation. the Eh value is useful in deter-

mining how much iron will stay in solution and not

deposit in the wellbore.

Organisms that consume oxygen cause a lowering of

the Eh. In buried scdimcnts, it is the aerobic bacteria that

attract organic constituents, which remove the free oxy-

gen from the interstitial water. Sediments laid down in a

shoreline environment will differ in degree of oxidation


I I191111 I I

1000 10,000

PRESSURE, PSILI

Fig. 24.8-Effect of pressure on the viscosity of water

compared with those laid down in a deepwater environ-

ment. For example, the Eh of the shoreline sediments

may range from -50 to 0 mV, but the Eh of deepwater

sediments may range from - 150 to - 100 mV.

The aerobic bacteria die when the free oxygen is total-

ly consumed; the anaerobic bacteria attack the sulfate

ion, which is the second most important anion in the

seawater. During this attack. the sulfate reduces to

sulfite and then to sulfide; the Eh drops to -600 mV,

H 2 S is liberated, and CaCO 3 precipitates as the pH rises

above 8.5.

Dissolved Gases

Large quantities of dissolved gases are contained in

oilfield brines. Most of these gases are hydrocarbons;

however, other gases such as CO2 , N?. and HzS often

are present. The solubility of the gases generally

decreases with increased water salinity, and increases

with pressure.

Hundreds of drillstem samples of brine from water-

bearing subsurface formations in the U.S. gulf coast area

were analyzed to determine their amounts and kinds of

hydrocarbons. 2o The chief constituent of the dissolved

gases usually was methane, with measurable amounts of ethane, propane, and butane. The concentration of the

dissolved hydrocarbons generally increased with depth

in a given formation and also increased basinward with

regional and local variations. In close proximity to some

oiltields, the waters were enriched in dissolved

hydrocarbons, and up to I4 scf dissolved gasibbl water

was observed in some locations. A more detailed discus-

sion of this topic is given in Chap. 22.

Organic Constituents

In addition to the simple hydrocarbons, a large number

of organic constituents in colloidal, ionic, and molecular

form occur in oilfield brines. In recent years, some of

these organic constituents have been measured quan-

titatively. However, many organic constituents are pre-

sent that have not been determined in some oilfield

TEMPERATURE , .F

Fig. 24.9-Viscosity of sodium chloride solutions as a function of temperature and concentration at 14.7 psia.

brines primarily because the analytical problems are dif-

ficult and very time-consuming.

Knowledge of the dissolved organic constituents is im-

portant because these constituents are related to the

origin and/or migration of an oil accumulation, as well

as to the disintegration or degradation of an accumula-

tion. The concentrations of organic constituents in

oilfield brines vary widely. In general, the more alkaline

the water, the more likely that it will contain higher con-

centrations of organic constituents. The bulk of the

organic matter consists of anions and salts of organic

acids: however, other compounds also are present.

; 0.611 I I / I 1

i- m 0 0.5. ,o

\

TEMPERATURE, ‘F

Fig. 24.10-Effect of temperature on viscosity of water.


Knowledge of the concentrations of benzcnc. toluene,

and other components in oilfield brines is used in ex-

ploration. The solubilities of some of these compounds

in water at ambient conditions and in saline waters at

elevated tern eraturex

determined. x3. f: ’

and pressures have been

However. the actual concentrations of these and other organic constituents in subsurface oilfield brines is

another matter. It has been shown experimentally that

the solubilities of some organic compounds found in

crude oil increase with temperature and pressure if

pressure is maintained on the system. The increased

solubilitiea become significant above 150°C. The

solubilities decrease with increasing water salinity.

Waters associated with paraffinic oils are likely to con-

tain fatty acids. while those associated with asphaltic oils

more likely contain naphthenic acids.

Quantitative recovery of organic constituents from

oilfield brines is difficult. Temperature and pressure

changes. bacterial actions. adsorption. and the high

inorganic/organic-constituents ratio in most oilfield

brines are some reasons why quantitative recovery is

difficult.

Interpretation of Chemical Analyses Oilfield waters include all waters or brines found in

oilfields. Such waters have certain distinct chemical

characteristics.

About 70% of the world petroleum reserves are

associated with waters containing more than 100 g/L

dissolved solids. A water containing dissolved solids in

excess of 100 g/L can be classified as a brine. Waters

associated with the other 30%’ of petroleum reserves con-

tain less than 100 g/L dissolved solids. Some of these

waters are almost fresh. However, the presence of

fresher waters usually is attributed to invasion after the

petroleum accumulated in the reservoir trap.

Examples of some of the low-salinity waters can be

found in the Rocky Mt. areas in Wyoming fields such as

Enos Creek, South Sunshine. and Cottonwood Creek.

The Douleb oil field in Tunisia is another example.

The composition of dissolved solids found in oilfield

waters depends on several factors. Some of these factors

are the composition of the water in the depositional en-

vironment of the sedimentary rock, subsequent changes

by rock/water interaction during sediment compaction.

changes by rock/water interaction during water migra-

tion (if migration occurs), and changes by mixing with

other waters, including infiltrating younger waters such

as meteoric waters. The following are definitions of

some types of water.

Types of Water

Meteoric Water. This is water that recently was in-

volved in atmospheric circulation: furthermore, “the age

of meteoric groundwater is slight when compared with

the age of the enclosing rocks and is not more than a

small part of a geologic period.” ‘I

Seawater. The composition of seawater varies

somewhat, but in general will have a composition

relative to the following (in mg/L): chloride--19.375,

bromide-67, sulfate-2,712. potassium-387. sodium

- 10,760, magnesium- 1,294, calcium-4 13, and stron-

tium-8.

Interstitial Water. Interstitial water is the water con

mined in the small pores or spaces between the minute

grains or units of rock. Interstitial waters are .snl,yc,,trric'

(formed at the same time as the enclosing rocks) or

cyigcrwric (originated by subsequent infiltration into

rocks).

Connate Water. The term “connate” implies born.

produced. or originated together-connascent. There-

fore. connate water probably should bc considered an in-

terstitial water of syngenetic origin. Connate water of

this definition is fossil water that has been out of contact

with the atmosphere for at least a large part of a geologic

period. The implication that connate waters are only

those “born with” the enclosing rocks is an undesirable

restriction. ”

Diagenetic Water. Diagenetic waters are those that have

changed chemically and physically, before. during, and

after sediment consolidation. Some of the reactions that

occur in or to diagenetic waters include bacterial. ion ex-

change, replacement (dolomitization). infiltration by

permeation, and membrane filtration.

Formation Water. Formation water. as defined here, is

water that occurs naturally in the rocks and is present in

them immediately before drilling.

Juvenile Water. Water that is in primary magma or

derived from primary magma is juvenile water. ”

Condensate Water. Water associated with gas

sometimes is carried as vapor to the surface of the well

where it condenses and precipitates because of

temperature and pressure changes. More of this water

occurs in the winter and in colder climates and only in

gas-producing wells. This water is easy to recognize

because it contains a relatively small amount of dis-

solved solids, mostly derived from reactions with

chemicals in or on the well casing or tubing.

Water analyses may be used to identify the water

source. In the oil field one of the prime uses of these

analyses is to determine the source of extraneous water

in an oil well so that casing can be set and cemented to

prevent such water from flooding the oil or gas horizons.

In some wells a leak may develop in the casing or ce-

ment, and water analyses are used to identify the water-

bearing horizon so that the leaking area can be repaired.

With the current emphasis on water pollution prevention.

it is very important to locate the source of a polluting

brine so that remedial action can be taken.

Comparisons of water-analysis data are tedious and

time-consuming; therefore. graphical methods are com-

monly used for positive, rapid identification. A number

of systems have been developed. all of which have some

merit.

Graphic Plots

Graphic plots of the reacting values can be made to il-

lustrate the relative amount of each radical present. The

graphical presentation is an aid to rapid identification of

a water and classification as to its type. Several methods

have been developed.


Tickell Diagram. The Tickell diagram was developed

using a six-axis system or star diagram. X5 Percentage

reaction values of the ions are plotted on the axes. The

percentage values are calculated by summing the equivalent proton masses (EPM’s) of all the ions.

dividing the EPM of a given ion by the sum of the total

EPM’s, and multiplying by 100.

The plots of total reaction values, rather than of

percentage reaction values, are often more useful in

water identification because the percentage values do not

take into account the actual ion concentrations. Water

differing only in concentrations of dissolved constituents cannot be distinguished.

However, with time and tectonic events plus transgres-

sion and regression of oceans and seas, even these

sediments probably were subjected to marine waters by

infiltration.

In any event. the petroleum, which formed from

organic matter deposited with the sediments, migrated

from what usually is called the “source rock” into more

porous and permeable sedimentary rock. Petroleum

(i.e., oil and gas) is less dense than water; therefore, it

tends to float to the top of a water body regardless of

whether the water is on the sutiace or in the subsurface.

is an oilfield water.

The question of the origin of oilfield brines is difficult

to answer in a general manner. The water involved and

the constituents dissolved in the water to form the brine

can involve divergent histories. Subsurface water is there

either because it originally was there or because it in-

Therefore, water associated with petroleum in a sub-

surface reservoir is called an “oilfield water.” By this

definition, any water associated with a petroleum deposit

filtrated to the subsurface from the surface. If it was

there originally, it would be endogenetic, whereas if it

infiltrated from the surface and/or penetrated with sedi-

Stiff Diagram. Stiff plotted the reaction values of the

Reistle Diagram. Reistle devised a method of plotting

ions on a system of rectangular coordinates. 87 The cat-

water analyses by using the ion concentrations. *’ The

ions are plotted to the left and the anions to the right of a

vertical zero line. The endpoints then are connected by

data are plotted on a vertical diagram. with the cations

straight lines to form a closed diagram, sometimes called a “butterfly” diagram. To emphasize a constituent that

plotted above the central zero line and the anions below.

may be a key to interpretation, the scales may be varied

by changing the denominator of the ion fraction. usually

This type of diagram often is useful in making regional

in multiples of 10. However, when a group of waters is

being considered, all must be plotted on the same scale.

correlations or studying lateral variations in the water of

a single formation because several analyses can be plot-

ted on a large sheet of paper.

ment accumulations, it would be exogenetic.

Obviously these two types of waters could meet and

mix in the subsurface and thus the mixture would contain

water of two separate origins. The problem could multi-

ply if more than one exogenetic water were involved.

The chemical composition of an oilfield brine is an end

product of several variables. These variables include (I)

dissolved ions, salts, gases, and organic matter, (2) reac-

tions between these dissolved constituents, and (3) in-

teraction of the brine with the surrounding rocks,

petroleum, etc. There are a number of pertinent reactions

that could cause the composition of a subsurface oilfield

brine to change in composition, including leaching of the

rocks, ion exchange between water and rock, redox,

mineral hydration, mineral formation and/or dissolution,

ion diffusion, gravitational segregation of ions, and

membrane filtration, or other osmotic effects.

Many investigators believe that this is the best method

of comparing oilfield water analyses. The method is sim-

ple. and nontechnical personnel can be easily trained to

construct the diagrams.

Other Methods. Several other water identification

diagrams have been developed, primarily for use with

fresh waters, and they are not discussed here. The Stiff

and Piper diagrams, 87~88 were ada ted to automatic data

processing by Morgan et al. *B and Morgan and

McNellis. ‘* The Piper diagram uses a multiple trilinear

plot to depict the water analysis. and this quaternary

diagram shows the chemical composition of the water in

terms of cations and anions.88 Angino and Morgan ap-

plied the automated Stiff and Piper diagrams to some

oilfield brines and obtained good results.“’

Occurrence, Origin, and Evolution of Oilfield Waters The sedimentary rocks that now consist of stratified

deposits originally were laid down as sediments in

oceans, seas. lakes. and streams. Naturally. these

sediments were filled with water. This water is still pres-

ent in the stratified sediments and millions of years later

would be considered truly connate water.

Many large sedimentary strata originally were

associated with oceans and seas. The original associated

water. therefore. was marine in such sediments.

Sediments laid down by lakes and streams would not

contain a marine water during their initial deposition.

It is rather difficult to rank the factors that might be

more important for general consideration. However. two

of the more important factors probably are the original

composition of the water and interaction of that water

with the rocks. If one assumes that the original water was

a marine water and that the associated sediments (subse-

quently sedimentary rocks) were marine, then the

original composition of the marine water could be an im-

portant factor.

However, even the salinity in the various oceans and seas is not constant. For example. the salinity of the

waters in the major oceans ranges from 33,000 to 38,000

mg/L, about 40,000 mg/L in the Mediterranean Sea, up

to 70,000 mg/L in the Red Sea. about 18,000 to 22,000

mg/L in the Black Sea, and only about I .OOO mg/L in the

Baltic Sea. Some land-locked waters. such as the Dead

Sea. Great Salt Lake, etc., contain waters that are nearly

saturated with dissolved solids.

Studies of formation waters in the western Canada

sedimentary basin indicate that 85% of the strata were

deposited under marine conditions, while 15% were

deposited under brackish-water and possibly under

freshwater conditions. y2 These investigators estimated

that 80% of all the sedimentary strata in Alberta were


deposited under marine conditions. This led to the con-

clusion that one could assume with negligible error that

all sedimentary strata originally contained seawater.

Further, the study indicated that evaporites form an

important volumetric part of several of the stratigraphic

units. Some of the stratigraphic units possibly contain

bitterns subsequent to halite precipitation but preceding

precipitation of potassium salts. They calculated an

average formation water salinity of about 46,000 mg/L

TDS. which indicated a net gain of dissolved salts. Of

the major and some minor components, all showed a net

gain with the exception of Mg and SOa.

Factor analysis was used in interpretation of the

analyses. and the following factors were considered to be

major controls: composition of the original seawater,

dilution by freshwater recharge, membrane filtration,

solution of halite. dolomitization, bacterial reduction of sulfate. formation of chlorite. cation exchange on clays,

contribution from organic matter, and solubility

relationships.

It was concluded that (I) the formation waters of

western Canada are ancient seawaters in which the

deuterium concentration was changed because of mixing

with infiltrating fresh water, (2) oxygen-18 was ex-

changed with carbonates in the rocks, and (3) dissolved

salts are in equilibrium with the rock matrix subsequent

to their redistribution by membrane filtration and/or dilu-

tion by freshwater recharge. Equilibrium was attained by

such processes as dissolution of evaporates, new mineral

formation. cation exchange on clays. desorption of ions

from clays and organic matter, and mineral solubilities.

The majority of the published research studies seem to

agree that all these controls and/or reactions are involved

in establishing the composition of oilfield brines. Fur-

ther. most investigators agree with the assumption that

marine water usually is a part of the original material

from which formation waters evolve. Opinions,

however, are not unanimous with respect to how they

evolved. The major disagreements are related to the

membrane filtration theory and to other modes of con-

ccntrating the dissolved solids such as seawater

evaporation.

It is possible to reconstruct the evolution of some

oilfield brines in sedimentary basins if one reasons that

they are genetically related to evaporites. For example.

geochemical and geological studies of some very con-

centrated brines indicate that in deep quiescent bodies of

water. strong bitterns can persist for long periods of time

under a layer of near-normal seawater. As a result, car-

bonates can precipitate from the less saline water and fall

through the bittern at the bottom, and. as compaction

proceeds. the pore spaces remain filled with bitterns.

Some fossil brines once trapped have not moved very far

or very fast.

A geochemical model can be built to represent the

origin and evolution of this type of brine by using the

relatively simple operations and processes of (I)

evaporation. (2) precipitation, (3) sulfate reduction, (4)

mineral fomlation and diagenesis. (5) ion exchange. (6)

leaching. and (7) expulsion of interstitial fluids from

evaporites during compaction.

Experimental work indicated that about 14% of the

bromide in seawater precipitates with the halite as

seawater evaporates. The average concentration of

bromide in the Smackover brines is 3,100 mg/L.

Therefore. the average degree of concentration of these

brines compared to seawater is 3,100+65 =48. Assum-

ing that seawater is concentrated 50-fold, the approx-

imate composition of a brine can be calculated. 26

Shale Compaction and Membrane Filtration

Some investigators believe that the salinity variations

found in oilfield waters are the result of filtration of

water through shale.“’ The membrane filtration theory

first was suggested by De Sitter.“” Laboratory ex-

periments indicated that natural shales can act as

semipermeable membranes. ys.y6 This system working in

nature should cause a water to be more saline on one side

of the shale membrane and almost fresh or less saline on

the other side. This follows because the shale membrane

should filter out the dissolved ions on the upflow side.

causing the water on the downflow side to contain few or

no dissolved ions.

Quantities of Produced Water

An analysis was made of the approximate amount of

water produced with crude oil in I4 states. The states and

their percent of total U.S. crude oil production in 1981

are: Alabama, 0.3%; Alaska, 19.9%; California,

I I .7%; Colorado, I .O%; Florida, I .4%; Louisiana.

13.4%; Montana, 1.0%; Mississippi, 1.2%; Nebraska,

0.2%; New Mexico, 2.3%; North Dakota, 1.4%;

Texas, 31.2%; Utah, 0.8%: and Wyoming, 4.2%.

Fig. 24.1 I indicates the crude oil and water production

from wells in the 14 states. The figure indicates produc-

tion of about 4.3 bbl water/bbl oil. Fig. 24.12 is a

similar graph for 13 states excluding Alaska. This figure

indicates production of about 5.2 bbl wateribbl oil. Fur-

ther. it can be shown that oil wells produce more water

as cumulative oil production increases. In other words,

the older the well, the higher the WOR.

Recovery of Minerals From Brines Extraction of minerals from oilfield brines should be

considered in production planning (I) to recoup explora-

tion and development costs, (2) to prevent environmental

damage from brine, (3) to produce potable water. and (4)

to conserve all valuable minerals and energy.

Precipitation is the most common separation process

used in separating minerals from any type of brine.

Minerals recovered from brines in the U.S. include com-

pounds of iodine, bromine. chlorine, sodium. lithium.

potassium, magnesium, and calcium.

Evaporation of a saline water or brine will cause the

precipitation of calcium carbonate. calcium sulfate,

sodium chloride, magnesium sulfate, potassium

chloride, and finally magnesium chloride. These are the

major chemicals in most brines, and this is the sequence

order in which these compounds will precipitate. Mere

preclpltation will not produce a very pure chemical from

a brine; therefore, other chemical or physical processes

arc used.

For example. iodine, which is in the foml of iodide in

a brine. is recovered by these steps: (I) the iodide is ox-

idized to iodine, (2) the iodine is stripped from the brine,

(3) the iodine then is reduced back to iodide, (4) the

iodide is oxidized again to iodine, (5) the iodine is


D 2700C

2

6

6 2 2600C

E

ZSOOC

BOO<

700(

6OOt

H---L,-

--4 ,/ Crude

I I I I

1975 76 77 78 73 80 YEAR

Fig. 24.1 I-Crude oil and water produced ( x 1,000 B/D) from wells in 14 states including Alaska.

crystallized and filtered, and (6) the iodine crystals are

purified further.

Bromine is recovered by a similar though, of course,

different process. It is present in a brine as bromide. The U.S. Bureau ofMines Yearbook9’ contains information

on general recovery technology, domestic production,

consumption and uses, prices, stocks, etc., of minerals

recovered from brines as well as minerals recovered

from other sources.

The first plant in the U.S. in more than 40 years built

solely to produce iodine from brine went on stream in

1977 near Woodward, OK. It has a design capacity of 2 million lbm iodineiyr or about 30% of the annual U.S.

demand. Some smaller-scale operations to recover

iodine started in 1982 near Kingfisher, OK.

Several plants recover bromine and other constituents

from brine near El Dorado, AR. The brine is produced

from the Smackover formation.

Magnesium and other chemicals are recovered from

lake brines, well brines, and seawater in plants located

near Ogden, UT; Ludington, MI: Freeport, TX; and

Port St. Joe, FL. Lithium is recovered from brine near

Clayton Valley, NV. 98

Economic Evaluation

It is true that market demand fluctuates with supply;

therefore, any company considering an enterprise to

30000

29000

27000

g o 26000

z I

25000

c

7000

6000

5000 I!

13 Stclcs (ercludlng Aiasio)

5 76 77 70 79 YEAR

80

Fig. 24.1 P-Crude oil and water produced ( x 1,000 B/D) from wells in 13 states excluding Alaska.

recover minerals from brines should make an in-depth

study of the current and potential economics. Some of

the factors that must be determined are (1) concentm-

tions of valuable minerals in a brine, (2) amount of brine

available, (3) costs of gathering the brine, (4) costs of

recovering the minerals from the brine, (5) present and

potential market demand for the recovered minerals, and

(6) costs of delivering the minerals to the market. 26

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McGrain. P. and Thomas. G.R.: “Preliminary Report on the Natural Brines of Eastern Kentucky,” Kenluck?/ Geol. Sur~je> Report (1951) 3. McGrain, P.: “Miscellaneous Analyses of Kentucky Brines.” Kentucky Geol. Survey Report (1953) 7. Lambom. R.E.: “Additional Analvses on Brines from Ohio.” Ohio Grol. Surveys Report (1952) li. Stout, W., Lambom. R.E., and Schnaf, D.: “Brines of Ohio.” BUM., Ohio Geol. Survey, 4th Series (1932) 37. Barb, C.F.: “Oil-field Waters of Pennsylvania.” Penn. Slate. Cdl. BUU. (1931) 8. Torrey, P.D.: “Composition of Oil-Field Waters of the Ap- palachian Region,” Sidney Powers Memorial Volume. AAPG (1934) 84-53. Price, P. er al.. “Salt Brines of West Virginia,” Wrsr Virginra Cd survqv (1937) 8. Rogen. G.S.: “Chemical Relation of the Oil-Field Waters in San Jaaquin Valley, Calif.,” Bull.. U.S. Geol. Survey (1917) 653. 5.

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246. Dotaon, C.R. and Standing. M.B.: “Pressure. Volume, Temperature and Soluhility Relation5 for Natural Gas-Water MIX- turcs:’ Drill. t/d Prod. Prw.. API (1944) 173-79. Rowe, A.M. Jr. and Chou. J.C.S.: “Pressure-Volume- Temperature-Concentration Relations of Aqueous NaCl Solu- tion\.“ J. Chw~. Dutcr (1970) 15, 61-66. Ashhy. W.H. Jr. and Hawkins, M.F.: “The Solubility of Natural Gas in Oil-Field Brines.” paper presented at the 1948 SPE Annual Meetmg. Dallas. Oct. 4-6. Roger\. P.S.Z. and Pitzer. K S.: “Volumctnc Propcrtlc5 of Aqueous Sodium Chlonde Solutions.” J. Ply.\. Clrtwr. Rcf: D~rt<r (1982) 11. No. I. 15-81. Wy II ie. M. R.J.: 77w F[rn~~~rr,lrnr~r/s of WC,// Lo,q //lrc,rpn,ta/i/,/r, wcond edstnn. Academx Press [nc.. New York CQ (1954) ret. 1957. Amyx. J W.. Bass. C.M. Jr.. and Whiting, R.L.: Pcrrolrwi Rccr~~vir Fqi,wcv%,q. McCrdw~Hill Book Co. Inc., New York

City (1960). K&in. J.. Khahfa. H.E.. and Co&a, R.J.: “Tables of the Dynamic and Kinematic Viscosity of Aqueour NaCl Solutitrn\ in the Temperature Range 2Ol5O”C and the Pressure Range 0 I-35 MPa.“J. fhrs. Chcwr. Rrf Dmtr (1981) 10. No. I, 71-87. McAuliffe. C.D.: “Solubiiity in Water of Paraffin, Cycloparat’iin. Olefin. Acetylene. Cycle-olefin and Aromatic Hydrocarbons,” J. Phy. C/w,,,. ( 1966) 70, 1267-75. Prince, L.C.: “Aqueous Solubility of Petroleum as Applied IO Its Ongin and Primary Migration.” &t/l.. AAPG t 1976) 2 13-44 Tickell, F.G.: “A Method for Graphical Interpretation of Water Analy\i\.” Co/,/: Sfrw Oil Gr~r Suprrv. (1921) 6. 5-I I

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Reistlc. C.E.: “ldentlt’icatwn of Oilficld Water\ bp Chcnwal Analysi\.” U.S. Bur. Min. Techmcal Paper, 404 (1927). Stllf. H.A. Jr.: “The Intcrprctntion of Chemical Water Analysis by Mean5 of Patterns.” J. Pet. Twh. (1951) 192. 15-17. Piper. A.M.: “A Graphic Proccdurc m the Geochemical Inter- pretation of Water Analyw.” U.S. Geol. Sun: Ground Water Note 12, (1953). Morgan. C.O.. Dingman, R.J.. nnd McNelli\. J.M.: “Digital Computer Methods fur Water-quahty Data.” Griwrcl wow, (1966) 4, 35-42. Morgan. C.O. and McNellis. J.M.: “Still Diapraut~ ul Wnter- quality Data Programmed for the Digital Cumputer.” Kanses State Geol. Sun,. Spec. Dtstrib. Publ. 43 (lY6Y) Angino. E.E. and Morgan. C.O. ’ ‘Appllcotlon of Pattcm Analysi\ to the Classification of Oilfield Brine\.” Kanw Slale Cc01 Sure. Comput. Contrlb. 7 (1966) 53-56. Hitchon. B.. Billings. G.K., and Klovan. J E.: “Geochemlwy and Origin of Formation Waters in the Western Canada Sedimcn~ tary Basin-Ill. Factors Controlling Chemical Compovt~on.” G<w/?i/,~ Cmr,wc~hi~,~. Am, ( I97 I ) 35. 567-98. Clayton. R.N. c’t r/l. : “The Origin 01‘Snline Fomwion Waters. I. Isotopic Composition.” J. G~qdi,u Rc.\. (1966) 71. 3869-112 De Sitter, L.U.: “Diagene\ir of’ Oil-field Bnnes.” &f/I. AAPG ( 1947) 2030-40. Kharaka. Y.K. and Berry. F.A.F.: “Simultaneous Flou of Water and Solutes Through Geological Membranes 1. Experimental In- vestigations.” Geoc~hiul. Co.\r,?oc~/iil,i. AC ICI. ( 1973) 37. 2.577~260.7. McKelvey. J.G. and Milne. J.H.: “The Flow of Salr Solution Through Compactrd Clay. in Clays and Clay Mmen~l\.” 9th Natl. Conf. Clays and Clay Mineral\ (1962) 24X-59. U.S. Bwwrrc c~fh4irw.s Minertrlc Yrwrhd. Ah/d\. Miwn~l~. mrl

Fwk. U.S. Bureau of Mine\. Washinztcm. D.C. (Yearlv). Vine. J.D.: “Lithntm Resources and Requirements by the Year 2000.” U.S. Geological Survey Professional Paper 1005, U.S. Gwemment Printini Office. iahhingtun D.C. t i976)

Chapter 25 Phase Behavior of Water/Hydrocarbon Systems Riki Kobayashi, Rice U. * Kyoo Y. Song, Rice U. E. Dendy Sloan, Colorado School of Mines

Introduction The occurrence of water with hydrocarbons both in the reservoir and in the produced states represents the norm. Even though streams saturated with water enter the producing tubing, subsequent cooling generally produces separate phases of low mutual solubilities. Nevertheless, the mutual solubility of water and hydrocarbons is extremely significant in the processing of produced fluids. In the reservoir, their mutual solubilities increase as the temperature increases, either as a result of reservoir depth or external heating, as in the case of a steamflooding operation. Thus, the definition of the saturated water content in the equilibrium phases is the subject of this chapter. The coexisting phases may be gas, G, hydrocarbon-rich liquid, LHC, water-rich liquid, L,, or hydrate, H, although the coexisting phases are seldom pure. The advent of EOR processes that use CO 2 gives rise to the occurrence of a CO*-rich liquid phase, which we designate Lco2 .

General Hydrocarbon/Water Phase Diagrams and Equilibrium Data Sources For a given mixture of oil, water, and gas, the definition of the phases in equilibrium at any given pressure and temperature is of importance to the reservoir engineer. The prediction of the extent, composition, and other equilibrium properties of the phases in equilibrium is the objective of thermodynamic calculations. Given the number of components in the mixture and the number of coexisting phases, the number of independent variables that must be specified to describe the system (thcr- modynamically) is given by the phase rule of Gibbs. ’

‘Authors of the onginat chapter on this topic in the 1962 edltwn were John J McKetta and Albert H Wehe

which states that the “degrees of freedom” or number of independent variables required to define the system, F, equals the number of components, C, minus the number of phases, P+2, or F=C-PC2. A few examples given this important relationship are summarized in Ta- ble 25.1.

The phase rule is essentially a “rule of algebra” applied to equations of equilibrium and as such does not specify which phases are in equilibrium or their equilibrium concentrations. Nevertheless, its value in the organization of knowledge regarding phases in equilibrium and their relationship is important and always should be respected and used.

The pressure-temperature projection of the univariant coexistence lines of binary hydrocarbon/water systems represents a unique way of summarizing the phase behavior of the system. The methane/water system is one in which the critical point of the gas falls far below the ice point. With high pressures, even at moderate temperatures, solid hydrates are formed. The pressure- temperature projection of the system is given by Fig. 25.1 .2 Of particular interest to petroleum production engineers is the precise location of the L,.-H-G line or the initial hydrate formation condition. Since natural gases vary in composition, the L,-H-G line is usually compositionally dependent.

Fig. 25.2 shows a constant-pressure trace of the saturation conditions of the methane/water binary system at a constant pressure exceeding the critical pressure of methane. Among the important features of this diagram are the dissolved gas concentration of the water-rich liquid phase (e.g., at Point 4), the equilibrium dewpoint locus, the initial hydrate formation temperature along the horizontal line 7-2-5-6, and the equilibrium and

25-2

TABLE 25.1-SUMMARY AND MEANING OF DEGREES OF FREEDOM

Number of Equilibrium Comoonents Phases

Number of Independent

Variables Required To

Represent each Locus of States

metastable dewpoint locus (Line 7-8) below the initial hydrate formation temperature and below the stable dewpoint line. The definition of the equilibrium dewpoint water content for methane has been determined by Olds et al. 3 and the initial hydrate formation condition by Villard,4 Deaton and Frost, 5 Kobayashi and Katz, ’ and Marshall et al. 6

The definition of the gas-hydrate equilibrium locus, as distinguished from the metastable equilibrium locus erroneously reported in most dewpoint charts, has been reported by Sloan et al. ’ The measurement of the gas hydrate compositions or hydrate numbers for methane was conducted successfully by Galloway et al. 8 and found in essential agreement with the statistical


mechanical theory of van der Waals and Platteeuw,” as applied by Saito et al. ‘O” as well as Panish and Prausnitz, ” and other subsequent workers.

The second type of pressure-temperature projection presented is for the propane-water system in which the critical temperature of the hydrocarbon exceeds the ice point. Since the aqueous and hydrocarbon-rich phases exhibit low mutual solubilities, a three-phase H-L,-G condition occurs in the neighborhood of the vapor pressure of condensable hydrocarbons such as propane.

Fig. 25.4 presents a constant-pressure trace of Fig. 25.3 at a pressure less than the critical pressure of propane (Kobayashi t t ), The principal qualitative difference between Figs. 25.2 and 25.4 is the existence of the LHC-G region in the latter that is absent in the former, at least at moderate temperatures. Note that in the LH~-G region of Fig. 25.4, the water concentration of the gas phase is larger than in the equilibrium liquid phase at the same temperature. On the contrary, in the G-L,,, region, the water concentration in the saturated gas is rather less than in the equilibrium water-rich liquid phase.

Owing to the differences in the molecular sizes of methane and propane, the hydrate structures of methane hydrate (Structure I) and of propane hydrate (Structure II) are quite different.

By using phase diagrams such as Figs. 25.2 and 25.4, it is possible to trace the phase transitions one would expect to encounter for various composition mixtures as the temperature of the system is lowered. It is important to note that hydrates can form directly from the fluid hydrocarbon phase (i.e., in the absence of free liquid

600

KEY

TEPPERATURE, “F - Tw C@+MENTS

-- @iE CCh'FOdEM

------ CRITICAL LrK"S

0 ~TVANE CRIT~L -300

El WATER CRITICAL c. -9 QsLwPLE PolNl

v THREE PHASE CRITICAL

G - L, I

_ ,; -HETASTABLE DEW PT. '-%

$:I i LOCUS

I

03) N-H

PURE METHANE I’ERCENT t'LIRE WATER

Fig. 25.1-Pressure-temperature projection of univariant Fig. 25.2-Constant-pressure trace of the methane/water heterogeneous equilibrium in the methane-water system at a pressure greater than the methane system. critical pressure.

PHASE BEHAVIOR OF WATER/HYDROCARBON SYSTEMS

-400 0 400 ml TEWERATLUE, ‘F

Fig. 25.3-Pressure-temperature projection of univariant heterogeneous equilibrium in the propane-water system.

water at low water compositions) provided that the temperature is sufficiently low and turbulence is present or the equilibration times are large, as shown by Cady ‘* The metastable dewpoint line shown in Fig. 25.2 (Line 7-8) rather than the true equilibrium state may be attained under certain situations to give a false or metastable indication of equilibrium (Kobayashi and Katz 13).

References for aqueous/volatile-gas systems related to petroleum production are listed in the references at the end of the chapter. These are for methane/water system (Refs. 3 and 14 through 44), natural-gas/water (Refs. 13 and 45 through 52), COz/water (Refs. 31, 44, and 53 through 96). and for nitrogen/water (Refs. 24. 31( 33 through 36. 62. and 97 through 120). References for other binary and ternary hydrocarbon/water systems are listed in the general references.

References for hydrate/volatile-gas systems are for methane/water (Refs. 2,4,6 through 8. and 121 through 129). natural-gas/water (Refs. 126 and 130 through 135). CO?/water (Refs. 5 and 136 through 139), and nitrogen/water (Refs. 6, 140, and 201). References for other binary and ternary hydrocarbon/hydrate systems are listed in the general references.

25-3

P -l-l I

PERCENT WATER I-lJKt WAlltft

Fig. 25.4-Constant-pressure trace of the propane/water system at a pressure less than the propane critical pressure.

As shown in Figs. 25.1 through 25.4 for the methane/water and propane/water systems, the phase behavior of such systems is complicated by the existence of multiphase equilibria, including solid phases such as hydrate or ice. The former phase is particularly troublesome in petroleum production since solid hydrates can form at temperature above the ice point wherein the concentration of water in the system is quite low. Fig. 25.5 presents the univariant three-phase loci for various binary hydrocarbon/water systems and shows their critical hydrate formation loci (solid lines).

The variability of the water content of hydrocarbon- rich phases for a condensable system perhaps is illustrated best by Fig. 25.6, which shows the concentration of water in the propane-rich phases in the propane/water system. In the low-pressure gaseous region the water content is determined primarily by the vapor pressure of water, whereas in the condensed propane region the solubility of water in the propane-rich liquid phase is determined by the strong repulsion of water by the hydrocarbon owing to the thorough hydrogen-bond- breaking ability of the condensed hydrocarbon phase. This phenomenon can be illustrated further by Fig. 25.7, a composite plot of the activity coefficient of water at

25-4

10 50 70 93

TWERAW, ‘F

Fig. 25.5-Hydrate-forming conditions for paraffin hydrocarbons.

moderate pressures from hydrocarbon molecules vs. temperature for molecules ranging from propane to li uids as heavy as naphtha and SAE 20 lubricating oil. 7

- I4

Fig. 25.7 also shows that at higher temperatures water becomes increasingly miscible with hydrocarbons, with total miscibility conditions having been reported for intermediate-range hydrocarbons. This phenomenon, which is relevant to high-pressure steamfloods, also is illustrated by Fig. 25.8, which gives their three-phase miscibility conditions. 14*

In addition to fluid condensed phases, as the pressure is increased and the temperature decreased, nonpolar molecules and weakly ionizing molecules of appropriate molecular sizes form solid gas hydrates. Davidson’43 presents the approximate molecular diameters and structure type of the hydrate formers and their theoretical hydrate chemical formulas.

Hydrate Stability Conditions Table 25.2 presents the physical data of the two known hydrate lattices, the diamond type or structure II hydrate, and the body-centered type or Structure I hydrate. Owing to their critical sizes, some molecules, such as cyclopropane, stabilize both hydrate Structures I and II at higher temperatures but only Structure II at lower temperatures with a phase transition temperature in between (see Sloan l”).


1 ax 400 lml 2cm 4col I%ESSUE, PSIA

Fig. 25.6-Concentration of water in propane-rich fluid phases in the two- and three-phase regions.

-

\ -

-

-

40 TEJEMTIBE, 'C

\

2

Fig. 25.7-Composite activity coefficient plot for water in hydrocarbon systems.

PHASE BEHAVIOR OF WATERlHYDROCARl3ON SYSTEMS 25-5

Estimating Initial Hydrate Formation The estimation for the stability conditions of the hydrates when liquid water is present, the L,-H-G equilibrium locus, can be estimated by various means.

Sweet Natural Gas Systems Method. The initial hydrate formation condition can be estimated for sweet natural gas systems by using pressure, temperature, and gas gravity as parameters (see Katz’45.‘46) as shown in Figs. 25.9 and 25.10. These figures should be confined for usage when the natural gas mixtures are similar to those used in developing them, with data taken from Deaton and Frost,” Wilcox ef al., “’ Kobayashi and Katz, 2 and Katz!45 Typical compositions of natural gases corresponding to gas gravities of Fig. 25.9 are given in Table 25.3. It should be noted that no H2S or CO1 content is tolerated by the correlations.

Vapor/Solid Equilibrium Ratios Method. The second approach involves the development and application of vapor/solid equilibrium ratios for gas/liquid/hydrate equilibrium (Carson and Katz, I47 Unruh and Katz, ‘39 Noaker and Katz, ‘48 Robinson, ‘49 and Robinson and Ng”‘), as shown in Figs. 25.11 through 25.16. The development of the vapor/solid K-values involved experimental hydrate formation conditions for mixtures of methane with other gas(es) and the hypothesis that hydrates could be treated as solid solutions, in hindsight a brilliant hypothesis. The vapor/solid Ki(,.,) values are used to calculate the hydrate “frost point” in direct analogy with dewpoint calculations:

where Ki(,,.rj is the vapor/solid equilibrium values of component i, yi is the mole fraction of component i in the vapor phase, and xi is the mole fraction of component i in the solid phase, so that

f; yiiKic\>.n=l.O. . . . . . . . (1) i= I

An example calculation for a complex mixture is presented in Table 25.4. ‘44 As suggested, the K-value of n-butane is taken numerically as that for ethane.

Statistical Mechanics for Adsorption Approach. A third method of estimating initial hydration formation involves the application of statistical mechanics (van der Waals and Platteeuw 15’ m well-defined hydrate cages as determined by X-ray crystallography by von Stackelberi and Miiller ) ‘52,‘53 and others. The theory of van der Waals and Platteeuw was applied to predict the initial hydrate formation of pure gases at temperature above the ice point by Marshall et al. 6 and later to binary mixtures by Saito and Kobayashi. ‘54 Nagata and Kobayashi ‘55 used the Kihara potential to calculate the dissociation pressures of hydrates, following the earlier work of McKay and Sinanoglu. ‘56 A more convenient estimation method for hydrate decomposition conditions

1.0 .n -

- HYDROCARBON - WATER SYSTEtlS .’ ,&iii-

0.4 ,

‘C

Fig. 25.8-Composition of hydrocarbon-rich phase at three- phase critical conditions.

was developed by Parrish and Prausnitz, lo using the Kihara potential and the method of van der Waals and Platteeuw . 9

Computer Method For Hydrate Dissociation Predic- tions. Pam’sh and Prausnitz Development. lo The method of van der Waals and Platteeuw as developed by Parrish and Prausnitz is slightly more complex than the previous method, but it has two considerable advantages: (1) the equations are related to the microscopic hydrate structure, and (2) the theoretical nature of the model allows it to be extended beyond the G-L,-H region.

TABLE 25.2-PHYSICAL DATA OF TWO KNOWN HYDRATE LATTICES

Water molecules per unit cell

Cavities per unit cell Small Large

Cavity radius, rc Small Large

Typical gases that form in each cavity of this structure

‘Small. “Large.

Structure I Structure II

46 136

2 16 6 a

3.97 3.91 4.30 4.73

methane* propane” ethane’ l i-butane’ l

n-butane’ * neo-pentane* l

40 60

TDJPERAIIE, ‘F

I T

Fig. 25.9-Initial hydrate-formation conditions for natural gases with varying gas gravities.

In the late 1940’s and early 1950’s the molecular structures of hydrates, shown in Table 25.2, were studied through the use of X-ray diffraction. ‘52,‘s3 The structural determination enabled van der Waals and Plat- teeuw 9 to develop a model for the prediction of hydrate dissociation pressure at any temperature. Their basic equation looks complex until one considers it as being very similar to the basic equation for the chemical potential of Component I in a mixture of Components 1 and 2. This equation, which relates the chemical potential of


TABLE 25.3-TYPICAL COMPOSITIONS AND COR- RESPONDING GAS GRAVITIES OF NATURAL GASES OF

FIG. 25.9

;“A C;H; I-C,H ,0 n-C,H,, CsH,z + Gravity

calcu-

Mole Fraction

0.9267 0.8605 0.7350 0.6198 0.5471 0.0529 0.0606 0.1340 0.1777 0.1745 0.0138 0.0339 0.0690 0.1118 0.1330 0.00182 0.0084 0.0080 0.0150 0.0210 0.00338 0.0136 0.0240 0.0414 0.0640 0.0014 0.0230 0.0300 0.0343 0.0604

0.603 0.704 0.803 0.906 1.023

component i, pi , to the activity of a component is

pj=pjO+RTln a. (, . . . . . . . . . . . . . . . . . . . . . . (2)

where p o = chemical potential of pure component i, I

R = universal gas constant, T = absolute temperature, and

ai = activity of component i in mixture.

Van der Waals and Platteeuw used theory to derive a similar equation for the chemical potential of water in the hydrate structure as follows.

where p,,,H = chemical potential of water in filled

hydrate, pw~r = chemical potential of water in empty

hydrate, n,i = number of cavities of type i per water

molecule in basic lattice, and yji = fractional occupancy of type i cavity by

type j molecule.

- 30 43 4) 60 xl

TDQERATU~ ‘F

Fig. 25.10-Initial hydrate-formation condition.

PHASE BEHAVIOR OF WATER/HYDROCARBON SYSTEMS 25-7

Fig. 25.11-Vapor/solid equilibrium constant for methane.

m

1.0 -

<OS6

i 5 0.4 Bi 2 3

0.2

0.1

Fig. 25.12-Vapor/solid equilibrium constant for ethane

0.02

0.01 t 30 40 M 60 70 80

TOYPERITIRE, ‘F

Fig. 25.13-Vapor/solid equilibrium constant for propane.


V v A /A / I A A /I//I// I

T-W& ‘F TEFPERATUIE, ‘F

Fig. 25.14-Vapor/solid equilibrium constant for isobutane. Fig. 25.15-Vapor/solid equilibrium constants for CO,.

TABLE 25.4-CALCULATION OF PRESSURE FOR HYDRATE FORMATION OF A COMPLEX MIXTURE

EHA &I: I-C,‘-‘,o n-C,H to N2 co2

Total

Mole Fraction in Gas

0.784 0.060 0.036 0.005 0.019 0.094 0.002

1.000

AT 50°F’

At 300 psia

K Y/K 2.04------- 0.3841 0.79 0 0759 0.113 0.3186 0.046 0.1087 0.79 0.024

3.: 0 0.0007

0.912

At 350 osia

K Y/K 1.90- 0.4126 0.63 0.0952 0.085 0.4234 0.034 0.1471 0.63 0.030

cc 0 2.3 0.0008

1.10

‘The linearly mterpolated anwer is 322 ps~a and the experimentally observed hydrate formatcn pressure at 5O“F was 325 ps,a.

Fig. 25.16-Vapor/solid equilibrium constants for hydrogen sulfide.

The second term on the right accounts for hydrocarbon filling of the lattice. The term yii is given by

cjifi Yii = ) . . . . . . . . . . . . . . . . . . . (4)

I+ C Cki.fk k

where Cji is a unique function of temperature for each guest molecule in each size cavity, fi and fk are the fugacities of j and k in the gas phase, and k is ordered from one to the number of components.

The fugacity term is determined by an equation of state (EOS), such as Peng-Robinson (PREOS). Is7 The Cji functions may be calculated using the Lennard-Jones- Devonshire spherical cell model. The interaction between the guest molecule and a uniform spherical surface representing the cage commonly is described by a Kihara potential function. The method is described by Parrish and Prausnitz. lo The Kihara parameters are determined from single or binary gas dissociation conditions and then may be used to predict dissociation conditions for multicomponent gases. A fit of Cji for common gases is given in Table 25.5.

To predict hydrate formation conditions from liquid water and gas, the following conditions must be satisfied.

p,,,L =p,,,H=pwg, . . . . . . . . . . . W

TL=TH=Tg, . . . . . . . . . . . .(5b)

and

pL =P,T, =pg, . . . . . . . . . . . . . . . . . (k)

where p is the absolute pressure and subscripts L, H, and g are liquid water, hydrate, and gas, respectively.


TABLE 25.5-PARAMETERS FOR THE HYDRATE DISSOCIATION MODEL

Structure I* Structure II**

~I,,,(T,,~P~), Jlmol 1297 874 PI,. Jlmol 1389 1624.6 AV,, cm3/mol 3.0 3.4

Parameters for Calculating Langmuir Constant Between 260 K and 300 K

C,, = A/T exp (B/T)atm -’

Small Cavities of Large Cavities of Small Cavities of Large Cavities of Structure I Structure I Structure II Structure II

AxlO B AxlO B AxlO B AxlO’ 8

CH.4 2.7711 2752.8047 1.4865 2878.0682 2.1778 2713.4259 6.6777 2310.0682

E$; 0.0 0.0 0.0 0.0 0.4071 0.0 3820.7119 0.0 0.0 0.0 0.0 0.0 2.9157 1.3212 3277.9254 4506.9810 n-C,H 1o 0.0 0.0 0.0 0.0 0.0 0.0 0.0404 2687.9744 i-C,Hlo 0.0 0.0 0.0 0.0 0.0 0.0 0.0788 3083.9044 N2 17.7986 1931.5130 5.7883 1669.2292 14.8724 2002.6644 15.6182 1319.4734 co2 1.5227 2943.9948 1.0242 3172.6655 1.1620 2837.3018 5.3986 2478.0545 H*S 2.3458 3701.3170 1.3532 3739.3355 1.8306 3671.9126 6.4567 2976.4243

‘Dharmawatdhana “’ “Weller ‘%

Eq. 5a may be combined with Eqs. 3 and 2 to obtain

APLW- -P~'MT-P~L=-RT C i n,i ln (l- 7 Yji)

+RT In a;, . . . . .(6)

where APT is the difference in chemical potential of pure water and ai accounts for the normally small solubility of the guest gas in the aqueous phase. Now given T, p, and&, one may calculate Ap,., in Eq. 6 by using Eq. 3 and the Kihara potential. However, the AP,~ obtained are useless until they arc matched to the AfiLM. from the following equation.

AP~VP) A~WVorpo) Tuh, RT = RT s -dT+ ~pI‘I-dp,

-T RT2 po RT 0

..,__ ___. __ ___ __ (7)

where T,, = reference temperature. I’0 = reference pressure,

Ah,,. = specific enthalpy difference, and AI.,, = specific volume difference.

Eq. 7 corrects a chemical potential difference at a standard T,, (0°C) and I>,, (0 atm). ApcL, (T,,.p,,) for the change in temperature and pressure of the hydrate of interest. The constants .Ip ), (T,, ./I,,) and Al? ,,. (T,,), meax- ured recently by Dharmawardhana “’ and Weiler. Is’ and parameters for Langmuir constants arc fivcn in Table 25.5.

Procedure for Determining Hydrate Formation Pressure. The procedure for determming hydrate formation pressures for a given gas at a given temperature IS as lhllow\.

1. Estimate a pressure, p. 2. At the estimated pressure, for the given temperature

and gas mole fraction of component j, determine the fugacity ofj from an EOS, such as PREOS. 15’

3. By using Cj; values from the Kihara potential and yji values from Eq. 4, determine Ap,, from Eq. 3.

4. By using constants from Table 25.5, calculate Ap w from Eq. 7 at the temperature and estimated pressure.

5. If the A,u, values for Eqs. 6 and 7 are equal, then the p value is correct for hydrate formation. If not, estimate a new value of p and return to Step 2.

A computer program that performs the above procedure has been written by Ng and Robinson and is available commercially through the Gas Processors Assn. (GPA). A second hydrate program generated by Erickson and Sloan I60 at the Colorado School of Mines is also available through GPA.

That the model predicts the three-phase data accurately is demonstrated in Fig. 25.17 for the methane/propane system. The dramatic decrease of dissociation pressure for a 1% addition of propane is evidence that the hydrate has changed structure (from I to 11) as mentioned earlier. In other words, as small amounts of propane are added, a greater temperature at constant pressure is tolerated for hydrate formation.

Fig. 25.18 also demonstrates the accuracy of the model while indicating that hydrates denude the gas of propane. At 5 atm, while the gas phase has about 8% propane, the solid phase has 50% propane. From Figs. 25.17 and 25.18 and typical earth temperature gradients, Davidson 16’ proposed the following in-situ, onshore hydrate conditions.

Going toward the center of the earth, one may encounter Structure II hydrate at relatively shallow depths until the point at which the hydrate denudes the gas of propane. No more hydrate is encountered until the range of Structure I stability conditions is obtained. Continuing downward from the Structure I region no hydrates are encountered. Finally, a Structure II region is realized for gases rich in propane.


m%kCfWE IN VAFm PHASE

0 DATA OF DEATON AND FROST5

- cALcuATED I

40 xl TEWEFS?~E, “F

Fig. 25.17-Hydrate formation conditions for the methane/ Fig. 25.18-Pressure-composition diagram for the methane/ propane/water system. propane/water system.

Determining the Water Content of Gas (or Hydrocarbon-Rich Liquid) in Equilibrium with Hydrates The position of lines G-H and LHc-H in Figs. 25.2 and 25.4 determines the extent to which the hydrocarbon must be dried to prevent the formation of hydrate from the gas phase, The water content in this region is relatively small and difficult to measure. Until recently, straight lines (log water content vs. l/T from the gaslliq- uid region were extrapolated into the gas/hydrate region with only limited experimental justification. However, as indicated by Kobayashi and Katz, I3 thermodynamics tells us that such concentration extrapolations across phase boundaries yield severe errors. This observation, that straight-line extrapolation into the gas hydrate region represents gas in equilibrium with metastable liquid water, explains the field data anomalies observed by

l DATA OF VAN DER WAALS AND PLATTEEUW’ -

- CALCULATED T= -3 “C

U xl 40 60 El lu.l

mE%PuoPANE

(WATER-PREE BASIS)

Records and Seely . ‘Q Laboratory confirmation that the water content of gas in equilibrium with hydrate should be much different from the extrapolated values has been verified by Sloan et al. 7 for methane hydrates, and Song and Kobayashi 163 for methane/propane hydrate!:

When one predicts the water content of a singie fluid phase, such as a fluid, in equilibrium with hydrates, the basic equation is as follows.

fw.=fwH , . . . . . . . . . . . . . . . . . . (8)

whemf,,,, is the fugacity of water in the fluid phase and f WH is the fugacity of water in the hydrate phase.

In this equation the fugacity of water in the fluid phase is determined from

fwf=ywKwfp, . . . . . . . . . . . . . . . . . . (9)


Fig. 25.19-Structure I empty hydrate vapor pressure as a Fig. 25.20-Structure II empty hydrate vapor pressure as a function of reciprocal temperature. function of reciprocal temperature.

where K,,,, is the fugacity coefftcient* of water (determined by an EOS) and y, is the mole fraction of water in the hydrocarbon.

The value y,,, is the solution to this problem, stated as: given a flowing hydrocarbon at T and p, determine how much the fluid should be dried to prevent hydrate formation.

The quantityfWH in Eq. 8 is determined by

fwH =fwMT exp(-Ap,IRT), . . . . . . . . . . .(lO)

where f,,,HT is the fu acity of water in empty hydrate. Ng and Robinson k4 give an expression for fW~r in

both structures, obtained by fitting the vapor/hydrate data of Kobayashi et al. 7~12i*165 Therefore, their method may be considered a correlation of existing two-phase (vapor/hydrate) data.

By equating the fugacity of hydrate to ice in three- phase data, Dharmawardhanat58 showed that fwMT of Eq. 10 can be expressed as an empty hydrate vapor pressure as follows:

P y~Kg exp Vl(P-Pf)

RT =P~MTK~MT exp@WW,

. . . . . . . . . . . . ..I..... (11)

where pvf = vapor pressure of ice, Kg = fugacity coefficient of ice, VI = volume of ice, pI = vapor pressure of ice,

pvMT = vapor pressure of empty hydrate, and KIT = fugacity coefficient of empty hydrate.

*In some prior publications, 0 was used as the symbol for fugaclty ccefhcient.

In this equation, all of the ice properties are well known, the Ap is obtained from three-phase data fit to Eqs. 3 and 4; the only unknown is P”MT, which was fit to a number of hydrates’ three-phase data below 273 K and found to be a single function of temperature; Figs. 25.19 and 25.20 show these values for empty hydrate vapor pressure as determined from a number of hydrates. Re- cent work at the Colorado School of Mines has shown the method represented by Eqs. 9 and 10 and Figs. 25.19 and 25.20 to represent the water-in-liquid hydrocarbon/hydrate equilibria accurately.

Hydrate Formation on Expansion of Gases The simultaneous solution of the isoenthalpic (throttling) expansion of natural gases with initial hydrate formation conditions, Fig. 25.9 yields a first approximation of the prediction of permissible expansions. Katz ‘45 presented a useful chart for various gas gravities of natural gases.

Definition of the Saturated Water Content of Natural Gases in Equilibrium With Aqueous Phases

The saturated water content of natural gases in equilibrium with aqueous phases generally is presented in the familiar dewpoint chart. Fig. 25.21 presents a dewpoint chart for methane-rich gases synthesized from several sources of data. The upper limit of the dewpoint chart given in Fig. 25.21 is defined by the properties of steam. Fig. 25.22 presents a correction to Fig. 25.21 caused by the hydrate formation of methane gas, and a mixture of methane and propane gas. The water content at temperatures above the hydrate stability conditions up to 10,000 psia are based primarily on the data of Olds et al. 3 At temperatures below the initial hydrate formation


TEMPERATURE, 103/K

IOOC 44 4.2 4.0 30 36 3.4 I I I I I ' I f-1

10303

lo

4

1

lFJ’T%m ‘F

Fig. 25.21~Dewpoint water content chart for methane-rich gas.

conditions, the data are primarily those measured by Skinner. ‘66 However, below the initial hydrate formation conditions, as initially observed (in the gas fields) by Records and Seely , ‘Q Fig. 25.21 presents metastable values. Using the hydrate theory discussed previously, and recent measurements on the water content of two gases (a methanel5.3 1-mol % propane and a pure methane in the gaseous state in equilibrium with hydrates), a corrective correlation to Fig. 25.21 in the gas/hydrate region was developed.

A typical replacement chart is shown in Fig. 25.22. 163 In this figure the high-temperature vapor/liquid-water region is separated from the low-temperature vapor/hydrate region by a line representing the three- phase (vapor/liquid-water/hydrate) boundary. The isobaric data in the vapor/hydrate region follow semilogarithmic straight lines when plotted against reciprocal temperature, but these lines have slopes different from the straight lines in the vapor/liquid-water region. In addition, the three-phase lines are indicated to be a function of gas composition, so that the change in the slope of an isobar from the vapor/liquid region occurs at different temperatures. With the above complex- ities, a comprehensive water content chart (or series of charts) for gases of differing compositions would be cumbersome. Instead, a mathematical method for determining the water content of gases in the vapor/hydrate region is used.

c &y/9”” oto-C!i4-C~H8(531% mold- Hz0

EXPERIMENTAL

----- CH4-H20 AOYAGI et al.“’

--*--DEW POINT LOCUS _

CALCULATED FOR

0.01 I I I CH, - C,H, (5.31%)

-50 -30 -10 14 40 70

TEMPERATURE, “F

Fig. 25.22~-Depression of metastable dewpoint below initial hydrate temperature.

Steps in Determining the Water Content of Vapor in Equilibrium with Hydrates The method for determining the water content of vapor in equilibrium with hydrates, at a given temperature and pressure, is composed of six steps.

1. Calculate the metastable water content at the temperature and pressure of interest by using Eq. 12.

2. Calculate the three-phase temperature at the pressure and gas gravity of interest by using Eq. 13. Ob- tain the temperature difference (AT) by subtracting the temperature of interest from the calculated three-phase temperature.

3. Calculate the displacement from the metastable water content (AW) at the above A’f and pressure of interest using both Eq. 14a for methane and Eq. 14b for a 94.69-mol% methane/5.31-mol% propane mixture.

4. Calculate the AW for the gas composition of interest by a linear interpolation between the AW for methane (gravity =0.552) and the A W for the mixture containing 5.31% propane (gravity=0.603), using gravity as an interpolation parameter.

5. Calculate the equilibrium water content by subtracting the AW value obtained in Step 4 from the metastable water value obtained in Step 1.

6. Consider the range of data used to tit Eqs. 12, 13, 14a, and 14b, as discussed later, to determine whether the answer obtained in Step 5 is within the bounds of the correlation.


TABLE 25.6-COEFFICIENTS FOR ECWATIONS

C,

Eq. 12

2.8910758E + 1 C, - 96681464E + 3 C3 - 1.6633562E + 0 Cd - 13082354E + 5 c5 2.0353234E + 2

2 3.8508508E - 2

d c9 C 10 C,,

Eq. 13 Eq. 14a

2.7707715E - 3 - 1.605505E + 3 - 2.782238E - 3 - 5649288E - 4 - 1.298593E - 3

1.407119E - 3 1.785744E - 4 l.l30284E-3

5.9728235E - 4 - 2.3279181 E - 4 - 2.6840758E - 5

4.6610555E-3 5.5542412E - 4

- 1.472776% - 5 1.3938082E - 5 1.488501 DE - 6

Equations for Determining the Water Content of Vapor in Equilibrium with Hydrates In the following equations, the pressure is expressed in psia, the temperature in degrees Rankine, and the water content is expressed in pounds of water per million cubic feet of gas at 1 atm and 60°F. A listing of the coefficients in each equation is found in Table 25.6.

Fit of Methane-Rich Gas (Fig. 25.21). The following equation, which is a fit of Fig. 25.21, is in the pressure range of 200 to 2,000 psia, and in the temperature range of -40 to 120”F, for metastable water content, IV,,,, , as a function of temperature, T, and pressure, p:

W,,,=exp[C1 +C~lT+C3(lnp)+Cq/P

+CS(lnp)lT+Cg(lnp)Z],. _. _. .(12)

where Cl . C6 are obtained from Table 25.6.

Fit of Three-Phase (Vapor/Liquid/Hydrate) Forma- tion Conditions. The three-phase condition was fit in the temperature range of 34 to 62”F, the pressure range of 65 to 1,500 psia, and the gas gravity, y. range from 0.552 to 0.9. Only hydrocarbons were used in the fit, and gases containing CO, and hydrogen sulfide were ex- cluded specifically.

T=lI[C, +CZ(lnp)+C3(ln +y)+Cq(lnp)*

+cS(]" p)(ln Y)fC6(ln ?)*

+C,(ln pj3 +Cs(ln p12(1n y)

+C9(lnpMln y12+C10Cln Y)"

+C~~(lnp)4+C~2(lnp)'(]ny)

+C,30np)‘(ln ~)~+C~14(lnp)(ln r13

+C,s(ln -y)4],. . . . .(13)

where CI Cl5 are obtained from Table 25.6.

Fit of Water Content Suppression. The suppression of the water content from the metastable region, AW, was

8.181485E+2 9.289352E + 2

- 1.578381 E + 2 - 3.899544E + 2 - 2.009926E + 1

1.368723E + 1 5.500387E i- 1 4.068990E + 0 1.517650E + 0

- 4.524342E - 1 - 2.590273E + 0 - 2.465SSE - 1

- 7.543630E - 2 1.034443E - 1

Eq. 14b

2.59097E + 3 -1.51351E+3 - 1.16506E + 2

3.26066E + 2 6.65280E + 1

- 1 .17697E + 1 - 3.05SSOE + 1 - 1.20352E + 1

2.94244E + 0 7.83747E - 1 i.O4913E+O 7.23943E - 1

- 2.94560E - 1 7.087SSE - 2

- 1.24938E - 1

fit as a function of pressure and of the temperature difference from the three-phase condition, AT, for both methane and a mixture containing 5.3 1 mol% propane. The fit for methane was in the pressure range of 500 to 1,500 psia and in the temperature range of -28 to 26°F; coefficients for methane in the following equation are labelled Eq. 14a in Table 25.6. The fit for the mixture was in the pressure range of 500 to 1,500 psia, and in the temperature range of -38 to 40°F; coefficients for the mixture are labelled Eq. 14b in Table 25.6. The general regression equation for both gases is:

AW=exp[C, +C:!(lnp)+C3(ln AT)+Cq(lnp)*

+ C5 (In p)(ln AT)

+Cg(ln AT)*+c,(ln~)~

+Cg(ln p)2(1n AT)

+Ct2(lnpJ3(ln AT)+C13(lnp)*(ln AT)2

+C,4(lnp)(ln AT)3+C15(ln AT)4]. . .(14)

Example Calculation of Water Content of a Vapor in Vapor/Hydrate Region. Determine the water content of a gas whose gravity is 0.575 in equilibrium with hydrate at 1,000 psia and 8.4”F.

1. The metastable water content of the gas is calculated from Eq. 12 at 1,000 psia and 8.4”F as 2.745 lbm/106 scf.

2. The three-phase temperature at 1,000 psia is calculated to be 60.35”F from Eq. 13. The AT value is 51.95”F.

3. The displacement from the metastable condition is calculated for methane to be 0.653 lbm/106 scf from Eq. 14a. The displacement from the metastable condition is calculated for the mixture containing 5.31 mol% propane as 1.55 lbm/106 scf from Eq. 14b.

4. An interpolation between the values obtained in Step 3 (based on gas gravity) is done to determine the displacement for a gas with a gravity of 0.575. The resulting displacement is 1.0575 lbm/106 scf.

25-14

. . . . --Pf3STAEJLEL

LINE FROM FIG.21

- STABLE ICE LINE

mPER4lURE, "F P-r,

Fig. 25.23-Depression of metastable dewpoint below ice temperature.

DISXMD XlXE, FM

Fig. 25.24-Correction to water content for natural gas in equilibrium with brines.


8 0 200 UN

-. PSIA

Fig. 25.25-Water content per cubic feet of volume occupied by various gases at system pressure and temperature.

5. The displacement in Step 4 is subtracted from the metastable value in Step 1 to obtain a water concentration of 1.687 lbm/106 scf. The 0.575gravity gas must be dried to less than 1.687 lbm/106 scf to prevent hydrate formation at 1,000 psia and 8.4”F.

6. A check of the conditions of regression of Eqs. 12 through 14 indicates that the correlation should apply for the conditions of the example.

Fig. 25.23 presents the corrective correlation below the ice/gas region, Fig. 25.24 gives corrections to Fig. 25.21 from the salinity of the aqueous phase. The work of Deaton and Frost’ indicated that the water content of gases in equilibrium with liquid water fall in the order

where y is the mole fraction of water in each subscripted gas at the same pressure and temperature as shown in Fig. 25.25. The water content of nitrogen up to moderate pressures has been repotted by Rigby and Prausnitz. 34 No data exist, however, on the water content of nitrogen in equilibrium with hydrates.

The water content of liquid and gaseous CO2 in equilibrium with hydrates has become increasingly more important in the development of EOR technology.

Fig. 25.26 presents a pressure-temperature projection of the univariant loci for the COz/water system. It defines both the univariant and two-phase regions presently being studied and the regions over which the various combinations of binary equilibrium exist. Like


TABLE 25.7-VAPOR PRESSURE OF WATER USEDTOCALCULATEENHANCEMENT

OF THE WATER CONTENT OF THE CO,-RICH FLUID PHASES

T 0 ,., (OF) (psia)

0 0.02215 * 15 0.04352” 30 0.08162” * 45 0.1487+ 65 0.30a9+ 77 0.4641 + 87.8 0.6518%

122 1.789%

‘Extrapolated lo kwer temperat”re from hl9h temperatures Of ** “Data from Perry, R.H. and Chtlton, C H. Chemvsal Engineer’s Handbook, llfth edl-

bon, McGraw-HIV Book Co Inc., New York City (1973). Table 3-4 ‘Data from “Tables of Thermal Propertles of Gases,” U S Dept of Commerce, Washtngton DC. (1955) Circular 564, Table 9-9/a

bla from “Tables of Thermal Properlles of Gases.” U S Dept of Commerce, Washmgton D C. 1,955) Crcular 564, Table 3-5

propane, the location of the critical point of CO* relative to the H-L,-G line results in an invariant quadruple point in which H-L,-LCO, -G coexist, the hub from the other four univariant three-phase lines emanate.

A second quadruple point involving H-I-L,-G exists at lower pressure in the neighborhood of the ice point.

The pioneering work of Wiebe and Gaddy provides extensive data on the solubility of CO2 in wate&” and the vapor-phase composition of CO 2 /water mixtures. s* The measurements were confined to temperatures exceeding the initial hydrate formation condition. Measurement of the water concentration of gas and liquid in equilibrium with hydrates currently is being pur- sued by Song and Kobayashi. ‘37,‘38 By using the vapor pressure of water or metastable liquid water given in Table 25.7, the experimental data from several sources have been presented as enhancement of the vapor pressure resulting from the CO2 pressure on the system (Fig. 25.27). In Fig. 25.27, p is the total pressure,p?,, is the saturation pressure of water, and yw is the mole fraction of water. The water content of coexisting COI-rich liquid and gas along the three-phase region is shown as a loop terminating at its three-phase critical point in the neighborhood of the critical temperature of CO2. Fig. 25.27 shows that the enhancement of the water vapor pressure is favored by lower temperatures and high pressure, variables that also favor a substantial increase in the density of fluid CO*. It is noted that the solubility of water in liquid CO* is greater than in gaseous CO1 at the same pressure and temperature, precisely the reverse of the solubility sequence for liquid and gaseous hydrocarbons, This phenomenon is related to the excessive collection of water in the middle of a distillation column separating a COz-rich feed from its associated LPG constituents.

Fig. 25.28 presents the water content of CO2 vs. inverse absolute temperature along isobars demonstrating the complexity of the system. The curves show a break downward at the initial hydrate formation conditions as methane and natural gases.

ml T H-%(1

lEWFMW, “F

Fig. 25.26-Pressure temperature projection of univariant loci for COalwater system.

2m

x0

Fig. 25.27-Enhancement of the vapor pressure of water caused by CO, total pressure at various temperatures.

Fig. 25.28-Water content of CO, vs. inverse absolute temperature along +sooars.


UOll

um

B

I” Kn

lol 0.m o.au O.Dlr 0.01 0.04 0.1

Fig. 25.29-The effect of molecular weight on the water content in the vapor phase (from Ref. 167).

Quantitative Prediction of Water Content in Light Hydrocarbon Systems A systematic study of the effect of molecular weight on the water content of the vapor phase made by McKetta and Katz52,167 is given in Fig. 25.29. The effect of molecular weight is seen to be most pronounced at the highest temperature of the study, 280°F.

The solubility of water in various liquid hydrocarbons at their vapor pressures is presented in Fig. 25.30.

In recent years estimations of water in both the non- aqueous and aqueous phases in both the two- and three- phase regions have been carried out successfully b? Peng and Robinson, ‘68 Baumgaertner et al., l6 and Moshfeghian et al. “O In these exercises various EOS’s were used-the PREOS (Peng-Robinson equation of state), 157 the.Schmidt-Wenzel EOS, 169 and the PFGC- MES (Parameter from Group Contribution-Mosh- feghian, Erbar, Shariot) EOS. “’ Collectively, these correlation procedures are able to describe vapor/liquid equilibria in systems as diverse as CHd/H*O, C~H~/HZO through n-CgH,a/H20, Nz/HzO, C021H,0, CO/H20, 02/H20, H2/H20, C~H~/HZO, air/HzO, H2S/H20, andNH3/H20. Both the PREOS and PFGC-MES EOS require temperature- dependent interaction arameters, while the method of Baumgaertner et al. I6 8 describes the water structure in terms of its degree of polymerization in the liquid as a function of the temperature. Examples of the successful application of the calculational method to multicomponent systems by Moshfeghian et al. I” are reported.

Quantitative Predictions of Solute Concentrations in the Aqueous Phase General references are presented for the solubility of various gases in water, along with other types of data on aqueous systems. The low-pressure references are included because of their contributions to calculational methods for sour water systems.

5.6

1.6

008

TEFfMTlJRL ‘F

Fig. 25.30-The solubility of water in various liquid hydrocarbons at their vapor pressures.

FLg. 25.31-The solubility of methane in water.


Fig. 25.31 presents the volumetric solubility of methane in water to 10,ooO psia as measured by Culber- son and McKetta. t7 The solubility of methane increases monotonically with pressure but shows a relative minimum with respect to temperature as do the Henry’s law constants. 14* Dodson and Standing,45 on the other hand, presented the solubility of a typical natural gas in water and gave corrections for the solubility due to brine salinity, Fig. 25.32. The relative solubility of gas in brine relative to its solubility in pure water is given in Fig. 25.32.

The analytical prediction of the solubility of nonpolar or low-polarity solutes in water can be used by the application of the relationships introduced by Krichevskii and Kasamovskii I” and Wiebe and Gaddy,90 which were later applied by Kobayashi and Katz 14* and Leland et al. i7* to condensing light-hydrocarbon systems.

The expression is given as follows.

A p,p,,s ) (15)

where f, = partial fugacity of the solute in water at T

and pt, KH = an empirical constant that is a function of

temperature only but is equal numerically to Henry’s law constant for noncondensable gases and a hypothetical Henry’s law constant for condensable gases,

Xl = mole fraction of the dissolved solute, R = gas constant per mole, ^

VA41 = partial molal volume of components in the solution,

T = absolute temperature, pt = total pressure, and

P “3 = vapor pressure of the solvent for a noncondensable gas, but equal to some constant pressure slightly above the three- phase pressure determined from experimental data.

The usual absence of values for the partial volume of the solute P,,, precludes the application of Eq. 15. However, given a good set of experimental data to moderate pressures, Eq. 15 provides a good method of extending the solubility data to higher pressures, particularly if the solute remains essentially pure at the higher pressures. Fig. 25.33 gives an application of Eq. 15 to the aqueous phase of the propane/water system. 142

Examples of the agreement in the experimental and predicted water compositions are

B iven for the

methane/water38*40 and ethane/water ’ 3s’74 and propane/water 142 systems in Figs. 25.34 through 25.36 by Peng and Robinson. 16*

Both the Peng-Robinson 16* and the Baumgaertner er al. ‘69 methods present successful predictions of the aqueous-phase concentrations as well as in the nonaque- ous phase.

TCVbL SOLIDS IN BRINE, PF?l X U3

Fig. 25.32-SoIubilityof natural aas in water with correction for bnne SalirGy.

6.6

6.4

9

,> 6.2

6.0

0 0.w a.aa o.l.2 0.16 0.20 0.24 o.zB

P/L 2.303 R T )

Fig. 25.33-Solubility of prop≠i water to determine partial molar volume and Henry’s law constant.

Sour Water Stripper Correlations With the development of a collective environmental con- sciousness, waste disposal has become an integral part of


W IN LIGlJlD W IN LIGlJlD

- CALmTICN - CALmTICN

1 " 1,O

Fig. 25.34-Experimental and predicted vapor and liquid phase compositions for methane/water system at 25ooc.

FOWE IN LIQUID -

I III I Ill

l - REF 1 73

m.E FRWICN

Fig. 25.35-Experimental and predicted vapor and liquid phase compositions for the ethanelwater system at 220°F.

a

ul

/ - /’ s’ o’r / vm 0,.- DATA OF KOBAYASHI &

KATZ “*

- CALCULATION

I I I I 0 2 4 6 8 lo I2 14

NlEFlWICNWERXld

Fig. 25.36-Experimental and predicted water content of propane liquid and vapor phases along three-phase locus.

petroleum production and processing. From an experimental standpoint the developments have been spurred by the accumulation of experimental data typically encountered in sour water processes. ‘75~178 Meanwhile, basic theoretical work had been laid for the interpretation of such data. 179-‘82 Interpretations of these and other theories are reviewed by Friedman and Krishnan, 179 Newman, lg3 and Knapp and Sandler. Is4

Thus, predictive methods have been developed to estimate vapor/liquid equilibria in complex mixtures containing such components as NH 3 /CO 2 /H 2 S (Wilsont75), N2/C02/H2S/CH40H (Moshfeghian et al. “O), NH31H2S/H20, NHs/S02/H20, and NHs/C021H20 (Renonlg5), NH~/COI/H~S/H~O (Mauererlse), CO~INaClIKClIH20 (Chen et al. lB7), and many others. tg3 The calculations now enable the estimation of physical and chemical equilibria from purely aqueous to strong electrolyte solutions.

Oil and Gas Reservoirs That Exist in the Gas Hydrate Region In recent years an increasing number of oil and gas reservoirs in the hydrated state have been discovered by Katz, 18’ St011 er al., Is9 Makogon Dick,19’ Verma et al.,

et al., ‘90 Bily and 19* Holder et a[., 193 and

Trofimuk er al. 194 In fact, hydrate cores have been recovered from below the ocean floor in the Mid- American Trench off Central America. ‘95 A review of geologic occurrences of hydrates is presented by Kven- volden and McMenamin. 196

In Feb. 1982 a hydrate core was recovered by the Deep Sea Drilling Project from the Mid-American Trench off Guatemala in 1718 m of water. All evidence to date indicates that these hydrates are of biogenic origin, since they are composed mainly of products from anaerobic digestion. These hydrates are of the Structure I form.

In May 1983 a second hydrate core was recovered by a Getty drilling operation from the Gulf of Mexico in 530 m of water. These hydrates are thermogenic in origin with probable prior biogenesis and have substantial amounts of ethane, propane, and isobutane. These hydrates are of the Structure II form.

PHASE BEHAVIOR OF WATERIHYDROCARSON SYSTEMS 25-19

Fig. 25.37-Effect of GOR on hydrate formation conditions for a 46B0API oil in the presence of excess fluid brine.

Fig. 25.39-Crystallization t8matures of aqueous diethylene glycol solutions

These natural hydrates bring many imphcatlons to mind; however, only a few will be outlined.

1. The simultaneous solution of hydrate formation for the ocurrence of hydrates and earth temperature gradients yields possible environments for the occurrence of hydrates.

2. The potential reserve of natural gas existing in nature as solid hydrates is probably very enormous.

3. Petroleum reservoirs existing in the hydrate region may be denuded of a substantial amount of the lighter constituents and, thus, will be energy deficient for production by a gas-drive mechanism.

4. Waterflooding of dissolved gas reservoirs with near-freezing water may cause hydrate formation in the reservoir.

5. A tremendous amount of technological development will be necessary to unleash hydrocarbons from hydrated reservoirs.

0 81 100

M

u1

.u- 20 ,,I t “1

I I I I I

I

c I I i I I -I

Hydrate Inhibition

While crude oils may not inhibit hydrate formation per se, their oils with dissolved gases affect the initial hydrate formation significantly, as shown in Fig. 25.37. ‘97

Under some circumstances it may be advantageous to inhibit hydrate formation rather than dehydrate oil and/or gas streams. While many ionic and hydrogen-bonding substances inhibit hydrate formation, the two compounds that are used most frequently for hydrate inhibition are methanol and ethylene glycol. Natural brines cause only a few degrees of hydrate depression. ‘34 Figs. 25.38 through 25.40 present the freezing points of aqueous glycol solutions showing their eutectics in the absence of gas. 198 Fig 25.41 presents the freezin . point depression of diethylene/glycol/water solutions. ’ 8 7

ul I ’ I I I ’ 1

Fig. 25.38-Crystallization temperatures of aqueous ethylene glycol solutions.

Fig. 25.40-Crystallization temperatures of aqueous trieihyl- ene glycol solutions.

lo 30 50 70

lElWRMW, ‘F

Fig. 25.41-Effect of dlethy.len@ glycol on conditions for hydrate fopation’s.

The inhibition effect of methanol and ethylene glycol on the hydrate formation condition of a methane/ 12-mol% propane mixture is currently under study at Rice U.

Recently, Ng and Robinson”” have presented the hydrate formation conditions of methane, ethane, propane, COz, hydrogen sulfide, methane/10.49-mol% ethane, 90.09-mol% methane/9.91-mol% CO2, 95.01-mol% methane/4.99-mol% propane, a synthetic natural mixture, and a synthetic natural gas mixture containing CO?, each in the presence of methanol solutions of 10 to 20 wt % methanol in water. With the increasing amount of oil and gas transmission along ocean floors prior to dehydration, such data are of increasing usefulness.

Nomenclature ai = activity of component i in mixture

Cj; = a unique function of temperature for each guest molecule in each size cavity

?; = fugacity of j in the gas phase fl = partial fugacity of the solute in water at T

and pf fwj = fugacity of water in the fluid phase

A/z,+ = enthalpy difference K1 = an empirical constant that is a function of

temperature only but is equal numerically to Henry’s law constant for noncondensable gases and a hypothetical Henry’s law constant for condensable gases

Kg = fugacity coefficient of ice


KIT = fugacity coefficient of empty hydrate K;c,,.s, = vapor/solid equilibrium values of

Component i K wf = fugacity coefficient of water n,; = number of cavities of type i per water

molecule in basic lattice PO = reference pressure

pvl = vapor pressure of ice pb,~T = vapor pressure of empty hydrate

P “S = vapor pressure of the solvent for a noncondensable gas, but equal to some constant pressure slightly above the three-phase pressure determined from experimental data

To = reference temperature Av, = specific volume difference

V,l = partial molal volume of components in the solution

W ms = nkastable water content Xl = mole fraction of the dissolved solute

Yji = fractional occupancy of type i cavity by type j molecule

pi = chemical potential of Component i pi0 = chemical potential of pure Component i

&Lw = difference in chemical potential of water /J,+,H = chemical potential of water in filled

hydrate p,,,,+,T = chemical potential of water in empty

hydrate

Subscripts

L = liquid water H = hydrate g = gas

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198.

100.

Culherson, O.L. and McKetta. J.J.: “Phase Equilibria in Hydrocarbon-Water Systems. 11. The Solubility of Ethane in Water at Pressures to 10,000 psi.” Truns., AIME (1950) 189, 319-22. Reamer. H.H. et crl. : “Composttion of Dew-Point Gas in Ethane-Water System,” Ind. Eng. Chrm. (1943) 35, 790-93. Wilson, G.M.: “A New Correlation of NH,. CO, and H?S Volatility Data from Aqueous Sour Water Systems,” API Data Eooli, API, Dallas (Feb. 1978). Otsuka, E.: “Measure Vapor Liquid Equilibria of NH,-CO,-H,,” Kogyo Kogcrke Zashi (1960) 63, 1214. Yasunishi, A. and Yashida, F.: “Solubility of Carbon Dioxide in Aqueous Electrulyte Solution,‘. 3. Chem. Eng. Data (1979) 24, 11-14.

200.

201.

207.

Trofimuk. A.A.. Cherskii. N.V . and Tsarw. V.P. “Ga\ Hydrates-New Sources of Hydrocarbon\.” Priodu. Moscow (1979) 1. 18-27. Ceo/irnrt (1979) 24. No. 12. 18-10. Kvenvolden. K.A. and McMenamin. M.A.: “Hydrate\ ot Natural Gas: A Review of Their Geologic Occurrence.” Gr,,/. Sun,. Circ. (1980) 825. 14. Scauzdlo. F.R.: “Inhibiting Hydrate Formatlow in Hydrocarbon Gases,” Chem. Eng. Progr. (1956) 52, No. 8. 324-2X. Gab Conditioning Fact Book, Dow. Chemical Co., Mldland, Ml ( 1962) 69-7 I. Ng. H.-J. and Robinson. D.B.: “Equilibrium Phase Composi- lions and Hydrating Conditions m Sy\tcm\ Containmg Methanol. Light Hydrocarbons. CO? and H: S,” Rese,mh Report, GPA. Tulsa (Feb. 1983). Salto, S., Marshall. D.R.. and Kobaya\hi. R. “Hydrates at High Preswre Part Il. Application of Swi\tical Mechanic3 to the Study o(‘ the Hydrates of Methane. Argon. and Nitrogen.” .AIC/rEJ. (1964) 10. No. 5. 734-40. \an Cl&f, A. and Diepen. G.A.M “Gab Hydrate\ olNitrogen and Oxygen,” Rec.. True,. Chim. ( I9601 79, 5X2-86 Kobnya\hi. R. er cri.: “Final Rcwrcd Report on the Water Con- tent of C,lrbon Dioxtde Gas and Llquld Equlllbrlum with Liquid W&r and with Gas Hydrates.” Rcpori to ARC0 Oil and Ga\ C(1.. Dallas (June 1979).

Malinin, S.D. and Kumvskaya, N.A.: “Soiubility of CO2 in NaCI-H,O Solutions at Elevated Temperatures and Pressures.” Go. Chem. Anal. Chem. (1975) 4, 547-50. Friedman, R.L. and Krishman, C.V.: Water-A Comprehensive Treatise, Vol. S, F. Franks (ed.) Plenum Press, New York City (1973) 55-59.

General References Water/Volatile Gas Systems

Pitzer. K.S.: “Thermodynamics of Electrolytes 1. Theoretical Basis and General Equations,” J. Phys. Chem. (1973) 77. 268-77.

Acctylenc/Water -.

Billitrct-. I.: “The Acid Nature of the Acetylcnc\.” Z. P/IV\. C/wm ~lY)oZJ 30. 5x-44.

Pitrer. K.S. and Mayorga. G.: “Thermodynamics of Elec- trolytes. Il. Acuvity and Osmotic Coefficients for Strong Elec- trolytes with One or Both Ions Univalent.” J. Phys. Chem. (1973) 77, No. 19, 2300-08 Pitzer. K.S and Kim. J J.’ “Thermodynamics of Electrolytes. IV. Activity and Osmotic Coefficxnts for Mixed Electrolytes,” J. Am. Chem. So,. (1974) 96, 5701-07. Thrrmodwumics of Aqueous System5 wrth hdustn’ul Appliu- tions, S.A. Newman (ed.), Symposium Senes 133, ACS (1980) Knapp, H. and Sandier, S.: “Phase Equilibna and Fluid Propcr- ties in the Chemical Industry.” paper presented at the 1980 Sec- ond Intl. EFCE Conf., West Berlin, March 17-21. Renon, H.: “Representation of NH,-H,S-H,O, NH ,-SO,- H,O, and NH,-CO?-H?O Vapor-Liquid Equilibrium,” Thrr- modynamics of Aqueous Systems with Industrirrl Applications. S.A. Newman (ed.). Symposium Series 133, ACS (1980) 173-86.

bled. K.M. and Golynets. Y.F.: “Soluhility of Acctylenc I” ,Aqueou\ Solutwns ot‘ Electrolytes in Relation to the Tcmpcraturc and Con- xntration of Salt.” /x l+.ct/r. U&/w. Zolr,t/. K/,r,ri. /+c~h,ir~/. ( IYSY 1 2. 173.

HiraoL,l. H.: “The Solubilities of Compre\wd Acetylens Ga\ in Li- quid\. 1. Water.” f?c’~. Ph!,. C&w ./[xr. (105-l) 24. Ii.

SW also Rel’. 30.

EthylcneiWater

Br,IJhul>. E.J. (‘I (I/ : “Soluhility of Ethylene in Water-Ettcct ot Temperature and Prcssurc.“ hid. EQ Clw~l. j lY52) 44. 2 I I - 17.

D,lvi\. J.E. and McKetta. J J. “Solubdlty of Ethqlcnc in Water.” J. Chetu. Eu,y. Durrr (lY60) 5. 371-75.

Mauerer. 0.: “Einnchtung zur Messung des Wasserdampf- Sonctw. M and Lentr. H.: “Phahc Equtlibrium of Water~Propene

anteils in Gasen.” Auslegcxhrift DE 2713617 B2. Deutsches and Wdtcr-Ethcne Sy\~em\ at High Tcmpcraturc\ ,~nd Pw\w~-cs.“

Patentamt (1981). Hiri/ 7iwp -Hi,qh Pre.$ww\ ( lY73) 5. No. 6, 68Y~YY.

Chen. C.-C.. Bntt, H.I., Boston, J.F.. and Evans, L.B.: “The New Actlvlty Coefficient Models for the Vapor-Liqutd Equilibrium of Electrolyte Systems.” Thrrmod~~mtnrc.\s of Aqueous Systems with lndustriul Applications. S.A. Newman (ed.) Symposium Series 133. ACS (1980) 61-89. Katz, D.L.: “Depths to Which Frozen Gas Fields (Gas Hydrates) May be Expected.” 3. Pet. Tech. (1971) 23$ 419-23. Stall, R.D., Ewing, J., and Bryan. G.M.: “Anomalous Wave Velocities in Sediments Contaming Gas Hydrates.” J. Geophy.\. Res. (1971) 76, 2090-94. Makogon, Y.F. PI ui. : “Detection of a Pool of Natural Gas !n a Solid (Hydrated Gas) State.” (in RussIan) D&i. AX&. A’wk SSSR (1971) 196. 203.

See al\o Rcl\ 30. 3 I, and 97

Blly, C. and Dick, J.W.L : “Naturally Occumng Gas Hydrates m the Mackenzie Delta. N.W.T..” Bull.. Cdn Pet. Geol. (1074) 22, No. 4, 340-52. Venna. V.K et crl.: “Dcnudlng Hydrocarbon Liquids of Natural Gas Conatltuents by Hydrate Formation,” J. Per. Tcvh. (Feb. 1975) 223-26.

Dwpcn. G.A.M and Schcffer. F.E.C. “The Soluhdltj (11 Water ,n Supercntul Ethane.” R<,c. l>iw C/r;,,, ( IY50) 69. 6OJ~OY.


Gjaldbaek. J.C. and Niemann. H.: “The Soluhllity ofh+trogen. Argon PropaneiWater and Ethane m Alcohol! and W&r.” Am Chow. SC mci. (1958) 12. 1015-23. Chdddock. R.E. : “Liquid-Vapor Equilibrium m Hydrocarbon Water

Systems [Propane-Water].” PhD dissertation. U of Michigan, Ann

Murzin. V.I. and Afanas’eva. N.L.: “Solubility of Water m L~qurf~cd Arbor (1442).

Ethane near its Cntlcal Point.” Zh Fi:. Khim (1968) 42. No. 8. 194245. DeLoo\, T.W., Wijen, A.J.M., and Diepen. G.A.M.: “Phase

Eauilibna and CritIcal Phenomena in Fluid (Pronanc +Wateri at See alsoRefs. 14. 15. 16. 18. 21, 28. 30, 31.41.42, 53. 54. 173. and Hi’gh Pressures and Temperatures.” J. Chum Ti~~rr~~ntl~ricir,~ic.\

174. (1980) 12. 193-204.

Propylene/Water Goldup, A. and Wcstaway. M.T.: “Detemlination of Trace Quantities

Azamonsh. A. and McKetta, J.J.: “Solubility of Propylene in Water.” of Water in Hydrocarbons. Application of the Calcium CarbIde-Gas

J. Chrm. Eng Darrt ( 1959) 4. 2 1 I- 12. Chromatagraphic Method to Streams Containing Methanol.” An& Chwm (1966) 38. No. 12. 1657-61.

Kazaryan. T.S. and Ryabtsev, N.1.: “Solubility of Saturated Pro- pylene. Iaobutylene. Isobutane, and n-Butane in Water and Aqueous

Hachmuth, K.H.: “Dehydrating Commercial Propane.” 1.1’(1.\1cm Grr.3

Snlulionr.” A’+. Kho:. (1969) 47, No. IO. 54-S6. (1931) 8. No 1, 55-56. 62. 64.

Klausutis. N.A.: “Phase Equilibrium in the Propane-Propylene-Water Perry, C.W.: “Determining Dissolved Water in Llquetied Case+.”

System in the Three-Phase Region,” PhD dissertation. U. ofTexas. M. Eyq. Chm And Ed. (1938) 10. 513-14.

Austm (I 968). Kre\heck. G.C.. Schneider, H.. and Scheraga. H.A.: “The Effect of

LI. C.C. and McKetta. J.J.: “Vapor-Liquid Equilibriums in the D,O on the Thermal Stability of Proteins. Thermodynamtc

Propylene-Water Systems.“ J. Chetn. Eng. Dutu (1963) 8, 271-7.5. Parameter for the Transfer of Model Compounds from H ,O to D,O.” J. Phy. Chrm. (1965) 69, 3132

McBam. J.W. and O‘Connor, J.J.: “The Effect of Potassium Oleate Upon the Solubility of Hydrocarbon Vapors m Water.” J. ,4rn. Pocttmann, F.H. and Dean. M.R.: “Water Content of Propane.” Ppr.

Chmt. SM. (1941) 63. 875-77. Rejner (1946) 25. No. 12. 125-28.

McBam. J.W. and Soldate. A.M.: “The Solubility of Propylene Vapor Sanchez. M. and Coil. R.: “Propane-Water System at High Pressures

in Water aa Affected by Typical Detergents.” J. Am. Chem. Sot,. and Temperatures. I. Two-Phase Region,” Am. Quirn. (1’178) 74.

(1942) 64. 1556-57. No. 11. 1329-3.5.

Oleinikova. A.L. and Bogdanov. M.I.: “Solubility of Propylene m Wehe. A.H. and McKetta. J.J.: “Method for Determining Total

Water and Aqueous Sulfuric Acid Solutions.” Uch. .X$X. Yaroslav. Hydrocarbons Dissolved in Water.” Am. Chm. (1961) 33. No. 20.

Tekhno. Inst. (1971) 27. 28-31. 291-93.

Petrw. A.N.. Pankov. A.G., and Bogdanov, M.I.: “Liquid-Gas Wetlaufer. D.B. rt crl.: “ Nonpolar Group Participatwn m thr

Chmmatographic Determinatmn of the Solubility of Hydrocarbon Gases in Water.” Uch. .%p., Yaroslav. Tekhnol. Inst. (1970) 13, 186-90

Desaturation of Proteins by Urea and Guanidinium Salts Model Compound Studies.” J. Am. Chern. Sm. (1964) 86. SO8- 14.

See Propene/Weter: Azamoosh and McKetta.

Slemikova. A.L.. Pctroc. A.N.. and Bogdanov. M.I.: “Ther- modynamic\ of Dwwlution of Unsaturated C,-C, Hydrocarbons in See also Refs. IS. 28, 30, 31, 41. and 142.

Water.” Uch. Zup.. Yaroslav. Tekhnol. Inst. (1971) 26. 35-41. 1.3.ButadieneiWater

See Ethylene/Water: Sanchez and Lentz.

See Ref. 30. See also Ref. 30.

PropyneiWater

Inga, R.F. and McKetta, J.J.: “Solubility of Propyne in Water,” J. Chrm. Eng. Dota (1961) 6, 337-38.

I-Butene/Water

Brooks. W.B. and McKetta. J.J.: “The Solublllty of I-Butene tn Water at Pressures to loo0 pbia.” Per. Refinrr (19%) 34. No. 2. 143-44.

Simpson, L.B. and Lovell, F.P.: “Solubility of Ethyl, and Vinyl Acety- lene in Several Solvents,” J. Chum. Eng. D&o (1962) 7, 498-500. Brooks, W.B. and McKetta, J.J.: “The Solubiltty ol Water in

I-Butene,” Pet. Rejner (1955) 34. No. 4, 138.

Cyclopmpane/Water Brooks, W.B., Haughn. J.E., and McKetta, J.J.: “The I-Butene-

Hafemann. D.R. and Miller, S.L.: “The Clathrate Hydrates of Water System in the Vapor and Three-Phase Regions.” Prr. /&finer Cyclopropane.” J. Phw. Chem. (1969) 73. No. 5. 1392-97. (1955) 34, No. 8. 129-30.

Imal, S.: “Biophysicochemical Studies on Cyclopmpane. 1. Solublhty Coefticient of Cyclopropane for Various Solutions.” ~liartr. I,qclku Zmshi. (1961) 12, 973-79.

See also Ref. 172.

lsobutaneiwater

Thomson. ES. and Gjaldbaek. J.C.: “Solubility of Cyclopropane m Pertluoro-Heptane, n-Hexane, Benzene, Dioxane. and Water,”

Razaryan, T.S. and Ryabtsev. N.I.: “Solubility of Saturated Pro-

Dan. Tidsskr. Furm. (1963) 37, 9- 17. pylene. Isobutylene. Isobutane. and n-Butane in Water and Aqueous Solutions,” Nef. Khoz. (1969) 47. No IO. 54-56.

‘See also Ref. 30 Black, C., Joris, G.G., and Taylor. H.S: “The Snlubility of Water in Hydrocarbons,” J. Chwn. Ph~s. (1948) 16, No. S, 537-43

Cyclopropane/KCI/Water Nosov. E F. and Barlyaev. E.V.: “Solubillty of Hexafluoropropylene

Zerpa, C. of rri.: “Solubility of Cyclopropane in Aqueous Solutions of and Isobutane in Water.” Zh. Otnhtl~. Khirn. (1968) 38. No. 2, Potassium Chloride.” f. Chern. Enx. Data (1979) 24. No. I. 26-28. 211-12.


Reed. C.D. and McKetta. J.J.: “The Solubtltty ot Isobutane m Methylcyclopentane/Water; 2.4.Dtmethylpentaneiwater; and Water,” Pet. Refiner (1959) 38. No. 4, 159-60. 2.2.4.Tnmethylpentane:Water

See also Ref. 28

Jordan, D. (‘I a/.: “Vapor-Liquid Equilibrium of C, Hydrocarbon- Furfural-Water Mixtures. Experimental and Theoretical Methods for Three- and Four-Component Systems.” Chem. Eq. Pro‘yr. ( 1950) 46. 601-13.

n-Butane/Water

Brooks, W.B., Gibbs, G.B.. and McKetta. J.J.: “Mutual Solubility of Light Hydrocarbon-Water Systems.” Per. Refiner (1951) 30. No 10. 118-20.

LeBreton, J.G. and McKetta. J.J.: “Low Pressure Solubilrty of n-Butene in Water.” Hydrocarbon Proc. PEWO. Ref: (1964) 43. No. 6.

136-38.

Reamer. H.H. et al.: “Composition of Co-Existing Phases of n-ButaneWater System in the Three-Phase Region.” I&. E~IR. C&w

(1944) 36, 381-83.

Reamer, H.H. er al.: “n-Butane-Water System in the Two-Phase Region,” Ind. Eng. Chem. (1952) 44, 609-15.

Rice. P.A., Gale, R.P.. and Barduhn. A.J.: “Solubility of Butane in Water and Soft Solutions at Low Temperatures.” J. Chern. Eng. Dam (1976) 21, 20406.

Tsikiis, D.S. and Maslennikova, V.Y.: “Limited Mutual Solubility of Gases in the Water-Butane System,” Pokl. Akad. Nuuk SSSR (1964) 157, 426-29.

See Ethane/Water: Danmel cf al.

See Propane/Water: Goldup and Westaway; Kresheck et al.: and Wetlaufer er al.

See IsobutaneiWater: Black er ui. and Kazaryan and Ryabtsev

See also Refs. 14. 15. 28, 30, 31. 41, and 55

2-2-Dimethylbutane/Water and Cyclop-entaneiWater

See Ref. 28.

n-PentaneiWater

Connolly. J.F.: “Solubility of Hydrocarbons in Water Near the Critical Solution Temperature,” J. Chem. En,q Dora (1966) 11. 13-16.

Fuhner. H.: “Water Solubility in Homologous Series,” Ber. Dew. Chrm. Ges. (1924) 5713. 510-15.

Liabastre. A.A.: “Experimental Determination of the Solubility of Small Organic Molecules in Water and Dideuterium Oxide and the Application of the Scaled Partrcle Theory to Aqueous and Non- aqueous Solutions.” PhD dissertation. Georgia Inst. of Tech., Atlanta (1974).

Namiot, A.Y. and Beider. S.Y.: “The Water Solubility of n-Pentane and n-Hexane, Khim. Tekhnol. Top/iv. Masel (1960) 5, 52-55.

See Isobutane/Water: Black et al.

See Ref. 28

2.McthyloentaneiWater and n-Her&me/Water

See n-PentanelWater: Connolly, J.F.

See also Ref. 28.

IsopentanelWater

Pavlova. S.P. er crl.: “Mutual Solubihty of C, Hydrocarbons and Water,” Prom. Sin Kauch. (1966) 3. 18-20.

See tsobutane/Water: Black er u/

See also Ref 28

NeopentaneiWater

See Refs 30 and 37

CyclohexaneiWater

Farkas. E.J.. “New Method for Determination of Hydrocarbon-in- Water Solubilities.” Am/. Cbem. (1965) 37. No. 9, 1173-75.

Roddy. J.W. and Coleman, C.F.: “Solubility of Water m Hydrocar- bons as a Function of Water Activity.” Trr/r~n/n (1968) 15, No. I I. 12X1-86.

Sultanov, R.G. and Skripka. V.G.: “Solubility of Water in n-Hexane. Cyclohexane, and Benzene at Elevated Temperatures and Pressures,” Z/t. Fiz. Khmz. (1973) 47, No. 4, 1035.

See also Ref. 28

n-HexaneiWater

Gester. G.C.: “Design and Operation ofa Light Hydrocarbon Distilla- tion Drier.” Chrm. Eng. Pro,yr. (1947) 43, 117-22.

See Cyclohexane/Water: Roddy and Coleman, and Sultanov and Skripka.

See also Ref. 28

Methylcycloheptane/Water and n-Octane/Water

See Ref. 28.

n-DecaneiWater

Latter, Y.G., Asymyan, K.D., and Skripka, V.G.: “The Volume Pro- perties of the Coexisting Phases of the n-Decane-Water System at 275°C.” Zb. Fiz. K/rim. (1976) 50. 2171.

MethaneiEthaneiWater

Amitijafari, B. and Campbell. J.M.: “Solubility ofGaseous Hydrocar- bon Mixtures in Water,” So,. Per. EUK. J. (Feb. 1972) 12, No. I. 21-27.

Villameal. J.F., Bissey, L.T., and Nielson, R.F.: “Dew Point Water Contents of Methane-Ethane Mixture\ at a Series of Pressures and Temperatures,” Prod. Month!? (1954) 18. No. 7. 15- 17.

Methane/Propane/Water; EthanelPropaneiWater; and

MethaneiEthanelPropaneiWater

See MethaneiEthanelWater: Amirijafari and Campbell

Methane/n-Butane/Water

Anthony, R.G. and McKetta, J.J.: “How to Estimate H,O in Hydrocarbons,” Hydrocarbon Proces.s. (1968) 47. No. 6, 131-34.

See also Refs. 28 and 44. See also Refs. 52 and 167.


Methane/n-PentaneiWater Hydrate/Volatile Gas Systems

See Ref. 44 Methane/Brine (NaCl)/Water and MethaneiEtOHIWater

EthyleneiEthaneiWater

Anthony, R.G. and McKetla. J.J.: “Phase Equilibrium in the Ethylene-Ethane-Water System.” J. Chem. Eq. Data (1967) 12. No: 1. 21-28.

See Ref. 134

Ethylene/Water

van Cleef, A. and Diepen, G.A.M.: “Ethylene Hydrate at High Presaurrs,” Rec. Trai,. Chim. (1962) 81, 425-29.

Aromatic-Hvdrocarbon/Water

Eganhtruae. R.P. and Calder. J.A.: “The Snlubility of Medium Diepen. G.A.M. and Scheffer. F.E C.: “The Ethylene-Water

Molecular Weight Aromatic Hydrocarbon(s) and the Effects of System,” Rec. Truv. Chim. (1950) 69, 593-603.

Hydrocarbon Co-Solutes and Salinity. ” Geochim. Cmmochim Actu. (1976) 40, No. 5, 555-61. See also Ref. 122.

Kerosme/Water and OlliWater EthylenelEtOH/Water

Griswold, J. and Kasch, J.E.: “Hydrocarbon-Water Solubilities at Reamer, H.H., Selleck, F.T.. and Sage, B.H.: “Some Properties of

Elevated Temperatures and Pressures.” Ind. Eng. Chrm. (1942) 34, Mixed Paraffinic and Olefinic Hydrates,” Trans.. AIME (1952) 804-06. 195, 197-201.

Groschuff. E.: “Solubility of Water in Benzene. Petroleum and Paraf- See also Ref. 129 and 140.

fin Oil.” Nckrrochern. (191 I) 17. 348. EthaneiWater

Naphtha/Warcr See EthyleneiEtOHiWater: Reamer er cri.

Amero, R.C.. Moore, J.W., and Capell. R.G.: “Design and U&e of Adaorptwe Drying Units.” Chrrn. E~IR. fro$!r. (1947) 43, 349-70. Set also Refs. 4. 8, 123, 124, 126, and 128.

See Kerosine-Water: Griswold and Kaach

Naiur;ll-GasiGlvcollWarer

Ru\wll. G.F.. Reid. L S., and Huntington. R.L : “Experimental Determinanons of the Vapor-Liquid Equilibria Between Natural Gas and 95% Dlethylene Glycol up to a Pressure of 2COO psi,” Trtrns., AlChE (1945) 41, 3 15-25.

GdwlineiWater

Derr. R.B and Willmore, C.B.: “Dehydration of Organic Liquids wth Activated Alumina,” Ind. Eng. Chem. (1939) 31. 866-68.

Wachter. A. and Smith, S.S.: “Preventing Internal Corrosion of the Pipe Lmcs-Sodium Nmite Treatment for Gasoline Lines,” Azd. hg. C~PIPI. (1943) 35. 358-67.

Argon/Methane/Water and Helium/Methane/Water

Namiol. A.Y. and Bondareva. M.M.: “Solublhty of Helium-Methane Mixture m Water at High Pressures.” N(zuch. Tekhn. SB. PO Dob~chemf/r l’wv. A’rfiqw: Nauch h/d. hr. ( 1962) 18, 82-9 I

Nllrogcn/MethanelWater

Maharajh. D.M. and Walkley. J.: “Thermodynamic Solubility of Gas Mixture\. I Two Component Gas Mlxturcs in Water at 25 deg. ,‘. J. Chm. SCM.. Fur. Trmc. (1973) 69, No. 5. 842-48.

Mahara.jh. D.M. and Waikley. J.: “Lowering of rhe Separation Solubility of Oxygen by Presence of Another&s,” Nutuw. London (1972) 236. No 5343, 165.

CyclopropaneiWater

Callahan. J.E. and Sloan, E.D.: “Heat Capacity Measurements on Structure I and II Pure Hydrates at Low Pressures and Below Room Temperature.” Research Repon, Gas Research Inst. (Sept. 1982) Contract No. 5081-360-0487.

Dhannawardhana. P.B., Parrish, W.R. andSloan. E.D.: “Experimen- tal Thermodynamic Parameters for the Prediction of Natural Gas Hydrate Dissociation Conditions, fnd. Eng. Chrm. Fund. (1980) 19, 410-14.

Hafemann. D.R. and Miller, S.L.: “The Clarhrate Hydrates of Cyclopropane.” J. Phys. Chem. (1969) 73, No. 5. 1392-97.

CyclopropaneiKCIIWater and CyclopropanelCaCl z /Water

Menten. P.D.. Pamsh, W.R. and Sloan. E.D.: “Effect of Inhibitors on Hydrate Formatmn,” Id En,q Chem Proressrs Des. Dev (1981) 20. No. 2. 399-401.

CyclopropaneiMethanoliWater

Giussani, A.: “Inhibition of Natural Gas Hydrates,‘. MS thesis, Col- orado School of Mines. Golden (1981).

See Cyclopropane/KCI/Water: Menten et a/

PronaneiWater

Miller. B. and Strong. E.R. Jr.: “Possibilitiesof Strong Natural Gas in the Form of a SolId Hydrate; a Method for Delerminmg the Ratio of Hydrocarbon to Water in a Solid Hydrate of a Normally Gaseous Hydrocarbon. and ita Application to Propane Hydrate,” Prot. Anz. Cu.\ Acroc. (1945) 27. No. 2. 80-94.

See NitropcnlMethanelWater: Maharajh and Walkley.

Hydrogen-Sulfide/Carbon-Dioxlde/Merhane/Wdter

Set: EthyleneiEtOHIWater: Reamer e/ a/.

See also Refs. 5, 122, 126, 134, and I35

Froning. H.R.. Jacoby. R.H., and Richards, W.L.: “Vapor-Liquid Equillhnums of rhe Methane. Carbon Dioxide, Hydrogen Sulfide. Water System and Apphcation to the Design of a Water Wash System for Removing Acid Ga\e\.” Pwr., Annual Convention of the Natural Ga\ A\wc. Am. (I9631 42. 32-39.

lsohutaneiwater

Rouher. O.S. and Barduhn. A.J.: “Hydrates of Iso- and Normal Butane and Their Mixtures.“ D~.\c/ir/urr/on (1969) 6. 57-73.

See also Refs. 126 and 149.

Hydrogen-SulfideiWater 1 .l-DioxaneiWater and I .3-DloxanelWater

Selleck. F.T.. Cannichacl, L.T.. and Sage. B.H.: “Phase Behavior In the Hydrogen Sulfide-Water System.” /mu. E/l,q. Chrru. (19.52) 44. Davidwn, D.W. and Ripmeester. J.A.: “Clathrate Ices-Recent 2219-26. Results,” J. Glacial. (1978) 21. No. X5. 33-49.


Methane/Ethylene/Water and MethanelEthyleneiPrcIpylene/Water

See Ref. 129

Methane/Ethane/Propane/COz/Water

See Refs. 164 and 165.

MethanelEthaneiWater MethaneiEthaneiPropanelIsobutaneln-Butane/Water

Holder, G.D. and Gngoriou. CC.: “Hydrate Dissoctation Pressures of (Methane-Ethane-Water). Existence of a Locus of Minimum Pressures,” J Chem. Thrnnnclwumrcs (1980). 1093- 1104.

See Ref. 127.

See ~1s~~ Rcf\. 5, 127, and 128.

Methane/Propane/Condensate/Water and

Methane/Propane/Crude-Oil/Water

See Ref. 192.

Methane:Propylene/Water

Otto, F.D. and Robmson. D.B.. “A Study of Hydrates in the Methane-Propylene-Water System,” AlChE J. (1960) 6. No. 4. 602m05.

MethaneiPropaneiHydrogenSulfideiWater

Schrocter, J.P., Kobayashi, R., and Hildebrand. M.A.: “Hydrate Decomposition Conditions in the System HzS-Methane-Propane.” fnd. Eng. Chem. Fund. (1983) 22, No. 4. 361-64

Carson. D.B. and Katz.. D.L.: “Natural Gas Hydrates.” Trunc., AIME (1941) 146, 150-53.

Verma, V.K., Hand, J.H., and Katz, D.L.: “Gas Hydrates from Liq- uid Hydrocarbons (Methane-Propane-Water Systems),” paper presented at the GVC/AIChE Joint Meeting, Munich, Germany, Sept. 17-21.

laobutylenelPropane/lsobutaneiWater and

Isohutylene/Propane/Isoheptane/Propylene/Water

See Propane/Propylene/Water: Fomina and Byk.

Cracked-Gas/Water

Byk, S.S.: “Experiments on the Conditions for the Formation ol Hydrates of Cracked Gases,” Gaz. from. (1957) 4, 33-35.

See alw Ref\ 5, 127, and 163. Oil/Water

Set Ref. 193 Methane!JsobutaneiWater

Ng. H.-J. and Robinson. D.B.: “The Measurement and Prediction of Hydrate Formation in Liquid Hydrocarbon-Water Systems.” lnd. En,q. Chmi. Fund. (1976) 15. No. 4, 293-98.

See ah Refs. 5. 127. and 149.

Methane/n-Butane/Water

John. V.T. and Holder. G.D.: “Improwd Predictions of Hydrate Equilibria,” paper presented at the 1981 AIChE Annual Meeting. New Orleans

Ng. H.-J. and Robinson. D.B.: “The Prediction of Hydrate Formation in Condensed Systems.” AlChE J. (1977) 23. No. 4. 477-82

See also Ref. 127

Methane/Pcntane!Water and MethaneiHexanelWater

See Methane-Propane-Water: Carson and Katz.

EthyleneiEthnneiWater

Koshelev. V.S. CI (I/. : “Study ot Hydrate-Gas Phase Equilihrtum m the Ethane-Ethylene System.” Zh. PM. Khirn., Lemgrad (1971) 44, 2573-74.

EthvlenelPmpaneiWater

Fomina. V.I. and Byk. S.S.: “Study of Hydrate-Gas Phase Equtltbrium m the Ethylene-Propane System.” Zh. Prilil. Khiw. Leningrad (1969) 42. 2855-58.

EthanelPropaneiWater and MethanelEthanelPropaneiWater

Holder, G.D. and Hand, J.H.: “Multiple-Phase Equilibria in Hydrates from Methane, Ethane. Propane and Water Mixtures.” AlCliE J. (1982) 28, No 3. 440-47.

Propane/PnlpylcnciWater

Fomina. V I. and Byk. S.S.: “Hydrate-Gas Phase Equilthrium m the Propane-Propylcne~Water System.” Go:. Pronr. (1967) 12, Nil. 3. X-56.

See Ref. 154.

Methane/Nitrogen/Water

Jhavcri, I. and Robmson. D.B.: “Hydrates in the Methane~Nitrogen System,” Cdn. J. Chew. Eng. (1965) 43, No. 2, 75-78.

ProoaneiNitrogeniWater

Ng, H.-J., Pettunia. J.P., and Robinson. D.B.: “Expenmental Measurement and Prediction of Hydrate Forming Conditions in the N,-Propane-Hz0 System.” Nuid Phasr Equil. (1978) 1. 2X3-91.

Methane/Carbon-Dioxide/Water

See Ref. 139.

Propane/Carbon-Dioxide/Water

Robinson. D.B. and Mehta, B.R.: “Hydrates in the Propane- CO,-H,O System,” J. Cdn. PH. Twh. (1971) 10. 33-35.

Propane/Hydrogen-Sulfide/Water

See Ref. 151.

MethaneiHvdroaen-Sulfide/Carbon-Dioxide/Water

Robinson. D.B. and Hutton. J.M.: “Hydrate Formatton m Systems Containing Methane. Hydrogen Sulfide and Carbon Dioxide.” J. Ch. Per. Tech. (1967) 6. No. I, 6-9.

Set Ref. 197

Natural-Gas/Ammonium/Water

Russell. J.T.: “Anhydrous Ammonia to Inhibit Gas Hydrate Forma- uon,” Cur (1937) 13. No. 6. 38-40.

Natural-GaslNaCliWater

See Ref. 134.

Natur&Gas/CaCl ,/Water

See Ethyletw’EtOHiWater: Reamer 01 o/. SW Ref. 5

Chapter 26 Properties of Reservoir Rocks Daniel M. Bass Jr., C~hado School of Mmea*

Introduction This chapter deals with the fundamental properties of reservoir rocks. The properties discussed are (1) pomsi- 8-a measure of the void space in a rock: (2) pertneahi/it~-a measure of the fluid transmissivity of a rock; (3) fluid saturutim-a measure of the gross void space occupied by a fluid; (4) cupillaryprrssure rek- rim--a measure of the surface forces existing between the rock and the contained fluids; and (5) electrical cm- clucrivity offluid-saturated rocks-a measure of the conductivity of the rock and its contained fluids to electric current. These properties constitute a set of fundamental parameters by which the rock may be described quantitatively.

Typical core-analysis data are presented to illustrate the description of porous media by these fundamental properties.

Porosity Porosity is defined as the ratio of the void space in a rock to the bulk volume (BV) of that rock, multiplied by 100 to express in percent. Porosity may be classified according to the mode of origin as primary and secondary. An original porosity is developed during the deposition of the material, and later compaction and cementation reduce it to the primary porosity. Secondary porosity is that developed by some geologic process subsequent to deposition of the rock. Primary porosity is typified by the intergranular porosity of sandstones and the intercrystalline and oolitic porosity of some limestones. Secondary porosity is typified by fracture development as found in some shales and limestones and the vugs or solution cavities commonly found in limestones. Rocks having primary porosity are more uniform in their

‘Thts author also Wrote the orlglnal chapter on this topic m the 1962 edition with coauthor James W. Amyx (deceased] D.M Bass Jr IS currently a petroleum COnSUltant

characteristics than rocks in which a large part of the porosity is induced. For direct quantitative measurement of porosity, reliance must be placed on formation samples obtained by coring.

Unit cells of two systematic packings of uniform spheres are shown in Fig. 26.1. The porosity for cubical packing (the least compact arrangement) is 47.6% and for rhombohedral packing (the most compact arrangement) is 25.96%. ’ Considering cubical packing, the porosity may be calculated as follows. The unit cell is a cube with sides equal to 2r where r is the radius of the sphere. Therefore, Vh=(2r)3=8r3, where V,] is the bulk volume. Since there are 8% spheres in the unit cell. the sand-grain volume, V,, , is given by

4ar’ v, = -

3

The porosity, $, is given by

where L’,, is PV. Therefore,

8r” -413irr3 4=

8r3 X100=(1--&00

=47.6%.

Of particular interest is the fact that the radii cancel and the porosity of uniform spheres is a function of packing only.


POROSITY: 47.6 % POROSITY= 25.96%

CuB~~~KXE;IDE RHOMBOHEDRAL OR CLOSE PACKED

Fig. 26.1-Unit cells and groups of uniform spheres for cubic and rhombohedral packing.

Tickell et al.’ has presented experimental data indicating that, for packings of Ottawa sand, porosity was a function of skewness of the grain-size distribution (see Fig. 26.2). Skewness is a statistical measure of the uniformity of distribution of a group of measurements. Other investigators have measured the effects of distribu-

In dealing with reservoir rocks (usually consolidated sediments), it is necessary to define total porosity and ef-

tion, grain size, and grain shape. In general, greater

fective porosity because cementing materials may seal off a part of the PV. Totalporosity is the ratio of the total

angularity tends to increase the porosity, while an in-

void space in the rock to the BV of the rock, while effective porosity is the ratio of the interconnected void space

crease in range of particle size tends to decrease

in the rock to the BV of the rock, each expressed in percent. From the reservoir-engineering standpoint, effec-

porosity.

tive porosity is the desired quantitative value because it represents the space that is occupied by mobile fluids. For intergranular materials, poorly to moderately well cemented, the total porosity is approximately equal to the effective porosity. For more highly cemented materials and for limestones, significant differences in total-porosity and effective-porosity values may occur.

-.08 -.04 0 +.04 +.08 SKEWNESS

Fig. 26.2-Variation of porosity with skewness of grain-size distribution.

Photographs of oilwell cores are presented in Fig. 26.3. 3 The pore configuration of the sandstones shown is complex, but the pores are distributed relatively uniformly. Complex pore configurations arise from the interaction of many factors in the geologic environment

Material having induced porosity, such as the carbonate rocks shown in Fig. 26.3, have even more com-

of the deposit. These factors include the packing and

plex pore configurations. In fact, two or more systems of pore openings may occur in such rocks. The basic rock

particle-size distribution of the framework fraction, the

material is usually finely crystalline and is called the “matrix.”

type of interstitial material, and the type and degree of

The matrix contains uniformly small pore openings that comprise one system of pores. One or

cementation. The influence of these various factors may

more systems of larger openings usually occur in carbonate rocks as a result of leaching, fracturing, or

be evaluated as statistical trends.

dolomitization of the primary rock material. Vugular pore openings are frequently as large as an ordinary lead pencil and usually are attributed to leaching of the rock subsequent to deposition. Fractures also may be quite large and contribute substantially to the volume of pore openings in the rock.

(b) (d)

Fig. 26.3-Oilwell cores. Consolidated sandstone: (a) wireline core, Lower Frio; (b) whole core, Seven Rivers. Vugular, solution cavities, and crystalline limestone and dolomite: (c) whole core, Devonian; (d) whole core, Hermosa.

PROPERTIES OF RESERVOIR ROCKS 26-3

Laboratory Measurement of Porosity

Numerous methods have been developed for the determination of the porosity of consolidated rocks having intergranular porosity. Most of the methods developed have been designed for small samples, roughly the size of a walnut. Since the pores of intergranular material are quite small, determining the porosity of such a sample involves measuring the volume of literally thousands of pores. The porosity of larger portions of the rock is represented statistically from the results obtained on numerous small samples.

In the laboratory measurement of porosity, it is necessary to determine only two of the three basic parameters (BV, PV, and grain volume). In general. all methods of BV determination are applicable to determining both total and effective porosity.

BV. Usual procedures use observation of the volume of fluid displaced by the sample. This procedure is particularly desirable because the BV of specially shaped samples may be determined as rapidly as that of shaped samples.

The fluid displaced by a sample may be observed either volumetrically or gravimetrically. In either pm cedure, it is necessary to prevent fluid penetration into the pore space of the rock. This may be accomplished by (1) coating the rock with paraffin or a similar substance, (2) saturating the rock with the fluid into which it is to be immersed, or (3) using mercury, which by virtue of its surface tension and wetting characteristics does not tend to enter the small pore spaces of most intergranular materials.

Gravimetric determinations of BV may be accomplished by observing the sample’s weight loss when immersed in a fluid or the difference in weight of a pycnometer when filled with a fluid and when filled with fluid and the core sample. The details of gravimetric determinations of BV are best summarized by Example Problems I through 3.

Example Problem l-Coated Sample Immersed in Water. Given that the

weight of dry sample in air. A=20.0 g. weight of dry sample coated with paraffin, B=20.9 g

(density of paraffin=0.9 gicmj), and weight of coated sample immersed in water at 40°F.

C= 10.0 g (density of water= 1 .OO g/cm3). we can then calculate that

weight of paraffin=&A=20.9-20.0=0.9 g.

0.9 volume of paraffin = - = 1 cm3 ,

0.9

weight of water displaced=B-C=20.9- 10.0 = 10.9 g,

10.9 volume of water displaced = ~ = 10.9 cm3,

1 .o

volume of water displaced-volume of paraffin =10.9-1.0=9.9 cm3, and

BV ofrock, Vb,=9.9 cm3.

Example Problem 2-Water-Saturated Sample Im- mersed in Water. Given that

weight of saturated sample in air, D=22.5 g, and weight of saturated sample in water at 40”F,

E= 12.6 g. we can calculate that

weight of water displaced=D-E=22.5- 12.6 x9.9 g, and

9.9 volume of water displaced= - =9.9 cm3.

1.0 Therefore,

BV rock, If,,, =9.9 cm3.

Example Problem 3-Dry Sample Immersed in Mer- cury Pycnometer. Given A from Example Problem I and the following values,

weight of pycnometer filled with mercury at 20°C. F=350.0 g and

weight of pycnometer filled with mercury and sample at 20°C. G=235.9 g (density of mercury= 13.546 g/cm3).

we can calculate that weight of sample + weight of pycnometer filled with

mercury=A+F=20+350=370 g, weight of mercury displaced =A+F-G=370-

235.9= 134.1 g. and

134.1 volume of mercury displaced = - =9.9 cm3

13.546

Therefore, BV of rock=9.9 cm3. Determinations of BV volumetrically use a variety of

specially constructed pycnometers or volumeters. An electric pycnometer from which the BV may be read directly is shown in Fig. 26.4. The sample is immersed in the core chamber, causing a resulting rise in the level of the connecting U tube. The change in mercury level is measured by a micrometer screw connected to a low- voltage circuit. The electric circuit is closed as long as the measuring point is in contact with the mercury. The travel of the measuring point is calibrated in volume units such that the difference in the open-circuit readings with and without the sample in the core chamber represents the BV of the sample. Either dry or saturated samples may be used in the device.

Sand-Grain Volume (GV). The various porosity methods usually are distinguished by the means used to determine the GV or PV. Several of the oldest methods of porosity measurement arc based on the determination of GV.

The GV may be determined from the dry weight of the sample and the sand-grain density. For many purposes, results of sufficient accuracy may be obtained by using the density of quartz (2.65 g/cm3) as the sand-grain density.

For more rigorous determinations either the A.F. Melcher-Nutting4 or Russell’ method may be employed. The BV of a sample is determined: then this sample, or an adjacent sample, is reduced to grain size and the GV is determined. In the M&her-Nutting technique, all the measurements are determined


Type of sampling

Functions measured

Manner of measurement

Errors

TABLE 26.1~METHODS OF DETERMINING POROSITY

Effective Porosity Methods

Washburn-Bunting Porosimeter

One to several pieces per increment (usually one).

Solvent extraction and oven drying. Occa- sionally use retort samples.

PV and BV.

Reduction of pressure on a confined sample and measurement of air evolved. BV from mercury pycnometer.

Air from dirty mercury; possible leaks in system; incomplete evacuation caused by rapid operation or tight sample.

Stevens Porosimeter



Sand grain volume and unconnected PV and BV.

Difference in volume of air evolved from a constant-volume chamber when empty and when occupied by sample. BV by Russell tube.

Mercury does not become dirty. Possible leaks in system; incomplete evacuation caused by rapid operation or tight sample.

Kobe Porosimeter






Boyle’s Law Porosimeter






MICROMETER SCALE

ADJUSTING SCREW

OH INDICATOR

LIGHT

gravimetrically, using the principle of buoyancy (Exam- ple Problem 2). The Russell method uses a specially designed volumeter, and the BV and GV are determined volumetrically. The porosity determined is total porosity, $r. Thus,

Vb - vs +r=- x loo.

vb

From the data of Example Problem 2 and using a sand- grain density of 2.65 g/cm3,

vb =9.9 cm3,

20 v,=- =7.55 cm3,

2.65

and

9.9-1.55 +r= x 100=23.8%.

9.9

Fig. 26.4-Electric pycnometer The Stevens6 porosimeter is a means of determining the “effective” GV. The porosimeter (Fig. 26.5) consists of a core chamber that may be sealed from atmospheric pressure and closed from the remaining parts of the porosimeter by a needle valve. The accurate volume of the core chamber is known. In operation, a core is placed in the core chamber; a vacuum is established in the

PROPERTIES OF RESERVOIR ROCKS

TABLE 26.1-METHODS OF DETERMINING POROSITY (continued)

Effective Porositv Methods Total Porosity Method

26-5

Core Laboratories, Core Laboratories, Dry Sample


Saturation* One to several pieces per increment (usually one).

Wet Sample Sand Density Several pieces per increment.

Several pieces for retort; one for mercury pump.

Solvent extraction and overy drying. Occa- sionally use retort samples.

PV and BV.

None. Solvent extraction and oven drying. Occa- sionally use retort samples.

Solvent extraction; then, in second step, crush sample to grain size.

Volumes of gas space, oil, and water. BV.

Sand-grain volume and unconnected PV, and BV.

BV of sample and volume of sand grains.

Weight of dry sample; weight of saturated sample in air: weight of saturated sample immersed in saturated fluid.

Weight of retort sample; volume of oil and water from retort sample; gas volume and BV of mercury-pump sample.

Difference in volume of air evolved from a constant-volume chamber when empty and when occupied by sample.

Weight of dry sample; weight of saturated sample immersed; weight and volume of sand grains.

Possible incomplete saturation.

Obtain excess water from shales. Loss 01 vapors through con- densers.

Possible leaks in system; incomplete evacuation caused by rapid operation or tight sample.

Possible loss of sand grains in crushing. Can be reproduced most accurately.

system by manipulating the mercury reservoir; the air in the core chamber is expanded repeatedly into the evacuated system and measured at atmospheric pressure in the graduated tube. The Stevens method is an adaptation of the Washburn-Bunting7 procedure, which will be discussed with the measurement of PV.

Example Problem 4-Determination of Grain Volume by Gas Expansion (Stevens Porosimeter). Given that

volume of core chamber, H= 15 cm3 and

total reading, 1=7.00 cm3 where

volume of air (first reading)=6.970, volume of air (second reading)=0.03, and volume of air (third reading)=O,

we can calculate effective grain volume=H-Z=8 cm3, bulk volume of sample (from pycnometer)= 10 cm3,

and effective porosity, 4, =[(lO-8)110] X 100=20%.

PV. All methods of measuring PV yield “effective” porosity. The methods are based on either the extraction of a fluid from the rock or the introduction of a fluid into the pore space of the rock.

The Washburn-Bunting 7 porosimeter measured the volume of air extracted from the pore space by creating a partial vacuum in the porosimeter by manipulation of the attached mercury reservoir. In the process, the core is exposed to contamination by mercury and, therefore, is

PULLEY.

MERCURY - RESERVOIR

--P GTOPCOCK

;RADUATED TUBE

-CORE :HAMBER

--CRANK

\ BRAKE

CONNECTING HOSE -

Fig. 26.5-Stevens porosimeter


Sample Number Type of Material

Approximate Gas Permeability

(md)

1 LImestone 1 2 Fretted glass 2 3 Sandstone 20 4 Sandstone 1,000

BZE Semiquartzltic sandstone 0.2 0.x Semlquartzitic sandstone 0.8 61-A Alundum 1,000 722 Alundum 3 1123 Chalk 16

1141-A Sandstone 45

TABLE 26.2-CHARACTERISTICS OF SAMPLES USED IN POROSITY-MEASUREMENT COMPARISONS

Porosity (O/O)

Average From Average From Value From

Average

17.47 28.40 14.00 30.29

3.95 3 94

28.47 16.47 32.67 19.46

not suitable for additional tests. The previously described Stevens method is a modification of the Washburn-Bunting procedure especially designed to prevent mercury contamination of the samples.

A number of other devices have been designed for measuring PV; these include the Kobe8 porosimeter, the Oilwell Research porosimeter, and the mercury-pump porosimeter. Kobe and Oilwell Research porosimeters are Boyle’s-law-type porosimeters designed for use with nitrogen or helium with negligible adsorption on rock surfaces at room temperature. The mercury-pump porosimeter is designed so that the BV may be obtained as well as the PV.

The saturation method of determining porosity consists of saturating a clean dry sample with a fluid of known density and determining the PV from the gain in weight of the sample. The sample usually is evacuated in a vacuum flask to which the saturation fluid may be ad- mitted by means of a separatory funnel. If care is exercised to achieve complete saturation, this procedure is believed to be one of the best available techniques for intergranular materials. Example Problem 5 illustrates the saturation technique of measuring PV.

Example Problem G-Effective Porosity by the Saturation Method. From the data of Example Prob- lems 1 and 2, we can calculate

weight of water in pore space=D-A=22.5-20 =2.5 g.

EXPANSION CHAMBER

KNOWN VOLUME COMPRESSED GAS SOURCE

CORE CHAMBER OF

KNOWN VOLUME

Fig. 26.6-Gas-expansion porosimeter for large cores.

Gas Saturation High Methods Methods Observation’

17.81 16.96 18.50 26.60 27.97 29.30 14.21 13.70 15 15 31.06 29.13 31.8

4.15 3.66 4.60 4.10 3.71 4.55

28.70 28.00 29.4 16.73 16.08 17.80 33 10 32.03 33.8 19.68 19.12 20.2

Value From Low

Observation”

16.72 27.56 13 50 26 8

3 50 3.48

27.8 16.00 31 7 100

2.5 g volume of water in pore space = ~

1 g/cm3 =2.5 cm3,

effective PV=2.5 cm’, and BV (Example Problem 2)=9.9 cm3.

Therefore,

2.5 ~,=~x100=25.3%.

Several methods of determining effective porosity are compared in Table 26.1.

Precision of Porosity Measurements. A group’ of major company laboratories conducted a series of tests to determine the precision of porosity measurements. The method used was either gas expansion or a saturation technique. Table 26.2 summarizes the results of these tests. Note that the gas-expansion method is consistently higher than the saturation method. This undoubtedly results from the fact that the errors inherent to each tend to be in opposite directions. In the case of the gas- expansion method, errors caused by gas adsorption would cause high values to be obtained while, for the saturation techniques, incomplete saturation of the sample would result in low values. The difference in the average values obtained by the two methods is about 0.8% porosity, which is approximately a 5% error for a 16% porosity sample. However, it is felt that all the methods commonly used to determine effective porosity yield results with the desired degree of accuracy if carefully performed.

Carbonate Rocks. Small samples, such as used in the routine techniques already discussed, yield values of porosity that do not include the effect of vugs, solution cavities, etc. The saturation methods of determining PV and BV are unsatisfactory because drainage will occur from the larger pore spaces. Therefore, it is necessary to use larger core samples and to determine the BV by measurement of the core dimensions or after coating the sample. The effective grain volume is obtained by using a large gas-expansion porosimeter of the type shown in Fig. 26.6. This porosimeter is based on Boyle’s law in


50

0 0 1000 2000 3000 4000 5000 6CCO

DEPTH OF BURIAL IN FEET

Fig. 26.7-Effect of natural compaction on porosity.

which high-pressure gas is equalized between two chambers. The porosity may be calculated from the measured pressures, the volume of either chamber, and the bulk-sample volume by the use of Boyle’s law.

Keltont” reported results of whole-core analysis. a method utilizing large sections of the full-diameter core. The following table of matrix vs. whole-core data summarizes a part of Kelton’s work. lo

Grollp

1 2 3 4 Matrix porosity, % bulk 1.98 1.58 2.56 7.92 Total porosity, % bulk 2.21 2.62 3.17 8.40

Matrix porosity is that determined from small samples; total porosity is that determined from the whole core. Whole-core analysis satisfactorily evaluates most carbonate rocks. However, no satisfactory technique is available for the analysis of extensively fractured materials because the samples cannot be put together in their natural state.

Compaction and Compressibility of Porous Rocks

The porosity of sedimentary rocks has been shown by Krumbein and Sloss ” to be a function of the degree of compaction of the rock. The compacting forces are a function of the maximum depth of burial of the rock. The effect of natural compaction on porosity is shown in Fig. 26.7. This effect is caused principally by the resulting packing arrangement after compaction; thus, sediments that have been buried deeply, even if subsequently uplifted. exhibit lower porosity values than sediments that have not been buried at great depth.

Geertsma12 states that three kinds of compressibility must be distinguished in rocks: (I) rock-matrix compressibility, (2) rock-bulk compressibility, and (3) pore compressibility. Rock-bulk compressibility is a combination of pore and rock matrix compressibility.

Rock-matrix compressibility is the fractional change in volume of the solid rock material (grains) with a unit change in pressure. Pore compressibility is the fractional change in PV of the rock with a unit change in pressure.

POROSITY-PER CENT

Fig. 26.8-Effective reservoir-rock compressibilities

The depletion of fluids from the pore space of a reservoir rock results in a change in the internal stress in the rock, thus causing the rock to be subjected to a different resultant stress. This change in stress results in changes in the GV, PV, and BV of the rock. Of principal interest to the reservoir engineer is the change in the PV of the rock. The change in rock-bulk compressibility may be of importance in areas where surface subsidence could cause appreciable property damage.

Hall I3 reported PV compressibility as a function of porosity. These data are summarized in Fig. 26.8. The effective rock compressibility in Fig. 26.8 results from the change in porosity caused by grain expansion and decrease in pore space because of compaction of the matrix.

Fatt I4 indicates that the pore compressibility is a function of pressure. Within the range of his data, he was unable to find a correlation with porosity.

725 Gradient (North

4 Gradient Sand 4 W.M.L(S.W.Tex.1

6 I I I I I I

35 30 25 20 15 IO 5 Formation Compressibility(Microsip1

1

Fig. 26.9-Depth vs. formation compressibility in abnormally pressured segment of an abnormally pressured reservoir.


/ I I

l l \eet

-I

l

l

l 0

J 35

Fig. 26.10-PV compressibility at 75% lithostatic pressure vs. initial sample porosity for limestones.

I I I I I I

0

Fig. 26.11-PV compressibility at 75% lithostatic pressure vs. initial sample porosity for consolidated sandstones.

100 I I I I I I

0 0 0

0 O 0” 08 0 0

0 O 0 0 00 0 0

0

00 00

@ OQ

0 0

0

B 0

\ 0 0 O 0 0 0 0 l

COR RELPlTlON \

0 0

H& LL�S -- 0 00 Oo o 0 0

@ >& . 0 00:

0 0 0 I

0 0

Fig. 26.12-PV compressibility at 75% lithostatic pressure vs. initial sample porosity for friable sandstones.

The additional significance of changes in porosity with the discovery of oil at deeper depths and new geological areas resulted in the need for a better understanding of the changes in porosity with the depletion of reservoir fluid pressure.

Hammerlindl I5 developed a correlation from measured field data that indicates the change in porosity compressibility with depth of burial of an unconsolidated sand (Fig. 26.9). Similar correlations have also been presented by others in the technical literature.

Considerable laboratory work has been performed recently in an attempt to understand better the effect of formation compaction on porosity. Newman I6 performed measurements on samples of limestone and consolidated, friable, and unconsolidated sandstones. He compared his results with those of Hall I3 and van der Knaap, ” as illustrated in Figs. 26.10 through 26.13. As noted in his data, an approximate correlation may exist between PV compressibility and porosity for limestones and consolidated sandstones. Little or no correlation exists between PV compressibility and porosity for friable and unconsolidated sandstones. By averaging the PV compressibility in 5% ranges of porosity, Newman at- tempted to correlate all four types of porous media. The results of this averaging technique are presented in Fig. 26.14.

The methods used to measure PV compressibility have come under discussion. PV compressibility can be measured in the laboratory by the hydrostatic (same pressure in all three directions) or the triaxial (different pressure in the z direction than in the x and y directions) techniques. The test samples also can be stress cycled


Fig. 26.13-PV compressibility at 75% lithostatic pressure vs. initial sample porosity for unconsolidated sandstones.

until the strain resulting from a supplied stress is constant, or the sample can be placed under stress and the strain measured for purposes of calculating PV compressibility.

Krug I8 and Graves I9 demonstrated that when a formation sample was stress cycled to a stable strain condition, the sample gave repeatable values of PV compressibility even when the sample was left in an un- stressed condition for 30 days or more. The data reported by Newman were for samples that were not stress cycled.

Lachance*’ compared PV compressibilities obtained by the hydraulic and triaxial methods. The reported results (Fig. 26.15) indicate a large difference in the magnitude of PV compressibilities obtained by the two methods. The triaxial data indicate that PV compressibility is essentially independent of the sample porosity. Newman’s I6 data were obtained by the hydrostatic method, whereas Krug’s I8 and Graves’ I9 data were obtained by the triaxial method.

In summary, rock compressibility is an important factor in reservoir evaluation. Oil reservoirs with high initial pressures and low fluid bubblepoint pressures are sensitive to the true value of PV compressibility. Gas reservoirs with initial reservoir pressures in excess of 6,000 psi are also sensitive to the value of PV compressibility. Newman, I6 Krug, I8 and Graves I9 all recommend that PV compressibility be measured on

Fig. 26.14-Class averages of PV compressibility vs. initial sample porosity.

Fig. 26.15-Calculated PV compressibility (porosity 2 8%).


-- . . --- Lf _-- -_- 6 3

II -- --- ] -_- ---I - _- --- --_ r/--i a t h,

.--------_

;

h-h,

Fig. 26.16-Schematic of Henry Darcy’s experiment on flow of water through sand.

samples from the reservoir in question when the PV compressibility may be significant in reservoir evaluation.

Permeability Introductory Theory

It is the purpose of this section to discuss the ability of the formation to conduct fluids. In the introduction to API Code 27,” it is stated that permeability is a property of the porous medium and a measure of the medium’s capacity to transmit fluids. The measurement of permeability, then, is a measure of the fluid conductivity of the particular material. By analogy with electrical con- ductors, the permeability represents the reciprocal of the resistance that the porous medium offers to fluid flow.

The following equations for flow of fluids in circular conduits are well known.

Poiseuille’s equation for viscous flow:

d2Ap v=- 321.LL ) . . . . . . . . . . . . . . . . ..I.......... (1)

Fanning’s equation for viscous and turbulent flow:

2dAp $=- fpL , . . . . . . (2)

where v = fluid velocity, cm/s, d = diameter of conductor, cm,

Ap = pressure loss over length L, dynes/cm2, L = length over which pressure loss is

measured, cm, p = fluid viscosity, Pa’s, p = fluid density, g/cm’, and f = friction factor, dimensionless.

A more convenient form of Poiseuille’s equation is

ar4Ap 4= , . . . . . . . . . 8clL (3)

where r is the radius of the conduit, cm, q is the volume rate of flow, cm”/s, and the other terms are as previously defined.

If a porous medium is conceived to be a bundle of capillary tubes, the flow rate q1 through the medium is the sum of the flow rates through the individual tubes. Thus,

qr=s i lljrj4, . . . .

P I 1

where n,, is the number of tubes of radius rj. If

(T/8) $ njr j4

j=l

(4)

is treated as a flow coefficient for the particular grouping of tubes the equation reduces to

qr=c$; . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...(5)

where

k

The pore structure of rocks does not permit simple classification of the flow channels. Therefore, empirical data are required in most cases.

In 1856, Darcy investigated the flow of water through sand filters for water purification. His experimental apparatus is shown schematically in Fig. 26.16.” Darcy interpreted his observations to yield results essentially as given in Eq. 7.

ht --h2 q=KA- . . . . . . . . . . . . . . . . . . . . . . L (7)

q represents the volume rate of flow of water downward through the cylindrical sandpack of cross-sectional area A and length L. h 1 and h2 are the heights above the standard datum of the water in manometers located at the input and output faces and represent the hydraulic head at


Points 1 and 2. K, a constant of proportionality. was found to be characteristic of the sandpack. Darcy’s investigations were confined to flow of water through sandpacks that were 100% saturated with water.

Later investigators found that Darcy’s law could be extended to fluids other than water and that the constant of proportionality K could be written as klp, where p is the viscosity of the fluid and k is a proportionality constant for the rock. The generalized form of Darcy’s law as presented in API Code 27 is presented in Eq. 8.

u,yz-; ($-gp;). . .

where s = distance in direction of flow, always

positive, us = volume flux across a unit area of the porous

medium in unit time along flow path S, z = vertical coordinate, considered positive

downward, cm, p = density of the fluid, g = acceleration of gravity,

- = pressure gradient along s at the point to ds which u refers, p = viscosity of the fluid, k = permeability of the medium, and

dt -= sin 8, where fl is the angle between s and ds the horizontal.

u, may further be defined as q/A where q is the volume rate of flow and A is the average cross-sectional area perpendicular to the lines of flow.

The portion of Eq. 8 in parentheses may be interpreted as the total pressure gradient minus the gradient caused by a head of fluid. Thus, if the system is in hydrostatic equilibrium, there is no flow and the quantity inside the parentheses will be zero. Eq. 8 may be rewritten as

kd u, =--@gz-p). . . . . . . . . .

fib

The quantity d(pgz-p)lds may be considered to be the negative gradient of a potential function b, where

a=p-pgz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..(lO)

The potential function is defined such that flow will be from higher to lower values.

The dimensions of penmeabilit P

may be established from an analysis of Eq. 8 as k=L . In the cgs system of units, the unit of permeability would be cm*, a large unit for common usage; therefore, the petroleum industry adopted the darcy as the standard unit of permeability, which is defined as follows.

A porous medium has a permeability of one darcy when a single phase fluid of one centipoise viscosity that completely fills the voids of the medium, will flow through it under conditions of viscous flow at a rate of one cubic centimeter per second per square centimeter cross sectional area under a pressure or equivalent hydraulic gradient of one atmosphere per centimeter. ”

Fig. 26.17-Sand model for rectilinear flow of fluids.

Conditions of viscous flow mean that the rate of flow will be sufficiently low to be directly proportional to the potential gradient.

Darcy’s law holds only for conditions of viscous flow as defined. Further, for the permeability k to be a proportionality constant of the porous medium, the medium must be 100% saturated with the flowing fluid when the determination of permeability is made. In addition, the fluid and the porous medium must not react-i.e., by chemical reaction, adsorption, or absorption. If a reactive fluid flows through a porous medium, it alters the porous medium and, therefore, changes the permeability of the medium as flow continues.

Flow Systems of Simple Geometry

Horizontal Flow. Horizontal rectilinear steady-state flow is common to virtually all measurements of permeability. If a rock is 100% saturated with an incompressible fluid and is horizontal (Fig. 26.17), then dz/ds=O, dplds=dpi&, and Eq. 8 reduces to

4 -k dp ux=-=--3

A tth

which on integration becomes

kA(P I -P*) 9= cLL , .,.................... (11)

where k is the specific permeability. If a compressible fluid flows through a porous

medium, Darcy’s law, as expressed in Eq. 8, is still valid. However, for steady flow, the mass rate of flow rather than the volume rate of flow is constant through the system. Therefore, the integrated form of the equation differs. Considering steady rectilinear flow of compressible fluids, Eq. 8 becomes

b dp pux=---, .,..........,,........... (12)

ttb

or, for steady-state flow,

pux=p: =constant.


I

FREE FLOW

II FLOW UNDER

HEAD h

III FLOW UNDER

HEAD h

Fig. 26.1 E-Sand model for vertical flow

The density-pressure relationship for isothermal conditions of a slightly compressible fluid may be expressed as

p=poe(‘p

and

ap=a”, . . . . . .(13) CP

where c is the fluid compressibility. Thus,

P 0 9 0 -b dp -k dp -z--c--

A P dx pc dx’

where q. is the volume rate of flow of a fluid of density PO.

On integration,

WP I -02) PO90 = . . . . . (14) cLcL

If terms of cp of second and higher order are neglected, the density can be expressed as

such that Eq. 14 reduces to

k4P I -P2) 40=

d .

The density-pressure relationship for isothermal conditions of an ideal gas may be expressed as

P P PPb -=- orp=-. . ,(15) Ph Pb Pb

Thus,

t”bqb b dp -=-_-

A P dx’

where pb and qb are the density and volume rate of flow, respectively, at the base pressure, ph.

Substituting for p

Pbqb k dp -=--p-, . . . . . . . . . . . .

A cl&

which on integration yields

(16)

kA P,*-Pz~ q”=G . . . . . . . _. __ (17) Pb

Define p as (p, +p2)12, and yP as the volume rate of flow at p such that pqp =pbqh; then

k4PI -P2) 41, = uL .,.................... (18)

Therefore, flow rates of ideal gases may be computed from the equations for incompressible liquids so long as the volume rate of flow is defined at the algebraic mean pressure.

Vertical Flow. Fig. 26.18 shows three sandpacks in which linear flow occurs in the vertical direction.

First consider Case 1 (Fig. 26. IS)--when the pressure at the inlet and outlet are equal (free flow), such that only the gravitational forces are driving the fluids. Given

dz dp S=Z, -=l, and -=O, ds ds

the flow is then defined by

q&g. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .(19) P

Next consider Case 2-the case of downward flow when the driving head (difference in hydraulic head of inlet and outlet) is h (Fig. 26.18). We know that

dz, -ah z=l and z=-

L

Therefore, from Eq. 8,

. . . . . . . . . . .(20)


When the flow is upward and the driving head is h, Case 3 (Fig. 26.18), and z is defined as positive downward,

and

k u=+-

P

then

kApgh 4= . . .._.......................... (21)

Radial Flow. A radial-flow system, analogous to flow into a wellbore, is idealized in Fig. 26.19. If flow is considered to occur only in the horizontal plane under steady-state conditions, an equation of flow may be derived from Darcy’s law to be

2akMp, -P,, 1 4= ) . . . . (22) ~ ln rplr,,

where rI, is the radius at the external boundary at which pc (pressure at the external boundary) is measured, and r,v is the radius of the wellbore at which pa, (pressure at the wellbore) is measured. All other terms are as defined for linear flow.

Eq. 22 may be modified appropriately for the flow of compressible fluids. The details of modifying this equation are omitted because they are essentially the same as the ones used in the horizontal rectilinear flow systems.

After modification for variations in flowing volumes with changing pressures, Eq. 22 becomes for slightly compressible fluids

2xk&, -P,,,) h’ = . ,_..................... (23)

cp In r,,lr,,.

where w is the mass rate of flow, g/s, or

2mWpp -pw) 40 =

a~, In TJr,,.,

where q. is defined at the pressure p. where the density is po.

For ideal gases, Eq. 22 becomes

7rkh(p<,‘-~,,.~) 4/J = . (24) Wb ln r,,r,,

or

2dd-0, -p w) 911 = , . . . . cL ln r‘,,ra, (25)

Fig. 26.19-Sand model for radial flow of fluids to central wellbore.

Conversion of Units in Darcy’s Law

It is convenient in many applications of Darcy’s law to introduce commonly used oilfield units. The following is a summary of the more common equations with the conversion factors to convert to oilfield terminology.

Linear-Flow Liquids (or Gases with Volume at Mean Pressure). Rate, BID, is given by

q=1.1271 kA(p I-p21 . . . . . . . LLL (26)

Rate, cu ft/D, is given by

q=6.3230 Wp I -~2)

. . . . . . . . . AL (27)

Radial-Flow Liquids (or Gases with Volume at Mean Pressure). Rate, liters per day, is given by

q=92.349x 103 Wp, -PM’)

. . . . p In r,/r,

(28)

Rate, cu ft/D, is

q-92.349x 103 kh(p, -p,v) cc ln r,/r,, . . (29)

Gases at Base-Pressure, p,,, and Average Flowing Temperature, Tf. Linear flow rate, cu ft/D. is given by

where q,, is the volume rate of flow at the algebraic mean pressure (p, +p,,,)/2.

3.1615T,,kA(p, ’ -pz *) Yb = , . . . . . . . .

TfW&PlJ (30)


Pe

Fig. 26.20-Linear flow-parallel combination of beds. Fig. 26.21~Radial flow-parallel combination of beds.

and radial flow rate, cu ft/D, is given by*

19.88T~kh(p,2 -p,,,?) q/J= - .,............. (31)

Tfq.4,~p~ In rplr,,,

where k is in darcies; A is in sq ft; h is in ft; p , , p2, pp, p ,,.. and Ph are in psia; p is in cp; L is in ft; and re and T,, are in consistent units.

Since the previous equations describe the flow in the medium, appropriate volume factors must be introduced to account for changes in the fluids caused by any decrease in pressure and temperature from that of the medium to standard or stock-tank conditions. Permeability Conversion Factors. Following is a list of various unit conversions from darcy units to other systems of units.

kL!E- A(p/L) ’

1 darcy (d)= 1,000 millidarcies (md)

(cm3/s)cp =

cm ‘(atm/cm)

=9.869x 10 -’ (cm3/s) cp

,,* (dynIrm*)

=9.869x lop9 cm2

=1.062x IO-” sq ft

=7.324x lop5 (cu ft/sec)cp

sq ft(psi/ft)

(cu ft/sec)cp =9.697x10p4

cm’(cm water/cm)

=1.127 WD)cp

sq ft (psi/ft)

= 1.424 x 10 -’ (gal/min)cp

sq ft (ft water/ft)

Flow Systems of Combinations of Beds

Consider the case where the flow system comprises layers of porous rock separated from each other by in- finitely thin, impermeable barriers as shown in Fig. 26.20. The average permeability k may be evaluated by Eq. 32.

(32)

C hj j=l

Fig. 26.21 shows that the same terms appear in the radial-flow network as in the linear system. The only difference in the two systems is the manner of expressing the length over which the pressure drop occurs. Because all these terms are the same in each of the parallel layers, an evaluation of the parallel radial system yields the same solution as obtained in the linear case.

Example Problem 6-Average Permeability of Beds in Parallel. What is the equivalent linear permeability of four parallel beds having equal widths and lengths under the following conditions?

Pay Horizontal Thickness Permeability

Bed (ft) (md) 1 20 100 2 15 200 3 10 300 4 5 400

i: kihj j& j=l .

ihi ’ j=I

k= (100x20)+(200x15)+(300x 10)+(400x5)

20+15+10+5

10,000 =--200 md.

50


AP, AP, AP, h

Fig. 26.22-Linear flow-series combination of beds. Fig. 26.23-Radial flow-series combination of beds

Another possible combination for flow systems is to have the beds of different permeabilities to be arranged in series as shown in Fig. 26.22. In the case of linear flow, the average series permeability may be evaluated by Eq. 33.

Therefore,

j& 250+2.50+500+ 1,000

2.50 250 500 1,000

z+50+100+- 200

L 2,000

k= . . . . . . .(33) = 10+5+5+5 =80 md.

LJ lkj J==I For a radial system,

The same reasoning can be used in the evaluation of the average permeability for the radial system (Fig. k=

log 2.000/0.5

26.23) so as to yield log 25010.5 log 500/2so lop I .000/500 log 2.ooo11 .ooo + + +

25 SO loo 200

kc In r,,/r,,.

’ In rjlr, -1

= h, j&l ‘.I

Example Problem 7-Average Permeability of Beds in Series. What is the equivalent permeability of four beds in series, having equal formation thicknesses under the following conditions?

Assume Bed 1 adjacent to the wellbore (1) for a linear system and (2) for a radial system if the radius of the penetrating wellbore is 6 in. and the radius of effective drainage is 2,000 ft.

=30.4 md.

Permeability of Channels and Fractures

Only the matrix permeability has been discussed in the analysis to this point. In some sand and carbonate reservoirs, the formation frequently contains solution channels and natural or artificial fractures. These channels and fractures do not change the permeability of the matrix but do change the effective permeability of the flow network.

Circular Channel. Equating Darcy’s and Poiseuille’s equations for fluid flow in a tube, the permeability may be expressed as a function of the tube radius.

k=;, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..(35)

Length Horizontal of Bed Permeability

_ @I Bed (md) 1 250 25 2 250 50 3 500 100 4 1,000 200

where k and r are in consistent units. If r is in centimeters, then k in darcies is given by

r2 k=

8(9.869x 10 -9) I 12.50X 106r’,

where 9.869~ 1O-9 is a conversion factor from the previous list. Then, if r is in inches,

For a linear system, k= 12.50~ 106(2.54)*r2

k= ’

k Ljlkj j=l

=80~10~r*=20~10~d*,

where d is the diameter of the opening in inches.


(PI -P2YL (0)

~~~~~~

01 03 (p: -Op5:),2L

07 09

fb)

Fig. 26.24-Plol of experlmental results for calculation of permeability-(a) from k/F = qL/

VW, -P~)I; @I from ~~P=~~,P&L~P, 2 -P~*)I.

Therefore, the permeability of a circular opening 0.005 in. in radius is 2,000,OOO md.

Fracture. For flow throu 4

h slots of fine clearances and unit width, Buckingham’- reports that

12pL Ap=- h? ’

such that the permeability of the slot is given by

k=;. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..(36)

When h is in centimeters and k in darcies. the permeability of the slot is given by

k= 12(9.869x 10-9)

=84.4x 10’h2,

and when h is in inches and k is in darcies, permeability is given by

k=54.4 x 106h2,

so that the permeability of a fracture 0.01 in. in thickness would be 5,440 darcies or 5,440,OOO md.

Physical Analogies to Darcy’s Law

Ohm’s law as commonly written is

where I = current, A,

E = voltage drop, V, and r = resistance of the circuit, Q,

but

L L r=p- or r= -,

A OA

where p = resistivity, Q-cm, u = llp=conductivity, L = length of flow path, cm, and A = cross-sectional area of conductor, cmZ.

Therefore,

I& PL

Comparing with Darcy’s law for a linear system,

,=!A%. P L

Note that

4 = 1,

k 1 and

I* P

4 E - =- L L’

The Fourier heat equation may be written as

d=k,aF,

where Q= rate of heat flow, Btulhr,

A = cross-sectional area, sq ft, AT = temperature drop, “F,

L = length of the conductor, ft, and kh = thermal conductivity, Btu/(ft-hr-“F).

A comparison with Darcy’s law indicates that

s=Q,

k -=kl,, and P

Ap AT -=- L L’


Electrical and heat models (based on these analogies) of rock and well systems frequently are used to solve fluid- flow problems involving complex geometry.

Measurement of Permeability

The permeability of a porous medium may be determined from samples extracted from the formation or by in-place testing. The procedures discussed in this section pertain to the permeability determinations on small samples of extracted media.

Two methods are used to evaluate the permeability of cores. The method most used on clean, fairly uniform formations uses small cylindrical samples called perm plugs that are approximately % in. in diameter and 1 in. in length. The second method uses full-diameter core samples in lengths of 1 to 1% ft. The fluids used with either method may be gas or any nonreactive liquid.

Perm-Plug Method. As core samples ordinarily contain residual oil, water, and gas, it is necessary that the sample be subjected to preparation before the determination of the permeability. The residual fluids normally are extracted by retorting or solvent extraction. The core is dried before permeability measurements are taken. Air commonly is used as the fluid in permeability measurements. The requirement that the permeability be determined for conditions of viscous flow is best satisfied by obtaining data at several flow rates and plotting results, as shown in Fig. 26.24, based on either Eq. 17 or 18. For conditions of viscous flow, the data should plot a straight line, passing through the origin. Tur- bulence is indicated by curvature of the plotted points. The slope of the straight-line portion of the curve is equal to k/p, from which the permeability may be computed. To obtain k in darcies, 4 must be in cm3/s, A in cm’, p 1 and p2 in atm. L in cm, and ~1 in cp.

A permeameter designed for the determination of the permeability of rocks with either gas or liquid is illustrated in Fig. 26.25. Data ordinarily are taken from this device at only one flow rate. To assure conditions of viscous flow, the lowest possible rate that can be measured accurately is used.

Example Problem S-Permeability Measurement. The following data were obtained during a routine penneability test. Compute the permeability of this core.

1. Flow rate= 1,000 cm3 of air at 1 atm absolute and 70°F in 500 seconds.

2. Pressure, downstream side of core= 1 atm absolute; flowing temperature, 70°F.

3. Viscosity of air at test temperature=0.02 cp. 4. Cross-sectional area of core=2.0 cm*. 5. Length of core=2 cm. 6. Pressure, upstream side of core= 1.45 atm

absolute.

PI VI fP?V2 =Pv

where 1 is upstream conditions and 2 is downstream conditions, and

P +Pz 1.45+1 P=- E-=1.225,

2 2

Fig. 26.25-Ruska universal permeameter.

and

1 x 1,000=1.225 V.

V=816 cm3,

_ v 816 -=1.63, 4=;=500

1.63x2x0.02 = x 1,000

2 x0.45

=72.5 md.

Assuming that the data indicated were obtained, but water was used as the flowing medium, compute the permeability of the core. The viscosity of water at test temperature was 1 .O cp.

v 1,000 4’-‘50040

t

and

.-

k=!!kx,,)oO= 2X1X2 ~ x 1,000=4,450 md.

A AP 2x0.45

Whole-Core Measurement. The core must be prepared in the same manner as perm plugs. The core is then mounted in special holding devices as shown in Fig. 26.26. The measurements required are the same as the perm plugs but the calculations are slightly different.


AIR PRESSURE -GASKET OPENING

END VIEW

TOP VIEW

SPL’T - TELOWMETER

GASKET1

Fig. 26.26-Clamp-type permeameter for large cores.

In the case of the clamp-type permeameter, the geometry of the flow paths is complex, and an appropriate shape factor must be applied to the data to compute the permeability of the sample. The shape factor is a function of the core diameter and the size of the gasket opening. The shape factor affects the quantity L/A in the previous equations.

Factors Affecting Permeability Measurements

In the techniques of permeability measurement previously discussed, certain precautions must be exercised to obtain accurate results. When gas is being used as the measuring fluid, corrections must be made for gas slippage. When liquid is the testing fluid, care must be taken that it does not react with the solids in the core sample. Also, corrections may be applied for the change in permeability because of the reduction in confining pressure on the sample.

Effect of Gas Slippage on Permeability Measurements

Klinkenberg I4 has reported variations in permeability determined by using gases as the flowing fluid from that determined by using nonreactive liquids. These variations were ascribed to slippage, a phenomenon well known with respect to gas flow in capillary tubes. The phenomenon of gas slippage occurs when the diameter of the capillary openings approaches the mean free path of the gas.

Fig. 26.27 is a plot of the permeability of a porous medium as determined at various mean pressures using hydrogen, nitrogen, and carbon dioxide as the flowing fluids. Note that for each gas a straight line is obtained for the observed permeability as a function of the reciprocal of the mean pressure of the test. The data obtained with the lowest-molecular-weight gas yield the straight line with the greatest slope, indicative of a greater slippage effect. All the lines when extrapolated to infinite mean pressure (l/j=O) intercept the permeability axis at a common point. This point is designated as the equivalent liquid permeability, kL. Klinkenberg and

b CARBON DIOXIDE I / I I I I 1

0 2 0.4 0.6 0.8 1.0 12 1.4

1

J

RECIPROCAL MEAN PRESSURE (ATM)-’

k!

Fig. 26.27-Permeability constant of core sample L to hydrogen, nitrogen, and COP at different pressures (permeability constant to iso-octane, 2.55 md).

others established that the permeability of a porous medium to a nonreactive homogeneous single-phase liquid was equal to the equivalent liquid permeability.

The linear relationship between the observed permeability and the reciprocal of mean pressure may be expressed as follows.

kg kL=- 1 +blp

=k, -ml, . . . . . . (37) P

where kL = permeability of the medium to a single

liquid phase completely filling the pores of the medium,

k, = permeability of the medium to a gas

completely filling the pores of the medium,

j = mean flowing pressure of the gas at which k, was observed,

b = constant for a given gas in a given medium, and

m = slope of the curve.

Reactive Fluids. While water commonly is considered to be nonreactive in the ordinary sense, the occurrence of swelling clays in many reservoir rock materials results in water’s being the most frequently occurring reactive liquid in connection with permeability determinations. Reactive liquids alter the internal geometry of the porous medium. This phenomenon does not vitiate Darcy’s law but rather results in a new porous medium, the permeability of which is determined by the new internal geometry.

While fresh water may cause the cementation material in a core to swell because of hydration, it is a reversible process. A highly saline water may be flowed through the core and return the permeability to its original value. The effect of water salinity on permeability is shown in Table 24.3. 25


TABLE 26.3-EFFECT OF WATER SALINITY ON PERMEABILITY OF NATURAL CORES (Grains/gal Chloride ion’)

Field Zone ~ - S 34

: 34 34 S 34 S 34 s 34 S 34 S 34 S 34 S 34 S 34 S 34 s 34 S 34 T 36 T 36 T T ;: T 36 T 36

k a

4,080 24,800 40,100 39,700 12,000 4.850

22,800 34.800 27,000 12,500 13,600 7,640

11,100 6,500 2,630 3,340 2,640 3,360 4,020 3,090

k 1,000 k 500 k 300

1,445 1,380 1,290 11,800 10,600 10,000 23,000 18.600 15,300 20,400 17,600 17,300

5,450 4,550 4,600 1,910 1,430 925

13,600 6,150 4,010 23,600 7,800 5,460 21,000 15,400 13,100

4,750 2,800 1,680 5,160 4,640 4,200 1,788 1,840 2,010 4,250 2,520 1,500 2,380 2,080 1,585 2,180 2,140 2,080 2,820 2,730 2,700 2,040 1,920 1,860 2,500 2,400 2,340 3,180 2,900 2,860 2,080 1,900 1,750

k 200

1,190 9,000

13,800 17,100 4,510

736 3,490 5,220

12,900 973

4,150 2,540

866 1,230 2,150 2,690 1,860 2,340 2,820 1,630

k 100 k w 885 17.2

7,400 147 8,200 270

14,300 1,680 3,280 167

326 5.0 1,970 19.5 3,860 9.9

10,900 1,030 157 2.4

2,790 197 2,020 119

180 6.2 794 4.1

2,010 1,960 2,490 2,460 1,860 1,550 2,280 2,060 2,650 2,460 1,490 1,040

‘Far example. ks means permeablhty lo air, hSoo means permeablhty 10 iresh water

means permeablllty 10 500.gram/gal chloride solul~on, and kw

Care must be taken that laboratory permeability values are corrected to liquid values obtained with water whose salinity corresponds to formation water.

Overburden Pressure. When the core is removed from the formation, all the confining forces are removed. The rock matrix is permitted to expand in all directions, partially changing the shapes of the fluid-flow paths inside the core.

Compaction of the core caused by overburden pressure may cause as much as a 25 % reduction in the permeabil i- ty of various formations, as observed in Fig. 26.28.2h Note that some formations are much more compressible than others; thus, more data are required to develop empirical correlations that will permit the correction of surface permeability for overburden pressures.

Factors in Evaluation of Permeability From Other Parameters

,Permeability. like porosity, is a variable that can be measured for each rock sample. To aid in understanding fluid flow in rocks and possibly to reduce the number of measurements required on rocks, correlations among porosity, permeability, surface area, pore size, and other variables have been made. The reasoning behind some of the correlations among porosity, permeability, and surface area is presented here to enable the reader to gain some understanding of the interrelation of the physical properties of rocks. Although these relations are not quantitative, they are indicative of the interdependence of rock characteristics.

Use of Capillary Tubes for Flow Network. The permeability of a tube derived from Darcy’s and Poiseuille’s equation is

k=f x

If a porous system is conceived to be a bundle of capillary tubes, then it can be shown that the permeability of the medium depends on the pore-size distribution and porosity. A flow network of tubes would be similar to layers of different permeability in parallel, such that the average permeability could be calculated by adapting Eq. 32 to read

m

C kjAj J=I

WI . . . . . . . . ..I.............. (38)

J=l

where kj is the permeability of one capillary tube and Aj is the area of flow represented by a bundle of tubes of permeability ki.

lCURVE SOURCE PERMEABILITY POROSITY -- nr rr.n.- . .^ --l?rruT

ti d 60 zt I t 3 ~WXIERN CALIFORNIA 335 25

:z 4 LOS ANGELES BASIN

2 CALIFORNIA I10 22

y 50 I I 0 1000

5 2000 3000 4000 5000

OVERBURDEN PRESSURE-PSIG

Fig. 26.28-Change in permeability with overburden pressure.


The quantities k, and A, can be defined in terms of the Wyllie*’ derived the Kozeny equation from Poi- radius of capillary tubes. seuille’s law by using a specified flow network. The

resulting permeability for this flow network is given by

A,=sn r ’ I I

and

Eq. 43.

, . . . . . . . . . . . . . . . . . . . . . . (43)

7 k;+,

where k = permeability of the porous medium,

F,Y = shape factor,

where n, is the number of tubes of radius r,.

5 A,=$A,, J=l

L = length of the sample, and L, = actual length of the flow path.

If

Lo 2

where 4 is the porosity of the flow network and A, is the ( > T =T= tortuosity of the porous medium

total cross-sectional area of the flow network. By substitution, Eq. 38 reduced to

and K, =F,Y7=Kozeny constant, then Wyllie’s equation will reduce to the same form as Eq. 42.

j&f

,,1

c n/r, 3 j= I 111 ( . . . . . . c ,l/r; *

j=l

(39)

where li is the average permeability of the tube bundle. Note that the permeability of a bundle of tubes is a

function not only of the pore size but of the arrangement or porosity of the system.

Consider a system that comprises a bundle of capillary tubes of the same radii and length; k, the permeability, may be written from Eq. 39 as

7

k=$. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..(40)

The internal surface area per unit PV, A,,, may be defined in terms of the tube radius by

A,,=?. ,.,.....,.,,.,,_...,.........., .(41) r

Combining Eqs. 40 and 41 gives the permeability as a function of porosity and internal surface area. This function is

If l/K; is substituted for the constant l/z, the resulting expression is Kozeny’s equation wherein K; is defined as the Kozeny’s constant.

4 k=- K,A,” ~~~~..........,......___,,,,. (42)

Fluid Saturations In the previous sections of this chapter, the storage and the conduction capacity of a porous rock were discussed. To the engineer there is yet another important factor to be determined-i.e., the fluid content of the rock. In most oil-bearing formations, it is believed that the rock was completely saturated with water before the invasion of the rock by petroleum. The oil will not displace all the water from the pore space. Therefore, to determine the quantity of hydrocarbons accumulated in a porous rock formation, it is necessary to determine the fluid saturation (oil, water, and gas) of the rock.

There are two approaches to the problem of determining the fluid saturations within a reservoir rock. The direct approach is to measure. in the laboratory, the saturations of selected rock samples recovered from the parent formation. The indirect approach is to determine the fluid saturation by measuring some related physical property of the rock.

Factors Affecting Fluid Saturations of Cores The core samples delivered to the laboratory for fluid- saturation determinations are obtained from the ground by either rotary, sidewall, or cable-tool coring. In all cases, the fluid content of these samples has been altered by two processes. First, in the case of rotary drilling, the mud column exerts a greater pressure at the formation wellbore surface than the fluid in the formation. The differential pressure between the mud column and the formation fluids causes mud and mud filtrate to invade the formation, thus flushing the formation with mud and its fyltrate. The filtrate displaces some of the original fluids. This displacement process changes the original fluid contents of the in-place rock. Second. as the sample is brought to the surface, the confining pressure of the fluid column is constantly decreasing. The reduction of pressure permits the expansion of the entrapped water, ail, and gas. Gas. having the greater coefficient of expansion, expels oil and water from the core. Thus, the content of the core at the surface has been changed from that which existed in the formation. Because the invasion

PROPERTIES OF RESERVOIR ROCKS 26-2 1

of the filtrate precedes the core bit, it is not possible to use pressurized core barrels to obtain undisturbed samples.

Drill cuttings, chips, or cores from cable-tool drilling also have undergone definite physical changes. If little or no fluid is maintained in the wellbore, the formation adjacent to the well surface is depleted because of pressure reduction. As chips are formed in the well, they may or may not be invaded, depending on the fluids in the wellbore and the physical properties of the rock. In all probability, fluid will permeate this depleted sample, resulting in flushing. Thus, even cable-tool cores undergo the same two processes as was noted in the case of rotary coring, although in reverse order.

Sidewall cores from either rotary- or cable-tool-drilled holes are subjected to these same processes.

In an attempt to understand better the overall effect of the physical changes that occur in the core because of flushing and fluid expansion, Kennedy et al. 28 under- took a study to simulate rotary-coring techniques. The effects of both invasion and expansion because of pressure reduction were measured.

Schematics of the changes in saturation resulting from these two processes for oil- and water-based muds are shown in Fig. 26.29. For the water-based mud, the original displacing action of the water filtrate reduced the oil saturation by approximately 14%. The expansion to surface pressure displaced water and additional oil. The final water saturation was greater than the water saturation before coring. With oil-based mud, wherein the filtrate is oil, the displacing action did not alter the initial water saturations but did result in replacement of approximately 20% of the initial oil. On pressure depletion, a small fraction of the water was expelled, reducing the water saturation from 49.1 to 47.7 % The oil saturation was reduced by both processes from 50.9 to 26.7%. Thus, even when high water saturations are involved, up to approximately 50%, the water-saturation values obtained with oil-based muds may be considered to be representative of the initial water saturations in the reservoir. Hence, it is possible to obtain fairly representative values of in-place water saturations by using oil-based muds.

Attempts have been made to use tracers in the drilling fluid to determine the amount of water in the core that is caused by mud-filtrate invasion. The theory was that mud filtrate displaced only oil. Thus. upon recovering the core to the surface, the salt concentration of the core water could be determined. Thus, if the salt concentration in the reservoir water and the tracer concentration in the drilling fluid were known, the volume of filtrate and reservoir water in the core could be calculated. Because a large fraction of the initial reservoir water may have been displaced by the invading filtrate, the tracer method results in incorrect values for reservoir-water saturation.

To obtain realistic values of fluid saturation, it is necessary to choose the proper drilling fluid or to use indirect methods of saturation determination.

Determination of Fluid Saturations from Rock Samples

One of the most popular means of measuring fluid saturations of cores is the retort method. This method takes a small rock sample and heats the sample to

SATURATION AFTER MUD FLUSHING BEFORE PRE :SSURE REDUC TION

RESIDUAL SbTUkATlON SATURATION

WATER BASE MUD (a)

ORIGINAL SATURATION

T---l

SATURATION AFTER

RESIDUAL SATURATION

MUD FLUSHING BEFORE PRESSURE REDUCTION

OIL BASE MUD (b)

Fig. 26.29-Typical changes in saturations of cores flushed with water-based and oil-based muds.

vaporize the water and the oil, which is condensed and collected in a small receiving vessel. The retort method has several disadvantages as far as commercial work is concerned. The water of crystallization within the rock is driven off, causing the water-recovery values to be too high. The second error that occurs from retorting samples is that the oil, when heated to high temperatures, has a tendency to crack and coke. This change of hydrocarbon molecules tends to decrease the liquid volume. The fluid wetting characteristics of the sample surface may be altered during the retorting process as a result of the two previous factors. Before retorts can be used, calibration curves must be prepared for water and oils of various gravities to correct for losses and other errors. These curves can be obtained by running “blank” runs (retorting known volumes of fluids of known properties). The retort is a rapid method for determining fluid saturations and, if the corrections are used, yields satisfactory results. It gives both water and oil volumes such that the oil and water saturations can be calculated from the following equations.

S&, “P

S, +,

P


and

S,=l-S,-S,,

wheres, =s, =s, =v, =VP =

v, =

water saturation,oil saturation,gas saturation,

The otherextraction

Fig. 26.30—Laboratory layout for performlng routine core analysis

water volume, cm3,pore volume, cm3, andoil volume, cm3.

method of determining fluid saturation is bywith a solvent. Extraction may be accom-

plished by a modified ASTM distillation method or acentrifuge method. In the standard distillation test, thecore is placed such that a vapor of either toluene, pen-tane, octane, or naphtha rises through the core. Thisprocess leaches out the oil and water in the core. Thewater and extracting fluid are condensed and collected ina graduated receiving tube. The water settles to the bot-tom of the receiving tube because of its greater density,and the extracting fluid refluxes over the core and intothe main heating vessel. The process is continued untilno more water is collected in the receiving tube. Thewater saturation may be determined directly by

S,,=v,;.VP

The oil saturation is an indirect determination. The oilsaturation as a fraction of PV is given by

so= w,, - w,, - w,VP-P* )

whereW‘II’ = weight of wet core, g,W td = weight of dry core, g,W, = weight of water, g,

VP = PV, cm3, andPO = density of oil, g/cm3.

The gas saturation is obtained in the same manner as theretort.

Another method of determining water saturation is touse a centrifuge. A solvent is injected into the centrifugejust off center. Because of centrifugal force, it is thrownto the outer radii and forced to pass through the coresample. The outflow fluid is trapped and the quantity ofwater in the core is determined. The use of the centrifugeprovides a very rapid method because of the high forcesthat can be applied. In both extraction methods, at thesame time that the water content is determined, the coreis cleaned in preparation for the other measurementssuch as porosity and permeability.

There is another procedure for saturation determina-tion that is used in conjunction with either of the extrac-tion methods. The core as received from the well isplaced in a modified mercury porosimeter in which theBV and gas volume are measured. The volume of wateris determined by one of the extraction methods. Thefluid saturations can be calculated from these data.

In connection with all procedures for determination offluid content, a value of PV must be established in orderthat fluid saturations may be expressed as percent of PV.Any of the porosity procedures previously described maybe used. Also, the BV and gas volume determined fromthe mercury porosimeter may be combined with the oiland water volumes obtained from the retort to calculatePV, porosity, and fluid saturations.

Porosity, permeability, and fluid-saturation determina-tions are the measurements commonly reported inroutine core analysis. A laboratory equipped for suchdeterminations is shown in Fig. 26.30.

Interstitial Water SaturationsEssentially, three methods are available to the reservoirengineer for the determination of interstitial water satura-tions. These methods are (1) determination from corescut with oil-based muds, (2) determination fromcapillary-pressure data, and (3) calculation from electric-log analysis (see Chap. 49).

Oil-Based Mud. The obtaining of water saturations byusing oil-based muds has been discussed. A correlationbetween water saturation and air permeability for coresobtained with oil-based muds is shown in Fig. 26.31.29


A general trend of increasing water saturation with decreasing permeability is indicated. It is accepted from field and experimental evidence that the water content determined from cores cut with oil-based mud reflects closely the water saturation as it exists in a reservoir, except in transition zones where some of the interstitial water is replaced by filtrate or displaced by gas expansion.

Fig. 26.32 shows permeability/interstitial-water relationships reported in the literature for a number of fields and areas. There is no general correlation applicable to all fields; however, an approximately linear correlation between interstitial water and the logarithm of permeability exists for each individual field. The general trend of the correlation is decreasing interstitial water with increasing permeability.

2 2 4 6 4 6 II t tic: t t ttn I 20 40 60 100 200 400

AIR PERMEABILITY, MILLIDARCYS

Fig. 26.31--Relation of air permeability to the water content of the South Coles Levee cores.

Capillary Pressure. Capillary pressure may be thought of as a force per unit area resulting from the interaction of surface forces and the geometry of the medium in which they exist. Capillary pressure for a capillary tube is defined in terms of the inter-facial tension between the fluids, a. the angle of contact of the interface of these two fluids and the tube. 0(., and the radius of the tube, VI.

vature (these radii touch at only one point), r, and r7 _ and the interfacial tension of the fluids. This relationship is given in Eq. 4.5.

(45)

This relationship is expressed in Eq. 44.

P,. = 20 cos 8,.

, ,,..,..................... (44) rt

Comparing Eq. 4.5 with the equation for capillary pressure as determined by the capillary-tube method, it is found that the mean radius U is defined by

where the angle 0,. is measured through the more dense fluid.

I 1 I 2 cos 0‘ _=-+-=-.--.-------' r rt r2 rf

In a packing of spheres, the capillary pressure is expressed in terms of any two perpendicular radii of cur-

rir2 rf y=-=-.---

rl +r2

2cos*,.. . . . . . . . . . . . . . . (46)

0 IO 20 30 40 50 60 70 80 90 100

LEGEND

I = HAWKINS 2: MAGNOLIA 3= WASHINGTON 4=ELK BASIN 5= RANGELY 6: CREOLE 7= SYNTHETIC ALUNDUM 8: LAKE ST. JOHN

C 9= LOUISIANA GULF COAST MIOCENE AGE-WELL A

IO=DITTO-WELLS BAND C

fil = NORTH BELRIDGE-CALIFORNIA

CORE ANALYSIS DATA

% INTERSTITIAL WATER

Fig. 26.32-Interstitial water vs. permeability relationships.


MEASURING APPARATUS

Fig. 26.33-Schematic of porous-diaphragm method of capillary pressure.

It is practically impossible to measure the values of rl and t-2 ; hence, they generally are referred to by the mean radius of curvature and empirically determined from other measurements on a porous medium.

The distribution of the liquid in a porous system depends on the wetting characteristics. It is necessary to determine which is the wetting fluid so as to ascertain which fluid occupies the small pore spaces. From packings of spheres, the wetting-phase distribution within a porous system has been described as either funicular or pendular in nature. In funicular distribution, the wetting phase is continuous, completely covering the surface of the solid. The pendular ring is a state of saturation in which the wetting phase is not continuous and the nonwetting phase is in contact with some of the solid surface. The wetting phase occupies the smaller interstices. As the wetting-phase saturation progresses from the funicular to the pendular-ring distribution, the volume of the wetting phase decreases and the mean radius of curvature or the values of rl and r2 tend to decrease in magnitude. Referring to Eq. 46, we see that if r I and r2 decrease in size, the magnitude of the capillary pressure would have to increase in value. Since r , and r2 can be related to the wetting-phase saturation, it is possible to express the capillary pressure as a function of fluid saturation when two immiscible phases are within the porous matrix.

Laboratory Measurements of Capillary Pressure

Essentially, five methods of measuring capillary pressure on small core samples are used. These methods are (1) the desatumtion or displacement process, through a porous diaphragm or membrane (restored-state method of Welge3’), (2) the mercury-injection method, (3) the centrifuge or centrifugal method, (4) the dynamic- capillary-pressure method, and (5) the evaporation method. *

Porous Diaphragm. The first of these, illustrated in Fig. 26.33, is the displacement or diaphragm method. The essential requirement of the diaphragm method is a

‘Since the method IS seldom used today, it WIII not be dwzussed The procedure con- slsts ot continuously monitoring the decrease m weight caused by evaporabon of a core sample lnitlally 100% saturated wlh a wetltng fluld. See Messner, E S : “Intetsbtial Water Determmation By An Evaporatmn Method.” Trans, AIME (1951) 192,269-74

permeable membrane of uniform pore-size distribution containing pores of such size that the selected displacing fluid will not penetrate the diaphragm when the pressures applied to the displacing phase are below some selected maximum pressure of investigation. Various materials including fritted glass, porcelain, and cellophane have been used successfully as diaphragms. Pressure applied to the assembly is increased by small increments. The core is allowed to approach a state of static equilibrium at each pressure level. The saturation of the core is calculated at each point defining the capillary-pressure curve. Any combination of fluids may be used: gas, oil, and/or water. Although most determinations of capillary pressure by the diaphragm method are drainage tests, by suitable modifications imbibition curves similar to Leverett’s may be obtained.

Mercury Injection. The mercury-capillary-pressure apparatus was developed to accelerate the determination of the capillary-pressure/saturation relationship. Mercury is normally a nonwetting fluid. The core sample is inserted in the mercury chamber and evacuated. Mercury is forced into the core under pressure. The volume of mercury injected at each pressure determines the nonwetting-phase saturation. This procedure is continued until the core sample is filled with mercury or the injection pressure reaches some predetermined value. Two important advantages are gained by this method: (1) the time for determination is reduced to a few minutes, and (2) the range of pressure investigation is increased because the limitation of the diaphragm’s properties is removed. Disadvantages are the difference in wetting properties and permanent loss of the core sample.

Centrifuge Method. A third method for determining capillary properties of reservoir rocks is the centrifuge method.3’ The high accelerations in the centrifuge increase the field of force on the fluids, in effect subjecting the core to an increased gravitational force. By rotating the sample at various constant speeds, a complete capillary-pressure curve may be obtained. The speed of rotation is converted into force units in the center of the core sample, and the fluid saturation is read visually by the operator. The advantage of the method is the increased speed of obtaining the data. A complete curve may be established in a few hours, while the diaphragm method requires days.

Dynamic Method. Brown3* reported the results of determining capillary-pressure/saturation curves by a dynamic method. Simultaneous steady-state flow of two fluids is established in the core. By the use of special wetted disks that permitted hydraulic pressure transmission of only the selected fluid phase, the difference in the resulting measured pressures of the two fluids in the core is the capillary pressure. The saturation is varied by regulating the quantity of each fluid entering the core. Thus, it is possible to obtain a complete capillary- pressure curve.

Comparison of Methods of Measurement

Intuitively, it appears that the diaphragm method (restored state) is superior in that oil and water are used; therefore, actual wetting conditions are more nearly ap-


proached. Hence, the diaphragm method is used as the standard to which all other methods are compared. The mercury-injection test data must be corrected for wetting conditions before they can be compared with results from the restored-state method. If it is assumed that the mean curvature of an interface in rock is a unique function of fluid saturation, then the ratio of mercury to water capillary-pressure data is given by

+-+f+6.57. . . . . (47) ‘M’ 0,.

DEPTH FEET BELOW SEA-LEVEL

where urn is the surface tension of mercury and u, is the surface tension of water. Experimentation has shown the ratio to vary between 5.8 (for limestones) and 7.5 (for sandstones). Thus, no conversion factor can be defined

Fig. 26.34-Comparison of water saturation from capillary pressure and electric log.

that will apply to all rocks. Good agreement of centrifuge data with those from the

diaphragm method was reported by Slobod. 31 Unlike the mercury-injection method, there is no need of conversion factors to correct for wetting properties. The same fluids are used in the centrifugal and diaphragm methods.

Excellent correlation was obtained by Brown3’ between the diaphragm and dynamic methods. The dynamic data were obtained by simultaneous steady flow of oil and gas through the porous sample at a predetermined level of pressure difference between the fluids. Care was taken to maintain uniform saturations throughout the core as well as to conduct the test such that a close correspondence to drainage conditions existed.

If capillary-pressure data are to be used for determining fluid saturations, the values obtained should be comparable with those of other methods. Water distributions, as determined from electric logs, and capillary-pressure data are normally in good agreement. A comparison of these methods is shown in Fig. 26.34. 33 Shown also is the approximate position of the gas/oil contact as determined from other test data. In the gas-bearing portion of the formation there is no significant variation in water saturation with depth or method of determination. However, in a thin oil zone, such as that shown in Fig. 26.34. there is a significant variation in the water saturation with depth. Variations in water saturations with depth within an oil zone must be taken into account to determine accurately average reservoir interstitial-water saturations.

Water Saturation from Capillary-Pressure Data. In oilfield terms, the capillary pressure may be stated as

gas/water or an oil/water system that normally does not have the same physical properties as the reservoir water, oil, and gas.

Essentially two techniques, differing only in the initial assumptions, are available for correcting laboratory capillary-pressure data to reservoir conditions.

p,..R= uw><, cos 0,.,,

uwg cos 0,., p,., L

or

P,..R=~P& . . . . . . (49) (JL

where fJ wo = interfacial tension water/oil,

UWR = interfacial tension water/gas, Ocwo = water/oil contact angle, e,.,, = water/gas contact angle, subscript

R = reservoir conditions, and subscript

L = laboratory conditions.

Since the interfacial tensions enter as a ratio, pressure in any consistent units may be used together with the interfacial tension in dynes/cm.

Averaging Capillary-Pressure Data. Two methods have been proposed for correlating capillary-pressure data of similar geologic formations. The first correlating procedure is a dimensionless grouping of the physical properties of the rock and the saturating fluids. This function is called a J function34 and is expressed as

P,.=+(p, -p2), ....................... (48)

, ...................... .(SO)

where h is in feet and p, and p2 are the densities of Fluids 1 and 2, respectively, in lbmicu ft at the condi- where tions of the capillary pressure. S,,, = water saturation, fraction of PV,

P,. = capillary pressure, dyne/cm*, Converting Laboratory Data. To use laboratory u = interfacial tension, dyne/cm, capillary-pressure data, it is necessary to convert them to k = permeability, cm*, and reservoir conditions. Laboratory data are obtained with a C#I = fractional porosity.


90 The results of the statistical correlation previously

81 z discussed applied to the capillary-pressure data presented

72 I+

in Fig. 26.35 are shown in Fig. 26.36. The reader should

2 note the linearity of the curves for each value of capillary

63 3 g

pressure and the tendency of all capillary-pressure curves

54 a’ i: to converge at high permeability values. This behavior is

3; what normally would be expected because of the larger 45 2 ,o capillaries associated with high permeabilities.

732 36 gs

To convert capillary-pressure saturation data to height

2, 2 2 saturation, it is necessary only to rearrange the terms in

3- &

Eq. 48 so as to solve for the height instead of the I8 z capillary pressure-i.e.,

3 P,. x 144

20 30 40 50 60 70 80 90 IO8

h,,=-, . . . . . . . . (52) PW -PO

WATER SATURATION,%

RESERVOIR FLUID DISTRIBUTION CURVES where

Fig. 26.35~Series of capillary-pressure curves as a function of hh = height above the free-water surface, ft,

permeability. P II’ = density of water at reservoir conditions,

lbm/cu ft, PO = density of oil at reservoir conditions,

lbm/cu ft, and

Some authors alter the above expression by including the cos f3(. (where 8,. is the contact angle) as follows.

P,. = capillary pressure at some particular saturation for reservoir conditions (it must be converted from laboratory data first, psi).

Example Problem 9-Calculation of Saturation Plane From Laboratory Capillary-Pressure Data. If

The J function originally was proposed as a means of converting all capillary-pressure data to a universal curve. There exist significant differences in correlation of the J function with water saturation from formation to formation such that no universal curve may be obtained, but the / function may be used to correlate the data from one formation.

The second method of evaluating capillary-pressure data is to analyze a number of representative samples and treat the data statistically to derive correlations that, together with the porosity and permeability distribution data, may be used to compute the interstitial-water saturations for a field. A first approximation for the correlation of capillary-pressure data is to plot water saturation against the logarithm of permeability for constant values of capillary pressure. A straight line may be fitted to the data for each value of capillary pressure, and average-capillary-pressure curves may be computed from permeability-distribution data for the field. The resulting straight-line equation takes the general form of

Fluid-distribution curves are reported for several values of permeability, ranging from 10 to 900 md in Fig. 26.35.” These data also may be considered to be capillary-pressure curves. The ordinate on the right reflects values of capillary pressure determined by displacing water with air in the laboratory. The ordinates on the left include the corresponding oil/water capillary pressure that would exist at reservoir conditions and the fluid distribution with height above the free-water surface.

P<.,L = 18 psi for S,.=O.35, CJ 11’0 = 24 dynes. P M’ = 68 lbmlcu ft,

is “‘8 = 72 dynes, and PO = 53 lbm/cu ft,

then, from Eq. 49,

P(.,R = 18(24/72)= 18/3=6 psi,

and

Pc,R x 144 6 x 144 h= =-=58 ft.

P II’ -PO 68-53

Thus, a water saturation of 35 % exists at a height of 58 ft above the free-water surface.

To calculate the fluid saturation in the gas zone, it is necessary to consider all three phases: oil, water, and gas. If all three phases are continuous, it can be shown that

where PC., “‘R = capillary pressure at a given height above

the free-water surface determined by using water and gas,

PC, H%) = capillary pressure at a given height above the free-water surface, using water and oil, and

pC.O,q = capillary pressure at a given height above the free-oil surface, using oil and gas.


If the wetting phase becomes discontinuous, then the wetting-phase saturation takes on a minimum value, and, at all heights above the point of discontinuity, the wetting-phase saturation cannot be less than this minimum value. It is then possible to calculate the fluid saturations above the free-oil surface by the following relations.

1. S,. at h is calculated using oil and water as the continuous phases.

2. SL at h is calculated using oil and gas as the continuous phases and height denoted by the free-oil surface.

3. S,=l-SL andS,=SL-S,, where SL is the total liquid saturation, oil plus water, fraction.

Example Problem lo-Calculation of Water and Oil Saturation in Gas Zone From Capillary-Pressure Data. Let oil-zone thickness, h,, equal 70 ft and

u “‘R = 72 dynes, (JOf = 50 dynes, (J I,‘0 = 25 dynes,

P II = 68 lbm/cu ft

Pn = 7 Ibm/cu ft, and PO = 53 lbm/cu ft.

From Fig. 26.28 for a 900-md sample, let PI,,L = 54 psi by the method illustrated in

Example Problem 9, Pc,R = 18 psi,

h fi = height above free-water level= 120 ft, and S,,. = 16% at a height of 70 ft or greater (read

from curve).

Since the oil zone is only 70 ft thick, the height of 120 ft above the free-water surface must be at least 50 ft into the gas-saturated zone. The first step is to calculate the total fluid saturation, SL, using gas and oil as the continuous phases.

h,,,=h,,-h,=120-70=50 ft;

hj, Pc,.R = IJ~(PI, -P,h

where h&, is the height above free-oil level, ft.

P<,.R = 50/144x(53-7)=501144x46. P<,.R = 15.97,

and

P,.,[, = Pr-,R~=15.97~72!50=23 psi. 0 og

From Fig. 26.35, for a laboratory capillary pressure of 23 psi and a permeability of 900 md, the total wetting saturation, SL, equals 18 % Therefore.

S,,=SL-S,,,=18-16=2X

)- IOOC

700

500

400

300

__ u-l $ 200 Q: 8

3

2 IOC

z 2 7c s 2 50

% 40

3c

2c

I-

)-

I-

I-

IO- 0

-

- -

-

-

-

- -

-

-

- 20 40 60 80 WATER SATURATION (%)

Fig. 26.36-Correlation of water saturation with permeability for various capillary pressures.

and

It must be understood that the relationships used in Ex- ample Problem 10 for calculating the fluid saturations in the gas zone were based on continuity of all three phases. Since this is not normally the case, it might be expected that saturations somewhat different from the calculated values exist. Because the capillary pressure for a discontinuous phase could vary from pore to pore, it is impossible to ascertain the exact relationships that should exist. Hence, the preceding method of calculating fluid distributions is not exact but is usually as accurate as the data available for making the computation.

Electrical Conductivity of Fluid-Saturated Rocks Porous rocks comprise an aggregate of minerals, rock fragments, and void space. The solids, with the exception of certain clay minerals, are nonconductors of elec- tricity. The electrical properties of a rock depend on the geometry of the voids and the fluids that fill the voids. The fluids of interest in petroleum reservoirs are oil, gas, and water. Oil and gas are nonconductors. Water is a


Fig. 26.37-Core-sample resistivity cell

The second fundamental notion of electrical properties of porous rock is the resistivity index, IK, which is defined as

(55)

where R, is the true resistivity of the rock system at some particular value of water saturation and Ra is as previously defined.

Three idealized representations have been introduced in the literature from which the formation resistivity factor, FR, and the resistivity index , f~, have been related to the porosity, 4, and the rock tortuosity, 7.

From Wyllie’s2’ analysis the relations are

F& 4

and

IR =7(,--r-, SW

conductor when it contains dissolved salts. Current is conducted in water by movement of ions and therefore may be termed electrolytic conduction. The resistivity of a material is the reciprocal of conductivity and commonly is used to define the ability of a material to conduct current. The resistivity of a material is defined by the F,=d-

following equation. 4

and

where T,, is the effective rock tortuosity at some water saturation.

Cornell and Katz3’ presented an analysis of a slightly different model. The relationships developed are as follows.

p=*A. ._.,.,.,,...,...,,.,,_,....,,.,, (53) L JR=&&

se where

p = resistivity. I’ = resistance,

A = cross-sectional area of the conductor, and L = length of the conductor,

Wyllie and Gardner 37 later presented an analysis based on a probability theory from which the following relationships were obtained.

FK=;

For electrolytes, p is commonly reported in Q-cm, and r is expressed in ohms, A in cm’, and L in cm. In the study of the resistivity of soils and rocks. it has been found that the resistivity may be expressed more conveniently in n-m. To convert to 9-m from O-cm, divide the resistivity in Q-cm by 100. In oilfield practice. the resistivity in Q-m commonly is represented by the symbol R with an appropriate subscript to define the condition to which R applies.

Fundamental Concepts

The definition of electrical formation resistivity factor is perhaps the most fundamental concept in considering electrical properties of rocks. The formation resistivity factor as defined by Archie” is

4’ and

I IR=--

s,,.’

From the analysis of the electrical properties of the foregoing idealized pore models, general relationships between electrical properties and other physical properties of the rock may be deduced. The formation resistivity factor has been shown to be some function of the porosity and the internal geometry of the rock system. In particular, the formation resistivity factor may be expressed in the following form.

FK=I@ -“I, (56)

F/$5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..(54) where K is some function of the tortuosity and VI is a R \I’ function of the number of reductions in pore-opening

sizes or closed channels. It is suggested that K should be where R. is the resistivity of the rock when saturated I or greater. The value of rn has been shown from theory with water having a rcsistivity of R,, to range from I to 2.


Both the formation resistivity factor, F,, and the resistivity index. IR, depend on ratios of path length or tortuosities. Therefore, to compute the formation resistivity factor or resistivity index from the relations derived from models, it is necessary to determine the electrical tortuosity. Since direct measurement of the path length is impossible, reliance has been placed primarily on empirical correlations based on laboratory measurements. Winsauer et al. 3X devised a method of determining tortuosity by transit time of ions flowing through a rock under a potential difference. The data obtained were correlated with the product FR+. The resulting correlation of formation resistivity factor, porosity, and tortuosity is given in Eq. 57.

1.67

=F,&

where L, is the actual length of flow path, and L is the length of the sample, or

$ IO II: 0 k-

6

T’.~“? =F&. . . . . . .(57) 4 1 HUMBLE RELATION F= 5 ,t-j&tt-

The deviation from the theory is believed to be an indication of the greater complexity of the actual pore system than that of the models on which the theory was based.

Archie suggested that the formation resistivity factor could be correlated with porosity and have the form

FR=c#-“‘, . . . ., ._.. . . .(58)

where 4 is the fractional porosity and m is the cementation factor. Archie further reported that the cementation factor probably ranged from 1.8 to 2.0 for consolidated sandstones and, for clean unconsolidated sands, was about 1.3.

Measurement of Electrical Resistivity of Rocks

Laboratory measurements of electrical properties of rocks have been made with a variety of devices. The measurements require a knowledge of the dimensions of the rock, the fluid saturation of the rock, the resistivity of the water contained in the rock, and a suitable resistivity cell in which to test the samples. A simple cell is shown in Fig. 26.37. 39 A sample cut to suitable size is placed in the cell and clamped between electrodes A. Current is then passed through the sample and the potential drop observed. The resistance of the sample is computed from Ohm’s law,

E r=-.

I

and R (the resistivity) is computed from

R,‘A L’

where A is the cross-sectional area of the sample and L is the length of the sample. The saturation conditions of the test may be established at known values before measurement or determined by an extraction procedure after measurement.

-- 5 60 5 2 40

zi

5 20

F TIXIER S RELATION FOR UNCONSOLIDATED

2p-M CONSOLIDATED FORMATIONS 1,

2 4 6 8 IO 20 40 60 80 POROSITY, =/a

Fig. 26.38-Comparison of various formation resistivity factor correlations.

Empirical Correlation of Electrical Properties Archie, as previously mentioned, reported the results of correlating laboratory measurements of formation factor with porosity. He expressed his results in the form FRz4-m.

Winsauer et al. ” reported a similar relationship based on correlations of data from a large number of sandstone cores. This equation, commonly referred to as the Hum- ble relation, is

FR=0.62q!-2.‘5. . .(59)

In discussing the theory of the formation resistivity factor, it was stated that K should be greater than 1 and that m should be 2 or less. At this time, the discrepancy between theory and experiment must be attributed to the possible effect of conducting solids.

Improved correlations should result from considering other parameters, such as permeability, as variables in the relations.

A comparison of suggested relationships between porosity and the formation resistivity factor is shown in Fig. 26.38.


A COMPARABLE CLEAN SAND I

4 !,

1.0 IO 100

R,-WATER RESISTIVITY, OHM-METERS

Fig. 26.39-Effect of Interstitial clay on formation resistivity factors.

Effect of Conductive Solids

Investigations by Wyllie4’ Indicate that clays contribute substantially to the conductivity of a rock when the rock is saturated with a low-conductivity water. The effect of water resistivity on the formation resistivity factor for sands containing clay minerals is shown in Fig. 26.39. The formation resistivity factor for a comparable clean (clay-free) sand is a constant. The formation resistivity factor for the clayey sand increases with decreasing water resistivity and approaches a constant value at a

water resistivity of about 0.1 Q-m. Wyllie proposed that the observed effect of clay minerals was similar to having two electric circuits in parallel-the conducting clay minerals and the water-filled pores. Thus,

Ro.\/z 1 1 1 FRO=- and -==++ FRR,,, \ . (60)

R, Roslr R,./ where

FRO = apparent formation resistivity factor, Rosh = resistivity of a shaly sand when 100%

saturated with water of resistivity R,,., R,., = resistivity caused by the clay minerals, R,,. = resistivity caused by the distributed water,

and FR = true formation resistivity factor of the rock

(i.e., the constant value of formation factor approached when the rock contains low-resistivity water).

The data presented in Fig. 26.40 represent graphically the confirmation of the relationship expressed in Eq. 60. The graphs were plotted by deWitte@ from data presented by Hill and Milburn.“3 The plots are linear and are of the general form

1 1 -=m-+b, . . . . . . . . . . . . . . . . . . . (61) Rosh R,i

where m is the slope of the line and h is the intercept. Comparing Eq. 60 with Eq. 61, note that m= ~/FR and b= l/R,.[. The curve labeled Suite 1 No. 40 indicates a clean sand because the line passed through the origin, thus having a zero intercept b= l/R,.,=O. Then l/Rosh =m(l/R,,)=(l/FRR,,), or Ro=F,R,,.. The remaining samples are from shaly sands, which have a finite conductivity of the clay minerals, as indicated by the intercepts of the lines. The linearity of the plots indicates that l/R,, is a constant independent of R,,. This phenomenon may be explained in terms of the ions absorbed on the clay. When the clay is hydrated, the absorbed ions form an ionic conducting path, which is closely bound to the clay. The number of absorbed ions is apparently little changed by the salt concentration of the interstitial water.

Eq. 60 may be rearranged to express the apparent formation resistivity factor in terms of R,., and FRR, .

K O”’ = R,. +R,.,/FR

and

FRY = &I

R,, +(R,.,IF,) ’

As R,,-+O,

I -+ Rw

Fig. 26.40-Water-saturated rock conductivity plotted against water conductivity yields these measurements: (A) Suite 1 No. 40; (X) Suite 1 No. 21; (0) Suite 1 No. 4; (0) Suite 2 No. 13: (II!) Suite 6 No. 2.

RCl lim FRY =-

R,IIFR

=FR.

Therefore, FRY approaches FR as a limit as R, becomes small. This behavior was observed in Fig. 26.39.


Hill and Milbum43 evaluated 450 samples from both sandstone and limestone formations. The formation resistivity factor was determined at a water resistivity of 0.01 R-m, a value at which the apparent formation resistivity factor, FRa, approaches the formation resistivity factor, FR. They designated the formation resistivity factor as FR,O,oI The data were fitted by the method of least squares to yield

F R.0,0,=1.4+-‘.78. . . . . ._ .(62)

This equation conforms to the theory previously discussed. They also fitted the data with K in Eq. 56 restricted to a value of 1. This yielded FR,P,o, =$ -’ 93, which corresponds closely to Archie’s onginal expression F=$ -‘,

In summary, Eqs. 58 (with m=2.0) and 59 have been used widely to represent the relation between formation resistivity factor and porosity. Both equations yield results satisfactory for most engineering purposes. However, we propose that Eq. 62 be considered as more valid because the data were taken to minimize the effect of clays. The selection of a particular relation should be based on independent observations on the formations or formations of interest in a given geologic province.

Resistivity of Partially Water-Saturated Rocks

A rock containing both water and hydrocarbon has a higher resistivity than when fully saturated with water. The resistivity of partially water-saturated rocks has been shown to be a function of the water saturation, S,,. . From theoretical developments, the following generalization may be drawn.

IR=K’S,,/‘, . . . (63)

where 1~ = R,/Ro, the resistivity index; K’ is some function of tortuosity; and n is the saturation exponent.

Archie compiled and correlated experimental data from various sources from which he suggested that the data could be represented by

IR =S,,. G. . . . (64)

Wyllie confirmed the suggested relationship for clean sands but found that the presence of clays [conductive solids) altered the relationship. A comparison of Ar- chic’s relationship and that for a core containing conductive solids is shown in Fig. 26.41. The change in the relationship depends on both the amount of clays and the water resistivity. Therefore. a general correlation for sands containing conductive solids is not available, although dewitte”’ has proposed a method of using Eq. 64 for evaluation of shaly sands.

Use of Electrical Parameters in Characterizing Porous Media

In the section on permeability, the Kozeny equation was developed as follows.

4 k=- F,A,‘7, . . . ..~~~~.... (65)

loo \

60 \

40 I \ I

z 20 2- WITHOUT CONDUCTIVE k ; IO m 56 ii

4

SOLIDS 2

I.01 .02 .04 08 .20 40 .80 WATER SATURATION

Fig. 26.41-Effect of conductive solids on the reslstivity-index- vs.-saturation relationship in Stevens sandstone core.

where k = permeability, C#I = porosity, fraction,

F, = shape factor, A,v = internal surface area/unit PV, and

r = Kozeny tortuosity.

7 has been shown to be a function of FR+i.e., 7= (FR#)-‘, where x ranges between 1 and 2. If the internal surface area is expressed in terms of the mean hydraulic radius, rH, by

A,& . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..(66) rH

the general form of the relationship may be stated as

or

@H) 2 k

=F. (FR)X & . . . . . . . . . . . . . . . . . .._. (67) ~

Eq. 67 perhaps provides an improved basis for the correlation of characteristic physical data of porous media with the electrical formation resistivity factor.

The electrical properties of porous rocks, as discussed in the foregoing sections, form the basis of quantitative evaluation of electrical-logging records. In particular, the Humble relation (Eq. 59) has been used widely by service companies in estimating porosity from measurements made with “contact” resistivity devices such as the Microlog.‘” Eq. 64 forms the basis of interpretation of water saturations from deeper-penetration


resistivity devices such as the conventional resistivity curves of the standard electrical log or from the various “focused” electrical-resistivity devices.

Improvements in the statistical correlations of electrical properties of rocks will improve the results of such analyses.

Nomenclature A = cross-sectional area

A., = area of flow represented by a bundle of tubes of permeability k,

A, = internal surface area/unit PV h = constant for a given gas in a given medium c = fluid compressibility C = flow coefficient d = diameter E = voltage drop f = friction factor

F, = shape factor FR = formation resistivity factor

F~ri = apparent formation resistivity factor K = acceleration of gravity h = driving head

I? to = height above free-oil level IT,,~ = height above free-water level

/f, = thickness ofjth layer I = current

IH = resistivity index J = J function, Eq. 48 k = permeability of the medium

k,, = permeability to air k,y = permeability of the medium to a gas com-

pletely filling the pores of the medium kl, = thermal conductivity k, = permeability of one capillary tube kL = permeability of the medium to a single

liquid phase completely filling the pores of the medium

k,,. = permeability to fresh water km = permeability to 500-grain/gal chloride

solution K = constant of proportionality, Eq. 7

K’ = some function of the tortuosity. Eq. 63 K; = Kozeny’s constant

f. = length of flow path or length of the sample L,, = actual length of the flow path L.; = length ofjth layer UI = slope of the curve or cementation factor

n/ - ~ number of tubes of radius r, p = mean flowing pressure

A~YI = pressure loss over length L ~1~ = base pressure

Pe = pressure at the external boundary p,\. = pressure at the wellborc P,. = capillary pressure

Pc.,l, = capillary pressure. laboratory conditions P,.,,, = capillary pressure of mercury

pc~.i,,y = capillary pressure at height above free-oil surface, using oil and gas

P c .R = capillary pressure, reservoir conditions P,.,,. = capillary pressure of water

P c I,‘(, = capillary pressure at a given height above the free-water surface determined by using water and gas

P,,,,,, = capillary pressure at a given height above the free-water surface, using water and oil

q/, = volume rate of flow at the base pressure 40 = volume rate of flow of oil

q/J = volume rate of flow at the algebraic mean pressure (p, +p,, )/2

qr = total flow rate Q = rate of heat flow r = radius or resistance Y = mean radius

r, = radius at the external boundary TH = hydraulic radius r 1,’ = radius of the wellbore

R,., = resistivity caused by the clay minerals Rn = resistivity of the rock when saturated with

water having a resistivity of R,, Ro,I, = resistivity of a shaly sand when 100%

saturated with water of resistivity R,, s = distance in direction of flow, always

positive lTs = gas saturation SL = total wetting saturation S,, = oil saturation S,,. = water saturation T,f = average flowing temperature AT = temperature drop u., = volume flux across a unit area of the porous

medium in unit time along flow path s UY = volume flux across a unit area of the porous

medium in unit time along flow path x v = fluid velocity

Vh = BV V,, = oil volume VP = PV V, = sand-grain volume

V,,. = water volume w = mass rate of flow

WC.I, = weight of dry core W,.,,. = weight of wet core W,,. = weight of water

z = vertical coordinate, considered positive downward

0 = angle between s and the horizontal 19,. = angle of contact of the interface of two

tluids and the capillary tube Oc.,,,p = water/gas contact angle fI,.,,i, = water/oil contact angle

p = fluid viscosity p = fluid density or resistivity

~1, = fluid density at base pressure P 0 = oil density

u = IFT or conductivity ~I11 = surface tension of mercury


surface tension of water water/gas IFT water/oil IFT Kozeny tortuosity effective rock tortuosity fractional porosity effective porosity potential function

Key Equations in SI Metric Units

q=14.696x IO" k4p I -I+)

, . FLL

y=92.349x IO” MP, -P ,,.I c1 ]n r,lr,, ,

T/,kA(p, 2 -pz ‘) qb=23.1454x104 _

TfW<&P/, , .

4)) = I .4554 x 106 T/,vWp, * -P,, *)

ii.fzj~~pj, In rclr,, ’ ” ” ”

(26)

(28)

where q is in m”/d, k is in pm2, A is in m2, p is in kPa, p is in Pa’s, L is in m, I7 is in m, r is in m, and T is in “C.

References I.

2.

3 4:

5.

6.

7.

8.

9.

IO.

Il.

I?.

13

14.

15.

Fraser, H.J. and Graton, L.C : “Systematic Packing of Sphere-With Particular Relation to Porosity and Permeability,” J. G4. (Nov.-Dec. 1935) 785-909. Tickell. F.G., Mechem. O.E. and McCurdy, R.C.: “Some Studies on the Porosity and Permeability of Rocks,” Trmv.. AIME (1933) 103. 250-60. Core Laboratories Inc.. Dallas, TX. Nutting, P.G.: “Physical Analysis of Oil Sands.” Buli., AAPG, (1930) 14. 1337-49. Russell, W.L.: “A Quick Method for Determining Porosity,” B!i//ril.. AAPG (1926) 10, 931-38. Stevens, A.B.: A Luhoruror~ Munuulfor Perrdrum Eqinrerirzg 308. Texas A&M U., College Station, TX (1954). Washburn, E.W. and Bunting. E.N.: “Determination of Porosity by the Method of Gas Expansion.” J. Ant. Ccram. SW, 5. 48. Beeson. C.M.: “The Kobe Porosimeter and Oilwell Research Porosimeter.” Trms., AlME (1950) 189. 313-18. Dotson. B.J. et ni.: “Pomsity Measurement Comparison by Five Laboratories.‘. Trcins., AIME (1951) 192. 341-46. Kelton. F.C.: “Analysis of Fractured Limestone Cores,” Truns.. AIME (1950) 189. 225-34. Krumbein. W.C. and Sloss. L.L.: .Srrcui~rciph~ and .Scdiww~tu- rim, Appleton-CenturyCrofts Inc., New York City (1951) 218. Geertsma. J.: “Effect of Fluid Pressure Decline on Volumetric Changes of Porous Rocks,” Truns.. AIME (19.57) 210. 33 1 and 339. Hall. H.N.: “Compressibility of Reservoir Rocks.” Trmn.c., AIME (1953) 198. 309. Fatt. I.: “Pore Volume Compressibilities of Sandstone Reservoir Rocks,” Trun;. , AIME (1958) 213. 362-64 Hammerlindl, D.J.: “Predicting Gas Reservoirs in Abnormally Pressured Reservoirs.” paper SPE 3479 presented at the 1971 SPE Annual Meeting, New Orleans. Oct. 3-6.

16.

17.

18.

19.

20.

21.

22.

23.

24

25.

26.

21.

28.

29.

30.

31.

32.

33.

34.

35.

36.

37.

38.

39.

40.

41.

42.

43.

26-33

Newman. G.H.: “PowVolume Comprcshihllity ofConsol~datet1. Friable. and Unconwlidatcd Reservoir Rock\ Under Hydrostutlc Loading.” J. PH. T~I. (Feb. 1973) 129-34. Van der Knaap. W.: “Nonlinear Behavior of Elastic Porou\ Media.” Trcrns.. AIME (1959) 216. 179-87 Krug. J.A.: “The Effect of Stress on the Petrophyhical Propcrtics of Some Sandstones.” PhD dissertation (T- 1964). Colorado School of Mines. Golden. CO (1977). Graves, R.M.: “Biaxial Acoustic and Static Measurement ol Rock Elastic Properties.” PhD dissertation (T-2596). Colorado School of Mines, Golden. CO (1982). Lachance. D.P. and Anderson. M.A.: “Comparison of Uniaxial Strain and Hydrostatic Stress Pore-Volume Compre%\ibilitic\ in the Nugget Sandstone.” paper SPE 11971 prcscntcd at the 1083 SPE Annual Technical Conference and Exhibition. Sdn Francirco. Oct. S-8.

Hubben. M.K.: “Entrapment of Petroleum Under Hydrodynamic Conditions.” Bull., AAPG (Aug. 1953) 1954-2026 Croft, H. 0. : Thrnnr)fl~~~crt~li~.~, Fluid NON (UK/ Hotrr Trrr!wri.c- \io/l, McGraw-Hill Book Company Inc.. New York City (1938) 129. Klinkenberg. L-J.: “The Permeability of Porou\ Media to Liquids and Gates.” Drill. crrtd Prod. Pnrc.. API. Dallas ( lY4 1 ) 200- 13.

Johnston. N. and Beeson. C.M.: “Water Pemrcability of Rcxr- voir Sands,” Trw~s.. AIME (1945) 160. 43-S? Fatt. I. and Davis. D.H.: “Reduction in Permeability waith Ovcr- burden Pressure,” Trtrm.. AIME (19.52) 195. 329. Wyllie. M.R.J. and Spangler. M.B.: “Application of Electrical Resistivity Measurements to Problem of Fluid Flow in Porow Media,” Bull., AAPG (Feb. 19.52) 359-403. Kennedy. H.T., VanMeter, O.E., and Jones. R.G.: “Saturation Determination of Rotary Cores.” P<,f. Efr~r. (Jan. 1954) B.52-B.64 Gates, G.L., Morris, F.C., and Caraway. W.H.: f$cr oj’ Oil- Bose Drilhg Nuid Fihrurc on Aucr/~sis of Corr v ,frm Sour/~ C&s Lewe, Crdijimtiu urld Rcmgc/~. C&r&> /G/d, technical report, Contract No. RI 4716. USBM (Aug. 1950). Welge. H.J. and Bruce, W.A : “The Restored-state Method for Determination of Oil m Place and Connate Water.” Drill. crrrrl Prod Prm.. API, Dallas (1947) 166-74 Slobod. R.L., Chambers. A.. and Prehn. W.L. Jr.: “USC of Ccn- trifuge for Determining Connate Water. Residual Oil, and Capillary Pressure Curves of Small Core Samples.” Tram.. AIME (1951) 192. 127-34. Brown. H.W.: “Capillary Pressure Investigations.” Trms., AIME (1951) 192, 67-74. Owen, J.D.: “Well Logging Study-Quinduno Field. Roberls County, Texas,” paper 593-G presented at the 195.5 AIME For- mation Evaluation Symposium, Houston. Oct. 27-28. Leverett, M.C.: “Capillary Behawor in Porous Solids,” Trmv., AIME (1941) 142, 152-68. Wright. H.T. Jr. and Wooddy. L.D. Jr.: “Formation Evaluation of the Borregas and Seeligson Fields, Brooks and Jim Wells Cow- ties, Texas.” paper 591-G presented at the 1955 AIME FormatIon Evaluation Symposium. Houston. Oct. 27-28. Cornell, D. and Katz. D.L.: “Flow of Gases Through Con- solidated Porous Media.” hi. cd Etzgr. Chew (Oct. 1953) 45. Wyllie, M.R.J. and Gardner, G.H.F.: “The Generalized Kozeny Carman Equation.” World Oil (March and April 1958). Winsauer. W.O. PI ol.: “Rewtiwty of Brme-Saturated Sands in Relation to Pore Geometry.” Bull.. AAPG (Feb. 1952) 253-77. Rust. C.F.: “Electrical Resistivity Measurements on Reservoir Rock Samples by the Two-Electrode and Four-Electrode Methods,” Trms., AIME (1952) 195, 2 17-24. Tlxier. M.P.: “Porosity Index in Limestone from Electrical Logs-Part I ,” Odrmci Cm .I. (Nov. 15. 1951) 140. Wyllie, M.R.J. and Gregory. A.R.: “Formation Factors of Un- consolidated Porous Media: Influence of Particle Shape and Effect of Cementation,” Truns.. AIME (1953) 198, 103-09. dewitte. A.J.: “Saturation and Porosity from Electrical Logs in Shaly Sands-Part I,” Oil and GNS J. (March 4. 1957) 89. Hill, H.J. and Mdhum. J.D.: “Effect of Clay and Water Salinity on Electrochemical Behavior of Reservoir Rocks.” Tmm., AIME (1956) 207. 65-72.

Chapter 27 Typical Core Analysis of Different Formations R.E. Jenkins. cw Lahoracorie\ ~nc.’

Introduction The early-day analysis of cores was largely an art, a qualitative matter of odors and tastes, sucking on the rock, and visual examination. The science of core analysis has evolved from such early beginnings, using developments in instrumental methods of chemical and physical analyses as they became available. Electron microscopy, mass spectrometry, gas chromatography, high-frequency phase analysis, acoustic wave train analysis, and nuclear magnetic relaxation analysis are among the tools being used in the more sophisticated core testing today.

Many other techniques are available now to assist the geologist and petroleum engineer in the completion of wells and the evaluation and operation of oil and gas reservoirs, but core analysis still remains the basic tool for obtaining reliable information on the rock material penetrated. Study of representative core samples of an oil- or gas-bearing formation provides the only means for direct measurement of many important properties of the formation.

The minimum basic measurements made on cores generally comprise determination of porosity at no confining pressure, permeability at low confining pressure, and residual fluid saturations. Various supplementary routine tests such as chloride, oil gravity, directional permeability, grain density, and grain size frequently are made as an aid in interpretation and evaluation. These data are the subject of this chapter.

Porosity Porosity is a measure of the void space or storage capacity of a reservoir material. Normally it is expressed as a percentage of bulk volume (%BV). Porosity may be determined by measurement of any two of the three quantities-grain volume, void volume, and bulk volume. Various generally acceptable methods and techniques for determining porosity are used by different laboratories. The void volume may be determined on a previously cleaned and dried sample by extraction or gas or air con-

tent, by saturation with a liquid, or by calculation from Boyle’s law upon compression or expansion of gas in the pore spaces of the sample. The other widely used method involves the separate determination of the gas, oil, and water contents of the sample, and the summation of these three values to obtain PV.

Most of the porosity data reported in the tables here were determined by the summation-of-fluids method. Comparison of porosity values obtained on samples from several thousand feet of core where measurements were made by both the summation-of-j&ids method and by a Boyle’s law method showed agreements, in general, of 0.1 to 0.5% porosity. Extensive checks of porosity values by resaturation with brine have shown values slightly lower than by the other procedures, indicating approximately 98 to 99% resaturation.

Permeability The permeability of a formation sample is a measure of its ability to transmit fluid. The permeability determination involves measurement of the rate of flow of a fluid of known viscosity through a shaped sample under a measured pressure differential. Air is the fluid normally used because of its convenience, availability, and relative in- ertness toward the core material. For many years, air- permeability measurements were corrected to an “equivalent” liquid permeability by use of the well-known Klinkenberg corrections. The permeability values reported in Tables 27.1 through 27.11 have been corrected to the “equivalent” liquid-permeability values, except as noted in the next paragraph.

In the whole-core orfill-diameter core analysis procedures, permeability is frequently measured in two horizontal directions. One measurement is made in the direction of the major fracture planes and is reported as k. This value indicates the effectiveness of the fractures as flow channels. The core sample is then rotated 90” and the second measurement is made in a direction of flow perpendicular to the direction of the first measurement. This

(continued on page 9)


TABLE 27.1 -ARKANSAS

Fluid Production

Range of Production

Deoth

Average Range of Production Production

Deoth Thickness

Average Production Thickness

(fu 15 20 10 11 17 11 20 12 11 16 16 13 10 15

Range of Permeability

(md) 1.6 to 8,900 0.6 to 4,620 1.6 to 5,550 1.2 to 4,645

Formation

Blossom C/O’ 2,190 to 2,655 2,422 3 to 28 Cotton Valley Cl0 5,530 to 8,020 6,774 4 to 79 Glen Rose 0 2,470 to 3,835 3,052 5 to 15 Graves Cl0 2.400 to 2.725 2.564 2 to 26 How Meakin

3: 145 to 31245 G/:0 l 2,270 to 2,605

31195 12 to 33 2,485 2 to 20

6.5 to 51730 3.0 to 6,525 0.7 to 6,930

5 to 13,700 0.1 to 698 0.1 to 980 0.1 to 12,600

Nacatoch Cl0 1,610 to 2,392 2,000 6 to 45 Paluxy 0 2,850 to 4,690 3,868 6 to 17 Pettit 0 4.010 to 5.855 4.933 4to19 Rodessa+ Smackover*

5:990 to 6;120 Gl:lO 6.340 to 9,330

61050 8 to 52 8,260 2 to 74

Tokio c/o 2,324 to 2,955 2,640 2to 19 Travis Peak c/o 2,695 to 5,185 3,275 3 to 25 Tuscaloosa Cl0 3,020 to 3,140 3,080 4 to 25

0.5 to 11,500 0.4 to 6,040 0.4 to 3,760

‘Indicates fluid Droduced: G = aas: C = condensate. 0 = oil “Specific zone not identified k&ally

‘Includes data from Mitchell and Glcyd zones. ‘Includes data from Smackover Lime and Reynolds zones

TABLE 27.2-EAST TEXAS AREA

Range of Production

Depth ffB


fmd)


Depth Thickness (W (ft)

7,138 3 to 24 8,458 7 to 59 2,356 5 to 8 5,897 3 to 35 6.020 3 to 52 5;928 3to 16 6,010 3 to 43 3,801 4 to 12

743 2 to 21 5.413 1:434

7 to 46 5 to 20

7,173 2 to 23 6,765 4 to 42 4.892 3 to 25 6,551 2 to 30 1,517 6 to 22 4,373 2 to 45 6,261 4 to 33


(fi) 11 33

7 19 12 9

21 8

12 27 13 11 17 12 11 13 14 17

Fluid Production

c/o C 0

Cl0 GICIO Cl0 0 0 0

: G/C/O

Formation

Bacon Cotton Vallev

6,665 to 7,961 8,448 to 8,647 2,330 to 2,374 4,612 to 6,971 5,976 to 6,082 4,799 to 7,666 5,941 to 6,095 3,742 to 3,859

479 to 1,091

0.1 to 2,040 0.1 to 352 0.1 to 4.6 Fredericksburg

Gloyd Henderson Hill Mitchell Mooringsport Nacatoch’ Paluxy Pecan Gap

0.1 to 560 0.1 to 490 0.1 to 467 0.1 to 487 0.4 to 55 1.9 to 4,270 0.1 to 9,600 0.5 to 55 0.1 to 3,670 0.1 to 1,180 0.1 to 9,460 0.1 to 180 0.3 to 470 0.1 to 13,840 0.1 to 610

4,159 to 7,867 1,233 to 1,636 5.967 to 8.379 4,790 to 81756 3,940 to 5,844 5,909 to 8,292

981 to 2,054 2,753 to 5,993 5,446 to 7,075

Pettit’* Rodessa Sub-Clarksvillet Travis Peak* Wolfe Citv Woodbine Young

Cl0 0

Cl0

C410 C

‘Small amount of Navarro data combined with Nacatoch “Data for Pinsburg, Potter, and upper Pettit combined wlfh Peltil

‘Small amount of Eagleford data combined with subClarksvW *Data for Page cambmed with Travis Peak.

TYPICAL CORE ANALYSIS OF DIFFERENT FORMATIONS 27-3

TABLE 27.1- -ARKANSAS (continued)

Range of Calculated Interstitial-

Water Saturation

VW 24 to 55 21 to 43 28 to 50 19 to 34 26 to 34 24 to 63 41 to 70 28 to 43 25 to 44 25 to 38 21 to 50 17 to 43 16 to 48 31 to 63

Average Calculated Interstitial-

Water Saturation

w 32 35 36 30 27 43 54 35 30 31 31 27 36 45

Range of Oil

Average Oil

Saturation (W 20.1 13.1 21 .o 16.8 19.9 12.9

Average Range of Permeability Porosity

(md) w 1,685 15.3 to 40

333 11.3 to 34 732 17.3 to 38

1.380 9.8 to 40

Average Porosity

w 32.4 20.3 23.4 34.9 30.9 31.8 30.5 26.9 15.4 16.5 14.2 32.1 24.3 27.3

Saturation w

1.2 to 36 0.9 to 37 4.0 to 52 0.3 to 29 2.6 to 56 0.6 to 43

1;975 1,150

14.4 to 41 17.1 to 40

142 9.9 to 41 1,213 15.1 to 32

61 6.2 to 28

0.2 to 52 4.9 7.5 to 49 21.2 9.1 to 29 12.7 0.7 to 26 14.8 0.7 to 41 12.8

135 5.1 to 28 850 1.1 to 34

2,100 13.6 to 42 460 9.4 to 36 506 15.6 to 39

0.9 to 57 25.6 0.5 to 36 14.3 0.3 to 53 14.0

TABLE 27.2-EAST TEXAS AREA (continued)


Water Saturation

toa 9 to 22

13 to 32 35 to 43 16 to 45 21 lo 44 23 to 47


Water Saturation

to4 16 25 41 31 27 33 29 40 41 30 46 23 23 33 28 46 35 21

Average Oil

Saturation Wol

Range of Oil

Saturation W)

2.7 to 20.6 1.1 to 11.6 3.3 to 39.0

trace to 24.3 0.8 to 23.3 0.9 to 26.7

Average Porosity

Pi8

Range of Porosity

w 1.5 to 24.3 6.9 to 17.7

11.9 to 32.6 8.0 to 24.0 7.0 to 26.2 6.4 to 32.2

Average Permeability

0-W 113 39

1.2 21 19 70 33

5 467 732

6 65 51

599 42 32

1,185 112

15.2 11.7 23.1 14.9 15.2 15.6

8.6 2.5

20.8 8.2

10.6 12.2

7.2 to 29.0 15.5 1.8 to 25.9 12.5 15 to 47 5.3 to 19.6 14.6 2.8 to 26.6 13.8 29 to 48

13.4 to 40.9 27.1 0.6 to 37.4 14.5 24 to 55 6.3 to 31 .l 21.6 2.2 to 48.7 24.1 22 to 47

16.3 to 38.1 26.8 3.5 to 49.8 12.9 30 to 56 4.5 to 25.8 14.7 0.9 to 31.6 9.8 10 to 35 2.3 to 29.0 14.5 trace to 25.3 5.3 6 to 42 6.2 to 38.0 24.8 1.4 to 34.6 17.9 12 to 60 5.6 to 25.8 15.0 0.1 to 42.8 12.5 17to 38

17.1 t0 38.4 27.9 1.5 to 37.4 15.6 23 to 68 9.7 t0 38.2 25.5 0.7 to 35.7 14.5 14 to 65 4.4 to 29.8 19.7 trace to 4.5 0.8 13 to 27


Formation

Annona Chalk Buckrange Cotton Valley a Eagleford’ Fredericksburg Haynesville Hosston Nacatoch Paluxy PettitC Pine Island d Rodessae Schuler’ Sligog Smackover Travis Peakh Tuscaloosa

Fluid Production

0 c/o

GlClO C

G/C C

Cl0 0

Cl0 c/o 0

G/C/O GICIO

Cl0 Cl0 c/o

GICIO

TABLE 27.3-NORTH LOUISIANA AREA

Range of Average Range of Average Production Production Production Production

Depth Depth Thickness Thickness m (fu vv m

1,362 to 1,594 1,480 15 to 69 42 1,908 to 2,877 2,393 2 to 24 13 3,850 to 9,450 7,450 4 to 37 20 8,376 to 8,417 8,397 9to11 10 6,610 to 9,880 8,220 6 to a 7

10,380 to 10,530 10,420 22 to 59 40 5,420 to 7,565 6,480 5to 15 12 1,223 to 2,176 1,700 6to 12 8 2,195 to 3,240 2,717 2 to 28 16 3,995 to 7,070 5,690 3 to 30 14 4,960 to 5,060 5,010 5to 13 9 3,625 to 5,650 4,860 6 to 52 18 5,500 to 9,190 8,450 4 to 51 19 2,685 to 5,400 4,500 3 to 21 7 9,960 to 10,790 10,360 6 to 55 24 5,890 to 7,900 6,895 7 to 35 18 2,645 to 9,680 5,184 4 to 44 24

iDat. reported where member formatlon of Cotton Valley group not readlfy tdentlflable Data reported as Eutaw in come areas

‘Includes data reported es Pettlt. Upper Petilt, and Mid-Pettit. eometlmes considered the same as Sllgo ‘Sometimes referred to as Woodruff. ; Includes data reported localy for Jeter, HIII. Kllpatrlck, and Fowler zonee

includes data reported focally for Bodcaw, Vaughn, Doris, McFerrin, and Justiss zones. ; Includes data reported as BIrdsong-Owens

Frequently considered the same as Hosston

TABLE 27.4-CALIFORNIA

Formation Area

Range of Average Range of Average Production Production Production Production Range of Average

Fluid Depth Depth Thickness Thickness Permeability Permeability Production (fi) (ft) (ft) (fi) (md) (md)

Eocene, lower San Joaquin 0 Valley a

Miocene Los Angeles 0 Basin and Coastal b

Miocene, upper San Joaquin ValleyC

Los Angeles 0 Basin and Coastal d

Miocene, lower San Joaquin 0 VaIleye

Los Angeles 0 Basin and Coastal’

Oligocene San Joaquin 0 Valleyg Coastal h 0

Pliocene San Joaquin 0 Valley’

Los Angeles 0 Basin and Coastal’

6,820 to 8,263

2,870 to 9,530

1,940 to 7,340

2,520 to 6,860

2,770 to 7,590

3,604 to 5,610

4,589 to 4,717

5,836 to 6,170 2,456 to 3,372

2,050 to 3,450

7,940

5,300

4,210

4,100

5,300

4,430

4,639

6,090 2,730

2,680


W) 0.1 to 2 5 0.1 to 2,430 0.1 to 7,350 3.5 to 3,040 1.6 to 163 0.1 to 235 0.4 to 1,500 27 to 5,900

0.2 to 3,060 0.1 to 587 0.2 to 1,100 0.1 to 2,190 0.1 to 3,180 0.1 to 1,810 0.1 to 6,190 0.1 to 2,920 0.1 to 5,750

-

60 to 450

10 to 1,200

5 to 1,040

30 to 154

20 to 380

-

- 5 to 80

-

aMainiy dala from Gatchell zone %zludes Uooe, and Lowe, Terminal. Umon Paclflc Ford. 237. and Sesnon zonee clnctudes Kernco, Repubhc, and 26R zo”ee. d Includes Jones and Maw zO”eS ; Includes JV. Obese. and Phamdes zones

Manly data from Vaqueros zone z Manly data from Oceanic zone

Mmly data fro Sespe zone lnciudes Sub Mullma and Sub Scaler No 1 and No 2 zones

: Includes Ranger and Tar zone?, O&based data show high oil ?.at”,at,o” [average 61%) and low water ( 3 to 54%. average 15%)

’ O,l-based data show range 27 6 to 52 4 and average of 42.3% not Included I” above 011 Saturation Values

-

165

245

130

76 15 to 4,000 700

134 256 to 1.460 842

- 10 to 2,000

- 20 to 400 33 279 to 9,400

100 25 to 4,500

35 to 2,000

IO to 4.000

4 to 7,500

86 to 5.000

518

300

1,000

1.110

528

107 1,250

1,410


Average Range of Average Gil Oil - Water Permeability Porosity Porosity Saturation Saturation Saturation

b-4 - (O/o) (O/o) - W) (ON to4 0.7

305 135 595

z; 140 447 490

26 285 265 104 156 220 357 706

14.3 to 36.4 26.8 6.0 to 40 22.0 24 to 40 13.4 to 41 31.4 0.7 to 51 22.6 29 to 47 3.5 to 34 13.1 0.0 to 14 3.1 11 to40

12.8 to 28 22.9 1.6 lo 28 4.3 - 12.8 to 23.1 19.9 1.7 to 4.3 2.7 35 to 49 5.5 to 23.1 13.4 1.1 to 14.5 5.1 31 to 41 8.8 to 29 18.6 0.0 to 35 8.6 18 to 37

25.8 to 40 31.4 2.5 to 33 19.5 45 IO 54 9.6 to 39 27.2 0.1 to 48 11 .a 23 lo 55 4.5 to 27 14.3 0.1 to 59 15.6 10 to 43 8.5 to 27 20.6 13.3 to 37 24.1 16to30 5.1 to 34 19.1 0.0 to 31 2.9 21 to 38 3.6 to 27.4 15.0 0.0 to 24 4.8 8 to 51 7.3 to 35 21.1 0.6 to 27 9.8 12 to 47 3.4 to 23 12.9 1.1 to 22 7.2 9 to 47 7.0 to 27 19.4 0.1 to 35 8.6 26 to 38

10.7 to 36 27.6 0.0 to 37 8.5 31 to 61

Range of Average Porosity Porosity

(O/o) w 14 to 26 20.7

15 to 40 28.5 6 to 65

17 to 40 28.2

19.5 to 39 30.8

20 to 38 26.4 4 to 40 19 25 to 80 51 14to67 36 15 to 40 34

21 to 29 24.3 13 to 20 15.8 32 to 67 53 27 to 60 37 34 to 36 35

19 to 34 26.3

15to22 19.5 30 to 36 34.8

24 to 41 35.6

TABLE 27.3-NORTH LOUISIANA AREA (continued)

Range of

Range of Calculated

Average Interstitial-

Range of Oil

Saturation to4

8 to 23

9 to 72

10 to 55

12 to 40

6to 17 7 to 43’

15 to 80


Water Saturation

to4 37 35 24 36

:A 28 47 35 29 22 30 25 31 25 31 43

TABLE 27.4-CALIFORNIA (continued)

Range of Average Range of Average Calculated Calculated

Average Total Total Interstitial- Interstitial- Oil Water Water Water Water Range of Average

Saturation Saturation Saturation Saturation Saturation Gravity Gravity to4 to4 PM W) co4 (OAPI) (OAPI)

14.1 16 to 51 35 15 to 49 35 28 to 34 31

18.6 25 to 77 50 15 to 72 36 15 to 32 26

32k 20 to 6Bk 5ok 12 to 62 30 13 to 34 23

25 22 to 72 44 12 to 61 30 11 to 33 21

22 2 to 60 43 3 to 45 30 37 to 38 38

11.8 19 to 56 46 15 to 52 42 - 25 24.1’ 33 to 84 54 10 to 61 34 18 to 44 24

45 19 to 54 38 10 to 40 21 12 to 23 15


TABLE 27.5-TEXAS GULF COAST-CORPUS CHRISTI AREA’

Formation

Catahoula Frito Jackson Marginulina Oakville Vicksburg Wilcox

Fluid Production

0 Cl0 0 C

SO

Range of Average Production Production

Depth Depth (ft) m

3,600 to 4,800 3,900 1,400 to 9,009 6,100

600 to 5,OQO 3,100 6,500 to 7,309 7,800 2,400 to 3,100 2,750 3,000 to 9,000 6,280 6,000 to 8,000 7,200 1,800 to 4,000 3,BOo

Range of Average Production Production Thickness Thickness

(fo m 1 to 18 8 3 to 57 13 2 to 23 9 5to 10 7 5 to 35 22 4 to 38 12

30 to 120 60 3 to 21 7

Range of Average Permeability Permeability

(md) (md) 45 to 2,500 670

5 to 9,000 460 5 to 2,900 350 7 to 300 75

25 to 1,800 4 to 2,900 z 1 to 380 50 6 to 1,900 390

‘Includes counties in Texas Railroad Commission Dist. 4’ Jim Wells. San Patricia, Webb, Brooks, Nueces, Jim Hogg. Hidalgo, W~llacy, Starr. Aransas, and Ouval.

TABLE 27.6-TEXAS GULF COAST-HOUSTON AREA

Fluid


Depth Depth Thickness Thickness Range of Average

Permeability Permeability Formation

Frio

Marginulina

Miocene

Vicksburg

Woodbine Yegua

Production

C 0 C

: 0 C 0 C

: G/C 0

4,000 to 11,500 4,600 to 11,200 7,100 to 8,300 4,700 to 6,000 2,900 to 6,000 2,400 to 8,500 7,400 to 8,500 6,900 to 8,200 5,800 to 11,500 2,300 to 10,200 4,100 to 4,400 4,400 to 8,700 3,700 to 9,700

(fb 8,400 7,800 7,800 5,400 4,000 3,700 8,100 7,400 9,100 7,900 4,300 6,800 6,600

(W uu 2 to 50 12.3 2 to 34 10.4 4 to 28 17.5 4 to 10 5.7 3 to a 5.5 2to 16 7.2 1 to 6 2.0 3 to 18 9.3 5 to 94 19.1 3 to 29 10.0 6 to 13 8.2 3 to 63 11.0 2 to 59 8.5

TABLE 27.7-LOUISIANA GULF COAST


Fluid Depth Depth Thickness Thickness Formation Production (fi) (fi) (fi) (fi)

Miocene : 5,208 to 14,900 11,200 3 to 98 20.2 2,700 to 12,700 9,000 3 to 32 11.0

Oligocene C 7,300 to 14,600 9,800 2 to 80 14.6 0 6,700 to 12,000 9,400 2 to 39 8.3

Tuscaloosa G/C 17,533 to 18,906 17,742 15 to 94 61

18 to 9,200 33 to 9,900

308 to 3,870 355 to 1,210 124 lo 13,100 71 to 7,660 50 to 105

190 to 1,510 3.0 to 1,880 9.0 to 2,460 14 to 680 24 to 5,040 23 lo 4,890


(md) 36 to 6,180 45 to 9,470 18 to 5,730 64 to 5,410

1 to 2,000

(md) 810

1.100 2;340

490 2,970 2,140

86 626

96 195 366 750 903


Imdt

1,010 1,630

920 1,410

139

‘Water salurations from logs


TABLE 27.5-TEXAS GULF COAST-CORPUS CHRISTI AREA (continued)


Water Saturation

(ON 30 to 44 20 to 59 21 to 70 20 to 40 32 to 48 26 to 54 22 to 65 14 to 48


Water Saturation

tow 36 34 45 34

i;t

Range of Oil

Average Oil

Saturation (%I 14 13 15 2

18 7

Range of Porosity

I%1

Average Porosity

Range of Gravity (‘=API)

23 to 30 23 to 40 22 to 46 55 to 68

Average Gravity (OAPI)

29 41 37 60

fs5 58 32

w 30 27 27

W) 1 to 30 2 to 38 3 to 32 1 to 4 9 to 30 1 to 17 0 to IO 4 to 40

17 to 36 11 to 37 16 to 38 14 to 30 24 21 to 35 28 23 to 26

37 to 65 53 to 63 20 to 40

14 to 32 24 15 to 25 19 22 to 38 29 17

TABLE 27.6-TEXAS GULF COAST-HOUSTON AREA (continued)

Range of Average Range of Average

Calculated Calculated Range of Average Total

Oil Oil Water Saturation Saturation Saturation

VW (04 P4 0.1 to 6.0 1 .o 34 to 72 4.6 to 41.2 13.5 24 to 79 0.2 to 0.8 0.5 33 to 61 8.1 to 21.8 15.3 48 to 68 0.2 to 1.5 0.5 55 to 73

11 .o to 29.0 16.6 45 to 69 0.0 to 1.5 0.2 66 to 76

14.4 to 20.3 15.3 45 lo 55 0.2 to 10.0 1.5 27 lo 62

Total Interstitial- Interstitial- Water Water Water

Saturation Saturation Saturation w w (%I 54 20 to 63 34 52 12 to 61 33 46 14 to 31 21 59 25 to 47 36

23 to 53 :: 21 to 55 3”: 74 53 to 61 56 53 26 to 36 35 46 20 to 54 30

Range of Average Porosity Porosity

Range of Average Gravity Gravity (OAPI) (“API)

25 to 42 36

26

25

35

34 27

37

(Oh) 18.3 to 38.4 21.8 to 37.1 35.0 to 37.0 20.5 to 37.3 28.6 to 37.6 23.5 to 38.1 26.5 to 31.0 29.5 to 31.8 14.5 to 27.4 16.2 to 34.0

w 28.6 29.8 35.9 32.6 33.2 35.2 27.1 30.4 19.6 21.9 25.5 30.7 31.6

25 to 30

21 to 34

22 to 37

19 to 42 26 to 28

30 to 46

4.6 to 20.5 9.7 32 to 72 47 20 to 50 10.7 to 27.4 20.1 34.4 to 72.7 46 24 to 59 iz 0.1 to 15.5 1.2 26 lo 74 57 17 to 59 33 3.5 to 21.8 11.4 31 to 73 57 17 to 53 34

23.5 to 26.7 23.4 to 37.8 22.9 to 30.5

TABLE 27.7-LOUISIANA GULF COAST (continued)

Range of Average Calculated Interstitial-

Water Range of Average Saturation Gravity Gravity

(“w (OAPI) (=‘API) 35 - - 32 25 to 42 36 32 - 35 29 to 44 38 - 40 to 53 47

Range of Average Range of Average Cal&ated

Total Total Interstitial- Average oil Oil- Water Water Water Porosity Saturation Saturation Saturation Saturation Saturation

w (Oh) w W) w rw 27.3 0.1 to 4.7 1.5 37 to 79 53 20 to 74

Range of Porosity

Pw 15.7 to 37.6 18.3 to 39.0 16.7 to 37.6 22.1 to 36.2

5 to 29

30.0 6.5 to 26.9 14.3 30 to 72 51 18to50 27.7 0.5 to 8.9 2.3 33 to 71 51 19 to 57 29.0 5.2 to 20.0 11.1 34 to 70 23 to 60 18 26’ to 44’ - 36 to 60 55

27-8 PETROLEUM ENGINEERING HANDl3OOK

TABLE 27.8-COMPARATIVE DATA-SIDEWALL (S.W.) VS. CONVENTIONAL (CONV.) ANALYSIS, TEXAS AND LOUISIANA GULF COAST AREAS

Formation Area

Average Average Fluid Type Depth Permeability

Production Analysis (ft) W) Frio Houston

Corpus Christi

Yegua (includes Cockfield)

Louisiana

Houston

Corpus Christi

Miocene (includes Catahoula)

Louisiana

Corpus Christi

C

0

C

0

C

0

C

0

C

0

C

0

C

0

SW. 8,945 Cow. 9,037 SW. 7.174 Conv. 8.622 S.W. 4:902 Conv. 6,789 S.W. 5,456 Conv. 6,399 SW. 8.148 Conv. $826 S.W. 8,276 Conv. 8,415 S.W. 7,240 Conv. 7,693 SW. 7,369

Conv. 7,099 SW. 3,861 Conv. 4,194 SW. 2,824 Conv. 3,625 S.W. 10,664 Conv. 11,500 S.W. 8,996 Conv. 10,171 SW. 4,286 Conv. 4,040 S.W. 4,504 Conv. 4,383

second value is normally reported as kw , and it is usually representative of the matrix permeability. Values for kw are reported in the following tables for formations that are normally subjected to the whole-core or full-diameter core analysis procedures. These values are not corrected to “equivalent” liquid-permeability values.

Liquid Saturations In the coring process, the core is exposed to the drilling fluid at a pressure greater than formation pressure. If the core contains oil or gas, some portion of this is flushed out and replaced by the drilling-fluid filtrate. As the core is brought to the surface and the external pressure is reduced, the expansion of free gas or dissolved gas expels both oil and water from the core. As a result, the pore spaces of the cores recovered at the surface contain free gas, water, and oil if oil is present in situ. The oil and water contents normally are called “residual liquids.”

The residual oil and water contents of core samples normally are determined by retorting, vacuum distillation, or solvent extraction and distillation. The oil and water contents are converted to oil and water saturations as percentages of PV. The oil and water saturation values reported in these tables represent data obtained by the retorting or the vacuum distillation procedures.

The water content of the core as recovered is generally called ’ ‘tofal wafer, ’ ’ and it may include some drilling- fluid filtrate or invasion water. The water saturation actually existing at a given interval in a reservoir may be spoken of as the connate water or interstitial water. This interstitial-water saturation value, as reported in the ta-

62 813 317

1,895 238

1,496 681 641

75 235 176 791 147 277 302 603 119 558 634 576 312 748 327

1,300 180 578 346 867

Average Porosity

to4 27.5 26.7 30.8 27.7 27.2 26.5 29.5 28.5 27.3 26.8 27.1 28.7 27.9 29.7 29.9 31.6 58 26.8 68 31 .a 65 33.3 53 31 .a 57 28.2 63 27.4 52 28.2 62 26.6 49 28.5 69 29.0 61 30.4 60 29.8 53

Average Oil Saturation

(% pore space)

0.7 0.7

14.6 14.6 0.8 1.1

19.5 16.3 4.2 1.9

10.0 7.9 0.2 0.7

10.5 11.7 3.2 1.7

20.9 19.9 2.5 2.1

10.1 14.8 0.5 0.7

17.7 20.0

Average Total Water Saturation (O/o pore space)

64 49 56 47 64 53 53 51 69

Et 56 62 55 59

bles, was determined in some cases by an empirical correlation factor applied to the total water value and in some cases by the use of capillary-pressure data for the specific reservoirs.

The API oil gravity values reported normally were measured on the oil recovered in the retorting or vacuum- distillation procedures. Comparison of gravity values obtained in oil recovered from cores with values obtained on produced or drillstem test (DST) oil indicates general agreement to within f2” API.

The liquid saturation data presented in the tables are from formations interpreted to be hydrocarbon-productive to some degree. In some cases, it was feasible to make a distinction between gas-, condensate-, and oil-productive zone characteristics. Table 27.9 shows core analysis data for zones identified as “transition” zones. These represent intervals or zones where an appreciable water cut is encountered during the life of a field. Such transition zones are present in many other areas and fields, but the available data did not permit a similar breakdown. It should be pointed out that the relative average depths reported for the gas-condensate, oil, and transition zones do not contradict the basic premises that gas overlies oil and that oil overlies water. The condensate-producing zones in the major formations in the U.S. gulf coast area, as presented in Tables 27.6 and 27.7, frequently are found at greater depths than are the oil-producing zones of the same formations. In a similar manner, the gas, oil, and transition zones shown in Table 27.9 for the extensive geologic groups and formations in the Oklahoma-Kansas area are found at different subsurface depths in different parts of the area.


Percussion Sidewall Core Data Percussion sidewall sampling is used extensively in the U.S. gulf coast area, and in other areas where productive intervals are encountered in relatively soft formations and where this type of coring has been found satisfactory. The limited size of the individual samples has made it necessary to develop special procedures for handling

I nn.%+c...tl- T.6 tl.m.‘,

names were selected in an effort to represent generally recognized nomenclature over large areas rather than local terminology. Some important producing formations are not included because of the lack of sufficient data at this time or because of their proprietary nature.

and measuring the prope&es and fluio LvIIIGIIIJ oI I1lLJti EQ~~IPO A Im the novoussion-s~pling technic--- --’ rL-

:o a small distance fron

Data From Non-U.S. Areas The data from non-U.S. areas generally are lacking in pore liquid saturation values because of the formaTion evaluation practices in general use. The small quantity of data reported is a result of the problems of data being released. Data from Australia are presented in Table 27.13. Most of the Canadian data (Table 27.14) were provided by the Energy Resources Conservation Board of Alberta. The Middle East data are presented in Table 27.15. The North Sea data (Table 27.16) were published in the European Continental Shelf Guide. ’ Venezuela data presented in Table 27.17 were provided by Petrole- um de Venezuela S.A.

-“.ynuu. NUV, “LI yvL” 1°C anu UK

limitation of sampling 1 I the walls of the wellbore frequently result in questions of the degree to which sidewall core analysis data compare with data obtained on conventional wireline or diamond cores. Ta- ble 27.8 summarizes a study of core analysis results from more than 5,300 samples where approximately half were obtained by percussion-type sidewall sampling and the other half were obtained by conventional coring procedures.

Data From U.S. Areas Reference Data from areas in the U.S. including Alaska, are presented in Tables 27.1 through 27.12. The formation and zone

I. European Continenfd ShelfGuide, Oilfield Publications Ltd., Led- bury, Herefordshire, England (1982).

27.10 PETROLEUM ENGINEERING HANDBOOK

TABLE 27.9-OKLAHOMA-KANSAS AREA*

FormatIon Arbuckle

AtokaC

Bartlesville

Bois D’Arc

Booth

Burgess

First Brom!ded

Second Bromide”

Burbank

Chester

Cleveland ’

Deese 9

Hoover

Hoxbar

Hut-don

Lansing

Layton

Marmaton Misner

Mississippi Chat

Mississippi Lime

McLish

FluId ProductIon

G

To” G 0 T

: T ci 0

: T

2 G 0 T G 0 T 0 T G 0

L 0

a 0

E T

: T 0 T 0

a 0 T 0 G 0 T

E

L 0 T

Range of ProductIon

Depth IfU

2,700 to 5,900 500 to 6,900 600 to 11.600

3,700 to 3,800 500 to 4,500 300 to 3,700 700 to 7,400 200 to 5,700 500 to 2,600

4,800 to 5,100 3.700 to 7,800 2,600 lo 3,200 1,000 lo 3.800 2,700 lo 3,300

300 to 2,800 6,800 to 7,600 3,700 to 13,800 6,000 to 13,200 6,900 lo 16,200 4,500 to 11,200 4,400 to 13,300 1,300 to 4,500 2,800 to 3,700 4,200 to 6,700 4,700 to 6,700 4,800 lo 6,100 2,200 to 5,700

300 to 6,400 1,900 to 3,900 4,300 to 11,800

600 to 10,000 2,200 to 6,800 1,800 to 2.100 1,900 to 2,000 3,800 IO 8,800 1,000 to 10,300 2,900 to 3,000 1,800 to 9,600 2,500 to 8,700 1,900 to 5,800

- 700 to 6,100 500 to 6,300

1,800 to 5,700 4,300 to 4,600

8,100 2,600 to 6,500 4,900 to 6,200 1,800 to 5,100

800 to 5,200 1,200 to 5,200

900 to 8,800 600 to 6.600 400 to 7,200

3,600 to 17,000

Average Production

Depth (fU

4,500 3,500 3,600 3,700 2,600 2,100 2,600 1,500 1,200 5,000 6,500 2,900 2,600 3,000 1,600 1,800 7,200 8,600

11,500 12,800 9,000 9,700 2,800 3,000 5,700 5,700 5,700 3,500 3,200 3,100 6,500 5,200 4,000 2,000 2,000 6,300 4,200 3,000 4,600 4,900 3,800 3,300 3,900 2,900 3,200 4,400 8,100 4,300 6,000 4,000 3,100 3,900 4,600 4,100 4,000

10,100 1,600 to 11,200 8.100

Range oi ProductIon Thickness

(ft) 5.0 to 37 1 .O to 65.5 2.0 to 33 1 .O to 9.0 3.0 to 16 2.0 to to 1.5 to 42 1 .O to 72

4 to 40 4 to 48

2.3 to 50 5 to 8 2 lo 26.5 4 to 5

2.5 lo 9 3.0 10 19.5 2.0 lo 82 15 to 161.3 20 to 53.6

3.0 to 69 5 to 44.5 3 to 48 31019 2 to 45 2 to 23 4 to 20.5 2to17 1 to 70 3 to 22 5 to 55 2 to 60.3 4 to 49 3 to 37 2to17 9to 11 2 to 63 3to13 2 to 77.3 2 to 73 3 to 16.2

- 410 18 1 to 57 3 to 15.5

1.5 to 7.5 3to 14 2 to 56.5 8 to 21 2 to 34.4 2 to 48.1 1 to 43 3 to 27.1

1.5 to 95.3 4 to 70.1

14to58 3 to 42

Average ProductIon Thickness

m 18.3 11.8 14.3 4.0 7.8 6.5

11.4 14.0 14.5 19.0 12.5

6.5 8.8 4.5

20 5.8

11.3 18.7 65.1 37.9 16.2 18.4 17.3 9.1

10.9 8.6

10.0 9.0

13.4 7.7

19.3 11.7 16.6 11.9

8.4 10.0 14.4 9.3

14.0 14.7 6.5

22.0 9.3

10.3 7.4 4.7 8.5

10.6 15.8 16.1 12.2 10.9 13.3 12.0 17.4 35.3 12.2

Range of Average Permeablllty Permeablllty

(mdi (md) 3.2 to 544 131 0.2 to 1,530 140 0.1 to 354 57 1.3 to 609 174 0.3 to 920 144

9 to 166 67.3 0.2 to 36 10.4 0.2 to 537 32.7 0.1 to 83 18.2 0.1 to 43 24.4 0.3 to 664 36.0 1.4 10 6.6 4.0 0.3 to 160 19.3 3.1 to 13 8.0

- 142 0.2 10 104 19 0.6 lo 62 31.3 0.1 to 2,280 175 0.9 to 40 18.3 3.4 to 72 21.4 2.0 to 585 118 0.8 to 42 12.9 0.1 to 226 8.64 0.1 to 4.8 1.53 0.1 to 269 33.0 0.1 to 61 9.11 0.1 to 13 2.38 2.5 to 338 50.6 0.1 to 135 15.4 0.1 to 112 12.9 7.8 to 232 94.1 0.4 to 694 62.8 1.9 to 200 61.8 1.3 to 974 288 55 to 766 372

6.4 to 61 33.7 0.1 to 1,620 277 0.5 to 31 14.4 0.1 to 678 34.5 0.1 to 48 5.3 0.3 to 390 101

- 14 0.2 to 210 26.3 0.3 to 280 54.1 1.1 to 143 23.8 24 to 105 46.4 37 10 171 104

0.1 to 803 89.7 0.1 to 120 41.8 0.4 to 516 33.5 0.1 to 361 21.9 0.2 to 229 21.3 0.1 to 129 22.2 0.1 to 1.210 43.5 0.1 to 135 7.5 12 to 98 48.0

0.7 to 157 39.0

Range of Permeablllty

k,o Wi -

0.1 to 1,270 0.1 to 135

0.6 to 2.8 - 5.5 1.5

0.07 -

0.1 to 2.2 - - - - 22 0.4

0.2 to 7.4 1.40

0.3 to 0.9

- -

0.9 to 3.5 0 to 0.5

0.1 to 5.0 -

1.4 to 2.3

OYIO 1.10

- - - - -

0 to 77.0 0.1 to 7.9 0.3 to 162

- -

0.5 to 162 -

0.20 -

0 to 2.1 -

0.2 to 74 0 to 216 0 to 163

0.1 to 89 0.1 to 185 0.1 to 36

- -

6.2 to 8.8

TYPICAL CORE ANALYSIS OF DIFFERENT FORMATIONS 27-l 1

TABLE 27.9-OKLAHOMA-KANSAS AREA (continued)

Average Permeability,

$n?, -

67.8 21.6

-

1.7 -

5.5 1.5 0.07

- 0.45

- -

- 22

0.40 2.23 1.40 0.60

- - - -

1.67 0.21 1.18 -

1.65

oio 1.10 - - - - - -

5.24 2.04

52.3 6.7 -

23.3 -

0.20

0.62 -

13.9 13.7 14.2 13.2 9.44 4.23 - -

2.1 lo 24.3

Range of

3.7 to 23.1 8.5 to 17.3

Porosity

5.9 to 28.6 11.9 to 18.6

w

8.4 to 21.1

9.0 10 20.9

8.5 to 25.8 8.5 to 20.1 3.8 to 19.8 1.2 to 19.3

11.9 to 14.8 8.3 to 21.4

16.9 to 18.1 -

8.1 to 22.8 1.5 to 6.5 1.4 to 15.7 1.5 to 10.9 3.5 to 14.5 5.6 to 11.7 5.6 to 11.4 6.4 to 21.6 7.1 to 17.0 2.6 to 20.7 2.3 to 16.0 3.2 to 17.8 9.8 to 23.5 7.4 to 24.6

11.0 to 20.4 9.8 to 22.6 4.7 to 26.4

11.7to23.4 12.7 to 24.1 16.7 to 22.5 13.9 to 18.2 3.1 to 29.7

14.3 lo 22.7 1.6 to 33.6 1.1 to 19.5 8.4 to 16.0

- 5.1 to 25.9 4.6 lo 27.2

14.2 lo 21.3 1 8 lo 21.4

11.0 to 12.1 2.1 lo 20.9 1.9 lo 11.3 6 5 10 37.8 5.7 to 39.3 1 5 lo 38.0 1.5 to 23.6 1.3 lo 34.1 1 1 to 26 1 2.8 to 9 6 5.5 to 16.5

14.4

Average

12.0 9.2

Porosity

12.9 14.5 14.9

VW

15.8 17.6 14.6 12.2 7.2

13.4 15.6 17.5 14.2 13.2 4.0 9.8 6.5 6.8 9.3 7.4

15.7 13.7 12.2 10.1 7.7

16.9 15.2 15.6 16.7 17.4 16.3 19.7 20.5 16.1 16.5 18.5 10.9

7.3 12.2

7.2 14.5 17.8 17.1 140 11.6 11.9 8.1

21 .o 22.3 18.7 10.3 13.4 9.3 6.7

11.0

Range of Oil

Saturation PM

0.7 lo 9.4 5.2 to 42.3

0 to 23.6 0 to 8.1

5.1 to 35.1 5.8 to 21 .l

0 to 11.1 3.3 to 60.6 0.9 lo 35.7

0 lo 6.7 3.3 lo 25.8 4.6 IO 8.8 4.8 to 49.7 7.4 lo 7.8

- 16.2 lo 33

0 to 7.6 3.1 IO 24 0.4 to 6.8

0 lo 6.9 2.4 IO 24.2

0 Io 13.6 9.3 lo 26.6 2.0 to 15.7

0 lo 7.5 7.2 lo 35.9

0 IO 11.1 0 lo 7.1

5.8 lo 35.5 0 IO 21.1

2.2 lo 6.3 5.9 lo 46.4

0 to 7.0 126to231

6 6 to 17.1 0 7 to 4.4 3.2 to 48.7 3.3 lo 11.4 1.6 to 34.5

0 to 61.1 6.5 to 28.9

- Oto78

1.6 to 37.3 0 to 14.3

6.4 to 18.1 2.1 to 2.3 4.1 to 41.6

0 to 8.2 0 to 6.8

1.4 to 30.0 1.1 to 18.3

0 to 9.3 2.1 to 56.5

0 to 41.2 4.0 to 14.7 5 1 to 27.7

Range of Average Average Total Total

Oil Water Water Saturation Saturation Saturation

w w w 37 34.5 to 62.7

20.6 to 79.3 37.2 to 91.9 36.4 to 65.2

17.1 7.1 2.0

20.7 12.1

47 16.2 12.2

4.3 15.0

8.7 21.5

7.6 8.3

21.5 3.8

11 2.2 4.0

11.5 4.8

15.3 11.2

1.1 19.1

1.2 4.1

13.1 7.8 3.8

20.4 0.8

160 14.5 2.6

21.4 6.8

15.3 10.6 18.1 12.8 2.4

15.3 6.9

11.7 2.2

14.8 4.7 2.4

12.9 7.6 2.8

15.0 6.9 7.8

132

18.4 to 61.5 42.7 to 55.4 23.4 to 70.0 17.4 to 85.2 43.9 to 88.0 32.9 to 82.4 14.6 to 58.5 50.0 to 51.3 15.3 to 60.0 47.3 to 55.2

-

19.3 to 65.4 35.7 to 71.8 12.8 to 67.2 29.5 to 78.6 28.2 to 45.7

8.9 to 44.9 21 .l to 57.6 31.5 to 73.4 45.7 to 80.7 20.9 to 80.7 17.7 to 80.8 40.9 to 89.2 40.0 to 64.4 10.2 to 74.0 32.9 to 77.2 19.1 to 54.9 14.0 to 58.6 41 .l to 77.1 14.6 to 48.5 34.8 to 50.7 40.1 10 40.6 13.6 to 68.5 50.5 lo 69.8 16.7 to 93.4 160 lo 687 37.4 lo 68.6

38.2 to 83.7 28.0 lo 76.3 33.2 IO 69.4 42.8 to 66.4 19.8 to 22.9 16.9 to 86.7 21.4 to 51 7 60.3 to 93 4 27.1 to 94.8 47.4 lo 84.9 22.6 to 93.5 18.9 to 85.3 32 9 to 94.0 19.3 to 76.5 148to522

43.1 52.4 69.2 47.2 36.7 47.0 54.1 44.4 63.5 42.6 32.4 50.7 40.0 51.3 37.3 42.2 53.6 35.4 48.3 37.9 25.1 43.5 47.2 57.8 48.8 42.1 61.7 48.9 48.7 55.3 42.1 37.8 53.8 40.2 42.9 40.4 45.1 57.9 48.6 54.5 51.9 75.5 54.1 45.5 45.9 55.5 21.4 41.5 33.0 76.7 84.0 71.5 63.2 50.7 67.6 43.9 32.1


Water Saturation

PM 28 to 62 20 to 79 37 to 91 32 to 65 19 to 61

40 23 to 66 17to72 43 to 67 26 to 62 15to59

50 15to59

44 -

19to58 36to 72 12to87


Water Saturation

w 40 47 52 45 37 40 48 40 54 40 32 50 37 44 35 40 54 34

- 28 to 45

8 to 44 40

31 to 73 45to 81 19to81 17to81 40 to 89 30 to 64 IO to 74 32 to 77 19 to 49 13to57 19to76 14to47 31 to 42 34to 39 t3to68

- 32 25 - 43 51 43 33 61 42 44 49 37 33

Liz 35

ii - -

17to93 46 16to89 48 28 to 69 49

- - 34 to 83 47 23 to 76 41 31 to 69 43 42 to 66 53 18 to 22 20 14 to 87 38 20to 51 32 60 to 93 77 27 to 95 58 43to 85 63 22 to 93 53 16 to 85 46 32 to 94 61 19 to 77 44 14 to 52 31

Range of Grawty (OAPI) -

29 to 44 42 -

31 to 42

- 28 to 42

35 -

32 to 42 -

29 to 42 -

31 to 38

31 to 42 - 42

37 to 42 -

35to 41 - -

38 to 42 - -

27 to 56 - -

17 to 42 -

36 to 42 42 -

29 to 42 -

24to 42

3lto39 -

30 to 42 -

36 to 42 -

36 to 48 - -

22to 42 - -

22to 45 - -

35 to 48

Average Gravity (OAPI) - 37 42 -

38 - - 34 35 - 40 - 35 - -

38 - 40 - 42 41 - 39 - - 40 - - 42 - - 32 - 42 42 - 34 - 36

37 - - 37 - 40 - 42 -

35 - - 39 - -

38



FormatIon Morrow

Oil Creek

Oswego

Peru

Prue

Purdy

Reagan

Redfork

Skinner

Straw

Sycamore Tonkawa

Tucker

Tulip Creek

Viola

Wayside First Wilcox

Second Wilcox

Woodford

FluId ProductIon

G 0 T G 0

a 0 T G 0 T G 0 T 0

a 0

a 0

i 0

a 0 0

2 T 0

a 0 T G 0

A G 0 T G 0 T 0

Range of Producllon

Depth lfli

4,300 to 9,700 4,100 to 7,500 5,500 to 6,900 7,100 to 14,000 5,100 to 11,700 8,400 to 13,700 4,500 to 4,600

300 to 6,300 1,200 IO 5,800 1,200 to 5,300

200 to 3,200 700 to 2,500

3,000 to 6,600 600 to 6,700

3,000 to 5,400 4,200 to 7,400

- 3,500 to 3,600 2.100 to 3.700

3,600' 2,300 to 7,400

300 to 7,600 1,200 to 3,800 1,000 to 5,300 1,000 to 5,800 2,400 10 4,600

1,000 to 7,400 2,600 to 6,700 5.000 to 7,100 2,400 to 5,700 2,300 to 3,100 1,300 to 2,900 2,700 to 2,900 7,200 to 16,700

700 to 16,800 1,400 to 12,900 4,300 to 7,300 2,100 to 11,100 2,600 to 10,300

300 to 2,800 2,800 to 5,400 2.800 to 7,400 3,200 to 6,100 5,000 to 10,000 3,700 to 6,400 4,700 to 7,500 4,100 to 5,000

Average Production

Depth m

6,100 5.700 6.100

10,900 8,300

12,300 4,600 3,800 3,300 3,100 1,200 1,500 4,000 3.100 3:700 4.500 4:200 3,800 3,600 3,600 4.300 3,100 3,100 3,700 3,200 3,400 1,100 3,500 4,600 5,600 4,800 2,700 2,200 2,800

13,400 8,000 8,600 5,400 4,900 4,600

800 4,300 4,900 3,900 6,700 6,500 6.000 4,600

Range of Average ProductIon Producllon Thickness Thickness

(ff) (fU 2 to 64 11.0 2to37 9.8 3to 30 9.5

14 to 149 46.3 3to 71 12.6 8 to 27 15.0 8 to 9 8.5

3.6 to 34.1 12.3 2 to 21 10.6 4to17 9.8 2 to 42 12.4 4 to 21 10.3 5 to 22 13.6 2 to 81 14.6 3 to 18 11.7 3 to 30 14.8

- 4.8 2 to 13 7.4 t to 32 11.0 5 to 7 6.0 4to 19 7.9 1 to 63 10.5 2 to 9 5.3 4 to 29 11.8 1 to 42.5 9.2 6 to 35.9 11.5

- 12.0 2 to 40.5 12.4 2 to 84 26.4 2 to 27.5 9.8 2 to 28.5 8.7 4 to 9 7.0 2to 14 7.8

8.9 to 16 12.5 21 to 268.4 78. I

2 to 136 15.3 3 to 86.5 20.0 3to 73 39.1 2 to 111.7 17.2 2 to 117 19.6

3.1 to 34 10.8 2 to 35 11.3 2 to 28 10.0

t .9 to 29 7.7 5 to 28 13.4

1.3 to 32 11.3 1.5 to 5 4.4 2.6 to 30.4 16.2

Range of Average Permeabll~ty Permeablllty

(md) (md) 0.1 to 1,450 115 0.2 to 1,840 117 0.1 to 410 34.4 0.1 to 132 32.0 0.1 to 615 131 0.1 to 87 22.1 2.4 to 151 76.7 0.2 to 296 27.3 0.1 to 117 27.0 3.1 to 42 15.0 0.2 to 264 20.8 1.7 to 804 205 0.7 to 42 18.3 0.1 to 254 22.6 0.5 to 133 42.6 7.4 to 500 182

- 195 1.1 to 173 39.3 0.2 to 2,740 255

19.0 to 37 38.0 0.1 to 160 23.4 0.1 to 668 14.2

0 to 23 6.3 0.1 to 127 27.7 0.1 to 255 20.6 0.3 to 16 6.0

- 71.0 0.1 to 599 58.1 0.1 to 3.1 0.67 0.3 to 283 46.7 1.4 to 278 96.6 1.3 to 406 106 2.1 to 123 36 4.3 to 252 128 0.9 to 24 7.63 0.1 to 1,470 154.0 2.0 to 143 44.6 3.6 to 23 10.8 0.1 to 1,150 52.3 0.1 to 997 45.1 0.2 to 133 22.2 0.7 to 145 72.1 0.2 to 445 91.3 0.3 to 418 84.1 0.2 to 154 76.2 0.4 to 2,960 214.0 0.4 to 756 246.0 1.4 to 250 87.1

Range of Permeablllty.

k,o (md)

0.3 to 55 0.1 to 48

- 0.2 to 230

- -

0.1 to 86 0 to 41

-

- -

-

51 to 266 -

- - - - -

2 to 6.6 2.40 -

0 to 1.3 -

8 to 22 - - 53

0.5 lo 1.0 0.2 to 1.8

0.40 3.40

0.2 to 186 0.03 to 49

- - -

0.80 -

- 2.4 to 156


7.5 23.1 28.0

-

75.6 - -

9.24 11.5

- - - - - -

179 166

- - - - - - -

3.30 2.40

-

0.50 -

15.0 - -

53 0.40 0.80

0.40 3.40

18 3 4.38

-

-

0.80

- -

79.2

4.2 to 24.4 5.7 to 23.2 5.5 to 16.2 6.1 to 13.5 1.8 to 23.9 5.2 to 16.1

12.0 to 17.3 2.6 to 21.6 4.7 to 20.9

12.3 to 17 5 12.7 to 33 8 13.6 to 24.4 13.8 to 22.4

7.6 to 23.8 9.8 to 23 4

12.3 lo 18.8 -

9.3 to 12 7 6.9 to 21.5

10.6 to 12.8 3.8 to 21.2 6.6 to 26 1

10 1 to 16.6 13.3 to 19.6

7.4 to 21.7 11.7 to 19.0

-

8.2 to 23.5 7.2 to 16.4

11.7 to 21.4 13.2 to 22.9 15.4 to 16.9 12.4 to 20.3 11.8 to 19.5

2.0 to 11.9 2.5 to 25.0 0.7 to 26.0 6.1 to 10.1 1 .O to 16.1 0.6 to 18.8

13.2 to 24.9 5.2 to 15.6 5.4 to 20.5 6.8 IO 17.7 5.0 to 15.1 4.2 to 20.6 1.9 10 20.4 1.9 to 6.6

Average Permeability, Range of Average

Porosity Porosity w w


Range of Oil

Saturation w/o)

148 14.6 11 3 9.0

13 1 10.9 14.7 10.1

8.7 156 18.7

19.2 17.8 17.0 17.5 16.7 17.6 10.8 13.3 11.7 14.5 162 15.3 15.7 15.3 15.5 21.3 16.8 13.3 16.4 18.4 17.1 15.6 15.7

6.1 11.6

11 .o 9.3 8.4 7.1

16.6

10.8 12.0 10.9 11.2 12.4

12.9 4.4

0 to 33.0 0.7 to 44.5

0 to 15.2 0 to 6.5

1.3 to 29.5 0 to 5.6

5.1 to 6.4 0 to 27.1 0 to 14.5

0.1 to 7.9 6.7 to 36.8

2.6 to 25.5 2.3 to 9.1 4.7 to 34 1 3.7 to 34.3

10.1 to 27.2 -

1.1 to 7.9 3.0 to 42.0 1.8 to 10.5

0 to 21.7 5 4 to 30.8 0.3 to 36.3

0 to 9.9 2.5 to 39.7 4.9 to 18.2

-

5.7 10 31.1 9.2 to 33.5

0 to 6.1 7.5 to 16.5

6.9 to 17.3 7.3 IO 29.6 7.1 to 10.9

0 to 6.6 3.0 to 44.5

0.7 to 7.7 1.7 to 9.4 3.2 to 41 0

0 to 33.7 8.1 to 33.8 0.7 to 6.3 3.6 to 40.5

0 to 169 0 to 3.8

2.9 to 19 2 0 to 6.4

8.3 to 16 7

Range of Average Total

Oil Water Saturation Saturation

w W)

4.3 15 1

5.0 1.6

13.0 2.6 5.8

15.0 5.0 4.1

14.7

12.0 55

16.9 19.0 20.0 13.6

4.2

14.2 6.2 4.7

16.9 9.9 4.2

20.1 0.5 9.9

15.1 21.1

2.0 12.5

11.4 16.0

9.0 4.1

12.2

2.6 5.0

15.5 8.6

18.6 3.6

11.7 7.9 1.5

10.2

6.1 11.8

29.0 to 77.0 23.9 to 75.5 31.1 to 90.1 12.5 to 40.6 14.2 to 76.4 21.7 lo 74.9 39.8 to 55.5 16.2 to 73.4 41.7 to 89.7 44.3 to 59 4 34.4 to 73.1

38.0 to 60.4 31.4 to 53.4 24.4 to 73.1 40.7 to 60.9 31.4 to 58.1

26 4 to 66.4 17.5 to 72.9 33.3 to 46.7 16.2 to 63.6 29.5 to 57.7

41.4 to 69 7 30.6 to 48 14.3 to 78.7 39.9 to 71 .l

-

28.5 to 61.5 36.0 to 61.6 31.8 to 58.3 36.1 to 78.0 45.1 to 52.6 35.6 to 50.1 58.0 to 64.3 23.7 to 54.8 10.0 to 63.0 15.9 to 82.6 19.7 to 37.2 24 1 to 85.5 39.0 to 90.8 29.4 to 68.0 29 7 to 60.5 15.0 to 58.2 24.6 to 63.6 17.7 to 45.0 19 0 to 56.3

41.4 to 60.5 43.0 to 87.9

Range of Average Average Calculated Calculated

Total Interstitial- Interstitial- Water Water Water Range of

Saturation Saturation Saturation Gravity W) W) (%I (OAPI)

48.5 42.1 57.2 25.2 39.1 46.6 47.7

41.5 63.4 52.5 50.6

50.7 42.2 41.6 47.1 41.5 56.2 44.4

32.9 40.0 45.8 43.7

52.6 40.8 40.3 52.4 61.8

45.6 45.5 44.5 45.0

49.0 40.7 61.2 33.2 34.9

45.7 30.7 54.4 65.7 51.3 43.9 32.0 41.7 30.9 36.9

42.5 60.1

16 to 77 36 16 to 54 35 31 to 90 38 12 to 40 24 14 to 76 34 21 to 74 -

34 to 55 45

15 to 73 37 42 to 89 57 44 to 56 51 28 to 73 44

36 to 56 51 25 to 49 37 20 to 72 38 32 to 60 36 16 lo 50 29

- 28 lo 68 12 to 72 29 to 45 16 lo 63 27 to 55 41 to 69 26 to 47 14 to 78 39 to 71

-

22 to 56 32 to 62 27 to 56 31 to 78 4-4 to 52 33 to 43 52 to 62 23 to 55

9 to 63 15to82 19 to 37 24 to 88 39 to 90 28 to 67 29 to 80 14to58

40

31 29 39 41

49 38 38

ii

41 43 41 38

45 38 52

2

46 30

El 47 44 31

- 171043 18 to 58 40 to 60 43 to a7

29 34

- 33 to 43

- -

29 to 42

-

35 to 46 -

25 to 43

- 34 to 46

- 39 to 44

-

41

24 to 43 - -

32 to 48

- 30 to 46

-

31 to 44 33 to 36

- 40 to 45

-

29 to 40 -

49 5 32 to 50

- -

28 to 48 -

29 to 42 -

33 to 50 -

- 40 - -

36 - -

44 - -

36 - -

42 -

41 -

41

38 - -

37

- -

36 - -

40 35 -

43 -

38

49.5 40 - -

37

35

42 -

34 to 42 40

- -

41 41

Average Gravity (OAPI)

a General geologic sections take” at dtfferent points I” Oklahoma-Kansas areas lndlcate some var!at!o”s I” the properties and a” apprec~abfe variate” I” the occurrence and relative depths of many of the more m~portanl 011. and/or gas-producing zones. formations, geologic groups, and thelr members The general !de”tlflcatlo” of core samples from thee producing lntewals reflects local condmons or actlwt~es slgnlflcantly In the development Of average data values. an attempt has bee” made to combine data orlgmally reported for locally named zones Into more generally recognued formatlow or geologic groups In some mstances (I e Deese. Cherokee) data are reported for a major geologic group as well as for $ome of 11s vndlwdual members The values designated by the maw group name represent areas where the general character~stlcs permit Identlficatlo” as to the gealognc group but not as to group member In other areas the group members or zones are readily ldentfffable The combmatlons of data and the use of local rather lha” regmnal geologic names I” some instances are emplaned 1” the footnotes

b T represents transitlo” zone or productlo” of both water and &her gas or 011 ’ fncludes data reported as Dornlck Hllfs and Dutcher ’ Includes Bromide first and second as reported on McClaln County area g Data reported locally as Bromide third. Bromide upper third. and Bromide lower have bee” ConsIdered as part of the Tuhp Creek

Includes data reported as Cleveland sand, Cleveland lower. and Cleveland upper ’ fncfudes the numerous zones (Deese first. second. third, fourth, fifth, Zone A, Zone 6. Zone C. and Zone 1) reported locally for the Anadarko, Ardmore, and Marietta Basm

areas. I” northwest Oklahoma. these different zones are normally referred to as Cherokee In other areas the zones are frequently Identlftable and properties are reported as for Redfork. Bartleswlle. etc


FormatIon

Aneth Boundary Buite

Cliffhouse D Sand Dakota

Desert Entrada Frontier Sands Gallop

Hermosa

Hospa

lsmay J Sand

Leadville McCracken Madison’ Manefee Meeaverde

Morrison Muddy Nugget

Paradox

Phosphoria (formerly Embar)

Pictured Cliffs

Point Lookout

Shannon Sundance Sussex Tensleep Tocito

Fluid Production

TABLE 27.10~ROCKY MOUNTAIN AREA

Range of Production

Depth 0)

5,100 to 5,300 5.500 to 5.600 5,400 to 5,900 3,600 to 5,800 4,350 to 5.050

500 to 7,100 653 to 7,293

5,400 to 5,500 3,600 to 3.700

265 to 8,295 1,5M1 to 6,900

500 to 6,400 4,900 to 7,700 5,300 to 6,000 4,800 to 7,100 4,600 to 5,100 5,544 to 5,887 4,470 to 5,460 6,970 to 8.040 9,950 to 10,100 8,264 to 9,466 3,400 to 6,200 5,200 to 5,700 1,500 to 6,100

1,600 to 6.900 930 to 8,747

9,900 to 10,300 9,500 to 10,800 5,100 to 9,500 5,300 to 6,100

700 to 10.500 1,200 to 5,800

4,300 to 6.500

4,700 to 5,500 1,100 to 6,860 4,300 to 5,100

600 to 11,800

1,400 to 5,100

Average Production

Depth (fi)

5,200 5,600 5,600 4,800 5,800 5,700 5,600

3,640 2,950 5,000 4,600 5,600 5,600 5,500 4,800 5,707 4,900 7.500 9,950 8,820 4,900 5,400 4,700

300 4,500 1,845

10,100 10,375 6,900 5,700

4,600 3,400 2,900 5,500 4,700 4,900 3,100 4,500 4,700 7,900 4.600

Range of ProductIon Thickness

(f1) 3.8 to 23.1

8 to 27 2 to 68 2 to 56 7 to 33 2 to 75

13 to 75 11.6 to 18.3

4to10 8 to 100 5 to 25 2 to 43 5 to 30 3 to 36.2 3to17 6to 1El

10 to 90 151062 20 to 76

2 to 142 41 to 450

7 to 25 2 to 22

- 24 to 54

7 to 75 60 to 700

250 to 700 4 lo 44.2 2 to 66

5 to 100 3.0 to 72 0

2 to 101

10 to 20 5 to 100

10 to 30 IO to 200

- 4 to 58


(W


(md) 14.0 0.7 to 34 17.5 01 to20 16.2 0.1 to 114 13.7 0.1 to 3.7 15.0 0 to 900 32.0 0.1 to 915 32.0 0.1 to 915 14.9 1 .o to 11 6.0 5 to 300

46.0 0 to 534 11.6 0.1 to 324 12.4 0.1 to 2,470 .14.1 0.1 to 91 15.1 0.1 to 37 10.5 0.1 to 70 133 0 7 to 25 36.4 0 1 lo 142 25.0 0 to 1,795 45 0 0.01 to 0.50 15.0 0 lo 21 56 4 0.01 to 272

186.0 0 to 1,460 12.7 0 1 to 20 10.0 0.1 to 17

4.0 - 40.0 0 to 1,250 20.0 0 to 2,150

385.0 0.6 to 65 475.0 0.5 to 85

12.2 0.2 to 42 14.8 0.1 to 119

64 0 17.0 23.0 22.9

7.0 15.0 44.0 20.0

118.0 7.0

17.3

0 to 126 0.01 to 135

0.1 to 16 -

0.05 to 5.0 0 to 1,250

0.05 to 20 0 to 2,950

- 0 to 31


OW 9.35 1.05

13.3 0.94

192 106 106

4.4 100 105 26.5 48.2 18.6 7.32

18.2 8 63

to.4 330

0.20 3.0 5.8

13 5.04 3.57

60 43

173

: 11.6 10.4

3.7 7.7 0.5 1.74 2.90 0.8

100 1.0

120 230

3.36

Range of Permeablhty.

km VW

0.2 to 23 -

0.2 to 23 - -

- 0.4 to 2.4

- -

0.3 to 20 0.1 to 3.2

45.0 0 to 26

- - - -

- -

- - - - - -

0.1 to 28 0 to 57

- I

- -

- -

-


TABLE 27.1 O-ROCKY MOUNTAIN AREA (continued)

Average Perm_eability, Range of

Porosity W)

6.10

12.5

-

- 1 13 -

10.2 0.7

45.0 4.26

- - -

-

- -

-

-

4.43 4.57

-

- 2.40 - -

4.4 to 10.5 6.1 4.3 to 6.5 47 5.4 to 21 6 11 .o 7.0 to 16 2 11.3 8.6 to 29 5 21.6 4.5 to 21 6 14.8 5.0 to 23.3 t 1.2

11.9 to 13.6 12.7 12.0 to 27 0 25.0

6.3 to 29 6 20 0 8.5 to 20.8 t 3.3 6.9 to 23 1 12.5 5.5 to 16 5 to.2 2.7 to 17 9 8.3 7.4 to 11 9 10.5 6.6 to 14.8 11.3 0.5 to 22 2 7.6 5.9 to 32.7 19.6 3.0 to 20.0 10.0 2.0 to 16.0 3.0 0.5 to 15.1 6.5 1.6 to 26.4 11.9 8.7 to 13.5 11.2

10.0 to 19.8 146 - 26.2

9.9 to 25.5 17.5 2.3 to 32 9 22.3

10 0 to 18.0 13.7 10 0 to 18.0 13.4

1.4 to 19.4 7.4 3.3 to 21.8 10.5

2 0 to 25.0 3 1 to 31.0

5.6 to 21.6 -

6.0 to 15 0 15.0 to 25.0

8 0 to 20 0 5.0 to 27.0

- 12.6 to 17.8

8.9 3.0 to 40.0 22.5 - 17.5 0.0 to 21 .l 2.6 16.0 to 88.0 11.4 - 23.2 - 10.9 0 to 9.1 2.9 11.9 to 55.6 13.3 - 23.8 40 12.0 3.0 to 22.0 16.0 30.0 to 60 0 19.0 8.0 to 25.0 17.0 - 130 5 0 to 20 0 11.0 35.0 to 60 0 13.6 6.0 to 30.0 23.3 7.0 to 59 20.2 - 4.0 - 14.7 11 9 to 26.6 21.3 40.6 to 55

Range 01 Average Oil Porosity Saturation

W) W) 14.5 to 35.9

4.7 4 8 lo 26.7

0 to 19.8 8 4 10 39.5 0.0 to 7.8

13.8 lo 54.5 13.4 to 16.6

trace to 6.0 7 6 lo 37.6

0 to 25.6 0.5 to 43.7

0 to 6.5 3.9 to 29.1 0.5 to 23.6

20.4 to 29.8 1 6 to 26.4 8.8 to 46.5 0.0 to 22.2

trace to 6.0 0.0 to 50.1 6.0 to 43.5 0.3 to 5.3

Oto68

5.0 to 26.0 7.6 to 48.5 0.0 to 5.0 5 0 to 10.0

0 to 10.1 3 6 to 36.7

Range of Average Total

Oil Water Saturation Saturation

wd w 12.5 to 30.5 23.8 to 35.0

9.3 to 48.8 10.2 to 60.3

25.0 4.7

12 5 4.5

13.2 3.5

24.4 15.2 3.0

14.9 5.7

25.3 3.0

10.8 7.5

25.0 a.4

13.9 2.0 7.5

14.4 17.4

1.6 3.3 8.3

13.1 30.8

3.6 6.4 3.1

12 4

- 14.8 to 55.3 11.6 to 44.3 14.8 to 24.7

- -

20.7 to 59.2 17.2 to 76.9 14.2 to 45.3 11.6 to 60.0 8.7 to 49.7

32.3 to 44.6 - -

10.0 to 65 0 -

- 14.5 to 45.1 145to664

- - -

20.0 to 60.0 20.0 to 50.0

9.9 to 57.9 10.8 to 60 5

Range of Average Average Calculated Calculated

Total Interstltial- Interstitial- Water Water Water Range of

Saturation Saturation Saturation Gravity w W) W) (OAPI)

23.6 29.4 26.3 36.9 -

40.6 31 .o 19.2

- 40.0 35.7 32.7 35.6 36.1 36.0

-

3Co - - -

27.5 42 0 61 .O

- 28.0 32.5 34.7 33.6

- 47.0 40.9 36.7 40.9 45.0 -

45.0 25.7 51.6 46.3

13 to 31 24 23 to 35 29

7 to 45 27 lOto 36 9 to 46 23

- - -

14to22 -

26 to 45 20 to 54 14 to 77 12to45 12 to 60 8 to 49

31 to 45 -

6 to 42 -

- 16 - 33 37 34 32 35 37 35 - 20

- -

22 to 33 15 to 43 15 to 64

- 15 to 41 5 to 47

20 to 56 18 to 40 10 to 58 10 to 61

- - 27 27 40 44 35 19 26 26 34 33

5 to 30

- 121055

- -

20 to 49 -

5 to 50 -

40 to 55

21

- 36 41

35 - 19 43 46

41

40 to 41

36 to 42 -

38 to 43

- 31 to 50

39 36 to 42

- 41 to 42

- 40 -

36 to 42 -

45 to 46 21.6 to 30

- -

29 to 56 26 to 42

- -

40 to 43

15 to 42.3 f

- - -

22 to 63 40 to 43 17 to 56.5

36 to 40

Average Gravity (OAPI) 41

41 1

36 - 40 41 -

2 39 - 40 -

;: 38 - - 45.5 26 -

- 42 38

48

41

25.4 55 39 - 39 44 39 42 26.2 - 36


TABLE 27.11 -WEST TEXAS-SOUTHEASTERN NEW MEXICO AREAS

Form&on

Bend Conglomerate

Blwbry

Cambrran Canyon reef

Canyon sand

Clearfork

Dean Delaware

Ellenburger

Fusselman

Glorletta (Paddock)g

Granite wash

Grayburg

Pennsylvanta sand (Morto~)~

Queen (Penrose)g

San Andres

Seven Rivers

Sprayberry

Strawn llme

Straw sand

Tubb Wolfcamp (Abo)Y

Group”

1

2

- -

-

1

2

- - -

1

2

3

-

-

-

-

1

2

3 -

-

1 2 3

-

1 2 -

1 2 3

4

Area”

1.2.4 5.6.8

3 8

3 2.3.4 5.6.7

z3.4.7

3.4.7

mart) 5.6

2(w) 2.4.7

1C

2.50

2.5e

All

All

3.4.6.7

a

4 5.6.7

1.2.3 2.3.4

All

8 5.6 1.2.3 4.7

1 2.5.8

47 2

All

Others’ 1 2.5.8

2 4 5 6.7

wart)

FluId Production

0

0 G 0 0 0

G 0 G

:

0

E G 0 G 0 C 0 C 0

Ei G 0 G 0 G

: 0 0 0

G 0

: 0

: 0 0 G 0 G 0 0

: 0 G 0 0

Range of ProductIon

Depth llll

6.000 to 6.100

10.300 to 10.500 5 383 to 5.575 5 262 to 5.950 5 500 10 6.300 4.200 to 10.400

-

30001010000

1.500 to 6.800 5.400 to 8.300

7.700 to 9.100 4.700 to 5,000 3 500 to 5.100

11 20010 11,600 11,300 to 12.300

5.500 to 9.900 11 000 to 11:zoo

7 800 to 12.800 4 100 to 10.600 5.500 to 16.600 8.700 to 12,700 9.500 to 12.500 2200 to 2 600 2,300 to 6.000 3.000 to 8 600 2,300 to 3 400 3.600 to 4 200 2.400 to 4 500

4.400 3.000 to 4 800 1.300 to 3 900 4.100 to 11.400

3.000 to 3 200 f3ooto 4 900

3.900 to 4 700 4.100 to 5 300 1 500to 5 100

3.600 to 4 100 I300 to 4 000

4.800 to 8 500 5oooto 9 200

-

5.200 to 6 700 3.800 to 10.500 I.100 to 11.300

915to 7 366 6.100 to 7 300

-

8.400 to 9 200 2.500 to 4 100 2.400 to 4 100 9.000 to 10.600 1.400 to 3 500 1.4oa to 4 000

Average Production

Depth

(fl)

6.000

Range of ProductIon Thickness

lfll

Rangeof Average Permeablllty Permeability

(W (4

3 to 22

Average Productfan Thvzkness

(f1)

13.2 4 to 311 150

10400 10 to 28 20 0 16toll 5.7 5.480 23to 50 36 1.6 to 3 8 24 5.610 410 95 43 0.1 10 5 3 1.8 5.900 20 to 95 30 3 0.8 to 1,130 173 7.100 40 to 222 36 a 0.6 to 746 42

5,000 5 500 2,400 4.400 6,600

-

3010 57 -

40t0180 3010 259

80 - 17 16 9 01 to 477 38 95 - 11 41 0.1 to 43 4.6

33 <O 1 to 136 5.8

8.200 4.800 4.200

11.400 11.800

9.200 7.700

11.100

11.200 7400

10.100 10.300 12.000

2.400 4300 4.700 3.000 3.800 4.100 4.400 4400 2.700 9100

6 0 to 68 52 to 39 3 0 to 52 1410 117

8 to 299

<01to03 1.1 to 33 0.6 to 84 0.5 to 36 0.2 to 23

-

Et0 113 19 to 34

65 to 954 11 to 18

30 to 347 18 to 51

8 to 49 3to 44 3to 103 4 to 8 2 to 81

301050 30 lo 123 12 to 26

6 to 259 45 to 182 17to 77

26.2 18.6 14.5 54 99 17 34 27 69 14 3

55 34 32

16 3 22 3

51 15 6

42 274 20.8 45 50 22 3

-

2.5 to 50 <OllOZ2

1.0 to 2,840 203to 246 0 1 to 2,250 12 to 26 0.5 to 25 46to 12 04to 223 11 to 2,890 5 to 3.290

t6to93 05to159 0.6 to 3 7 02to 118 0 3 to 1.430 0.3 to 462

0.12 12.9 245 10.5

4.0 0.4

14.9 1.1

177 225

75 8.4

10.3 5.6

11.5 477 609

6.5 13.7 25 55

37.7 349

3100 4 0 to 29 99 loto 318 64 3500 15 to 38 10.2 0.2 to 4,190 123 4.500 610 39 18 6 0 3 to 461 61 4.500 47to124 40 1 0 3to 295 69 3.300 30 to 197 30 2 0 2to 593 9.7

3900 2.600 7100 6 900 5600 5.900 7.800 5.200 3938 6500 9 800 8.800 3.600 3.500 9700 2800 2.300

301080 40 to 136 2 0 to 59 20 to 120 11 to 57

2010101 3 0 to 39 20 to 76

6 to 21 1510 43

0.6 to 23 04to 428 0.2 to 71 0 1 to 124 4 5to 310 19to 196 0 3to 42 02to 718 1 oto 400 02to135

-

13 to 129 4oto119 20 to 114 45 to 204 30 to 53 30 to 66

56 1s 5 21 7 IS 5 34 4 36 7 16 8 15 1 14 335 10 6 41 7 22.5 28 0 59 10 8 16 6

-

23to9410 0 1 to 1.380 1 0 to 1,270 02to147 02to 145 1 oto 4 000

12.2 51.4

63 48

179 43 11 4 47 45 276

23 419

57 60 204 19.3 427

TYPICAL CORE ANALYSIS OF DIFFERENT FORMATIONS 27-l 7

TABLE 27.11-WEST TEXAS-SOUTHEASTERN NEW MEXICO AREA (continued)

Range of Average Permeabihty, Permeabtlity,

km (md)

-

09to51 -

ozto42 -

0 3 to 249

2.2

1.4

17

- - -

<O.l to 24 10.1 to 109

-

7.8 2.5 3.1

- - -

0.1 to 1.3 0.1 to 5.8

- - -

0.5 08

0.2 to 18 <O.l to 0 9

0.3 io 1,020 1.4 to 54

<Ol to396 03to13 02 to 17

02to126 - -

-

70 0.5

37 27 7 22.9

09 3.9 93 8.1

53 30

0 2 to 48 0.3 to 2 1 0 1 IO 110 0.1 to 228 0.1 to 168

-

52 13 27

143 147

- - - 10

0 1 to 462 53 0.1 to 208 38 0.2 to 510 84

- 03 80 40

-

27 to 189 0 6 to 148 01 too4 0 1 to 138

-

108 19 1

02 11 7

011011 05 - 04

1.5 to 6.210 274 - 34 - 43

0 2 to 36 54

- -

27 8

Range of Poroslly

P/o)

Range of Average Range of Average Total Total

Average 011 011 water water Saturation Saturation Saturation Saturation

1%) 1%1 &%I P/d

Range of Average Calculated Calculated Interstltlal- Intarstltlal-

water water Range of Average Saturation Saturation Grawty Gravity

Ml P/d iDAPIl YAPI\

13 8 lo 16.9

Porostty

(Oh)

150 8.1 lo 8 6 8.3 43 10 64

21 to 41 34 to 40 29 to 57 22 to 71

la 3 to 73

52 42 to 62

21 to 39 31 to 33 27 to 56 22 to 71 18 to 73

50

4 0 to 15.7 10 9 9.5to161 11.5 10 7 to 14 8 12 7 2.1 to 9 1 4.9

31 to 125 78 9.6 to 19 3 12.8 41 to 168 120 6.9 to 21 2 11 8 3.0 to 21.5 89 3 6 to 39 2 11 6

33 36 40 39 44

32

z; 38 43

-

5 5 to 22 1 15 1 14 3 13 5

92 58

4.8 lo 27 7 -

4 1 to 20.6 19to194

7.5 to 31 4 5.6 lo 27 1

58 13 7

57 156 16 5

-

21 to 72

18to84 22 to 69

46 - 44 -

43 21 to 72 41 37 to 43 50 - 50 -

54 18 to 84 53 23 to 42 47 21 to 69 47 28 to 40

75to127 138to218 152to254

17to53 13to68

5 5 to 27 7 2 2 to 7 7 1 e to 25 2 37to46 13to 138 26to37 14to107 14 to 182

5 2 to 20 9 121 to204

3 5 to 26 1 11 1 to 143

7 0 to 20 0 631066 27to162 5 3 lo 24 3 2710139

10 3 179 21 0

33 43 67

15 2 50 60 42 36 33 3.3

15.0 13 6 14.4 17.7 124 11 3

6.4 79

119 77

,22 to 44 2.0 to 103 3.910 156 2.1 to 6.6 3.3 to 16 7

6.8 to 22 9 3.1 to 4 8 5 3 to 24 6 08to76 1.010 192 02to39 5.2 to 16 39to44 3 1 to 22 1 29toa7 4 8 to 22.5 7 1 to 42 6.2 to 37 9 24to71 4.8 to 22 1 8 3 to 34 47to 188

33 7 20 to 52 60 45 to 66

11 2 33 to 65 37 37 to 68 92 19 to 53 57 -

11 0 41 to 76 40 45 to 69

129 22 to 65 42 47 to 67 a4 40 to 84 17 32 to 47

104 25 to 65 37 39 to 60

154 24 to 72 52 39 to 66

14 7 42 lo 71 18.6 22 to 53 176 26 to 56

47 55 to 68 13.9 32 to 84 182 31 to 78

97 28 to 58

34 53 49

ii 62 51 57 46 57 61 40 42 51 48 55 54

i: 60 55 58 42

19 10 51 36 lo 63 31 to 64 37 lo 68 19 10 53

-

41 lo 76 45 lo 69 22 lo 65 47 lo 67 40 to 84 32 lo 47 24 to 64 37 lo 60 24 lo 71 39 to 66 35 to 66 22 to 52 25 to 55 55 to 68 32 to 84 31 to 78 28 to 58

33 49 42

;: 61 51 57 46 57 60 40 38 50 47 53 49

:: 60 55 56 41

10 7 to 22 2 16.6 2.6 to 7 6 74 36 to 62 48 35 to 58 45 5 7 to 27 0 172 4.2 to 34 7 156 32 to 68 49 30 to 66 45 32to140 85 8 9 to 33 9 187 21 to 49 36 19 to 49 36 31 to128 71 4 9 to 30 6 147 26 to 69 52 25 to 69 51 3 3 to 25 1 15 5 3 5 to 24 2 132 39 to 74 58 37 10 74 56

15 5 to 16 6 5 9 to 28 9

101 to233 4 4 to 20 6

10 9 IO 14 8 31 I0126 21 to142 1 oto203 6 0 lo 27 2 5 to 7 1

-

4910185 7 2 to 24 5 5 4 to 26 3 26t0128

121 to274 2.4 to 27 0

160 16 5 158 11 7 129

72 6.9

126 16 2

49 43 99

153 15 5

81 179 18 8

34to95 42to41 7 7 0 to 24 5 7.0 to 30 55tof33 4 9 lo 26 3 17to52 2 7 to 279 5 0 to 27 8 5 to 25 3

66to 168 0510 161 1 6 to 26 8 5.3 to 23 6 13to 170 3 7 to 37 3

64 51 to 66 56 46 to 65 54 16.2 38 to 70 54 36 10 61 50 15 3 32 to 68 45 30 to 67 43 15.5 25 to 72 43 25 to 72 42

5.9 38 to 39 39 38 to 39 38 11 2 15 to 66 44 15 to 66 43

30 46 to 60 52 46 lo 60 52 122 23 to 77 43 23 to 77 41 14 1 25 to 60 43 23 10 59 41 12 9 37 to 64 54 37 to 64 54 19 6 - 25 - 25 97 32 to 56 44 31 to 56 44 46 30 lo 64 48 26 to 64 45

14.3 32 10 65 46 29 to 64 44 14.4 28 to 56 39 28 to 56 39 56 ‘id to 79 59 36 to 76 53

16 0 31 to 75 53 31 to 75 47

40 io 42 14

41 to 45 -

39 lo 42 44 to 51 30 to 47

43

40 46 42

40

28 32

37 to 40 -

35 to 42 -

48 lo 52 -

35 to 46 -

36 to 49 -

37 10 52 -

47 to 50 -

28 to 40 -

40 to 45 -

31 to 41

39

40

49

42

42

47

48

33

42

36

23 lo 40 32 28 to 35 31 38 to 47 41

30 to 42 33 34 to 38 37 30 to 37 33 26 to 37 32

28 to 38 32 36 to 42 39 36 to 43 38

39 to 47 41

29 to 48 -

38 42

36 to 45

42

38 42 40

40 to 50 48 40 to 44 42

27 to 41 32


Fig. 27.1-Area map for Table 27.11

TYPICAL CORE ANALYSIS OF DIFFERENT FORMATIONS

TABLE 27.1 P-ALASKA

27-19

Range of Production

Depth fftl


Depth Thickness (fo (fi)

5,640 40 to 106 8,600 20 to 1,300 6,200 30 to 80 8,600 350 to 630 6,230 22 to 130 7,200 36 to 92 6,150 90 to 1,000


(fi) 82

420 - -

t: 265


0-W 100 to 300

1 to 35 3 to 200

- 20 to 4,400

3.5 to 1,600 10 to 350


(md) 125

10 -

265 480 - 43

Fluid Production

G

: 0

E 0

Formation

Beluga Hemlock Kuparek’ Sadlerochit’ Sterling Tyonek Tyonek

‘Data from repon.

4,500 to 8,100 6,100 to 10,800 6,200 to 6.700 8,300 to 8,800 2,850 to 7,500 6,950 to 7,800 4,400 to 14,800

TABLE 27.12-ALASKA (continued)


Water Saturation

W) 35 to 50 35 to 46


Water Saturation

W) 40 39

Range of Average Oil

Saturation SatZion w W)

0.0 to 0.1 0.1 - 10.0 - -

Range of Average Gravity Gravity (OAPI) (OAPI)

30 to 38 37 - 23 - 28

Range of Porosity

to4 19.8 to 28.0 11.2 to 18.0

-

Average Porosity

w 23.0 14.6 23.0 22.0 30.0 16.0 16.0

Formation

Beluga Hemlock Kuparek’ Sadlerochit’ Sterling Tyone k Tyonek

- - -

28.0 to 34.0 11.0 to 21.0 14.0 to 26.0

- - - - - -

10 to 18 15.0

- - - - - -

35 to 44 40 - - - -

‘Data from repon

TABLE 27.13-AUSTRALIA (GIPPSLAND BASIN)


Water Saturation

w

f : 25 10 26 24 16 40

Range of Average Production Production Range of Average

Fluid Depth Thickness Permeability Permeability Production (m) b-0 VW VW

: 2,299 1,650 to to 2,396 1.950 80.4 6.0 600 800 to to 3000 3000 - - G 1.521 fo 1.556 7.5 2.occr

Average Average Porosity SatZion

(Oh) W) 22 - 21 - 25 0 21 0

2 27 0 25 -

Formation Production (Reservoir) Unit

L-l Mackerel L-l Tuna M-l Marlin M-l Tuna M-l Barracuda M-l Cobia N-l Snapper N-4 Barracuda

G 11299 to 1:377 59.1 - 3;oO0 : 2,352 1,018 to to 2,396 1,151 37.2 40.0 5,ocO 500 to5000

G 1,186 to 1,383 99.0 - 1,000 0 1,330 to 1,339 2.7 - 1,000


TABLE 27.14-ALBERTA. CANADA

Formation

Cardium A Cardium A Beaver Hill Lake A&B Father (conglomerate) Falher (sandstone) Gilwood Keg River Keg River Leduc 03 Leduc 03A Taber Viking Viking A

Pool

Barrington Willesden Green

Swan Hills Elmworth Elmworth

Nipisi Rainbow Rainbow

Red Water Bonnie Glen

Taber Viking Kimsella

Gilbey

Flutd Production

0

:

E 0 G 0 0

: G 0

Average Production

Depth WI

6,634 6,225 0,345 6,500 6,500 5,651 6,082 6,381 3,208 6,000 3,500 2,400 6,401

Permeaiility 0-4

3.7 7.4

32.2 1.0

40.1 208.0

95.0 187.0 302.0 682.0

1,000.0 14.0

238.0

TABLE 27.15~MIDDLE EAST

Range of ProductIon Range of

Fluid Depth Permeability Formation Locatton ProductIon (fo OW

Arab IV Quatar 0 7,400 10 7,980 0.3 to 6,000 ShubalbalWasal Oman 0 4,125 lo 4,422 2.0 to 10 Buhasa Abu Dhabl 0 10,000 to 12,000 0.5 to 1,000 Umm Shalff Abu Dhabi 0 10,000 to 12,000 0.2 to 500 Asab Abu Dhabi 0 10,000 to 12,000 0.5 to 1,500

Average Range of Permeability Porosity

Cm4 W) 300 5 to 34

8 27 to 37 20 15to22

8 lot020 25 15to30

TABLE 27.16-NORTH SEA’

Formation Field

Productton Range of Fluid Depth Thickness Permeability

Productton m (w WJ) (Paleocene) Forties 0 7,200 509 400 to 3,900 Brent Brent G&O - 740 10 to 8,000 Brent Statfjord 0 7,700 770 Statfjord Brent G&O 900 100 to 5,500 Statfjord Slatfjord es00 800 10 to 2,000 (Upper Cretaceous) lo Danian Ekofisk : 10:400 700

Average Porosity

(04 10.1 15.1

7.9 10.0

9.0 12.9 4.4

10.0 6.3 9.4

26.0 18.0 10.6

Average Oil

Saturation 37.9 30.3 13.3 0 0 9.3 0

16.1 19.4 4.7

20.0 0

13.0

Average Calculated

Water Saturation

22.9 23.3 21.9 23.0 35.0 42.5 14.0 19.9 25.6 24.2 25.0 35.0 35.6

Range of Average Reservoir Reservoir

Average Water Water Porosity Saturation Saturation

W) W) P/o) 21 9 to 100 25 33 8 to 16 10 18 151040 25 15 25 to 45 35 20 151035 20

Average Range of Permeability Porowty

WI W) - 25 to 30

7 to 37 3,000 -

- IO to 26 - - 12

Average Reservoir

Average Water Porosity Saturation

W) w/o) 27 23 - - 28 - - - 23 - 30 20

TABLE 27.17-VENEZUELA

Range of Average Range of Average Production Production Production Productson Range of Average Range of Average

Fluid Depth Depth FormatIon

Thickness Thickness Permeability Permeability Porosity Porosity Production (n) (fi) (fi) (4 (md) W-a w Wd

Upper Laguna 0 7,200 lo 10,900 9,500 20 to 170 06 100 lo 470 270 1ato35 30.3 Upper Lagumllas InferNor 0 8,100 10 11,400 10,000 20 lo 220 142 200 to 3.000 1,500 20 lo 32 20.7 Bachaquero inferior 0 9.000 lo 11,cOo 10,000 20 to 150 83 100 to 700 450 17 to 28 21.8

Chapter 28

Relative Permeability Walter Rose.con\ultant *

Introduction This chapter was written as an overview of relative permeability: the basic ideas are given and their evolution is traced. Also presented are some laboratory measurement details and comments on the use of relative permeability information in problem solving. Many unresolved issues still exist, regardless of the fact that the literature is quite rich with the descriptions of what previous workers have thought about this complex sub,ject

Fluid flow is the major transport process that is involved in the recovery of oil, gas, and associated formation waters from subsurface petroleum reservoirs. As a consequence, process descriptions are needed to understand. to forecast. to manage, and to control production operations. Relative permeability is the concept that is often used as a framework for describing two- and three- phase flow of immiscible fluids through porous sedimentary rocks.

The term permubility historically has been adopted as a measure of the porous rocks’ ability to conduct fluid. If only one fluid is present in the interstices, this transport coefficient is called the speciJi(, permeability, but otherwise one must make reference to the c$kcti\v permeability of each of the immiscible fluids in the connected pore space. Relative permeability by convention is the ratio of the effective to the specific permeability.

In transport theory one deals with U%.re.s. ,@(vs, and the coefficients by which these variables arc intcrcon- netted. As soon as the force-flux relationships are established for particular cases, they can be written in such a way that the various permeability functions will appear explicitly. In other words, just as specific

‘Aulhor of the chapter on ,h,s to~,c I” the ,962 ed,t,on was M R J Wyllle

permeability has the sense of a transport coefficient that appears in Darcy’s equation for single-phase flow, effective and corresponding relative permeability functions also can be thought of analogously as important transport coefficients by which multiphase flow processes are best described.

Central to the relative permeability idea is that we arc dealing with material response types of parameters that cannot be derived from theory alone. On the contrary. laboratory measurements generally also will have to be made. All measurements are to be made in accordance with how the experimental variables properly are defined and used later.

To simplify the discussion, assume that we are dealing with the steady flow of an incompressible fluid that is moving macroscopically in a horizontal direction. Then.

kAAp 4=- , . . . . . . . . . . . . . . . . . (1) I.IL

where Ap is the pressure drop that can be measured across a specimen sample of length L and cross-sectional area A. and q is the volumetric rate of discharge of the flowing fluid whose viscosity is CL. Eq. I serves to prescribe an experimental measurement methodology by which values for k can be determined unambiguously.

In particular. it is seen that a plot of q vs. AI, should be a straight line whose slope is proportional to the specific permeability. k, as long as certain limiting conditions prevail. These are that (1) the fluid is homogeneous: (2) the temperature is constant: (3) the transport process is free of electrokinetic effects (as occur when certain dilute electrolytes are being moved through electrically nonconducting media), and of film surface flow (as oc-


curs when a gas is moving at such low mean pressure that the frequency of molecular collisions at the interstitial surface boundaries becomes important); and (4) the porous rock is sufficiently rigid and inert to preclude rapid changes in the pore geometry.

Accordingly, in what follows, we adopt the idea that if Darcy’s law adequately describes single-phase flow, analogs of it can be postulated just as well as useful descriptions of multiphase flow phenomena.

Historical Background In the 1930’s and 1940’s, serious ideas about the meaning and measurement of relative permeability phenomena first appeared. Principal authors were Muskat, Botset. Hassler, Leverett, and perhaps a dozen more whose names punctuate the milestones described in the standard references. ‘.* These people were connected predominantly in one way or another with the U.S. petroleum industry at a time when quantitative study of recovery of hydrocarbon fluids from subsurface sedimentary environments was in its infancy. In focusing on how reservoir fields of fluid flow would be influenced by the nature and number of the coexistent interstitial fluids, the early workers took advantage of the fact that the existing and well-developed understandings about single-phase flow in porous rocks, when generalized. seemed to provide credible descriptions of multiphase flow situations. When L.A. Richards3 published his classic 1931 paper on the flow of capillary-bound moisture in so-called unsaturated soils, Darcy’s pioneering work already had stood the test of three-quarters of a century of scrutiny, use, and amplification by diverse groups of technologists that included groundwater specialists as well as petroleum, chemical, and civil engineers,

Framework Ideas By analogy to Eq. 1, a set of separate equations can be written to describe multiphase flow phenomena under the restricted conditions that no gravity forces are affecting the steady flow of each of the incompressible immiscible fluids, or

9, =(kjA)(AP,)l(~jLjL)=(Wc~jA)(APj)i(~jL),

where the subscript j refers to the jth fluid phase (oil, gas, water). Following the usual terminology. k, is called the effective permeability, krj is called the relative permeability, and Pj denotes values of pressure locally measured in the various fluid phases that are separated by interfaces of contact.

In particular, kj and kti are to be considered measures of the flow conductivity afforded by the porous rock when saturated with the immiscible fluid phases in some particular way. As will be seen, reference must be made to fluid saturation configurations and distributions as well as to fluid saturation levels. For example, and in analogy to the porosity concept where 4 is given by the local ratio of pore to bulk volume, the saturation of the jth fluid, Sj, is defined as

“8 SQV’ ,,...............................(3) /Jr

where Vfi is the volume of fluid j and V,,, is the total pore volume. In other words, the product C&S, can be thought of as an effective porosity of that portion of the partitioned pore space occupied by the jth fluid phase.

It follows that locally (i.e., in any representative volume element of the reservoir rock system of interest) Es,, = 1, even when saturation is changing with time and position. In any case, it would appear that the relative permeability, k,, has a first-order dependency on the saturation level, Si. But this is only one of the dependen- cies, because usually many interstitial fluid phase distributions are possible for each level of saturation. Also, the reduced pore space occupied by each of the several pore fluid saturants is not necessarily everywhere bounded by interstitial (solid pore wall) surfaces; hence, it is possible that the influence of prevalent fluid/fluid interfacial boundaries also may have to be considered. Thus, the statement

O<kr;<l forO<Sj<l, . . . . . . . . . . . . . . . . . . . (4)

while always true, ignores the fact that k,., may equal zero even when Sj is finite, and may be greater than unity even for values for S, less than unity.4.” Moreover, Eq. 4 is too crude to indicate explicitly that krj can have more than one value for each value of si (e.g.. because of hysteresis).

Hysteresis

From the thermodynamic point of view, the fluid flow processes under consideration are irreversible (i.e., nonequilibrium); therefore, they are inherently path- dependent. One consequence is that the equilibrium states approached in one direction can be different from those approached in another. This phenomenon is called hysteresis, and explanations for it are not hard to find. For example, while specific permeability depends mostly on the interstitial pore geometry, effective (hence, relative) permeability depends on the fluid saturation geometry as well. Usually there will be more than one way a given fraction of the pore space can be occupied by each fluid phase of interest. The result is that relative permeability data give values that are functions of the history and sequence of the prior saturation changes as well as being merely functions of the fluid saturation levels.

As will be seen later in this chapter, little laboratory work has been published to prove that Eq. 2 truly describes multiphase flow phenomena. Nor can much reassurance be taken from the fact that the validity of Eq. I as a description of the characteristics of single-phase flow has been confirmed experimentally for a large number of cases. This is because the unsteady states are of the greatest interest when dealing with petroleum recovery problems, but this aspect is ignored by the Dar- cian modeling.

In other words, Eq. 2 by itself does not make it possible to account for and to predict the saturation changes that occur as flood fronts move through reservoir space during production. And in the real processes to be modeled, the various phases may be flowing in separate directions rather than colinearly. The greatest limitation of Eq. 2, however, is that it gives no explicit prescription

RELATIVE PERMEABILITY 28-3

of how to avoid end effects (the buildup of wetting fluid saturation levels at surfaces of capillary discontinuity such as core end-faces) in laboratory work.

Immiscible Wetting and Nonwetting Pore Fluids Whenever wetting and nonwetting immiscible fluids compete to occupy the same pore space, it is clear that at inflow and outflow surfaces of so-called capillary discontinuity, there will tend to be a buildup of wetting fluid saturation levels during the course of multiphase flow processes. This has been understood from the earliest days. 3.6 The central idea is that immiscible fluids that are co-existent in contiguous capillary pore space generally will be separated by curved interfaces of contact instead of by stress-free flat interfaces at contacts that occur exterior to the flow system.

In fact, the inter-facial curved boundaries are a retlec- tion of the balance between capillary and gravity forces in the static (stationary) cases, and of the viscous forces as well in the dynamic cases. This means that locally there usually will be a pressure difference between the immiscible fluids. This pressure difference, commonly called the capillary pressure, P,., by convention is defined as the local difference between p,! and pIr (where the subscripts n and MJ refer to the nonwetting and the wetting fluids, respectively).

In systems at equilibrium. immiscible fluids tend to be distributed such that the free surface energy of the system is at a minimum, subject to the constraints imposed by the S, levels and by the hysteretic path of saturation change being followed as successive equilibrium states are being established. This usually means that the wetting fluid will be found in the smaller pore spaces, and that the interfaces of contact will be concave toward the nonwetting fluid (hence, P, will have positive values). In fact. capillary pressure, like kj and k, , frequently is assumed to be primarily saturation- dependent, but it depends substantially on the fluid/fluid interstitial configurations at each saturation level.

The Buckley-Leverett equation6 takes the following special form in describing two-phase displacement processes involving one-dimensional (horizontal) flow of incompressible fluids. With density p, =constant and aq,l&=O, we have

=o. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...(S)

where 4 is the local porosity independent of time, Af is the cross-sectional area of flow path, P,. is the capillary pressure, L,, is the horizontal distance parameter, and t is the time (both independent variables); and h4, and M,,. are the mobilities of the nonwetting and wetting fluids, respectively (i.e.. M, =k,llLj). As can be seen from the derivations of Eq. 5 given in Refs. 1, 2, and 6. the saturation levels vary with position and time in a way that depends on the variation of P,. with S,,.. on the inherent in the indirect nature of such measurements. To saturation gradient, on the relative permeabilities, and on expose the rationale for selecting one type of procedure the initial and boundary conditions of the problem [as over another, the ideas of recent authors are reviewed well as on certain controllable and disposable variables below.

As will be seen, the steady-state methods are more time-consuming than the unsteady-state methods; still, the data obtained by them are at least as believable as the plausible model on which they are based (Eq. 2), especially if convincing measures are taken to minimize the capillary end effects mentioned previously. On the other hand, the unsteady-state methods, comparatively speaking, supply the wanted data quickly and cheaply. This latter advantage, it may be argued, is only a partial compensation for the uncertainties in data interpretation

such as porosity, fluid viscosities, the specific permeability, and the total flow rate given by (q,,, +q,l)].

Indeed, the importance of having relative permeability information is to make it possible to solve reservoir engineering problems modeled by process descriptions such as given by Eq. 5. The more elaborate modeling technique involving equations with the transport and interaction coefficients described by Rose’ require considering more than simple relative permeability information, however. Even so, the experiments prescribed by the Buckley-Leverett’ and Rose’ equations will not be easy to perform. The laboratory difficulties obviously multiply if unsteady states are to be considered (where Sj changes with time and spatial position). This is why only state-of-the-art methodologies will be described here. Nonetheless, it is clear that future workers will continue to be challenged by the need to develop and to perfect measurement methods that are based on modeling that goes beyond the simplistic Darcian reasoning embedded in Eq. 2.

Measurement Methodologies A number of measurement methodologies have been described in the literature; these are classified and explained to some extent as follows, along with some of the data that have been reported. Two controversial questions are (1) do the various methods yield equivalent data, and (2) if not, which are the most trustworthy ones?

Laboratory measurement techniques for relative permeability determination are of two sorts. In the so- called steady-state methods, the effective permeability as a function of saturation is calculated from the flow data that are obtained on the assumption that Eq. 2 is correct in form. The trick is to make direct measurements prescribed by the theory, of parameters such as volumetric flow rates, pressure drops, and fluid saturation levels. In one variant of the method, known as the Hassler technique,’ provision also is made to control and to measure the local values of capillary pressure to avoid the troublesome end effects.

The so-called unsteady-state methods are based on using integrals of Eq. 5 as the process model. The idea is to observe the consequences (i.e., the outcomes in terms of cumulative production) of controlled multiphase displacement experiments, and then to back-calculate the relative permeability values that are consistent with, and serve to explain, those outcomes. The cumulative production data also are processed to provide a basis for calculating average saturation levels to be associated with the relative permeability values.


Fig. 2&l-Details of steady-state relative permeability apparatus.

Steady-State k, Methods Experimental Procedure. Blackwell and Braun” provide a comprehensive statement of how some people think the steady-state relative permeability method should be practiced when given the understandings and instrumentation opportunities available at the start of the 1980’s. Fig. 28.1 is a schematic ofthe laboratory system that can be used. Positive displacement or other types of constant-rate pumps, one for each fluid, discharge a fixed-ratio mixture into the core sample. Regardless of the initial saturation conditions within the core sample, the effluent fluid mixture eventually will be identical in composition to that being delivered by the pumps upstream. At this steady-state condition, effective permeabilities for the immiscible fluids can be calculated because the separate pump rates (4(, and q,,) will be known, and because an approximation of the pressure drop across the core sample can be used as the indicated driving force for each fluid.

For example, suppose that the reservoir process under consideration involves edgewater encroachment into a uniform sand that has a certain level of interstitial water saturation, with the rest of the pore space filled with an unsaturated oil. A core sample representative of the formation could be selected and. after cleaning. an appropriate initial condition with respect to water and oil \aturat(on could be established by the so-called restored- state capillaty pressure technique. Alternatively (and perhaps ideally), a “fresh” core sample could be brought into the laboratory as recovered by a pressure core barrel so that the wanted initial saturation conditions already would prevail. Or, as still another preparation

procedure, an “as-received” core could be processed so that the mud filtrate was replaced by simulated formation water that, thereafter, was displaced down to interstitial levels by flooding the sample with “live” oil. That is, in one way or another, the imbibition water/oil relative permeability data could be obtained where the experiment is started from a proper initial condition in fluid saturations and saturation distributions. And, if reservoir conditions of wettability were to be somehow preserved or restored as preparations for the experimental work are made, and if the ensuing displacement process were to be undertaken under conditions where reservoir-like overburden stress, pore fluid pressure, and/or temperature were simulated, then so much the better. However, the final saturation levels at steady state still would have to be measured. Several methods are available from which this information can be obtained.

Saturation Measurements. What the Braun and Blackwell method9 does is have a downstream water/oil separator where (as shown in Fig. 28.1) the bulk of each effluent phase is directed back to the inflow sides of the respective pumps, but where the differential amount between inflow and outflow of each phase is collected in a column and gravimetrically or volumetrically measured. In other schemes, X-ray absorbers or radioactive tracers can be added to one or more of the flowing fluids so that external instrument scans of the core will give the information that can be converted back to saturation levels. Even more simply, the core sample can be removed from the core holder after each steady-state condition is

RELATIVE PERMEABILITY

Fig. 28.2-The Hassler “sandwich.” C denotes the core sample of length L and 6 denotes the inflow and outflow capillary end barriers. NW and W designate the ports through which the nonwetting and wetting fluids are directed collinearly as shown by the arrows.

reached, and then weighed so that saturation values can be calculated from independent knowledge of fluid densities and core sample PV.

More details about the steady-state procedure under discussion are available in the references. Suffice it to say that entire curves of relative permeability vs. saturation are to be obtained. following well-defined imbibition or drainage paths, by proceeding stepwise from one steady-state condition to the next. For example, in the water influx experiment under discussion, the q,./q,, ratio delivered by the pumps could be set at succeedingly higher values while going from one steady state to the next until finally the high produced WOR’s would confirm that a condition of residual oil saturation had been achieved.

The previous discussion provides a brief description of the sense of the steady-state relative permeability measurement scheme as used when no special effort is made to control end effects (e.g., the buildup of wetting fluid saturation levels at surfaces of capillary discontinuity such as core end-faces). Early data obtained by equivalent steady-state procedures are reported in Muskat’s classic work. lo Remarkably, there does not appear to be much learned from more recently obtained data than was at least qualitatively apparent in the beginning.

For example, one conclusion that can be drawn consistently from laboratory observations is that the ine- qualities given previously as Eq. 4 can be written more exactly as

O<k,.;<l forS;j<Si<l, . (6)

where S;, is the minimum (irreducible) value of S, when the jth fluid of interest no longer has phase continuity over sensible distances within the pore space. On the other hand, the idea that relative permeability can be greater than unity for saturations less than unity has been reported”.’ and explained as a reflection of the “lubrica- tion” provided as one fluid slides by an adjacent immiscible one.

28-5

DRAINAGE CURVE

. . 1 I I \ ’ I

0 0.2 0.4 0.6 (0.8 1.0 SW E

Fig. 28.3-Schematic capillary pressure curves

On the other hand, when attention needs to be given to end effects, some workers have proposed that long cores be used so that measurements could be confined to an inner portion. ” Even in such a so-called Penn State arrangement, however, the pressure-drop terms of Eq. 2 still are not measured separately for each of the immiscible fluids, and that is why it makes sense to refer back to Hassler’s almost-forgotten work.

The Hassler method for relative permeability determination has had a curious history. The patent was granted in 1944’ and although cited occasionally, it has been ignored by most workers intent on developing simple state-of-the-art procedures. Scheidegge? referred to the method as superior, but difficult and time-consuming to apply, and at one point Rose I2 gave an analysis of why operational difficulties were to be expected in some applications. More recently, however, a patent has appeared that teaches how Hassler’s ideas indeed might be reduced to a practical operating scheme. I3 Whether or not these claims eventually are substantiated by the facts, it is nonetheless of interest to examine in some detail the principle of the Hassler method for relative permeability determination. Thereby, a reference frame can be established to which other steady-state relative permeability procedures can be compared.

0.6 -

kw k.

0.4 -

28-6

- 0.4

0 0.2 0.4 0.6 0.6 1.0

svl

Fig. 28.4-Schematic relative permeability curves

l------

0.3 0.4 0.5 0.6 0.7 0.8

5,

Fig. 28.5-Hysteresis in waterflood vs. oilflood relative permeability curves.


Fig. 28.2 is a schematic that shows the sandwich arrangement where the wetting fluid (denoted by W) passes in series through an inflow capillary barrier as it enters the core sample, and then exits through a similar downstream barrier. The nonwetting fluid (denoted by NW) flows in parallel with the wetting fluid in the core sample but does not enter the pore space of the barriers. This exclusion is achieved by never letting the pressure in the nonwetting phase locally be so great that the barrier threshhold pressure is exceeded; hence, the endflow barriers will always remain 100% saturated with the wetting fluid during the course of the test.

Fig. 28.3 is a schematic of a representative capillary pressure drainage and imbibition curve for the reservoir rock sample of interest where the relative permeability relationships are wanted. Suppose that, as an initial condition, the core (as well as the end barriers in series with it) is 100% saturated with water (say with a simulated oilfield brine). Let the threshold pressure for the core sample be PcA and that for the barrier material be greater than Pee. * Threshold pressure is being defined here as the lowest capillary pressure (P,., -PC.,,.), where the nonwetting fluid will enter a wetting-fluid-saturated porous medium. Since the capillary end barriers are made of material considerably less permeable than the core sample material, P,., $ P,,

Hassler’s way of performing the relative permeability experiment is to measure the effective permeability to each phase by using Eq. 2 at various successive capillary pressure conditions, such as PA, PSI, PSI PC, PDI, PD2. PE. The result is a succession of saturation states such as S,.,, , Ssl, SB2 SC,, SD,, SD2 SE in the sense that from A to C a drainage curve is being traced since the wetting-phase saturation is always decreasing, while from C to E an imbibition curve is being traced since the wetting-phase saturation is always increasing. Note that at A the wetting-phase saturation, S4, is 1 .O, at C the wetting-phase saturation is close to the interstitial water level, S;,,, while at E the wetting- phase saturation is (1 -S,,Z), where S,,, designates the residual (nonproducible) nonwetting fluid saturation level.

Corresponding to the saturation points where capillary pressure values have been measured and shown in Fig. 28.3 during drainage and imbibition, the associated relative permeability data to be obtained by the Hassler method are shown in Fig. 28.4 in schematic format. It is instructive to draw some comparisons between these presentations. Capillary pressure as well as relative permeability functions are saturation-dependent. They both appear as parameters in the Buckley-Leverett description of multiphase flow and displacement processes (Eq. 5). Both functions are a direct reflection of the network structure of the pore space (size, shape, orienta- tion, mode of branching, tortuosity, etc.). It is for these reasons that early workers were quick to search for the direct dependency between capillary pressure and relative permeability phenomena ” and that Hassler, with such great insight, was provoked to emphasize the interconnections that still earlier had been recognized by Leverett I5 and Richards. ’

*Pee IS the highest value of capillary pressure 10 be used I,, the exper,men, 10 ob,a,n Ihe lowest value of S,


The process under discussion is complicated and not OIL ISOPERMS GAS

easy to describe without many details. Since these are fully covered in the original references, ‘J.’ it is enough to end the discussion here with the observation that there are at least two ways, in principle. to practice the Hassler method. One is to impose fixed boundary conditions in pressure upstream as well as downstream, and then to observe flow rates needed for the calculations of permeability data. * The other” is to have constant flow rate as the upstream boundary condition while keeping constant pressure as the downstream boundary condition. What is gained thereby is circumvention of the practical difficulties of avoiding end effects encountered when the boundary conditions are set in terms of upstream and downstream pressure only. / \ \

YRTER / I ' OIL

Unsteady-State k, Method Compared to the unsteady-state methods to be described Fig. 28.6-Three-phase saturation trajectory and oil isoperms

now, the steads-state methods are suite straightforward rangingfrom 1x10-’ to2x10-3.

and involve few uncertainties. The following analyses will reveal why this is so.

Experimental Procedure. In so-called unsteady-state procedures, effluent production from a core sample during the course of an imposed displacement process is recorded, and relative permeability functions are generated on the basis of a mathematical modeling of the process that is supposed to be consistent with what is being observed. In practice, the mathematical model usually selected is a simplified form of an integral of the Buckley-Leverett Eq. 5. By linearizing the equation by dropping the capillary pressure (end effect) terms, back- calculating the relative permeability functions appears to be possible.

Since the aim is to get more resolution for calculation of intermediate values of relative permeability and for calculation of the associated saturation values, one needs to spread out the effluent production data. The whole enterprise is compromised, however. when a very unfavorable mobilit? ratio is chosen as the way to prolong the transient penod before total breakthrough of the displacing phase. The reader is referred to one analysis of this situation’ for further information.

Methods of Calculation Institut Francais du Petrole Method. The reader also is referred to the definitive paper by authors at the In- stitut FranGais du P&role I6 for full details about how to practice the unsteady-state method for relative permeability determination. Constant-flow-rate and constant-pressure schemes are described, precautions are enumerated, and calculation schemes are given. Fig. 28.5 is taken from another paper” that shows how representative data and the associated relative permeability curves might look in a representative case.

Automated Centrifuge Technique. To finish with the discussion of the variants of the unsteady-state methodologies, it will be useful to cite the work of O’Meara and Lease, I8 who gave three-phase data obtained with an automated centrifuge technique. By spin- ning core samples in a centrifugal field of known strength and observing effluent volumes as a function of

time, a back-calculation of relative permeability can be made (which, again, will be at most of qualitative value because of the limiting assumptions that have been used in the mathematical modeling).

Claims made for the centrifuge technique are (1) it does not suffer from viscous fingering distortions, as in the case of the conventional unsteady-state procedures, and (2) it is faster than the competing steady-state procedures. However, the capillary end-effect problem still has to be faced. Another disadvantage is that in any given run, the information obtained applies only to the relative permeability of the invading phase. Since the conventional unsteady-state procedures give relative permeabilities for the displaced (as well as the displacing) fluids, and since larger samples can be processed than is possible in the centrifuge, the conventional approaches are the ones that are considered to be state-of- the-art. In fact, the appeal that the centrifuge technique holds for experimenters is related to its suitability for automation, and to the fact that it is already generating three-phase data. Fig. 28.6, for example, is a display of some of the data that have been reported.

Critique of Methods To summarize what has been published about relative permeability measurement methodologies, the critique originally given by Scheidegger, 2 and more recently af- firmed, ‘* is accepted enthusiastically here. The consen- sus seems to be that the steady-state methods. Hassler’s in particular, give the most believable results since they are based on a plausible (however naive) definition of relative permeability (i.e., as embedded in Eq. 2). Unsteady-state methods, while quicker and easier to apply from the laboratory operational point of view, nonetheless are beset with enormous interpretation difficulties. This is mostly because they involve drawing in- ferences (by way of back-calculations) from a rough- integral form of the Buckley-Leverett Eq. 5. As noted previously, Eq. 5 is at most an imperfect model of the flow process under study. ’


t

0 i l 76 Cm. Hg.(Air Flow)

A P’=oO (Air Flow) 0 P’*CO (Hellurn Flow)

,THEORETICAL CURVE

2 .4 6 6

SL,- WETTING LIOUID SATURATION (fracl~onal)

Fig. 28.7-Gas relative permeability vs. total wetting-liquid saturation.

Other k, Methods Still other methods to arrive at relative permeability information remain to be cited for completeness. For example, there are the so-called stationary fluid methods I9 and the calculation methods based on capillary pressure and endpoint displacement data associated with Corey et al. *O and Stone.2’ Figs. 28.7 and 28.8 display some of the results given by these investigators.

In the stationary fluid methods, the effective permeability of one phase is measured by flowing that fluid at such a low pressure gradient that the contiguous immiscible fluid is left (it is hoped) unaffected. Clearly, the method can be trusted most when the stationary fluid has a saturation level close to its minimum (irreducible) value (i.e., Sj-+SV for the stationary fluid). Otherwise, it may be concluded that the data generated by applying the method will be distorted by the ever-present end effects. On the other hand, the method is easy to apply operationally, and the data generated giving k, at S;,, (irreducible water saturation) and k,. at S;, (irreducible oil saturation) are needed along with other parameters when calculated values of relative permeability are to be made by the popular Corey et al. and Stone methodologies. In any case, values for k, at Sit,. give an indication of the initial productivity of oil wells from horizons where there is only initial oil plus interstitial water saturation. Similarly, values for k, at Si, can be used to indicate the level of the effective water/brine permeabilities when residual oil saturation conditions are reached at the end of a waterflood recovery process.

To understand better the rationale for using relative permeability calculation schemes, reference can be made to the early papers where they were first advocated. 14~‘2 All along, the idea underlying them has been that petrophysical properties (e.g., relative permeability and capillary pressure relationships, specific surface area,

Fig. 28.8-Matching Corey et al. Berea sandstone data

electrical resistivity parameters, etc.) depend in one way or another on the nature of the pore structure, and on how it will be partitioned in representative cases between the intertwining filaments of the adjacent immiscible fluid phases. Of the pore textural properties enumerated previously, relative permeability turns out to be the most difficult one to measure in the laboratory. This has been the origin of the thought (and hope) that an economy could be expected if relative permeability information somehow could be extracted (by way of calculations) from the more easily obtainable data. Wyllie,” a foremost advocate of these ways of thinking, is the authority to be consulted when more information is needed.

Eqs. 7a and 7b are the ones given by Corey et al. 2o for calculating k, under three-phase saturation conditions, and Eq. 8 is the one proposed by Stone. I’ For SL > SLrr

k,.~~=(1-S,-S,V)3(1-SS,+S,,,-2SL,)/(l-SLr)4.

. . . . . . . . . . . . . ..I........... (74

and for SL 2 SLr

k,=(1-S,-S,.)/(l-SL,)4. . . . .(7b)

Also,

km =(k,w +k,)(k,, +k,)-(km, +k,), . (8)

where SL = total liquid saturation, fraction,

SLr = residual liquid saturation left in pore space, fraction,

k,,. = relative permeability to oil in a gas-free system, and

k i-q = relative permeability to oil in a water-free system.


0.6

A’ 0.5

0.4

0.3

0.2

0. I

0 40 50 60

.9,-x vp

Fig. 28.9-Gas/oil relative permeability in poorly consolidated Fig. 28.10-Unsteady-state. three-phase relative mobility sandstone. (relative permeability to oil, Berea sandstone).

The recommendation for using Eqs. 7 and 8 to obtain calculated values for the difficult-to-measure k,,, under three-phase saturation conditions is that one only needs to enter more easily obtained two-phase data. Inspection will show that while such equations give plausible results (e.g.. compatible with the indications of Eq. 6), the results are no more trustworthy than the modeling assumptions when measured relative permeability values are needed but are otherwise unavailable.

Comments. A conclusion to be drawn from this analysis is that if there is any merit to taking short-cuts, it is only when the benefits outweigh the risks. While many (perhaps most) of the readers of this chapter will never have to go to the laboratory to make relative permeability measurements, it is important for them to realize that someone, some day, has to make such measurements before any of the calculation schemes can be used with confidence. In other words, computer guesswork in general will be no substitute for laboratory work. This is because direct observations always will be needed before reliable predictions can be made for processes that inherently depend on material response parameters such as relative permeability.

Recent Literature More than 30 years have elapsed between an early and a later time when the author of this chapter was provoked to write papers on the then-current problems of relative permeability measurement. “X It is as though some of the problems have continued to be unsolved and/or un- solvable, while other vexing ones have emerged to take the place of any of the earlier ones that somehow were resolved. In the meantime. work continues on many fronts such as those critiqued in this paper. Note that all the papers now to be referenced have appeared after

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A w 2 .4 8.. A 5 d ?F �. ,� *� E yv . a A

.OOl I d f I I I 20 40 60 t

OIL SATURATION, PERCENT 1

80

60

‘I

0

I 0 I

0.11 2 I I I I

0 IO 20 30 40

0.2 0 cm t

7

GAS SATURATION. %

Fig. 28.1 l--Relative permeability to gas in three-phase flow as a function of gas saturation.


CONTACT ANGLE

- leo0 -- 410

Fig. 28.12--Relative permeability to oil and water showing the effect of displacement (Curve 1) vs. carbonated water displacement (Curve 2)

0 20 40 60 80

WATER SATURATION, PERCENT PORE VOLUME

1 10 0

Fig. 28.13-A comparison of restored-state and native-state water/gas relative permeability data.

0 20 40 w 80 1Ul WATER SATURATION. PERCENT PORE SPACE

Fig. 28.14-lmbibition relative permeabilities for two wetting conditions, Torpedo sandstone.

Wyllie wrote the original chapter on “Relative Permeability” in the first edition of this handbook (in 1962) referencing the literature through the 1950’s. z3

Critique of Recent Work Loomis and Crowe1126 present an early but extensive comparison of data obtained by various methods, and as calculated by various mathematical modeling schemes. The high degree of conformity reported makes suspect the objectivity of the work. On the other hand, the authors were quick to point out that wettability was an uncontrolled laboratory variable in their work. This dis- quieting contention was matched by the surprising result reported without explanation by other workers at the same time, namely that hysteresis effects were different for unconsolidated vs. consolidated core samples. ” Fig. 28.9 shows the trends observed.

The paper of SaremZs was one of several describing three-phase measurements by an unsteady-state method. One observation (see Fig. 28.10) of this work had to do with the important role played by the initial saturation conditions. At about the same time, Saref and Fatt29 reported success in the development of a nuclear magnetic resonance technique for measurements of fluid saturation levels. These workers, moreover, confirmed the long-held view that relative permeability to gas in three-phase systems depended mostly on the total liquid saturation. This calculation is supported by the data shown in Fig. 28.11.

Two papers appeared in the early 197O’s’o.” indicating that relative permeability to oil is greatly increased if CO* is present (see Fig. 28.12). At this same point in time, Lefebvre du Prey3* was dealing with the question of interfacial tension effects on relative


kro

Fig. 28.15-Gas/oil relative permeability calculated from production data from experiments.

permeability while Schneider and Owens3” and Owens and Archer34 were concluding that because of wettability effects, experimenters were advised to make use of so- called native-state cores. The work of Bardon and Longeron- ” also dealt with this subject. And somewhat later Sigmund and MacCaffery36 were trying to sort out the influence of reservoir rock heterogeneity on relative permeability characteristics. Some of the data presented by these authors are shown in Figs. 28.13, 28.14, and 28.15.

In the 1980’s, numerous relative permeability papers continue to appear as though a renascent interest in the old subject is developing. A noteworthy one was by Hagoort, 37 who used a centrifuge technique to show the high efficiency of the gravity drainage recovery process in water-wet cores. Bogdanov and Markhasin”* introduced the less familiar subject that speculated that viscosity changes (because of molecular-surface interactions with the rock matrix) could distort relative permeability data. At the same time, Ashford,j9 in a very comprehensive paper, was reopening the dubious issue of how relative permeability and capillary pressure data can be linked directly. (As implied above, it is nice to have a conceptual theory available to explain relative permeability effects, but to expect that calculations avoid the need for careful experimental work is a kind of wishful thinking that can be justified only when there is a great urgency to have qualitative inputs for reservoir process simulations). Fig. 28.16 is representative of the fits reported by Ashford between calculated and measured values.

Delshad et al.” currently have addressed the in- teresting question of whether the transport of low-tension micellar fluids will significantly change classical relative permeability trends. They show that the residual (endpoint) saturations decrease and relative permeabilities increase as interfacial tension decreases. The predicted nearly 45” relative permeability curves are shown for one case in Fig. 28.17. Yokoyama4’ has been dealing

28-11

Fig. 28.16~-Relative permeability relations for imbibition and drainage experiments, with values calculated by Naar et al. method.

Fig. 28.17~lmbibition relative permeability curves for microemulsion and decane vs. oil saturation in Berea sandstone.


with the equally complex problem of accounting for transverse and longitudinal capillary imbibition during displacements in stratified media.

In another direction, Carlson4* extends Land’s4’ earlier prescriptions for calculating flow from independent measurements of rock properties. Chierici4 does the same thing, on the basis of the “bundle of capillary tubes” model described earlier by Brooks and Corey. 45 Some of these data are shown in Fig. 28.18.

Finally, Lin and Slattety46 and Mohanty and Salterj’ carry pore structure (network) modeling as a basis for ar- riving at calculated relative permeabilities to still higher plateaus of sophistication. Extensive bibliographies are provided by these latter authors. Some of their results are given in Figs. 28.19 and 28.20.

For example, Fig. 28.20 indicates that (1) relative permeabilities to the nonwetting phase k, during secondary imbibition (SI) and imbibition (IM) are essentially the same but lower than the values that refer to the primary drainage (PD) conditions, and (2) relative permeabilities to the wetting phase k, during primary drainage is lower than that in either seconda drainage or imbibition. In other words, those authors conclude that “the ratio of conductivity or nooks and crannies to that of a full throat feature influences the wetting fluid permeabilities only at low saturation.”

Other recent papers are those of Salter and Moharty,48 who made observations to justify a modeling of multiphase flow that postulates flowing, dendritic, and isolated configurations for each phase, and of Maini and Batycky, 49 who claim (see Fig. 28.21) that temperature influences both the endpoint saturation and the shape of the relative permeability curves. A different view about the importance of temperature effects had been expressed earlier by Sufi et al. 5o

no I- -* /- -. 1

a2

0

Fig. 28.19-Comparison of drainage relative permeabilities from randomized network model with experimental data for 100 to 200 mesh sand.

The paper of O’Meara and Lease I8 has been cited previously in connection with the unsteady-state determination of three-phase relative permeabilities using the centrifuge technique. It, along with the Maini and Batycky paper, 49 are just two of nine other papers on relative permeability presented at the 1983 Society of Petroleum Engineers Annual Technical Conference and Exhibition in San Francisco, Oct. 5-8. Listing them by topic is one way to expose the depth and breadth of current interests in the subject. Thus, Kortekass”’ describes displacement in cross-bedded reservoirs. Meads and Bassiouni5’ speak of combining production history and petrophysical correlations to enhance the represen- tativeness of relative permeability data. Miller and Ramey 53 deal further with temperature effects for oil/water systems. Mohanty and Salters4 extend their work on oil mobilization, transverse dispersion, and wettability effects. Fulcher et al. ” and Harberts6 deal further with low interfacial systems. Heiba er al. 57 address the wettability uestions. Heaviside et al. 51

And in companion papers, cover the experimental and theoretical

aspects of relative permeability phenomena. Such are the extensive details currently being discussed.

Ramifications Needing Attention In summary, the reader who has studied the representative papers cited here, and the even larger number that are scattered in the literature at large, will conclude that this chapter is not the final one to be written on what amounts to be a very complex subject. Some of the ramifications that appear to need further attention include studies of the following effects: (1) phase changes such as gas evolution during multiphase flow, (2) non- collinear flow in a gravity force field between immisci-


ble fluids of differing densities, and counterflow imbibition. (3) reservoir rock anisotropy and heterogeneity by which sample size and sampling frequency requirements are to be determined, (4) “fines” movements. (5) overburden stress simulation and related stress-relaxation and creep compaction phenomena, (6) viscous drag at interstitial interfaces between contiguous immiscible fluids, (7) chemical precipitation and dissolution phenomena, (8) chemical reactions, (9) high Reynolds- number conditions (nonlinear laminar and turbulent flow regimes) (10) Klinkenberg gas-slippage effects. (I 1) concentration and/or thermal gradients being superim- posed on fields of flow primarily caused by mechanical energy gradients, (12) non-Newtonian rheology, (13) systems characterized by more than one local pore space type, (14) fluid/solid interactions, for example, as related to the mineralogy of interstitial clays, (15) viscous fingering, and (16) hysteresis related to wettability changes.

While theoretical considerations may permit a qualitative prediction of the nature of some of these effects, in the final analysis, any truly quantitative assessments should be based on directly undertaken experimental work, if possible. This is not to say that in every case the laboratory data obtained on small hand specimens will reveal everything that needs to be known about large composite petroleum reservoirs, but rather that observations generally are more trustworthy in- dicators than are blind guesses.

Conclusions Several questions come to mind whenever the subject of relative permeability is raised: how is it to be defined‘? where can the information be obtained? why is it needed and by whom? What are the proper (fruitful) ways to use it? Only partial answers to some of these questions have been given in this chapter. This is because the subject is too vast to be dealt with fully in limited space and because the details not covered are probably too specialized for the average reader, whose concern is only with the ordinary applications.

Here we have asserted that definitions of permeability (specific. effective, relative) are embedded in the differential equations that describe the transport equations governing fluid flow in petroleum reservoirs. Eqs. I and 5 are examples that apply to special situations (steady single-phase flow and unsteady multiphase flow of immiscible fluids, respectively). Obviously, the differential equations of transport will have other forms for more general cases of fluid flow, such as those observed when there is coupling with chemical diffusion and/or heat transfer processes. This is to say that there may be different kinds of relative permeability to deal with according to the nature of the process under consideration. In all cases. however, one must start by constructing the defining equations to be compatible with the underlying principles of nonequilibrium thermodynamics.

Relative permeability information can be obtained in two major ways. The preferred method is to have an cx- periment performed on a representative sample of the reservoir rock according to the procedure prescribed by the appropriate integral form of the defining differential equation. Eqs. 1 and 2 are examples of integrals that involve measurable terms (such as volumetric flow rates

0 50 100

NONWETTING PHASE SATURATION

Fig. 28.20~-Relative permeability curves.

RUN: I1 TEMPERARATURE: i 02' C

WATFP SATIJPATIZN

Fig. 28.21-High-temperature relative permeability curves for oil and water.

28-14

and pressures. pi, at bounding sample surfaces). Since the parent differential equations themselves have terms that cannot be directly measured in the laboratory (such as velocity and mechanical energy gradients), integral forms that apply to the particular initial and boundary conditions of the problem must be derived and used for each specific case.

In these connections. it will be revealing (and disturbing) to mention that the degree of equivalence of relative permeability functions obtained by different methods (e.g., the steady- vs. the unsteady-state schemes mentioned previously) so far has not been established fully. Eq. 2 prescribes how the steady-state results are to be obtained, while integrals of Eq. 5 prescribe how the unsteady-state results are to be obtained. Until the definitive laboratory work is done and the comparisons are reported in the literature, users of relative permeability information today will continue to be left in the dark as to which procedure can be used with the most confidence when applications are being made.

As for ordinary applications, relative permeability information is used by petroleum reservoir engineers when interpretations and assessments are being made about the outcomes of observed and probable petroleum recovery processes. These applications are referenced in other chapters in this handbook (e.g., on reservoir simulation. well testing analysis. etc.). and will not be discussed further here. Suffice it to say that the same governing transport equations and their integrals by which relative permeability is defined, necessarily are used again in the ensuing analyses of reservoir performance; hence, relative permeability will be needed as input data whenever analytical studies are undertaken. Among other things, this means that using drainage relative permeability data to describe an imbibition process (such as waterflooding) should be avoided.

A second way to obtain relative permeability information is to develop suitable models of the processes under consideration for use as calculation algorithms. Eqs. 7 and 8 are examples that in use require laboratory data more easily obtained than the relative permeability functions themselves. For example. to calculate three-phase oil relative permeability as a function of oil saturation (where S,, = I -S,,.-S,) by Eq. 7, all that is needed is prior knowledge of the interstitial water saturation. Naturally, such calculation schemes cannot be used blindly except for cases where it has been independently validated that calculated and experimental values are equivalent. In other words, even the most carefully constructed calculation scheme does not circumvent the need to have experimental measurement methods also developed and available.

However, calculation schemes usually involve analytical functions that can be entered directly into the computer software used for such things as qualitative economic forecasting. Similarly, the related way to obtain relative permeability information, namely by infer- ring it from the values that force history matches of observed field data, also has a utility when qualitative assessments are being made using reservoir simulators.

The points being made here are both subtle and self- evident. The aim has been simply to convey a certain set of useful ideas to users of relative permeability information such as (I) that relative permeability methodologies


are still in the developmental state even after more than a half century of well-intentioned labor by hundreds of workers and (2) that users of relative permeability information must put the burden of proof on those that supply it. to demonstrate that credible schemes have been used.

Acknowledgment Any author who has been writing narrowly on a specialized subject like relative permeability for more than a third of a century (specifically from 1948” to 1984l”) has to be deeply indebted to all those inspiring workers who have managed to keep the issues alive and in focus over such a long period. A few of them, but not all, are named in the abbreviated references that appear here. Likewise, any teacher for a similarly long period must be deeply indebted to the generations of inquisitive students who were willing to ask the provocative questions before they graduated and left to disappear into oblivion. What a lucky thing it was to have had so many companions on what otherwise would have been a dreary Orwellian journey.

Nomenclature A=

Af = k=

k, =

k,.i =

k ,-oh’ =

km,,. =

k,.,,. = K ,11<’ =

L=

L/l = M,, = M,,, =

P, = Ap = P,. =

4= s, = s”,l II

Sin = Sj =

SL = s1.r = SLU =

srr, =

s,,. =

s wr = I=

“J =

“p, = Ap =

c”=

cross-sectional area cross-sectional area of flow path specific permeability effective permeability, Fluid j (gas. oil. or

water) relative permeability, Fluid j (gas, oil, or

water) relative permeability to oil in water-free

system relative permeability to oil in gas-free

system relative permeability of wetting fluid microemulsion dispersion coefficient length horizontal distance mobility of nonwetting phase mobility of wetting phase pressure, Fluid j pressure drop capillary pressure volumetric flow rate residual gas saturation irreducible (minimum) value of S.; irreducible (interstitial) water saturation fractional saturation of jth fluid total liquid saturation residual liquid saturation wetting liquid saturation residual (nonproducible) nonwetting fluid

saturation water saturation residual water saturation time volume of Fluid j total PV pressure drop fluid viscosity


(T = inter-facial tension 6 = porosity

Subscripts

g = gas

j = jth fluid (gas, oil, or water) n = nonwetting 0 = oil M’ = water or wetting

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Chapter 29

Petroleum Reservoir Traps Raymond T. Skirvin, J.R. Butler and Co Brian E. Ausbum, J.R. Butler and CO.*

Introduction A reservoir trap is a combination of physical conditions that will cause hydrocarbon liquids and/or gases and water to accumulate in porous and permeable rock and prevent them from escaping either laterally or vertically because of differences in specific gravity, pressure, fluid/gas characteristics, and/or lithology. It has the capability of collecting, holding, and yielding hydrocarbon fluids and water.

The portion of the trap that contains oil and/or gas accumulations is the petroleum reservoir. It generally occupies a limited portion of the trap capacity, the remainder being occupied by formation waters that underlie and are interspersed within the petroleum accumulation.

Traps are formed by an infinite variety of structural and stratigraphic conditions of rock formations combined with pressure differentials among the various fluids within the reservoir rock. A trap consists of an impervious cover or roof rock overlying a porous and permeable rock. Reservoir pressure gradients and fluid flow within the reservoir rock can create traps that do not have structural closure. The boundary between oil and water or between gas and water need not be flat or level when these pressure gradients are present. Generally. however, traps do have structural closure, and as viewed from below, the impervious cover is concave, preventing the oil and gas, if present. from escaping vertically or laterally. The water underlying the oil and gas exerts a buoyant force on the oil/water boundary or contact, lifting and holding the oil and gas to the crest of the structure or area of minimum hydrostatic pressure.

Trap Classification Classification of traps logically falls into three broad general groups: (I) structural, (2) stratigraphic, and (3) combination. More detailed classifications have been

made by geologists attempting to include all factors and conditions that account for petroleum reservoirs. Many reservoirs have unique features that cause the oil to accumulate at a given location. The purpose of this chapter is to illustrate the more common geological conditions that cause traps and to point out a few of the infinite variety of minor variations that help create and hold petroleum accumulations in place.

Structural Traps Structure implies some form of rock deformation, commonly expressed as a positive uplift, which may result in four-way dip closure. With the proper stratigraphy, structural traps may be present. Domes, anticlines, and folds are common structures. Fault-related features also may be classified as structural traps if closure is present. Structural traps are the easiest to locate by surface and subsurface geological and geophysical studies. They are the most numerous among traps and have received a greater amount of attention in the search for oil than all other types of traps. In new areas of exploration the prime search is for potential reservoir rock, source beds for hydrocarbons, and structural deformation. This structural deformation provides opportunities for several types of structural traps.

Domes, Anticlines, and Folds. Domes, anticlines, and folds in general must have structural closure to become effective traps. The reservoir rock must dip away in all directions from the crest of the structure. If there is not dip in all directions away from the crest but hydrocarbons are present, there are other contnbuting physical factors that helped complete the trap.

Domes, anticlines, and folds caused by structural deformation of sedimentary rocks generally create many potential traps because the deformation extends vertically through potential reservoirs. Thus a single well can reveal many possible pay zones when drilled on the crest of a domal structure.


KREYENHAGEN KETTLEMAN HILLS PLAINS

KETHiXl-;AN SANvJL$+J’N

TEMBLOR SANDSTONE REEF R’DGE KETTLEMAN HILLS

KREYENHAGEN SHALE CROSS SECTION CRETACEOUS -UNDIFF

Fig. 29.1-Example of anticlinal folds creating structural traps; Kettleman Hills field.

L*IN 8Y 5NdO I -. - . - ..-- -,

IN PLVXEHE )IATOYITE SPELLACY ANTICLINE 1FII” rAtr

.’ ’ \ CROSS SECTION \

OF THE WILLIAMS AND TWENTY-FIVE’

HILL AREAS MIDWAY OIL FIELD

KERN CO., CALIFORNIA 500’ 0 aaa’lcm’ Imod 2500’

DONUIL HILLIS. NOV. 1941

Fig. 29.2-Example of anticlinal folds creating structural and stratographic traps: Midway oilfield.

1 3.000

SANTA FE SPRINGS FIELD, CALIFORNIA

Fig. 29.3-Example of anticlinal folds creating many separate reservoirs: Santa Fe Springs field.

Figs. 29.1, 29.2, and 29.3 are cross sections of Ket- tleman Hills, Midway, and Santa Fe Springs fields, CA. t These are examples of single folds creating many separate accumulations. The separation between the various reservoirs is demonstrated in each case by different oil/water and gas/oil contacts in most reservoirs. The Midway field also illustrates stratigraphic traps formed on the flanks of the anticlinal fold.

Folds, anticlines, and domes arc the easiest to interpret in subsurface studies. They vary in size from a few acres to several thousand acres. Folds and anticlines were created by compressional or tensional forces in the earth’s crust or by differential compaction of the sediments. Asymmetrical anticlines, overturned anticlines, thrust faulting, and fracturing generally indicate areas of compression. Symmetrical folds and anticlines, low-angle normal faulting, monoclines, homoclines, and low-relief domal structures generally indicate areas of tensional forces or compaction.

Mountainous areas usually result from compressional forces. Torsion and shearing help cause local complex structures but are generally forces resulting from the more regional compressional forces of the earth’s crust.

Stable areas or areas of subsidence ate the counterpart to mountain-building compressional areas. They are areas where structures arc caused by differential

PETROLEUM RESERVOIR TRAPS 29-3

m FAULT OF FAiLTED FAULT

REGIONAL DIP ANTICLINE STRUCTURE THRUSTWT;EVERSE GRABEN AND HORST

NORMAL FAULTING

Fig. 29.4-Examples of fault traps: Fig. 29.5-Examples of fault traps: normal or gravity faults. reverse or thrust faults.

downwarping, as in the midcontinent area of the U.S. and areas where structures are created by the lengthening of the earth’s crust, such as the gulf coast of Texas and Louisiana. This lengthening causes regional horizontal tensional forces that create simple and more predictable local structures. The many prolific structural and stratigraphic oil trends that parallel the U.S. gulf coast today are the result of regional downwarping and tensional forces.

tural closure.

Fault Traps. Fault traps are classified as structural traps where closure is effected in one or more directions by faulting or where faulting has caused definite changes in

Normal or gravity faults (Fig. 29.4) occur as a result

the reservoir configuration (such as along strike-slip faults). Many structures are faulted without being limited by the faults or without changing the reservoir configuration. Fault traps can occur in both the up- and downthrown blocks. Closure against the fault can result from faults striking across regional dip or across anticlines or domes. Horsts and grabens and other closed fault blocks can result in traps with relatively no struc-

the fault. This “downbending” creates a reversal in dip and this results in closure. This type of trap is extremely common in the Cenozoic formations of the U.S. gulf coast.

Reverse or thrustfaults (Fig. 29.5) result from compressional forces and involve horizontal shortening of the earth’s crust. The angle of the fault plane with a horizontal plane can vary from a few degrees to 90” and can be recognized in the subsurface by repetition of stratigraphic section in wells drilled through the fault plane. Structural traps of this nature are common on both the east and west coasts of North America. The occurrence of a trap against a fault depends on the fault plane sealing the porous reservoir rock and preventing migration across or along the fault plane.

solution and combine with primary and secondary porosity to give a greater effective reservoir porosity and

Fractured formations usually are caused by local deformation, faulting and folding, reduction in overburden permitting expansion of the underlying rock, and differential compaction. Brittle rocks are more commonly affected because of their inelasticity. In many cases minor joints, fractures, and fissures are modified by

of tensional or gravitational forces. The angle of the fault plane with the horizontal generally ranges between 25 and 60”. Normal faults involve horizontal lengthening of the earth’s crust and are recognized in the subsurface by loss of stratigraphic section in wells drilled through the fault plane. Geophysically, they are recognized by inter- ruptions in the continuity of reflective interfaces.

Two common types of normal fault-related traps are: (1) fault closures and (2) rollover fault closures. Any structural nosing cut at right angles by a fault results in a fault closure. The direction of throw on the fault is not important but the closure created by the fault is. For example, a south-plunging structural nose cut at right angles by a fault will result in a potential trap. The fault throw may be in either direction. A trap will result if the fault acts as a seal or if the potential reservoir is thrown against a shale or other impermeable member on the opposite side of the fault.

Gravity-type faulting commonly occurs in areas of tension and over the crests of domes and anticlines because of the stresses involved. Fault traps are common in such an environment, and hydrocarbon accumulations may occur on either the up- or downthrown blocks, in horsts,

permeability. Fractures in reservoirs increase the wellbore radius and permit extremely tight and impermeable areas to bleed into the fractures over a wide area and thus be connected with channels leading to the wellbore.

Production is sometimes obtained from igneous and metamorphosed rock as a result of fracturing. The fractures provide the reservoir space as well as the permeability to permit oil and gas migration, accumulation, and production from the reservoir.

For a trap to occur in a fractured formation, it must be overlain by a more pliable or less brittle rock that has not been fractured by the deformation. Otherwise, migration would occur up through the fractures and there would be no trap.

Where faulting caused the fracturing, production is limited to a narrow band along the fault. When folding or other deformation has caused the fracturing, the reservoir can become very complex in shape and unpredicta- ble in production performance. Generally, the areas of greatest deformation have the greater number of fractures, which results in better well performance and recovery of more oil or gas.

and/or in grabens. Rollover fault closures are common in sedimentarv Stratigraphic Traps

basins receiving great quantities of sediments. Closure $ Traps created by changes in stratigtaphy have the same created on the downthrown block by contemporaneous physical requirements as structural traps. There is an up- sedimentation and fault movement. Through this interac- dip limitation or termination of the reservoir rock, tion, more deposition takes place next to the active fault creating an area of minimum hydrodynamic potential or plane, resulting in a “downbending” of the deposits into .concave closure. In case of structural limitations, this is

Fig. 29.6-StructuraVstratigraphic interpretation; Northwest Atkinson field, TX.

obtained by faulting or a turnover of the reservoir rock. In stratigraphic traps, this limitation is accomplished by changes in porosity and permeability, which result from nondeposition, erosion and overlap, facies, and lithological changes caused by depositional variations, truncation, and differential compaction.


Stratigraphic traps can be classified as primary or secondary. Primary traps are those formed during sedimentary deposition: lenses, facies changes, shoestring sands, offshore sandbars, reefs, and detrital limestone or dolomite reservoirs can be classified as primary. Secondary traps arc those resulting from later causes such as solution, cementation, erosion, fracturing, and chemical alteration or replacement.

Primary Stratigraphic Traps. These traps result from deposition of elastic or chemical materials. Shoestring sands, lenses, sand patches, bars, channel fillings, facies changes, strand-line (shoreline) deposits, coquinas, and weathered or reworked igneous materials are classified as elastic sedimentary deposits and can result in stratigraphic traps. Fig. 29.6 is a structural/stratigraphic interpretation of the northwest Atkinson field in Live Oak County, TX. 2 An ancient sand-filled stream channel meander has cut into older south-dipping shales and created a perfect stratigraphic trap. Fig. 29.7 is a cross section3 across the Yoakum Channel in Lavaca County, TX. This is an example of a channel filled with shale. The shale plug served as the seal for reservoirs within a west-plunging structural nose. Hydrocarbons are trapped in the truncated updip portions of the reservoirs.

Organic reefs or biohenns and biostromes are the primary chemical stratigmphic traps; they are built by organisms and are foreign bodies to the surrounding deposits. A cross section of Scurry field in Scurry Coun- ty, TX (Fig. 29.8) gives an example of a primary chemical stratigmphic trap.4 The Strawn and Cisco- Canyon series are limestone reefs that have had younger sediments deposited on the flanks and eventually over the crest of the reef deposits. The shale serves as the seal. Differential compaction of the thicker shales on the

H.R. SMITH PURE PURE PURE CHAVANNE PURE WILSON TEXAS E. BOOTHE RICE CHANDLER REt-SE CARTER SCHULTZ OUOTA ORSAK

II ’ -1%0~l~....114 TOP OF WI, ,-nx 115J164V 118

LOG SECTION A-A’

CHANN

FILL

MIDDLE WILCOX CHAN

Fig. 29.7-Cross section showing stratigraphic position of upper Wilcox Yoakl urn channel.

NEL


Fig. 29.8-Example of a stratigraphic reef field; structure and cross section of Scurry field.

flanks of the reef as compared with the thinner shale at the crest has created structural closure in younger overlying formations. Hydrocarbon accumulations have occurred in the Cisco and Fuller formations as a result of this differential compaction. Additional traps in other reservoirs arc the result of updip permeability and porosity barriers and are either primary or secondary stratigraphic traps.

Secondary Stratigraphic Traps. Traps of this type were formed after the deposition of the reservoir rock by erosion and/or alteration of a portion of the reservoir rock through solution or chemical replacement.

Secondary stratigmphic traps actually should fall into the combination-trap classification because most are associated with or are the result of structural relief during some stage of development of porosity and permeability or limitation of the reservoir rock. However, many of the so-called typical “stratigraphic traps” fall into this category, and it is felt that it would be impossible to change the historical usage of this term. Therefore, secondary stratigraphic traps are defined for this discussion as those traps created after deposition and having limitations caused by lithology changes.

Erosion creates a major part of these through truncation of the reservoir rock. On-lap deposition (when the water is encroaching landward), off-lap deposition (when the water is regressing), and the chemical alteration of limestone result in many secondary stratigraphic traps.

The East Texas field (Figs. 29.9 and 29.10) is perhaps the most famous field in this classification. It is a truncation of the Woodbine formation as it approaches the regional Sabine uplift. 5 A certain amount of leaching of the cementing material by waters over the unconformity

has resulted in increased porosity and permeability in the field as compared with similar Woodbine sands in the deeper portions of the East Texas basin.

Combination Traps Combination traps are structural closures or deforma- tions in which the reservoir rock covers only part of the structure. Both structural and stratigraphic changes are essential to the creation of this type of trap. Traps of this nature are dependent on stratigraphic changes to limit permeability and structure to create closure and complete the trap. Updip shale-outs, strand-lines, and facies changes on anticlines, domes, or other structural features causing dip of the reservoir rock create many combination traps. Unconformities, overlap of porous rocks, and truncation are equally important in forming combination traps. Faulting is also a controlling factor in many of these traps. Asphalt seals and other secondary plugging agents may assist in creating traps.

Salt Domes. These structures are of enough importance to justify a separate classification. However, sometimes they are difficult to identify, and many of the traps result from both stratigraphic variations and structural deformation.

Intrusion of rocks into overlying sediments may result in many different types of traps. Salt intrusions are more commonly associated with petroleum traps, although some igneous intrusions have also resulted in the formation of petroleum traps.

Salt domes are classified as piercement, intermediate, and deep-seated domes. Salt plugs or masses have moved up from greater depths through overlying sediments, forming traps in the sediments that have not been penetrated by the salt. Most salt intrusions took


EAST TEXAS FIELD

IZONTAL SCALE

Fig. 29.9-Example of a secondary stratigraphic trap: structure and cross section

of East Texas field.

EAST TEXAS FIELD

CONTOURS ON ERODED SURFACE OF WOODBINE

Fig. 29.10-Example of a secondary stratigraphic trap: structure and cross section of East Texas field.

considerable geologic time to reach their cut-tent position in the crust of the earth. Some are still growing, and apparently all have grown intermittently, allowing sands to be deposited over the crest of the structure at certain times and limiting deposition to the flanks of the sttuc- ture at other times. The movement of the salt mass up through the surmunding rock creates many complex structures and sedimentary variations. Radial and peripheral faulting provide the avenue for the salt pushing up through overlying sediments. At times, the overlying formations were competent enough to stop or delay the growth of the salt plug. At other times, the salt

apparently grew steadily and contemporaneously with the deposition. Many times the salt masses of some domes must have reached the surface or near surface, where groundwaters could act on the intrusive salt mass. Some of the domes are very near the surface of the ground. Some have reached the surface and are currently extruding salt. In areas of very low rainfall, such as southwest Iran, salt has reached a height of 5,000 ft above the surrounding terrain.

Deep-seated salt domes are normally those at considerable depths where the salt may not have been penetrated by drilling. These can be identified by the overlying characteristic structure or by geophysical data, which help prove salt is present at depths of 12,000 ft or more and can be assumed to have caused the overlying complex structure. Intermediate domes can be defined arbitrarily as those where the salt is deeper than 2,500 ft but has been penetrated by drilling at depths less than 12,000 ft.

Traps occur on the flanks of salt domes where sands have been faulted and deformed or terminate against the salt mass and where facies changes have resulted because of the associated uplift. These conditions are illustrated in Fig. 29. 11.6 Traps occur in the cabrock, which consists of calcite, anhydrite, and limestone. Caprock is the insoluble residue on top of the plug that results from the dissolution of the salt from the crest of the plug. Porosity and permeability in the capmck result from fracturing, solution, chemical alteration, or any combination of these and are generally restricted to the calcite or limestone portions of the caprock.

Traps also overlie the salt mass and may result entirely from structural closure, faulting, differential compaction, or stratigraphic variations combined with the deformation, as indicated in Fig. 29.12.l

Characteristics of Reservoir Rocks Classification of reservoirs* can be made on the basis of the texture, composition, and origin of the containing rock or the geometric configuration of the reservoir trap. Classification of reservoirs on the basis of rock texture and composition can assist in the prediction of reservoir performance. Variations in the mineralogy of reservoir rocks can be as important in reservoir performance as structural configuration or area1 extent of the reservoir rock.

Sedimentary reservoir rocks can be divided into two groups: chemical and detrital. Sedimentary rocks are created by the weathering, disintegration, erosion, reworking, and deposition of material from older rocks.

‘For mm detailed coverage of this subject. refer to Aefs. S and 9.


A ,PLIESTOCENE

MIOCENE <

SALT

ifi OLIGOCENE-,- I\

i A -OLIGOCENE

‘JACKSON BARBERS HI1

cH,c,“,2~.T:As YEGUA -

GOUGE ZONE

YEGUA t 01

/ gL- 1000 FT

Fig. 29.1 l-Example of piercement-type dome showing termination of sands on- the flanks of the salt plug and the resultant reservoir traps.

Clastic or detrital rocks are created from fragments transported by wind or water and allowed to settle out of suspension when the weight of the fragments is sufficient to exceed the carrying capacity of the transporting agent (wind or water). Chemical rocks are the result of precipitation of materials out of aqueous solution by organic growth and deposition or evaporation of seawater in closed basins, which precipitates salt and other evaporites. A list of reservoir rocks is given in Table 29.1.

Detrital Reservoirs Clastic or Detrital Granular Reservoirs. These reservoirs can be classified according to rock types, depend-

ing on variations in source rock, transport distance, and depositional environment.

Quartzose-Type. Quartzose-type sediments occur in periods of geologic quiescence, with relatively flat coastal plains bordered by shallow seas. Weathering and chemical decay are at a maximum and erosion is at a minimum. Only stable minerals remain, and these are well sorted and generally uniform in texture and composition. Blanket sands and shales over extensive areas are general factors and the sandstones demonstrate high vertical as well as horizontal permeability. Waterdrive reservoir mechanisms can be expected and high recoveries by primary methods of production are the general rule because of the homogeneity of the reservoir rock. The coastal plains, embayments, and continental shelf along the Gulf of Mexico from Texas to Florida are typical of the physical requirements for this type of deposition.

Graywacke Sediments. These sediments occur in periods of moderate geologic disturbances. The coastal region is moderately uplifted and the depositional basins are somewhat deeper with a shorter continental shelf. More rapid erosion and shorter distances of transportation prevent the complete weathering and chemical decay of the sediments, and some of the more unstable minerals are able to remain. The land and adjacent basin areas are unstable, and minor isostatic adjustments occur from time to time, causing abrupt changes in the sediments being deposited. This causes poor sorting, lenticularity, irregular porosity and permeability variations, and heterogeneous deposition. Vertical permeability is poor, limiting water drive and gravity drainage. Production is normally gas-depletion drive, and the opportunities for secondary recovery operations are excellent. The New England coast is typical of the environment necessary for these types of deposits.

Arkose Sediments. Arkose sediments result from deposition during periods of intense erogenic movements. Certain land areas are sharply elevated above other land areas and/or the shoreline. Faulting and major isostatic adjustments occur frequently. The con-

ESPERSON DOME STRUCTURAL CROSS SECTION

Fig. 29.12-Example of traps caused by a combination of structural and stratigraphic varia-

tions and of the complex faulting occurring above an intrusive salt mass.


TABLE 29.1--RESERVOIR ROCKS

Clastlc and Detrttal Porosity

1. Sand, conglomeratic sand, and gravel (clean, argillaceous, silty, lignitic, etc.)

2. Porous calcareous sandstone and siliceous sandstone (incomplete cementation)

3. Arkosic (feldspathic) sand, arkose, arkosic conglomerate (granite wash)

4. Detrital limestone and dolomite, oolitic and pisolitic limestone, coquina, and shell breccia

Fractured Porosity

1. Fractured sandstone and conglomerate 2. Fractured limestone, shale, and chert

Crystalline Porosity

1. Crystalline limestone and dolomite 2. Sugary dolomite “saccharoidal” porosity

Solution Porosity

1. Crystalline limestone and dolomite 2. Cavernous limestone and dolomite 3. Porous caprock 4. Honeycombed anhydrite 5. Ooliclastic limestone

tinental shelf is extremely narrow or nonexistent. Max- imum erosion and the short distance of transportation virtually eliminate chemical decay and weathering. Sediments are deposited and covered over by younger sediments before any appreciable sorting and weathering can take place. Unstable minerals are present in the thick heterogeneous deposits. Highly porous stratigraphic traps are developed by lensing, pinchouts, and unconformities. Depletion-drive reservoirs are the general rule and recoveries are usually low. Much of the California coast is typical of the depositional environment for the deposition of arkosic sediments.

Chemical Reservoirs Limestones and Dolomites. Limestones and dolomites also are deposited in quiescent geologic environments. Deposition of limy deposits is occurring along the west coast of Florida and some of the Bahama Islands while elastic sediments are being deposited in other nearby local areas.

Carbonate Reservoirs. Carbonate reservoirs include reefs, elastic limestones. chemical limestones, and

dolomite. Porosity may be intercrystalline, intergranular, oolitic or ooliclastic, vuggy fractured, fossiliferous, cavernous, or saccharoidal. Production characteristics are highly variable in carbonate reservoirs. depending almost entirely on the type of porosity and fracturing developed and the resultant permeability.

Other types of reservoirs are given in Table 29.2.

Glossary of Terms Eioherm: A moundlike, domelike, lenslike. or reeflike mass of rock

built by sedentary organisms (such as corals, algae, foraminifers, mollusks, and gastmpods), composed almost exclusively of their calcareous remains and enclosed or surrounded by rock of different lithology.

Biostrom: A distinctly bedded and widely extensive or broadly len- titular, blanketlike mass of rock built by and composed mainly of the remains of sedentary organisms and not swelling into a

TABLE 29.2-TYPES OF RESERVOIRS

Shale Reservoirs

Sometimes present in brittle, siliceous fractured shales Anhydrite Evaporites

Develop porosity from leaching by circulating waters lqneous or Metamorphic Rock

1. Very uncommon 2. Sometimes contain oil when secondary porosity is

developed by fracturing or weathering 3. Best-known igneous reservoirs are the serpentine plugs of

Bastrop and Caldwell counties, Texas

moundlike or lenslike form. As an organic layer, such as a bed of shells, crinoids, or corals or a modem reef in the course of formation.

Brecciat A coarse-grained elastic rock composed of angular broken fragments held together by a mineral cement or in a fine-grained matrix.

Closure: In a subsurface fold, dome, or other structural trap, the vertical distance between the structure’s highest point and its lowest closed structllre contour. Four-way dip is determined by in-line and cross-line right angle control demonstrating dip in four directions away from the crest of the closure.

Coquina: A dettital limestone composed wholly or chiefly of mechanically sorted fossil debris that experienced abrasion and transport before reaching the deposition site, and weakly to moderately cemented but not completely endmated.

Deftifalr Pertaining to or formed from detritus of rocks, minerals, and sediments. The term may indicate a source outside or inside the depositional basin.

Facies: The aspect, appearance, and characteristics of a rock unit, usually reflecting the conditions of its origin; especially as differen- tiating the unit from adjacent or associated units.

Graben: An elongate, relatively depressed crustal unit or block that is bounded by faults on its long sides.

Horst: An elongate, relatively uplifted crustal unit or block that is bounded by faults on its long sides.

Minimum hydrodynamicpotential: As used here, a geologic position or condition due to impermeability in the reservoir rock where the dynamic action of fluid movement is abated.

Minor isosfafic adjustment: The minor adjustment of the lithosphere of the earth to maintain equilibrium among units of varying mass and density; excess mass above is balanced by a deficit of density below and vice versa.

Norn~lfuult: A fault in which the hanging wall appears to have moved downward relative to the foot wall. The angle of the fault is usually 45 to 90”. A low-angle normal fault is a normal fault with the angle of the fault less than 45”.

Ofilop deposirion: The progressive offshore regression of the updip terminations of the sedimentary units within a cornformable sequence. of mcks in which each successively younger unit leaves exposed a portion of the older unit on which it lies. The successive contraction in the lateral extent of strata (as seen in an upward sequence) resulting from their being deposited in a shrinking sea or on the margin of a rising land mass.

On-fop deposition: The regular and progressive pinching out toward the margins or shores of a depositional basin of the sedimentary units within a conformable sequence of rocks in which the boundary of each unit is transgressed by the next overlying unit and each unit, in turn, terminates farther from the point of reference.

PETROLEUM RESERVOIR TRAPS

Oolicnsr: One of the small, subspherical openings found m an oohtlc mck, produced by the selective solution of ooliths without destmc- tion of the matrix.

Oolicusric porosity: The porosity produced in an oolitic rock by removal of the ooids and formation of oolicasts.

Oolith: One of the small round or oval accretionaty bodies in a sedimentary rock resembling the me of fish, usually formed of calcium catbonate and having a diameter of 0.25 to 2 mm.

Pisolirh: One of the small, round or ellipsoidal accretionary boches in a sedimentary rock, resembling a pea in size and shape, and con- stituting one of the grains that make up a pisolite. It is often formed of calcium carbonate and some are thought to have been produced by a biochemical algae-encrustation process. A pisolith is larger and less regular in form than an oolith.

Pisoliric: Pertaining to pisolite or to the texture of a rock made up of pisoliths or pealike grains.

Pisolitic limestone: A limestone with pisolitic texture.

Saccharoidal: Said of a granular or crystalline texture resembling sugar.

Shell breccint A breccia composed of angular broken shell fragments.

Shoestting sands: A shoestring of sand or sandstone usually buried in the nudst of mud or shale as in a buried sandbar or channel fill.

Strand line: The ephemeral line or level at which a body of standing water meets the land; the shoreline, especially a former shoreline now elevated above the present water level.

Strike-slip fault: A fault on which the movement is parallel to the fault’s strike.

Torsion: The state of stress produced by two force couples of opposite movement acting in different but parallel planes about a common axis. Torsion faults are wrench faults or lateral faults in which the fault surface is more or less vertical.

Tnmcnrion: An act or instance of cutting or breaking off the top or end of a geologic stmcture or land form, as by erosion.

Unconformity: A substantial break or gap in the geologic record where a mck unit is overlain by another that is not next in stratigraphic succession, such as interruption in the continuity of a depositional sequence of sedimentary rocks or a break between eroded igneous rocks and younger sedimentary strata. It results from a change that caused deposition to cease for a considerable span of time, and it normally implies uplift and erosion with loss of the previously formed record.

References 1.

2.

3.

4.

5.

6.

7. 8.

Galloway, T.J.: Bull. 118, California Division of Mines, Sacramento (Aug. 1957). Sams, H.: “Atkinson Field; Good Example of “Subtle Stratigraphic Trap,” Oil and Gas J. (Aug. 12. 1974), 145-63. Hoyt, W.V.: “Erosional Channel III the Middle Wilcox Near Yoakum, Lavaca County, Texas,” Trans., Gulf Coast Assn. of Geological Societies (Nov. 1959) 9, 41-50. “Occurrence of Oil and Gas in West Texas,” F.A. Herald (ed.) Bureau of Economic Geology and West Texas Geological Sot. (Aug. 1957). “Occurrence of Oil and Gas in Northeast Texas,” F.A. Herald (ed.) Bureau of Economic Geology and East Texas Geological Sot. (April 1951). An Introduction ro Gu[fCoa~r Oil Fields, Houston Geological SOC. (1941). A Guide Book, Houston Geological Sot. (1953). Pirson, S.J.: Oil Reservoir Engineering, second edition, McGraw- Hill Book Co. Inc., New York City (1958).

29-9

9. Krynine, P.D.: “The Megascopic Study and Field Classification of Sedimentary Rocks,” J. Geol., 56, No. 2.

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Tulsa (1980).

Bates, R.L. and Jackson, J.A.: Glossary of Geology, second edition, American Geological Inst. (1980).

Beebe, Warren B.: “Natural Gases of North America, Vols. 1 and 2,” Memoir 9, AAPG (1968).

Bouma, H., Moore, G.T., and Coleman, J.M.: “Framework, Facies and Oil Trapping Characteristics of the Upper Continental Margin,” AAPG (1978) Studies No. 7.

Braunstein, J.: “North American Oil and Gas Fields,” AAPG (1976) Memoir 24.

Busch, D.A.: “Stratigraphic Traps in Sandstone,” AAPG (1974) Memoir 2 1.

“Geologic Formation and Economic Development of Oil and Gas Fields of California,” California Department of Natural Resources, Sacramento (1943).

Halbouty, M.T.: “Cilant Oil and Gas Fields of the Decade 1968-1978,” AAPG (1980) Memoir 30.

Halbouty, M.T.: “Salt Domes, Gulf Region, United States and Mex- ico,” second edition, Gulf Publishing Co., Houston (1979).

Halbouty, M.T.: “The Deliberate Search for the Subtle Trap,” AAPG (1982) Memoir 32.

Hanna, M.A.: “Gulf Coast Salt Domes,” Problems in Petroleum Geology, AAPG (1934).

Hubbert, M.K.: “Entrapment of Petroleum under Hydrodynamic Con- ditions,” Bull., AAPG (Aug. 1953) 37, 1954-2026.

King, R.E.: “Stratigraphic Oil and Gas Fields: Classification, Ex- ploration Methods and Case Histories,” AAPG (1972) Memoir 16, S.E.G. Special Publication No. 10.

Levorsen, A.I.: Geology of Petroleum, W.H. Freeman and Co., San Francisco (1954).

Mazzullo, S.J.: “Stratigraphic Traps in Carbonate Rocks,” AAPG (1980) Reprint 23.

Payton, E.: “Seismic Stratigmphy-Applications to Hydrocarbon Ex- ploration,” AAPG (1977) Memoir 26.

Russel, W, L. : Structural Geology for Petroleum Geologists, McGraw- Hill Book Co. Inc., New York City (1955).

Scholle, P.A., Bebout, D.G., and Moore, C.H.: “Carbonate Deposi- tional Environments, AAPG (1983).

“Structure of Typical American Oil Fields,” Bull., AAPG (1929).

Weeks, L.G.: “Habitat of Oil,” AAPG (1958).

Wilhelm, 0.: “Classification of Petroleum Reservoirs,” Bull., AAPG (Nov. 1945) 29, 1537-79.

Woodland, A.W.: Petroleum and the Continental Shelf of Northwest Europe, Vol. I, Geology, John Wiley Sons Inc., New York City (1975).

Young, A. and Galley, I.E.: “Fluids in Subsurface Environments,” AAPG (1965) Memoir 4.

Chapter 30 Bottomhole Pressures G.J. Plisga, Sbhio Alaska Petroleum Co.*

Introduction The practice of using bottomhole pressure (BHP) to improve oil production and to solve petroleum engineering problems started in about 1930. Pressures in oil wells were first calculated from fluid levels and later by injecting gas into the tubing until the pressure became constant. The earliest BHP measurements were made with pressure bombs and with maximum-indicating or maximum-recording pressure gauges that did not have the accuracy, reliability, or durability now demanded. These early pressure measurements were occasional. or spot tests rather than systematic diagnostic engineering measurements.

BHP Instruments The development of precision recording pressure gauges small enough in diameter to be run through tubing made it feasible to make BHP measurements in sufficient number to develop the science that now makes them in- dispensable to petroleum engineering. BHP now is determined with continuously recording pressure gauges, which are either self-contained or surface-recording.

Self-Contained Gauges Mechanical self-contained pressure gauges are used universally. The pressure element and recording section are encased and sealed against external pressure except for an opening to communicate the pressure to the element. The entire instrument is run to the depth at which the pressure is to be measured, allowed to stabilize thermally, and then returned to the surface and the pressure determined from the chart. Modem pressure measurement systems incorporate force summing devices that convert energy into physical displacement or deformation. These force summing devices can take many forms, three of which are shown in Fig. 30.1. Although there

‘The ongmat chapter on the topic bn the 1962 edition was written by C.V. Mfllikan.

are numerous mechanical self-contained pressure devices available (Table 30.1) only the most commonly used continuously recording BHP gauges are discussed fully. Regardless of the type of force summing device in- corporated into the BHP gauge, whether physical displacement (piston elements) or deformation (bellows/bourdon tubes), the generated force is coupled to a recording device.

The Amerada pressure gauge has a helical bourdon tube as a pressure element that is of sufficient length to rotate the stylus the full inside circumference of the cylindrical chart holder without multiplication of movement. A clock moves the chart longitudinally. The gauge is made in both 1% - and l-in. diameters with a length of approximately 74 in. A vapor-pressure-type recording thermometer can be run in combination with this to obtain continuously recorded temperatures and allow correction of pressure measurements. This will also ensure that thermal stabilization has occurred.

The Humble gauge pressure element has a piston, which moves through a stuffing box against a helical spring in tension. Attached to the inner end of the piston is a stylus that records longitudinally on a chart in a cylindrical holder, which is rotated by a clock. The instrument is made in two sizes, with 1 l/4- and 15/16-in. OD’s, and is approximately 60 in. long. Thermometer elements are available for both sizes.

Other recording gauges have been described in the literature, two of which were continuously recording, but they are no longer available on the market. The Gulf BHP gauge has a pressure element consisting of a long metallic bellows restrained by a double helical spring in tension. The recording mechanism is a cylindrical chart holder rotated by a clock. The USBM BHP gauge pressure element is a multiple-bellows type with a movement of about 0.6 in., which is multiplied through a rack and gears to about 5% in. of stylus movement. The stylus records longitudinally on a cylindrical chart that is


TABLE 30.

OD, in. Length, in. Type pressure element* Maxtmum pressure, psi” Accuracy, %FS t Resolution, %FSr Maximum service temperature, OF Maximum clock running time, hours

1

- RPG-3 RPG-4

--MECHANICAL RECORDING BHP GAUGES

Amerada

1.25 1 77 76 B B

25,000 25,000 +0.2 f 0.2

+0.05 f 0.056 500 500 360 144

‘B = bardon tube, AP = Rotating piston, P = Piston. “Normally, elements are avarIable in several ranges. tFS= Full scale. NS = Not stated

RPG-5

1.5 20 B

20,000 k 0.25 + 0.05 450 120

PRES.SU{~~- ;E

DIAPHRAGM BELLOWS

PRESSURE

SPIRAL BOURDON TUBE

Fig. 30.1-Force summing devices

rotated by a helical spring but controlled by a watch movement.

BHP gauges, although rugged and capable of service in severe conditions, must be considered precision instruments. Proper attention to adjustment, calibration, and operation is required to obtain consistently reliable and accurate pressure measurements. A comparison of the commonly used mechanical continuously recording BHP gauges is shown in Table 30.1.

Charts Charts used in a BHP gauge are paper or metal. Paper charts have an abrasive coating and are marked by a brass or gold stylus. Metal charts, which are made of brass, copper, or aluminum, are generally preferred because they are not affected by humidity. Plain metal charts require a sharp pointed stylus. Coated metal charts are generally preferred because they produce less stylus friction. Black-coated charts are marked with a steel or jewel stylus, which burnishes the coated surface. White- coated charts are used with a brass or gold stylus. A finer line can be made on the black chart, but it is more difficult to read. A brass or gold stylus used with white- coated charts, paper, or metal, must be sharpened very frequently.

Self-contained pressure gauges, like all pressure gauges used for precision work, must be calibrated on a dead- weight tester at regular intervals. To obtain maximum accuracy, the pressure gauge is calibrated before a survey at the anticipated bottomhole temperature, (BHT), the survey conducted, and then the chart read using the presurvey calibration lines. New pressure elements should be calibrated frequently until they have become seasoned in service and their ability to retain calibration has been established. Before calibration, pressure equal to the maximum range of the element should be applied and released several times. The number of calibration points should be more on a new element, and two or more curves should be run as a check. The element should also be calibrated at the reservoir temperature at which the pressures are to be determined, or a temperature-correction factor should be determined to correct pressures measured at other than calibration temperature (Fig. 30.2). During calibration, the gauge should be tapped lightly to relieve residual friction in the moving parts of the element. Under normal operating conditions, pressure determination in a well should have an accuracy within a range of 0.2% of the maximum range of the element. The pressure element range should be selected to operate in the upper two-thirds range when at bottomhole conditions. Greater accuracy can be obtained by greater attention to details of calibration and the use of instruments that are well- seasoned by service. Pressure increase inside the gauge caused by an increase in temperature is considered only when extra effort is made to obtain precision pressures.

Temperature Effect

A small magnifying lens and steel scale with O.Ol-in. Temperature effect is an inherent property of metals and divisions are most frequently used for reading charts is present in all gauges, although for some alloys it is with static pressure-i.e., where only one or two very small. Except for such alloys, temperature change

KPG

Kuster

AK-1 K-2 K-3

1.25 2.25 1 1.25 73 36 41 43 B B B B

30,000 30,000 20,000 20,000 * 0.2 * 0.25 f 0.25 f 0.25

* 0.05 f0.025 +0.05 -f 0.04 700 350 700 700 360 120 120 120

Leutert

1.42 139 RP

10,000 f 0.025 f 0.005

300

Johnston J-200

2.88 54 P

20,000 k 0.25

NS 400 192

pressures readings are made on a chart. When a number of readings are to be made from a chart, it is advantageous to use one of the several available chart scanners. Some engineers have used microscopic com- parators to read pressure deflection to 0.0001 in., but the inherent errors of a pressure element even under most careful handling are usually greater than the added accuracy of such precise measurement of the chart. New electronic chart scanners have improved the readability and accuracy of mechanical BHP gauges.

Calibration

BOTTOMHOLE PRESSURES

Input pressure - - - - _ _ - - - - - - - - - - - - -

konstanr~ t

TKlle

Jl~,“d,ur,r - - - - - - - - - - - - - - - - -

I Room ., Temo --

Time

--- 4

\ .--

outpur \ Temperature

Error , , ’ T,mE?

\ / \ /

/ \ / \ / \ , \ /

\ .II/’

Fig. 30.2-Temperature effect on pressure gauges.

must be considered in pressure measurements. The preferred method is to calibrate the pressure element at the temperature of the reservoir in which pressures are to be measured. The calibration curve for most pressure elements is practically a straight line; therefore, a temperature-correction coefficient may be determined for a given pressure element and used to correct for temperatures other than the calibration temperature as follows. For a given pressure, preferably about three- fourths of the maximum for the element, determine the pressure deflection and the temperature. For the same pressure, determine the deflection at a higher temperature, preferably 100°F higher.

Then ’

where CT = temperature coefficient, T, = lower temperature, T2 = higher temperature, dl = deflection at T, for given pressure, and d2 = deflection at T2 for same pressure.

The corrected deflection can be calculated as

d,.= “’ 1 +CT(To -T,) ’

, . . . . .

where d,. = deflection at calibration temperature, d, = observed deflection, T, = calibration temperature, and T, = observed temperature.

(11

(2)

t output

Marlmum

Input b

Maxtmum ~npui

Fig. 30.3-Hysteresis.

If it is more convenient, pressure readings may be substituted for deflections in Eq. 2. Gauges with a steel pressure element usually have a temperature coefficient of about 0.0002 in./“F.

When the pressure gauge is run to the depth of the pressure determination, it should remain long enough to stabilize thermally, usually 15 to 20 minutes. If the instrument cannot remain long enough to reach temperature equilibrium, a maximum-indicating thermometer run in a closed container as part of the gauge will give a satisfactory reading for temperature correction.

Many BHP gauge elements are made of an alloy with a very low temperature coefficient such as Ni-Span C@, and a temperature correction may be neglected up to 200°F except where extra precautions are taken to obtain very precise pressure measurements. For temperatuf?s above 2OO”F, most elements require a varying correction that can be determined only by actual calibration.

Hysteresis Hysteresis is a characteristic of metals under strain that must be recognized in pressure gauges. Because of hysteresis, the calibration of a gauge made with increasing pressures will differ slightly from a calibration made with decreasing pressures (Fig. 30.3). If only static pressures are to be determined, a calibration at increasing pressure is satisfactory. When a flowing pressure starting from a static condition is to be determined, hysteresis may be of sufficient magnitude to take into account. To determine the hysteresis effect, the pressure element should be pressurized somewhat higher than the highest anticipated well pressure and released several times before running the calibration, first with increasing pressures, then with decreasing pressures. Flexing the element several times will substantially reduce the hysteretic effect and should be done each time just before the gauge is run into a well.*

Operating Equipment The BHP gauge, a self-contained instrument, is run on a wireline and depth is measured by the line running in contact with a calibrated measuring wheel, which operates a counter. The most frequently used calibration of the measuring wheel is 2 ftirev. When the contact of the line is tangent to the measuring wheel, the wheel


TABLE 30.2-WIRELINE TENSILE STRENGTHS AND WEIGHTS

Nominal Tensile Strength (Ibf)

Tensile Strength Diameter Line (in.)

(Psi) 0.066 0.072 0.082 0.092

Plow steel 232,000 -945 794 1,225- 1,542

~ai$3ss steel 170,000 150,000 582 513 692 611 090 792 1,130 997

Nominal Weight per 1,000 ft of Line (Ibm)

11.4 14.0 18.0 22.8 Plow steel Stainless steel Monel

11.8 14.1 18.3 23.0 13.1 15.6 20.2 25.4

diameter in inches is 241~. When the contact is an arc of the wheel, the wheel diameter is D=(24/n)-d, where d is the diameter of the wireline. This applies if the greatest distance of the chord of the contact arc from the periphery of the wheel is greater than the diameter of the wireline. The measuring wheel diameter should be checked at reasonable intervals to maintain accuracy of depth measurements. A decrease in the diameter of the wireline caused by wear or by permanent stretch resulting from a hard pull will also cause errors in depth measurements.

The most common wirelines have diameters of 0.066, 0.072, 0.082, or 0.092 in. In areas having noncorrosive well fluids, plow steel lines are most satisfactory, but for corrosive conditions, stainless steel and Monel@ lines are used. Both plow steel and stainless steel are subject to hydrogen embrittlement, but are satisfactory for short runs such as static-pressure tests, except under severe conditions. For an operation that requires the line to be in the hole under corrosive conditions for several hours, a Monel line should be used. Nominal tensile strengths of wire lines and their weights are given in Table 30.2.

Equipment for operating a wireline varies greatly. The most frequently used unit is a trailer-mounted reel driven by a 2- to 4-hp air-cooled gasoline engine. Power is transmitted to the reel by V-belt, through a disk clutch, or by hydraulic drive. On smaller equipment, an idler pulley permits the V-belt to serve as a clutch also. Brak- ing may be by friction disk, brakeband, or hydraulic

pump. When the equipment is used for a continuous program it may be mounted in a pickup truck, with housing to protect against the weather.

Pressure Bombs Pressure bombs were used to some extent before recording pressure gauges small enough in diameter for oilwell use became available. They were usually made from tubing approximately 1 L/2 in. in diameter with a small needle valve in the top and a ball and seat in the bottom to hold maximum pressure in the well. When the bomb was recovered, the pressure was determined by attaching a pressure gauge to the valve. The bomb had to be long enough to leave a volume of gas (or air) in the top to reduce the error of filling the bourdon tube of the pressure gauge. There was also substantial correction for temperature unless the bomb was raised to BHT before the pressure was read. An ordinary commercial maximum-indicating pressure gauge enclosed in a pressure-tight container was used occasionally, and in some cases a recording mechanism and clock were added. Such instruments were 3 in. or larger in diameter, which limited their use to wells without tubing.

Surface Recording Gauges Surface recording pressure gauges can be used either permanently installed or wircline retrievable. All surface recording pressure gauges must be run on a single-

BOTTOMHOLE PRESSURES 30-5

SGTISOI Excitation

Capacitive AC-DC special

Differential transformer AC special

Force balance AC line power high level (5V) with servo

0.01

Piezoelectric DC amp and self-generating

AC

medium level with amp

1

Potentiometer AC-DC regulated

high level 1

0.01 to 5,000 0 to>100

30 to 10,000 >I00

1 to 5,000 oto <5

0.1 to 40,080 1 to > 100.000

5 to 10,000 oto >50

Strain gauge AC-DC regulated

Unbended IOV AC-DC low level 4 mVN 0.25 0.5 to 40,000 0 to >2,000

Bonded foil 1 OV AC-DC low level 3 mVN 0.5 5 to 10,000 0 to >I,000

Thm film IOV AC-DC 3 mVN 0.25 15 to 10,000 0 to > 1,000

Diffused semiconductor

Bonded bar semiconductor

Variable reluctance AC special 40 mVN

10 to 28 V DC

1OV AC-DC

Vibrating we and tube AC special

Vlbratlng quartz AC special

TABLE 30.4-SUMMARY OF TRANSDUCER CRITERIA

Pressure Frequency Temperature Range Accuracy Range Response and Effects

Output Level PM (Psi) (Hz) VI

high level (5V) frequency/bridge

htgh level (5V) phase

demodlbridge

medium level 3 mVN to 20 mVN

medium level 3 mVN to 20 mVN

high level and frequency

high level and frequency

0.02

0.5

0.25

0.25

0.5

0.02

0.01

Oto +I85

Oto +165 poor 0.5

4Oto +165 (O.Ol%I°F)

- 450 to + 400 (O.Ol%/~Fj

-85 to +300 (O.Ol%l°F)

- 320 to + 800 (0.005%/°F over

limited compensated

range)

-65 to +250 (O.O1%/°F over

limited

15 to 5.000 0 to > 1,000

5 to 10,090 0 to > 1,000

range)

- 320 to + 525 (O.OOS%/~F over

limited compensated

range)

- 65 to 250 (0.005%/°F over

limited

compensated range)

-65 to t250 (O.Ol%l°F over

limited

0.04 to 10,000 0 to > 1 ,OiJo

1t0100 oto >I00

range)

-320 to +800 (O.O2%/OF over

limited

compensated range)

-85 to +200 requires

temperature control

1 to 10,000 0 to >I00 oto +I302

Shock and Vibration

Sensitivity

@3X t0 QOod

Stability’

WY0

0.05

poor O.OS%/month

excellent

poor

good

very good

very good

“W QQQd

1

05

0.5

0.5

0.05

0.05

0.5

0.5

0.01

0.005

Lile or Calibration Shift

with Use’

> 10' cycles

with <0.05% calibration shift

> to6 cycles life

z 10’ cycles with ~0.5%

calibration shift

use effects

<IO@ cycles life

< 0.5% calibration shift after IO6 cycles

> lOa cycles

> 106 cycles with ~0.25%

calibration shift

< 0.25% calibration shift after 10 B cycles

< 0.5% calibration shift after lo6 cycles

> lo6 cycles life

> 106 cycles life

> lo6 cycles life

‘Stability and calibration shift should be considered together.


BOURDON TUBE

PRESSURE SENSING

DIAPHRAGM

L&g5

::::

q I

OUTPUT ..-.

/ BASE CRYSTAL

Fig. 30.5-Piezoelectric transducer.

Fig. 30.4--‘E’-Core transformer

Variable Inductance Transducer

conductor armored cable that carries a direct current from the surface to the transducer in the bottomhole instrument. Oscillating current returns through the same circuit from the transducer to surface instruments that determine and record its frequency. A transducer is any device that converts energy from one form to another. There is a large variety of transducers that allow nonelec- trical variations to be converted into changes in resistance, current, voltage, capacitance, etc. Some examples are the strain gauge, thermistor, and the microphone. Readings are made at selected intervals of 1 second to 30 minutes or more. The frequency recorded in cycles per second is translated to pounds per square inch from a calibration curve. Table 30.3 shows a comparison of commonly used surface recording pressure gauges.

A permanently installed surface recording pressure gauge requires a gauge carrier or receiver and either a single conductor line or small diameter tubing (0.092 in.) strapped to the production tubing. The pressure gauge can be run with the tubing or by wireline retrievable, which sits in a gas lift mandrel or some other device to complete the circuit. The surface instruments may be connected permanently, or one set can be used to monitor BHP in several wells.

Modem precision pressure-measuring systems incorporate force summing devices that convert gas or liquid entry into physical displacement or deformation. The following sections discuss various concepts of pressure transducer technology shown in Table 30.4.’

Pressure Transducer Technology Capacitive Transducer In a capacitive transducer, a diaphragm is spaced evenly between capacitor plates. BHP causes displacement of the diaphragm and a change in capacitance. The advantages of a capacitive transducer are excellent frequency response, low hysteresis, good linearity, and excellent stability and repeatability. Disadvantages are high sensitivity to temperature variations and vibration.

In the variable inductance transducer, a flux linkage bar is mechanically linked to a spiral bourdon tube, diaphragm, or bellows (Fig. 30.1). The flux linkage bar is in the magnetic path of an E-core transformer (Fig. 30.4). Displacement of the flux linkage bar by pressure changes the E-core flux density resulting in a transformer output proportional to the pressure applied. The advantages are medium-level output and rugged construction. Disadvantages are a requirement for AC excitation, poor linearity, and susceptibility to stray magnetic fields.

Piezoelectric Transducer The piezoelectric effect is the property exhibited by certain crystals of generating voltage when subjected to pressure (Fig. 30.5). When a strain is applied to an asymmetrical crystalline material such as barium, titanite, quartz, or rochell salt, an electrical charge is generated. When a piezoelectric crystal is connected to a diaphragm, bellows, or bourdon tube, the generated charge can be made proportional to the applied pressure. Advantages are very high frequency response (250 kHz), small size, rugged construction, and ability to accept large overpressures without damage. Disadvantages are temperature sensitivity, inability to make static measurements, and special electronics required.

Potentiometric Transducer This transducer is constructed by coupling the wiper of a multitum potentiometer to an amplifying mechanical linkage to a diaphragm, bellows, or bourdon tube. Ad- vantages are low-cost, high-level output and simple electronic circuits. Disadvantages are limited life, poor resolution, large hysteresis, and low frequency response.

Vibrating Wire Transducer A thin wire is connected in tension to a diaphragm, bellows, or bourdon tube and is caused to vibrate under the influence of a magnetic field (Fig. 30.6). The wire’s frequency of vibration is directly related to its tension.


TAUGHT M MAGNETIC <

OUTPUT

MAGNETS 0

AC CARRIER AND FREQUENCY

DETECTOR ELECTRONICS

/

Fig. 30.6-Vibrating wire transducer.

Advantages are very high accuracy, low hysteresis, and excellent long-term stability. Disadvantages are sensitivity to shock and vibration, temperature sensitivity, and additional electronics.

Strain Gauge Transducers A strain gauge transducer is a strain-sensitive resistor mounted to a diaphragm, bellows, or bourdon tube. When pressure is applied, the resistor changes its physical length thereby causing change in resistance. This effect is expressed by

Arlr F,=- . . ~,L, . . . . . . . . . . . . . . . . . . . . . . . (3)

where F, = gauge factor, Ar = change in resistance,

r = unstrained resistance, aL = change in length, and

L = unstrained length.

There are four basic types of strain gauge transducers; unbonded wire, bonded foil, thin film, and semiconductor. A rule that applies to strain gauge transducers is the larger the gauge factor, the higher the output of the device. For unbonded wire, the gauge factor is four. Bonded foil and thin film (Fig. 30.7) have factors of two. For semiconductor transducers, the factor ranges from 80 to 150.

Vibrating Crystal Transducer In vibrating crystal transducers, a crystal is forced by external electronic circuits to oscillate at its resonate fre quency when external stress is applied to the crystal by mechanical linkage to the diaphragm, bellows, or bourdon tube. The resonate frequency of the crystal shifts in proportion to the stress. In at least one transducer of this type, the pressure is applied directly to the crystal itself. The vibrating crystal is usually manufactured out of quartz because of its excellent elastic properties, long-

Fig. 30.7-Thin film strain gauge transducer.

Fig. 30.6-Cross-sections showing different modes of motion of quartz crystals.

term stability characteristics, and ease of vibrational ex- citement. Fig. 30.8 shows various modes of motion of quartz crystal. Advantages are excellent accuracy, resolution, and long-term stability. Disadvantages are sensitivity to temperature and extremely high costs.

New technology is constantly evolving a new generation of surface recording pressure gauges that are more and more advantageous to the petroleum engineer and petroleum engineering problems.

Calculated BHP BHP calculated from surface pressure and fluid level, although less accurate than measured pressure, is sufficient for many practical uses. In an open hole or open tubing, the fluid level can be determined by a float run on a measuring line.

In pumping wells, the fluid level can be determined by sound reflection. There are four types of commercial instruments available. These are the deptbograph, echometer, sonoloy, and acoustical well sounder. Each of these instruments records sound reflection initiated by firing a blank shotgun shell or pistol cartridge or venting pressure into a chamber attached to the casing head. A sound reflection is received and recorded from each tubing collar. By counting the collar reflections and knowing the tubing tally, the depth to the fluid can be calculated. In deep wells, attenuation of the collar reflection makes accurate counting difficult. In some oil wells,


usually those having considerable gas, a foaming condition makes the fluid level difficult to identify or may indicate a fluid level much higher than actual. A foaming condition is usually indicated when the fluid level changes several feet on tests made at short intervals of time. Fluid level can also be calculated from the time interval for the reflection to be received from the fluid level, but the variation in the speed of sound through gases of different compositions and the effect of temperature make the procedures more laborious and usually less accurate than the simpler method of counting collar reflections.

In calculating the pressure caused by the column of fluid, allowances should be made for gas in solution in the oil, which will reduce its specific gravity below that measured in the stock tank. This can reduce the gradient 5 psi/100 ft or more where much gas is in solution under high pressure. For wells producing water, it is customary to calculate the fluid head on a basis of a column of oil and water in the same ratio as normal production for the well, but this calculation is less reliable for low-capacity wells with high casinghead pressure and for pumping wells in which the pump is several hundred feet above the producing formation. If the surface pressure is low, the pressure caused by the weight of a column of gas may be too small to warrant consideration, but under high pressure it should be calculated and added to the hydrostatic head by the same equation used for calculating BHP in a gas well, where D is the depth of the fluid level.

Producing BHP of a pumping well that is sufficiently accurate for practical use may be calculated by shutting in the casing head until the gas pressure depresses the fluid level to the inlet of the pump, at which time fluid delivery is stopped. The casinghead pressure at that time, plus the head of the column of gas from the casing head to the pump inlet, plus the head of the column of liquid from the pump inlet to the producing formation is the producing BHP. A check of the determination should be made by releasing and controlling the pressure a few pounds less than the maximum pressure read and determining the rate of production under such conditions.

The BHP in a gas well can be calculated with an equation developed by Pierce and Rawlins4:

pw5=(pwh)e 0 m347y * D

) . . . . . . . I. I.. . . . . (4)

where p,,,$ = static BHP, psia, p,+h = wellhead pressure, psia,

e = base, natural logarithms,

YR = specific gravity of gas (air= l), and D = depth of well, ft.

This equation is based on an average temperature of the column of gas of 60°F. While the temperature gradient in a producing well is rarely a straight line, the average temperature at a depth below seasonal effect (20 to 30 ft) and at a depth of the pressure is sufficiently accurate for practical purposes. The equation can then be written5 :

or

YRD bgp,,s =logp,h +KT, . . . . (5)

where T is the average temperature in the borehole, “F+460.

Deviation of a gas from Boyle’s law will affect the calculated BHP enough to be considered only in high pressure deep wells. USBM Monograph 7 presents the following equation.’

where z is the deviation coefficient, deviation per psi expressed as a decimal.

Application of BHP The importance of pressure analysis in projecting and enhancing the performance of producing oil and gas wells emphasizes the need for precision pressure measurement systems. Today’s petroleum engineer must have sufficient information about the reservoir to adequately analyze current performance and predict and op- timize future performance. More specifically, such pressures are a basic part of reservoir calculations, rate of equalization of pressures, interference tests for well spacing or rate of development, formation damage during completion, rework or workover operations, and indication of deposition of salts, sediments, or other restrictions at the wellbore. Other applications are design of downhole equipment for artificial lifting, efficiency of operation of such equipment, and evaluation of drillstem test (DST) information.

Static Pressure Static pressure is the most frequent BHP measurement. Most such measurements are made as a pressure survey of a pool where the pressures in all wells are determined in a short period of time either by cooperation of the operators or by order of a conservation commission, usually as a result of a recommendation by the operators. Pressures are taken under reasonably uniform conditions after the wells have been shut in a specified length of time such as 24 or 48 hours, or longer, if the pressure buildup is at a slow rate. The pressures should be measured at or adjusted to a common data plane. In many pools, the pressures will not reach equilibrium in the specified shut-in time. However, if the pressures are determined for several surveys under the same conditions, the indicated rate of decline of the reservoir pressure should be reasonably accurate. Tests in representative wells which have been shut in long enough to reach pressure equilibrium will show the relation of the measured pressure to the actual reservoir pressure. Pressures in inactive wells may be used to confirm the actual pressure and the rate of decline.

Average Reservoir Pressure The average reservoir pressure for a pool may be determined by arithmetically averaging the pressures of all


wells. For some pools it is preferable to determine a weighted average by weighting each pressure by the productive thickness of the reservoir at that point. When for any reason the pressure cannot be determined in substantially all wells or where wells are irregularly spaced, a better average reservoir pressure is determined by recording the pressures, either actual or weighted, on a map of the area and drawing isobars from which the average pressure weighted for an area is determined by planimeter, grid system, or other means.

Static Pressure from Partial Buildup Many low-permeability reservoirs require excessive shut-in time to reach static or equilibrium pressure. Several methods have been proposed for calculating the reservoir pressure from partial buildup of pressure. Muskat proposed plotting log (p,,,$ -pr) vs. time, where pbrs is an estimated static BHP and pr is the measured pressure at different times, p,, , pt, , p,, , etc. When plotted on semilog cross-sectional paper with pressure on the log scale, the selected pws is the static pressure when the plot is a straight line.

Arps and Smith7 proposed plotting increments of pressure increase for uniform time periods against measured pressure on rectangular cross-sectional paper, and extrapolating the curve to intersect the zero line of the incremental-pressure scale, which gives the static pressure. Both the Arps and Smith and the Muskat methods are more commonly used in cases of rapid pressure buildu

Miller et al. .r presented an equation to calculate the static pressure from a partial buildup curve:

P~,~=P*+ (Psd-*!j')@ o~oo70* kh ) . . . . . . . .

where

PWS = static BHP, psi p* = last pressure on buildup curve, psi

psd = log,(rdlrw) for constant pressure at radius of drainage, or

= log,(rd/r,)-0.75 when no influx across external boundary,

4 = production rate at shut-in, B/D, p = reservoir fluid viscosity, cp, B = formation volume factor for total fluid

produced, RBISTB k = permeability of reservoir, md, h = effective thickness of reservoir, ft,

@ = dimensionless pressure variable from curves (see Fig. 30.9),

ds = Pnf-Pws, p4 = BHP during buildup, psi, PWS = BHP at time of shut-in, psi, and

t = time after well was shut in. hours.

The value of p* is determined by plotting the buildup pressure vs. the time on semilog paper, with time on the log scale. When afterflow is completed following shut- in, the points should fall on a straight line and p* is the

30-9

Fig. 30.9-Curves from which A@ is determined in the Miller et al. equation for calculating static pressure from buildup pressure curve. Solid lines assume influx at fd and dotted line indicates direction of curves when no influx at rd.

highest measured pressure lying on the straight line. This is the same straight line by which the slope, m, is determined in the equation for permeability from buildup pressures by the same authors and is discussed further under that topic.

The straight line by which the slope m is determined comes from the middle time region of a Homer plot. Afterflow causes lack of development of the middle time region (with long periods of aftefflow), early onset of boundary effects, and development of several false straight lines that could be mistaken for the middle time region. This makes the middle time region difficult for the buildup test analyst to recognize. Recognition of the middle time region is essential for successful buildup curve analysis based on Homer plot method. The line must be identified to estimate reservoir permeability, to calculate skin factor, and to estimate static drainage area pressure.

A log-log graph of the pressure change, pws -pwf (Q), in a buildup test vs. shut-in time t presents a good estimation of where the straight line portion, or middle time region, begins (Fig. 30. 1O).9 A log-log graph of pressure change pws -pwf vs. At I6 is an even more diagnostic indicator of the end of afterflow distortion. Fig. 30.11 shows a semilog plot of theoretical buildup test data. The use of type curves has greatly improved identification of the straight line portion of the buildup curve after wellbore storage effects have ended.

HomerlO plotted buildup pressure vs. (t+At)lAt on semilog paper with (t+At)lht on the log scale where t=total producing time since well completion, hours, and At=time since the well was closed in, hours. Ex- trapolation of the curve to a value of (t + At)/At = 1 is the approximate static pressure.


SEYKOG

ti t2 LOG t

Fig. 30.10-Log-log vs. semilog plots.

The value of I is determined by dividing the cumulative production of the well by the rate of production per hour at the time the well is ‘shut in. The uncertainty of the value oft increases with the age of the well. Experience indicates that using the time of the flow period before the well is shut in for the buildup test is often more reliable than’using the total time since completion provided fully stabilized conditions exist both when the well is opened and when it is shut in.

Thomas, l1 with Homer’s basic equation, preferred using the reciprocal of (t+At)lAt and therefore plotted pressure vs. At/(l+At) on semilog paper with Atl(t+At) on the log scale, and extrapolated the curve to a value of Atl(t+Ar)= 1, which gives the approximate reservoir pressure.

Hurst’* plotted the buildup pressure vs. the shut-in time in minutes on semilog paper with time on the log scale. A straight line is drawn through the points and extrapolated to an intercept time value of 1. The slope is the value of pressure change in one log cycle. Expressing his equation in English units, the static pressure is calculated:

p,,,=b+mlog625m, . . . . . . . . . . . . . . . . (8)

where pas = static BHP, psi,

m = slope of buildup curve, and h = intercept of curve with time value of 1

minute.

Correct identification of the straight-line portion of the buildup curve is necessary for the interpretation of pressure buildup data. The straight-line portion of the

Fig. 30.11-Plot of typical buildup with afterflow.

curve is frequently masked by one or more factors, such as skin effect, afterflow, and the early onset of boundary effects. Chap. 35, “Well Performance Equations,” ad- dresses these problems.

The capacity of a well to produce can be estimated from the BHP drawdown on a flow test. For gas wells, the open-flow capacity is calculated by the procedure proposed in Ref. 5 except that both the static pressure and the flowing pressure are measured with a BHP gauge. Open-flow capacity of oil wells having large capacity and high pressure is rarely of value, and little work has been reported on such determinations. Theoretically, so long as single-phase flow maintains, the rate of flow should increase in proportion to the drawdown pressure. But, because of gas coming out of solution below the bubblepoint, turbulence in the flow, and borehole restrictions, the flow conditions change and the proportionality does not hold. Engineers who have investigated the problem usually consider that little increase will be obtained after the drawdown pressure is one-half the static pressure. For low-pressure wells, the rate of production will usually continue to increase until the flowing pressure is equal to or close to atmospheric pressure.

Productivity Index

PI is defined as the barrels of oil produced per day per pound decline in BHP. To determine the PI, a well is shut in until static or reservoir pressure is reached. The well then is opened and produced until the BHP and rate of production are stabilized. Since a stabilized pressure at surface does not necessarily indicate a stabilized BHP, the BHP should be recorded continuously from the time the well is opened. The PI is then

. . . . . . . (9)

where J = PI, B/D-psi,

qO = rate of oil production, B/D, PWS = static BHP, psi, and p,,f = flowing BHP, psi.

BOTTOMHOLE PRESSURES 30-l 1

Fig. 30.12-Flow-test data on a well having a negligible transient or stabilization period.

Specific PI is defined as barrels of oil produced per day per pound decline in BHP per foot of effective reservoir thickness, and is expressed as

J,= " (p, -Pwf)h, . . . . , . . . . . . . . . . . . . (10)

where J,y is the specific PI and h is the effective reservoir thickness, ft.

On a flow test the time required for a well to reach a stabilized BHP and rate of production, that is, the transient period, may require several hours or even days and occasionally several weeks. The duration of the transient period and the rate of the pressure decline and the PI decline during the transient period will indicate the quality of the reservoir. A short transient period indicates a high-quality reservoir, and a long transient indicates a low-quality reservoir which will have a comparatively low recovery of the amount of oil calculated to be in place. Reservoir quality is not related to the numerical value of the PI. The nature of the transient period is most conveniently expressed by plotting the productivity index by hours on log-log paper.

Typical well test data are presented in Figs. 30.12 through 30.15. The negligible transient period of the test shown in Fig. 30.12 indicates a high-quality reservoir from which relatively high recovery may be expected. The short transient period in the flow test in Fig. 30.13 indicates a comparatively high recovery of the original oil in place. In Fig. 30.14, the transient period is quite long but the continuous flattening of the slope of the PI curve indicates eventual stabilization. Fig. 30.15 is the flow test of a well in which the continuous decline in pressure, production, and PI shows that the flow will not stabilize and therefore the ultimate recovery will be lower than that reasonably expected from a consideration of the producing formation and its apparent productivity.

Flow tests and PI tests are conducted by other procedures. Some prefer to run the test at two or more different rates of flow. There is usually some difference in the PI at different rates, sometimes more than can be accounted for by inherent limitation of accuracy of pressure measurement and production gauging. Chang- ing GOR or WOR will affect the relative permeability

and therefore the PI. Calculating a PI based on total fluid mass instead of liquid production has given more consistent results in some pools.

Permeability Permeability of the reservoir rock can be calculated from the PI. Wycoff et al. I3 used

=325 J,pB log=, . . . . . . . . . . . . . . . (11) rw

where k = permeability, md,

rd = radius of drainage area, ft, rw = wellbore radius, ft,

q = production rate, B/D, p = viscosity of produced fluid, cp, B = formation volume factor, RBISTB, h = effective reservoir thickness, ft,

Pws = static BHP, p,,,, = flowing BHP, and

J, = specific PI.

Permeability can be calculated from the buildup curve obtained when a producing well is shut in following a flow test. Muskat discussed this in 1937 and presented an equation in 1949. l4 The equation in commonly used units is

k= 40.37 wui*pB log(rdlr,.)

, ,,..........,.. (12) hy

where m =slope of log (p, -p,,,,) vs. t, d=diameter of flow pipe, in., t=time, hours, since well was closed in, and other parameters are as previously defined.

The equation has limitations, but it may be helpful in cases of severe reservoir damage such as interpretation of DST buildup curves where recovery is low.


HOURS

Fig. 30.13-Flow-test data on a well having a short transient period.

Miller et al. 8 calculated permeability from a BHP buildup curve with the equation

ko = 162.5qo~oBo hm ( .,,...._...........~.. (13)

where k, = effective oil permeability, md,

k = permeability, md, 40 = oil production rate, B/D,

= viscosity of reservoir oil, cp, i” = formation volume factor of oil RB/STB,

i = effective reservoir thickness, f;, and m = slope of buildup curve.

The slope m can be determined most conveniently by plotting BHP against time in hours on semilog paper, with time on the log scale. The initial part of the curve is affected by the afterflow into the wellbore, and the last part of the buildup curve may be too flat and therefore unreliable because of interference of drainage areas or limited reservoir. The calculation is simplified by extrapolating the buildup curve to encompass one complete cycle of the log scale. The slope is then the difference in the pressure reading at the beginning and at the end of the cycle.

The part of the curve representing the slope of the buildup curve is usually evident, but occasionally in- terferences and irregularities in the reservoir make the slope uncertain. We consider that if the value

0.0002637kt m=

4ct,rd2p ,,.__..,................. (14)

where k = permeability, md, t = time, hours, from closed in to end of

straight-line portion, 4 = porosity, fractional,

Cl. = liquid compressibility, psi -’ , p = viscosity, cp,

r d = drainage radius, ft,

falls to the range 10 ~ r to 10 p2, the slope m is proper and the calculated value of k is valid. This tacitly assumes that the values of the other factors are known and that the conditions exist for which the equation was derived. A valid calculation of permeability from buildup curves requires stabilized conditions of pressure and rate of production at the time the well is closed in.

These equations for calculating permeability are based on liquid single-phase flow. When a small amount of free gas is produced with the liquid, adjustment by the relative permeability will give an acceptable answer. When gas only is produced from the reservoir, the equa-

tions for permeability are as follows.

Radial flow equation:

k= qXpKTRz b&d~r,.)

O.OO~O~II(~,~,~*-~,~~)’ ““““““‘.’ . (15)

Pressure buildup t5 :

k= 1 ,637qgpgTRz hmg , ,.....,,.........,.... .(I61

where

k = permeability, md,

q&T = rate of production, Mcf/D at 14.7 psi and 60”F,

= viscosity of reservoir gas, cp, Fi = reservoir temperature, “F+460,

z = gas deviation factor, reservoir conditions, h = effective reservoir thickness, ft,

PWS = static BHP, psia, pwf = flowing BHP, psia,

rd = drainage radius, rw = wellbore radius, and,

mg = slope of pressure buildup curve, pw 2 vs. log t, where t=time after shut-in, hours, pw =BHP at t.


HOURS

Fig. 30.14-Flow-test data on a well having a long but finite transient period.

15-w DRAW-DOWN PRESSURE -e-t

I ‘bl / II1 I i 1 ‘hi I 1 /PRODUCTION I i tttl'

I 1w

IO

HOURS

Fig. 30.15-Flow-test data on a well having a very long transient period.

Permeability Damage

The permeability of the reservoir adjacent to the borehole is frequently reduced by the invasion of drilling mud, water blocking by invasion of filtrate water from drilling fluid or other source, swelling of clay particles, or deposition of salts or wax. Blinding or partial clogging of screens or perforations will give a similar effect. A substantial restriction of flow can be observed on the BHP chart by the straight-line buildup until near the maximum pressure instead of the normal exponential shaped curve. On the other hand, permeability adjacent to the borehole may be increased as a result of acidizing, fracturing, or shooting.

The amount of damage or improvement to the permeability adjacent to the borehole is determined by comparing the permeability calculated from flow test with the permeability calculated from the buildup and is expressed as the productivity ratio:

Fp=k’ ,............................. kb

. .(17)

where FP = productivity ratio, kj = permeability calculated from productivity

index, and kb = permeability calculated from buildup

pressure. Substituting the equated expressions of kj and kb and simplifying:

F, = 2m log(rdlrw)

. . . . . . . . . . . . . . . . . . (18) P ICS -P wj

A fractional Fp indicates restricted flow at the borehole and an Fp greater than unity indicates better permeability at the borehole, usually the result of stimulation.

Dolan et al. I6 presented an empirical equation to determine “damage factor” that does not involve the use of the amount of production. It is of particular value for interpretation of drillstem test charts that have an acceptable buildup but negligible fluid recovery. His equation expressed as productivity ratio is

Fp= 4

o.183(p, -pw~), . . . . . . . . . . . (19)

30-l 4 PETROLEUM ENGINEERING HANDBOOK

where FP = productivity ratio,

P W’S = static BHP, pti = flowing BHP, and Ap = slope of plot ofp vs. log (t+AtlAt),

where t = time well was open, minutes,

At = time after well was shut in, minutes, and p = pressure at t+At.

Hurst I2 has developed eq uations for calculating restrictions to flow through the reservoir adjacent to the borehole, which they have called “skin effect.” Ex- pressed in oilfield units, these equations are

for oil:

PS =m [

(Pr -Pwf> -log

(

93,

171 10.4mhqbc,r,,.’ >I . . . . . .

and for gas:

pS =mR [

(Pr-Pwf)

Mg

-log ,

(201

(21)

where

Ps = Pws = Pwf =

Pt = 40 = qg =

pressure loss due to skin effect, psi, static BHP, psi, flowing BHP, psi, well pressure 1 hour after shut-in, psi, production rate for oil, B/D, production rates for gas, Mcf/D at 14.7 psia

and 60”F, B, =

z= h=

TR =

4= co = rw = m=

mg =

formation volume factor of oil, RBISTB, compressibility factor (gas deviation factor), effective reservoir thickness, ft, reservoir temperature, “F+460, porosity reservoir rock, fraction, compressibility of reservoir oil, psi -’ , borehole radius, ft, slope, pt vs. log t, and slope pt2 vs. log t, where pt is the well

pressure at time t and t is time after well shut-in, hours.

Positive values of ps indicate damage and negative values of pr indicate improvement of permeability adjacent to the wellbore in terms of pressure loss due to skin effect.

It is usually difficult to delineate specific heterogeneities from well test results only because different heterogeneities may cause the same or similar well test response. A higher degree of confidence is achieved when the interpretation of test results is confirmed by geological and geophysical evidence of heterogeneities.

Linear discontinuities, faults, and barriers affect a pressure buildup behavior and are manifested by a second straight line, the slope of which is double the initial straight line. For a well near a linear fault, drawdown testing can be used to estimate reservoir permeability and skin factor in the usual fashion, as long as wellbore storage effects do not mask the initial straight-line section. If the well is very close to the fault, the initial straight-line section may end so quickly that it will be masked by wellbore storage.

As the drawdown proceeds and the pressure at the producing well falls below the initial semilog straight line, the following equation indicates that ~,,f vs. log t plot will have a second straight line portion with a slope double that of the initial straight line.

pi+m 0.86859s+log , . . (22)

-162.5qopoBo m=

kh ’

Plhr = pressure on straight-line portion of semilog plot one hour after beginning a transient test, psi,

pi = initial reservoir pressure, psi, s = skin effect, and L = distance to a linear discontinuity, ft.

However, the simple occurrence of a doubling slope in a transient test does not guarantee the existence of a linear boundary near the well.

To estimate the distance to a linear discontinuity, we use the intersection time, t,, of the two straight line segments of the drawdown curve. The following equation applies for drawdown testing. I7

(23)

where c, is compressibility of the total system, psi-’ The effects of reservoir heterogeneities and method of determining them are discussed in Chap. 26.

Lifting Equipment BHP measurements are valuable to the engineer for determining the size and type of artificial lift to install and to monitor the efficiency of such equipment.

The efficiency of a gas lift depends, among other factors, on the pressure at the depth of gas injection. From


the flowing pressure or PI, the pressure can be calculated for a given rate of production and after a gas lift is in operation. Knowing the PI, the producing efficiency can be calculated from the rate of production. The change in pressure gradient in a well being gas lifted will determine the point at which gas is entering the flow string, which is of interest where multiple flow or unloading valves are installed.

The PI is used to determine the amount of fluid available to be pumped from a well and therefore the size of the pump that should be run and the depth at which it should be set. After a well has been on the pump for some time and declined in production, the question frequently arises as to whether the productivity of the well has declined or the pumping equipment has decreased in efficiency. The correct condition can be determined by measuring the static and producing pressures, either with a bottomhole gauge or from fluid-level calculation by sound reflections as described previously. If fluid-level determinations are known to be unreliable for a given pool or are proved uncertain in a given well because of fluctuating fluid-level by several determinations, a BHP gauge should be run. Many operators have successfully run a pressure gauge in the annulus between the tubing and casing. During such runs the wireline will sometimes wrap around the tubing or the gauge will wedge between the tubing and casing. It can usually be released by starting the pumping equipment, but sometimes it is necessary to move in a pulling unit to lift the tubing to free the gauge. Many operators use an ec- centric tubing head to position the tubing against one side of the casing instead of its normal central position and thus minimize chances of the gauge’s becoming hung up in the annulus. The BHP gauge can be run on the rods in most wells by attaching it, preferably rigidly, to the standing valve. A pressure gauge under these conditions is subject to severe vibrations resulting from both the vibration of the pumping equipment and a “water- hammer” effect from the liquid at the pump level.

Drillstem Tests The most common use of BHP gauges in a drilling well is in evaluating DST’s. Pressure gauges were first used to determine that the valve functioned properly and was open during the test. Subsequently the pressure information has become important. The detailed pressure information obtained on a DST can be used to determine the productivity of the formation by calculating the PI from the amount of fluid recovered during the test and the static and drawdown pressures. A more recent use has been to confirm indicated productivity from the buildup after the valve is closed. It is not unusual to have a very poor recovery of fluid and obtain a good buildup curve such as can be obtained only when the producing capacity is much better than indicated by the quantity of fluid recovered. The permeability can be calculated from the buildup curve. While subject to a high probable error because of the short time of the test and usually high reservoir damage adjacent to the borehole, it is sufficient to indicate whether further testing may be warranted.

Mud Weight The pressure at the depth of a DST, before seating the packer and also after the test is completed and the packer

30-15

unseated, permits calculating the average weight of mud in the hole and is used to verify mud weight as measured by routine tests.

Nomenclature b = intercept of curve with time value of 1

minute E = formation volume factor for total fluid

produced B, = formation volume factor of oil CL = liquid compressibility CO = compressibility of reservoir oil ct = compressibility of the total system

C, = gas compressibility CT = temperature coefficient

d = diameter of flow pipe d,. = d, = d, = d2 = D= e=

F, = FP =

h= J=

J, = k=

kb =

deflection of calibration temperature observed deflection deflection at Ti for given pressure deflection at T2 for same pressure depth of well base, natural logarithms gauge factor productivity ratio effective reservoir thickness PI specific PI permeability of reservoir permeability calculated from buildup

pressure kj =

k, = L=

permeability calculated from productivity index

AL= m=

ml* =

effective permeability of oil distance to a linear discontinuity and

unstrained length change in length slope of buildup curve, pt vs. log I or

slope of log(p,, -pwf) vs. I slope of pressure buildup curve, pm,’ vs.

log t P=

Ap =

Lcp =

pressure at r+Ar slope of plot of p vs. log t+ Al/At or

AP=P~~-P~, dimensionless factor from curves

(see Fig. 30.9) p* = last pressure on buildup curve Pi = initial reservoir pressure PA = pressure loss due to skin effect

P.sd = log e rd/r,,, for constant pressure at radius

Pt = PI,’ = Pwf =

of drainage or log c (rd/r,.)-0.75 when no influx across external boundary

well pressure 1 hour after shut-in BHP at t flowing BHP

pKh = wellhead pressure pH.,, = static BHP

Plhr = pressure on straight-line portion of semilog plot one hour after beginning a transient test


4=

4K =

qn =

r= Ar = t-d = rw =

.Y= t= t=

production rate at shut-in rate of production rate of oil production unstrained resistance change in resistance drainage radius wellbore radius skin effect time

kt m=

+ct,rd ‘CL . . . . . (14)

254.359q,p,TRz log

k= h(p,&p,,f2) ““...’

(15)

time from closed in to end of straight-line

At = portion of buildup curve

time after well was shut in intersection time of the two straight line

k= 127.2q,~KTRZ

. . hm, .(16) t, =

T= T,. =

7-o =

segments of the drawdown curve average temperature in the borehole calibration temperature observed temperature reservoir temperature lower temperature higher temperature compressibility factor (gas deviation factor) specific gravity of gas (air=l) viscosity of produced fluid viscosity of reservoir gas viscosity of reservoir oil porosity reservoir rock

(20)

T, = T, = T, =

z= 142.817q,zTR

ps =mR Pt-P4 log

m<s $hm c r ,2j fi 8 II il .(21)

L= J kt, ,,78,~c,~, , (23)


f~,,,=p,~~ exp(l.l39XlO-“y,D). _, (4)

Y,D logp ,,.,, =logp ,,,, l+p. . . . . . . . . . . (5)

67.37T

p ,, =p*+ (P v/ -MqbB I, I (7) 2ahk

kz - . (II) 2*4p,,, -P,,t.) 27l

44.330 dtLB log

k= . . (12) hY

k,, = 4OtcOB~, 5,45751,n7 . (13)

where p’s are in Pa,

D is in m, yK is in kg/m3,

T is in K, I* is in Pa*s, h is in m, k is in m2, q is in m”/s,

r’s are in m, t is in s, and

c’s are in m3/m3.

References I.

2.

3.

4.

5.

6.

7.

Millikan, C.V.: “Bottom-Hole Pressures,” Petroleum Produc- tion Hundbook (1962) 2, 27-l-27-14. Brownscombe. E.R. and Cordon, D.R.: “Precision in Bottom- Hole Pressure Measurement.” Trans., AIME (1946) 165, 159-74. Bergman, J.C.. Guimard. A., and Hagernan, P.S.: “High Perfor- mance Pressure Measurement Systems,” Johnston-Macco (1980) 10. Pierce, H.R. and Rawlins. E.L.: “The Study of Fundamental Basis for Controlling and Gauging Natural Gas Wells, Part I ,” RI 2929, USBM (1929). Buck-Pressure Data on Natural Gus Wells and Their Application to Pmductiotz Pructices, USBM Monogrdph 7 (1935) 168. Muskat, M.: “Use of Data in the Build-Up of Bottomhole Pressures.” Trans., AIME (1937) 123, 44-48. Arps, J.J. and Smith, A.E.: “Practical Use of Bottom-Hole Pressure Build-Up Curves,” Drill. and Prod. Pruc., API (1949) 155.


8. Miller. C.C.. Dyes. A.B.. and Hutchinson. C A. Jr.: “Estimation 13. Wycoff, R.D. er 01.1 “Measurement of Permeability of Porous of Permeabihty and Reservoir Pressure from Bottomhole Preasurc Media.” Bull.. AAPG (1934) 18. 161. Bmld-Up Charactenstics,” Trum., AIME (1950) 189. 91-104.

9. Earlougher, R.C. Jr., Kench, K.M., and Ramey, H.J. Jr.: 14. Muskat, M.: Physical P&r&s ofOil Production. McGraw-Hill

Book Co. Inc., New York City (1949). “Well&e Effects in Injection Well Testmg,“J. Pet..Tech. (Nov. 1973) 1244-50.

10. Homer, D.R.: “Pressure Build-Up in Wells.” Proc.. Third World Pet. Gong. (1951).

11. Thomas, G.B.: “Analysis of Pressure Build-Up Data,” J. Pet. Tech. (April 1953) 125-28; Trans., AIME, 198.

12. Hurst, W.: “Establishment of the Skin Effect and Its Impediment to Fluid Flow into a Wellbore,” Pet. Eng. (1953) 25. No. 11, B-6.

15. Tracy, G.W.: “Why Gas Wells Have Low Productivity,” Oil and Gas .I. (Aug. 6, 1955) 54, No. 66, 84.

16. Dolan, J.P., Einarsen, C.A., and Hill, G.A.: “Special Applica- tions of Drill Stem Test Pressure Data,” J. Pet. Tech. (Nov. 1957) 318-24; Trans., AJME, 210.

17. Gray, K.E.: “Approximating Well-to-Fault Distance fmm Pressure Build-Up Tests,” J. Pet. Tech. (July 1965) 761-67.

Chapter 31

Temperature in Wells G.J. Plisga, Sohio Alaska Petroleum Co.*

Introduction Frequently, when working with a wildcat or deepening old production into zones that are relatively unknown, it becomes necessary to know the underground temperatures expected at a predetermined depth. In the 1920’s, API Research Project 25 investigated the relationship between geothermal gradients and the geologic structures of oil fields. ’ Initially, interest in subsurface temperatures in oil fields focused on high temperature in deep wells, which caused cement to take initial set before it was placed behind the casing. More recently, cements with low hydration heat have been developed to protect permafrost intervals in northern frontier areas. Temperature surveys in wells were used to determine the top of the column of cement behind the casing.2 With continual development of temperature devices, the reliability, accuracy, and speed of response have opened new horizons to temperature logging. Temperature logs are used currently to identify fluid entry into the wellbore, fluid migration behind the casing, tubing/casing leaks, and the extent of hydraulic fracturing and to monitor injectivity profiles.

Thermometers Self-Contained Recording Thermometers

Self-contained recording thermometers, as used in the oil fields, use the same mechanism to record as the bottomhole pressure (BHP) gauge, with a thermometer element substituted for a pressure element. Temperature elements are made for some of the commercially available BHP gauges.

Humble Gauge Temperature Element. The temperature element for the Humble gauge is a container filled with mercury. With an increase in temperature, the mercury expands into a small-diameter cylinder at the end of

‘Author of the original chapter on this topbc m the 1962 edltm was C.V. Mllhkan

a piston, which extends through a packing gland against a tense helical spring. A stylus arm attached to the end of the piston extends into the cylindrical chart holder of the recording mechanism. The temperature range may be changed by varying the diameter of the cylinder and piston. To prevent the well pressure from affecting the temperature element, the mercury container is enclosed within an outer tube, which is filled with mercury to reduce thermal lag. With reasonable care in calibration and operation, temperature readings are accurate to 2°F and differential temperatures of 0.5”F can be read.

Amerada Gauge Temperature Element. The temperature element for an Amerada gauge is a pressure element with a bulb attached to the pressure end of the helical Bourdon tube, but thermally insulated from the gauge to reduce thermal lag. The bulb contains a liquid that has a substantial vapor pressure in the temperature range of interest. For various temperature ranges, different liquids and different ranges of helical Bourdon tubes are selected, preferably in such a combination that the maximum temperature range is near the critical temperature of the liquid, which gives maximum defec- tion per degree change in temperature. Ranges of approximately 120 and 200°F are used most frequently, with the minimum or maximum temperature as requested on the order. For maximum chart readability, the span between the minimum and maximum should be no greater than 200°F. Thermometers with a range of 120 to 2OO”F, as ordinarily calibrated, have a sensitivity of about 0S”F and temperature changes of 0.1 “F can be detected. The absolute accuracy of the Amerada temperature gauges is +2”F. The time required for thermal equilibrium is 20 minutes, but some 70% of the change in temperature will be recorded in 30 to 45 seconds when the instrument is immersed in liquid. A faster-responding gauge design, which increases the


temperature sensing area and reduces the heated mass, reaches thermal equilibrium in 8 to 10 minutes. The response of a liquid-vapor element is not a straight line, and therefore the accuracy and sensitivity of the element depend on the temperature to be measured.

Time Response. The time response of a thermometer to a change in temperature is directly related to the rate of movement through fluid, or flow of fluid past the thermometer. When a long section of hole is to be surveyed for a possible anomaly, the thermometer can be run at 50 to 100 ftimin followed by a second nm at 2 to 5 ftimin through intervals of interest indicated on the first run.

Thermometers in Gas. The thermal conductivity of a gas is much lower than that of liquid. Therefore, a thermometer in gas has greater thermal lag for a given change in temperature. However, in most wells in which a thermometer is run through gas, any anomaly present is caused by expansion of gas, and the change in temperature is much greater than normally found when the anomaly is caused by migration of liquids. Because of the greater change in temperature, the presence of an anomaly is recorded as quickly in gas as in liquid. If a wellbore contains gas through the interval of interest and no gas expansion is present, such as a survey to determine migration of fluid behind the pipe, it is preferable to fill the well with liquid. If this is not feasible, then the thermometer must be run much slower (one-fifth to one- tenth) than the normal rate in liquid.

Electrical Surface-Recording Thermometers Electrical surface-recording thermometers have a ther- mocouple, resistance wire, or thermistor as a temperature element. As normally calibrated for oil well use, electrical surface-recording thermometers have a sensitivity of 0.5”F and a thermal lag of only a few seconds. They are run on armored, insulated cables and the measuring wheel is geared to drive a chart recorder, camera, or computer to record temperature against depth.

Differential thermometers have been developed that record very small changes in temperature, 0.1 “F or less, and are useful for identifying an anomaly in a long section when surveying at logging speeds of 100 to 150 ftimin. Once an anomaly is recorded, the thermometer can be run at slower speeds to completely define the anomaly. The differential thermometer is usually run in conjunction with an electrical thermometer to allow the absolute temperature to be measured in conjunction with the differential temperature.

By using electrical surface-recording thermometers, any temperature change noted can be checked by a rerun without returning the instrument to the surface. Very small anomalies under static conditions may be disturbed by the movement of the instrument, and therefore when a check of such condition is run, it should be delayed long enough to reestablish temperature equilibrium in the hole.

Advantages and Disadvantages

Self-contained thermometers and electrical surface- recording thermometers each have advantages and disad-

vantages. Self-contained thermometers have the advantages of portability and low investment. Disadvantages are much greater thermal lag and the necessity of retum- ing the instrument to surface and reading the charts before the results are known. Electrical surface- recording thermometers have the advantage of quick response to temperature change, which permits running faster, plotting temperature against depth as the survey progresses, and checking any temperature anomaly without having to recover the instrument from the well. Disadvantages include a much greater investment, larger and heavier equipment, and delicate instrumentation.

Thermometry Introduction Two types of temperature surveys are used in the oil fields. One determines the true temperature at the depth of interest, and the second determines the depth or interval of a change in temperature. Usually, true temperature is measured with a maximum-recording thermometer. However, the use of electrical surface-recording thermometers is becoming more widespread for measuring true temperatures. Determination of a change in temperature requires a continuous record some distance above and below (as well as through) the interval of interest. In this case, the use of a differential thermometer will show the existence of a change in temperature rather than the true temperature or the actual magnitude of the change.

Actual Temperature The geothermal gradient is very different in the various sedimentary basins, but within a given basin the change is gradual from one part to another.3b4 In most oil- producing areas, the gradient is usually within the range of 1 to 2°F increase for each 100 ft of depth. Temperatures just below the seasonal effect, ordinarily 30 ft below the surface, are about 1.5”F higher than the isotherms of the average annual temperature, as shown by climatological data of the U.S. Weather Bureau (Fig. 3 1. I). An exception to this is in northern latitudes where continuous permafrost exists. A geothermal gradient determined from such surface temperatures and the temperature of the producing formation is sufficiently accurate for most practical uses (Fig. 31.2). The rate of temperature increase in some areas is greater with depth, especially below 10,000 ft, and marked increases have been reported below 18,000 ft. When a precise geothermal gradient is to be determined, the hole selected must not have been disturbed for several months. In any event, the survey must be conducted while the well is in operation, since the passage of the thermometer will alter the static gradient.

The thermal conductivity of geological strata varies. The average heat conductivity of common sediments is given approximately by the figures in Table 3 1.1. 4

When fluid movement continues in a borehole for periods of time, such as in drilling operations or a producing well, the temperature effect will be different on each formation. Any effect on a given formation will depend on its thermal conductivity, the difference in temperature between the moving fluid and the formation, and the length of time such movement continues. When fluid movement is stopped, temperature equalization

TEMPERATURE IN WELLS 31-3

Fig. 31.1-Average annual temperature, OF, for the period 1899 to 1938. lsolines are drawn through points of approximate equal values.

begins, but considerable time, usually several months, is required to approach temperature equilibrium. In temperature surveys of wells, such temperature irregularities can be confused with an anomaly caused by some operating condition. Normally, however, the irregularities in the gradient resulting from normal operating conditions are small and the abnormal condition being investigated, such as a hole in the casing, fluid migration behind the pipe, or cement top, is of such size

or character that there is no uncertainty as to cause. The actual temperature at depth is very important in

many problems in drilling, production, and reservoir work. Drilling mud is often adversely affected by high temperature. The type of cement and additives are determined by the temperature at the casing seat or zone of interest. In oil reservoirs, the amount of gas in solution, the bubblepoint, and the viscosity are all related to the temperature, as is the amount of condensate formed and

CONTOUR VALUES ARE IN

DEGREES PER 100 FEET

MEAN SURFACE TEMP. 74-F

Fig. 31.2-Contour map of geothermal gradients in southwest U.S


TEMPERATURE INCREASES * TABLE 31 .I-AVERAGE HEAT CONDUCTIVITY OF COMMON SEDIMENTS (Btu/hr-sq ft-OF)

Rock salt Anhydrite Dense lime Sand Shale

36

;02 16 12

the amount that remains as a liquid wetting the reservoir rock. The volume of gas per unit of reservoir rock and the supercompressibility of the gas are also related to the actual temperature.

Temperature Surveys A temperature survey of a well is made either by running the thermometer continuously at a slow speed or by stop- ping it for a short time at regular intervals. For a survey through a long interval of hole, a continuous run is often preferred, while for a short interval numerous stops of 1 to 2 minutes are made. Temperature readings should be taken through the interval of interest, while running the thermometer in and while pulling up. Both runs should be at the same speed or at the same stops to determine more accurately the depth of any anomaly. On runs made very slowly, 2 to 5 ftimin, the actual thermal lag may be too small to warrant surveying the opposite direction. When a survey is started at a given rate, that rate should not be changed during the survey. To do so will cause a change in gradient or anomaly on the chart that may mask an actual anomaly or change in gradient in the well. Since the temperature chart is not available until the survey is completed and the thermometer is removed from the well, thorough notes that record time and depth of the instrument are required to correlate temperature and depth.

Fig. 31.3-(a) Example gradient gas flow. (b) Example gradient fluid flow.

The location of a temperature change on a temperature survey is, in most cases, much more significant than the actual temperature or the amount of change in temperature. Normally, the temperature gradient in a well is reasonably uniform, and any deviation is indicative of an abnormal condition at that depth. The deviation may be an irregularity or anomaly in an otherwise uniform gradient, or it may be merely a change in the gradient. The primary causes of temperature change in a wellbore are expansion of gas, hydration of cement, and migration of fluid. Expansion of liquids in producing wells and heat of solution and chemical reaction are often present, especially in drilling wells, but the net effect on the temperature in the borehole is normally too small to be recognized. Gas expansion will cause an anomaly on the gradient, and migration of fluid will cause a change in gradient.

ducing. When the tubing tail is below the producing interval, any gas produced that travels downward to the bottom of the tubing, then up the tubing past the thermometer, mixed with any other fluid that may be flowing into the wellbore, will mask anomalies that exist at the producing interval. With this type of completion, the tubing must be shut in and the annulus allowed to produce with the thermometer being run in the tubing. If a packer is set or, for other reasons, the well cannot be produced through the annulus, the survey can be run after the well is shut in. A temperature survey on a shut- in well relies on gas cooling by expansion to lower the temperature of that part of the formation producing gas below that of the formation not producing gas. Some time is required for the temperature to equalize, and a temperature survey run long enough after shut-in to complete afterflow will record lower temperatures in the principal intervals of gas production. A sequence of runs through the interval will permit a more reliable interpretation.

The lowest interval producing gas can be identified from a temperature survey by the cooling effect through the intervals producing the free gas and the return to the normal gradient below. Water-producing intervals can be determined only if enough free gas is produced with the oil to give a change in gradient at the lowest interval producing oil.

A hole in the casing through which fluid is moving can usually be found by running a temperature survey. In addition to the depth of the hole in the casing, the depth of the formation, which is the source of the migrating fluid, and the depth of the formation into which the fluid is moving must be determined when a hole is known or suspected to exist.

Gas expanding as it enters the borehole from the reser- A permeability or injectivity profile of a water- voir formation is much cooler than the adjacent forma- injection well can be determined from a temperature tions, and therefore the particular intervals from which survey. A typical temperature survey of a water-injection the gas is flowing can be identified by a temperature well with a homogeneous formation shows a cooling survey (Fig. 3 1.3A). A typical temperature survey con- across the injection interval (Fig. 31.4). Two procedures ducted in a well producing minimal or no gas can be are used to obtain injection-well temperature surveys. identified by a temperature survey (Fig. 3 1.3B). Greater After injecting water for a period of time, injection is detail will be recorded if the thermometer is run across discontinued and, after a few hours, the survey is run. A the open hole or perforated sections while the well is pro- more reliable answer would be expected from a series of

TEMPERATURE IN WELLS

TEYPERATURE INCREASES -

INJECTING WATER

STATIC

12 HOUR SHUT-IN \ YJECTION ZONE \

\ \ - “-, \ ‘1

Fig. 31.4-Water-injection gradient.

surveys at intervals of a few hours. Continued injection for many months can cool the entire formation and make it difficult to identify the relative injection capacity of the different parts. Under some conditions, another method that may give more detail is to discontinue injection for a day or more, then run a survey while injecting water at a very low rate, such as 1 to 5 bbl/hr. Because of the residual variations of temperature from normal water- injection operations, a survey before injection is recommended for comparison.

If water were channeling from below, the temperature survey would show a warmer anomaly at the base of the producing interval (Fig. 31 S). Fig. 31.6 shows ideal- temperature curves for various conditions of migration of fluid through a hole in the casing. Certain assumptions were made in drawing these ideal curves. Where gas is migrating, some expansion and, therefore, cooling is presumed as the gas leaves the formation. Also, it is assumed there will be a drop in pressure and, therefore, expansion and cooling at the depth of the hole in the casing. If there is no expansion at either point, the curves for gas would have the same appearance as the curves for

31-5

TENPERATURE INCREASES -

2 HOUR SHUT - IN

PRODUCING ZONE

MELED ZONE

! \

Fig. 31.5-Fluid channel gradient.

liquid. In cases where both formations are either above or below the casing hole, the movement of fluid from the hole to the farthest formation will mask any gradient between the hole and the nearest formation.

There are times when the volume of migrating fluids is not sufficient to affect the temperature. Gas leaking through a small hole in the casing will cause a very sharp temperature drop, but the volume may be too small to affect the gradient. Migration of fluids behind the casing will create a lower rate of temperature change than the normal gradient. If the flow is upward the gradient temperature will be higher than the normal gradient, and for downward flow the gradient temperature will be lower.

Preparation of the well is essential for a successful and reliable interpretation of the survey results. Usually the maximum anomaly is of the order of 2”F, and under less than optimal conditions the anomaly may be so small or so masked that a reliable interpretation is impossible. In these instances, the use of an electrical surface-recording differential thermometer may be the only method of obtaining a successful survey.

Normal Temperature Gradient

-Formation from which fluld is migrating

-Formation into which fluld is migrating

(A] Gas migrating upward

(6) L!qud migrating upward

(C) Gas mtgrat,ng downward

(0) Liqwd migrating downward

(E) Gas rmgratmg downward to casmg hole, then up

(F) Llquld migrating downward to cas.mg hole. then up

(G) Gas m,grat,ng up to casmg hole. then down

(H) Liquid migrating up to casing hole, then down

Fig. 31.6-Ideal-temperature curves of fluid migrating through casing hole.


Casing-leak and channeling-of-fluid temperature surveys are run with the well shut in. The shut-in time must be long enough for the entire wellbore to approach an even temperature gradient. A minimum of 24 hours should be allowed. However, the shut-in time required should be determined from past experience, type of problem to be identified, and location. Gas production and water production intervals are located with the well flowing at the maximum practical rate. If the survey cannot be run while flowing the well, the time interval between shutting in the well and running the survey may be critical. All afterflow must have ceased, but not so long as to allow the temperature to approach the normal gm- dient, which would mask any anomaly.

A temperature anomaly can be created by injection of fluid, usually oil or water, when normal conditions will not give a temperature change. Examples of this are identifying a channel below the producing interval and locating a packer or tubing leak by pumping cool fluids.

The data required for this graph usually are obtained on successive openhole logging runs and allow an approximation of static BHT.5 Although this Homer-type analysis is not mathematically correct, when assuming short circulating times the technique provides reliable estimates of static temperature. This technique is most applicable in regions of high geothermal gradient, where log-recorded temperatures can be significantly lower than the static temperature. Drilling Wells

In drilling deep wells or wells that encounter high The hydration of cement is an exothermic reaction, temperatures, especially in excess of 250”F, a xepresen- and sufficient heat is generated that the presence of ce- tative bottomhole temperature (BHT) is required for ment behind a string of casing can be determined by a selection of a proper mud program, cement, and ad- temperature survey for up to several days after cement- ditives to ensure proper cementing of the casing. In ing. The character of the anomaly at the top of cement in development drilling, temperature data from neighboring a particular field is fairly uniform but varies greatly in wells can be used in estimating the BHT of a new well. different fluids. The anomaly may be a large, sharp in- In exploration drilling, an estimation of the BHT may be crease (Fig. 31.7A) in some cases 35 to 45”F, or it may all that is available. Unless offset data are available a be a very slight increase in gradient (Fig. 31.7B).

geothermal gradient must be assumed that will permit estimation of the BHT.

A technique exists for determining static BHT’s by plotting on semilog paper T,, vs. (tk + At)/At where

T ws = bottomhole shut-in temperature measured at At, OF,

tk = circulation time, hours, and Ar = time after circulation ceases or shut-in time,

hours.

TEMPERATURE INCREASES > TEMPERATURE INCREASES -t

Fig. 31.7A-Effect of cement behind casing on temperature gradient.

Fig. 31.7B-Effect of cement behind casing on temperature gradient.

TEMPERATURE IN WELLS 31-7

The principal influence on the survey is the time elapsed between placement of the cement and running the survey. Other influential conditions include fineness of cement, chemical composition, rate of hydration, mass of cement in place, and the thermal conductivity of the adjacent formation. The maximum temperature usually occurs 4 to 9 hours after cementing, but reliable data can be determined in most areas after 48 hours. Any temperature change is affected more by the rate of hydration than by the total amount of heat liberated. Although hydration continues indefinitely, the rate decreases rapidly from the peak. A washed-out section of hole may be responsible for a large, sharp increase in temperature and can indicate a false cement top. A small temperature change or slight change in gradient could be caused by a small annular area or dilution of the cement with drilling mud. These factors, which influence the size of the

temperature anomaly at the top of the cement in a given well, vary widely in their effect. However, even under an unfavorable combination enough heat is generated to

permit a determination of the cement top. A new cased-hole logging method exists for detecting

vertical flow outside the casing resulting from faulty cement. The radial differential temperature (RDT) log measures variations in temperature in the plane of the casing radius on the inside of the casing.6 Normally, two sensors are used, placed 180” apart; one sensor may be used at the wall of the casing and the other sensor in the body of the tool. An anchor spring at the top of the logging tools prevents the entire tool from turning as the sensors rotate. A motor rotates the tool at a speed of one revolution every 4 minutes. The RDT logging tools are designed to allow attachment of a perforating gun, which can be adjusted to perforate into the suspected channel or abnormality located by logging,

If a channel is suspected in a perforated well, the well should be produced long enough to ensure that channel fluid is being produced before running the RDT log. The RDT sonde is placed at depths in the well where the channel is suspected. The arms are extended and the instrument revolves once or twice. Before moving to another depth the arms are retracted. As many measurements as required to delineate the channel can be made on one run. In some cases better results are obtained by injecting fluids at the surface to cool the channel.

Temperature surveys can be used to locate depth of lost circulation in an area where formations above the depth of drilling are known to have taken fluid. The

temperature survey will show a sharp increase in temperature immediately below the point of loss of fluid. The temperature break will be even greater if slow losses are occurring while running the survey. At times when the hole is considered dangerous, the survey can be run through open-ended drillpipe over the suspected interval.

Summary Wellbore temperature surveys are an inexpensive method to determine problem well conditions. The data obtained from a temperature survey are often the only data available and usually are accurate and reliable. When an anomaly occurs, one of these conditions must exist: (1) expansion of gas, (2) migration of fluid, or (3) some type of chemical reaction. With the exception of measuring the actual temperature at a point in a wellbore, temperature surveying is highly qualitative. In the majority of surveys, consistency of procedures, past experience, and the engineer’s ingenuity allow reliable information to be collected and unique analyses to be performed. Since no quantitative relationship between temperature and depth exists that covers all areas and sedimentary basins, an assumed gradient of 1 to 2”F/lOO ft depth is appropriate.

References I. Heald, K.C.: “Study of Earth Temperatures m Oil Fields on An-

ticlinal Structures.” Bull. 205, API, Dallas (1930) I. 2. Leonardon, E.G.: “The Economic Utility of Thermometric

Measurements in Drill Holes in Connection with Drilling and Cementing Problems,” Geophysics (1936) 1, 115.

3. Van Orstrand. C.E.: “Normal Geothermal Gradient in the United States,” Bull., AAPG (1935) 19, 79.

4. Nichols, E.A.: “Geothermal Gradients in Midcontinent and Gulf Coast Oil Fields,” Trans. AIME (1947) 170, 44-50.

5. Dowdle, W.L. and Cobb, W.M.: “Static Formation Temperature From Well Logs-An Empirical Method,” J. Per. Tech. (Nov. 1975) 1326-30.

6. Cooke, C.E. Jr.. “Radial Differential Temperature (RDT) Log- gmg - A New Tool for Detecting and Treating Flow Behind Cas- ing,” J. Pet. Tech. (June 1979) 676-82.

General References Romero-Juarez. A. : “A Simplified Method for Calculating

Temperature Changes in Deep Wells,” J. Pet. Tech. (June 1979) 763-68: Trirrzs., AIME. 267.

Smith. R.C. and Steffensen. R.J.: “Interpretatwn of Temperature Pro- files in Water-Injection Wells.“J. Pet. Ted. (June 1975) 777-83: Trmu.. AIME. 259.

Wooley. G.R.: “Computing Downhole Temperature in Circulation. Injection, and Production Wells,” J. Pet. Tevh. (Sept. 1980) 1509-22.

Chapter 32

Potential Tests of Oil Wells J.D. Kimmel, Oilcovery Inc.* Richard N. Dalati, Cockrell Oil Corp.

A potential test is a simple production test under stabilized flowing conditions to determine the ability of a well to produce. Potential or production tests are used to determine the rate of production through a given size of choke. This production rate and GOR then are used to determine if the well is capable of producing the assigned daily allowable production rates.

Production-rate tests are conducted on a well so that its producing capabilities can be determined and a record of its producing abilities maintained. The results of these tests are used in diagnosing and evaluating a producing well. Their impottance cannot be overemphasized since they are used in every phase of reservoir and equipment analysis in which a knowledge of the productivity of the reservoir is essential. The test results aid in determining the parameters shown in Table 32.1.

Production tests usually are considered part of routine field operations. Because they are performed on every type of producing well, a standard method of procedure that would cover every well cannot be set forth in detail. In many cases, the method or procedure for obtaining the results desired is left to the engineer’s initiative and judg- ment and, in many cases, ingenuity.

In every production test an initial understanding of the equipment employed and the method of completion, and a general knowledge of the producing reservoir and the results of previous tests on the well or on comparable wells will greatly simplify the testing procedure and aid in obtaining the desired results.

Potential or production rate tests generally are required periodically by most state regulatory bodies in the U.S., such as the Texas Railroad Commission and the Loui- siana Dept. of Conservation. The state regulatory bodies, authorized by the various states to control the production of oil and gas, set up a daily allowable or maximum rate at which each individual well may be produced. The well and reservoir conditions are considered

in setting up this maximum producing rate. Usually one other condition is involved in setting the producing allowable: the produced or re$ned oil and gas storage or market capacity. These regulatory bodies meet periodically and set a maximum number of producing days for a given period. The allowable is specified in two ways: the maximum amount of oil that can be produced each day and the maximum number of days each set period (usually 1 month) that this maximum daily allowable may be produced.

It is a responsibility of the engineer or person in charge to set up and supervise the proper testing of all producing wells. When the production is controlled by state regulatory bodies, it is also the responsibility of the engineer or person in charge to find out the requirements set up by these regulatory bodies as to the proper method for testing and reporting the tests on producing wells.

The importance of testing and information required to be supplied to the state regulatory agencies cannot be overlooked. Form W-2 of the Texas Railroad Commis- sion’s Oil and Gas Div. is an example of the information required (see Fig. 32.1).

As a general rule in Texas and Louisiana, the daily allowable is determined by the producing horizon of the well, but there are exceptions to this rule. The reservoir characteristics, previous reservoir performances, and completion procedures are considered before a definite allowable is set for the well. The general case in Texas is covered by a depth allowable set up in 1947. These allowables are set up for wells completed in proven areas and known reservoirs.

Texas Allowable Rule

The Texas Allowable Rules of 1947 and 1965 were based on producing depth and well spacing. These are normally referred to as “yardsticks.” In 1966, another yardstick was established for offshore only (Table 32.2).


TABLE 32.1-DETERMINATIONS FROM TEST RESULTS The allowables set up by the state regulatory bodies are not necessarily the proper rate to produce the wells. The producer should work very closely with the reservoir engineers and geologists to see that the test data, along with all other information available, are used to determine the most efficient producing rate of the well or reservoir.

a.

9.

10.

Il.

Optimal or maximum efficient production rates. Correlation and identification of producing horizons. Results of recovery methods. Estimates of oil and gas reserves; for example, gauged rate production decline vs. time. Decline trends and performance productions in the ability of the reservoir to produce. Qualitative determinations of gas and/or liquid contacts. Determinations relative to artificially imposed harmful wellbore or reservoir conditions such as gas or water coning, sanding or bridging action, and paraffin depositions. Analyses and comparisons of well-completion practices and equipment. Performance of and comparison between subsurface well equipment and installation principles. Analyses and comparisons of artificial lifting practices and equipment. Determining the necessity of and evaluating the results of remedial measures.

The allowable given a well completed in a new field or new reservoir is called the “Discovery Allowable: ’ It is usually set up on a producing-depth basis. This allowable is for a certain period of time or until a certain number of wells are completed into the reservoir. For example, in Texas the onshore discovery allowable is for a 24-month period or until the 11 th well is completed into the reservoir. The offshore discovery allowable is for an l&month period or until the sixth well is completed into the reservoir. The discovery allowable in Texas is set up as in Table 32.3.

When several companies produce from the same reservoir, it is common procedure to combine their knowledge and arrive at a maximum efficient producing rate (MER).

It is permissible for a company to request a change of allowables to conform more closely to the MER as determined by the company’s engineers. Before any change in the allowables is made by the regulatory bodies, a meeting or hearing of all the companies involved in producing from the reservoir is proposed. At this time all the information available is evaluated to determine if a new and different allowable is warranted. This new allowable (to conform more to the MER) usually involves a reduction in the normal allowable set up by the regulatory body.

Productivity Index (PI)

It is desirable to be able to assign to a producing well a quantity that indicates the well’s ability to produce. It was once a common occurrence “to open the well up” and measure the amount of production under wide-open flow. Today it is realized that wide-open flow of an oil or gas well can be very harmful to future well conditions.

Fig. 32.1-Sample regulatory agency form.

POTENTIALTESTS OFOILWELLS 32-3

TABLE 32.2-ALLOWABLE “YARDSTICK” SCHEDULE

47 Yardstick 65 Yardstick' 66Offshore"

Depth (ft) 10 20 40

0 to 1,000 1,000 to 1,500 1,500 to 2,000 2,000 to 3,000 3,000 to 4,000 4,000 to 5,000 5,OOOto 6,000 6,oooto 7,000 7,000 to 8,000 a,oooto 8,500 8,500to 9,000 9,000 to 9,500 9,500 to 10,000 10,000 to 10,500 10,500 to 11,000 11,000 to 11,500 11,500 to i2.000 12,000 to 12,500 12,500 to 13,000 13,000 to 13,500 13,500 to 14,000 14,000 to 14,500 14,500 to 15,000

18 28 -

27 37 57 36 46 66 45 55 75 54 64 84 63 73 93 72 82 102 81 91 111 91 101 121 103 113 133 112 122 142 127 137 157 152 162 182 190 210 230 - 225 245 - 225 275 - 290 310

10 20 -- 21 39 21 39 21 39 22 41 23 44 24 4% 26 52 28 57 31 62 34 68 36 74 40 81 43 88 48 96 - 106 - 119 - 131

40 80

74 129 74 129 74 129 78 135 84 144 93 158 102 171 111 184 121 198 133 215 142 229 157 250 172 272 192 300 212 329 237 365 262 401

- 330 350 - 144 287 436 - 375 395 - 156 312 471 - 425 445 - 169 337 - 480 500 - 181 362 - 540 560 - 200 400 - - - - - -

‘1965 yardstick effective tt field d!scovered aiter Jan 1, 1965 “1966 offshore yardstick efiective Jan 1. 1966

Wide-open flow may cause water or gas coning, influx of sand into the wellbore, collapse of tubing or casing, and/or many other harmful results.

The ability of a well to produce usually is determined by use of the PI. The use of the PI was first mentioned by Moore in 1930. ’ In a 1936 paper M.L. Harder states that the relative ability of a well to produce shows the PI to be superior. 2

API states in Recommended Practice for Determining Productivity Indices3 that the PI is calculated from the observed production rates and subsurface pressure measurements obtained. Special applications and modifications by the user to conform to individual requirements and conditions are normally used. The following discussion of PI is not meant to cover all applications but only to show how the PI may be used.

By definition, the PI is equal to the barrels per day of stock-tank oil production per pound force of pressure differential between the wellbore opposite the producing horizon and the static reservoir pressure, which is the average pressure of the well drainage area. Therefore, the PI is, in barrels of oil produced per day per psi decrease in reservoir pressure, the difference between the average pressure in the drainage area of the well and the flowing bottomhole pressure (BHP) of the well. Ac- cording to the accepted concepts of flow, the rate of flow in a system containing a single fluid under steady-state conditions should be directly proportional to the pressure drop. Using this concept, the PI would be the slope of the line resulting from plotting the rate of flow against pressure drop. On such a plot the wide-open flow quantity or well potential would be measured at the maximum pressure drop available. Such a case is referred to as the “ideal PI.” Observed values of production rates vs. pressure differentials do not give straight lines. PI data on nonflowing wells are usually more linear than the data

506 543 600 -

160 40

238200 238 200 238 200 249 245 265 245 288 275 310 305 331 340 353 380 380 420 402 420 435 465 471 465 515 515 562 515 621 565 679 565 735 620 789 620 843 675 905 675

1,000 735 - 735

80 160 .-- 330 590 330 590 330 590 360 640 400 705 445 785 490 865 545 950 605 1,050 665 1,150 665 1,150 730 1,260 730 1,260 800 1,380 800 1,380 a75 1,500 875 1,500 950 1,625 950 1,625

1,030 1,750 1,030 1,750 1,115 1,880 1,115 1,880

on flowing wells. Experience has shown that the line will be curved. This is because PI is defined to occur under steady or pseudosteady-state flow conditions. The curvature results because pB is not constant if the flow is single phase and/or gas evolution or water coning exists around the wellbore - i.e., relative permeability effects. PI is higher than theoretical when calculated erroneously before pseudosteady-state flow exists. PI is meaningless unless the radius of wellbote damage is fixed - i.e., pseudosteady-state flow is established. The flow of compressible fluids (oil and water) into a wellbore after the drainage area has been established is, strictly speaking, described by a pseudosteady-state flow equation.

TABLE 32.3-DISCOVERY ALLOWABLES

Interval of Depth

(fu

0 to 1.000 1,000 to 21000 2,000 to 3,000 3,000 to 4,000 4,000 to 5,000 5,000 to 6,000 6,000 to 7,000 7,000 to 8,000 8,000 to 9,000 9,000 to 10,000

10,000 to 10,500 10,500 to 11,000 11.000to 11,500 11,500 to 12,000 12,OOOto 12,500 12.500to 13,000 13,000 to 13,500 13,500 to 14,000 14,000to 14,500

Daily Well Allowable

WI) 20 40 60 80 100 120 140 160 180 200 210 225 255 290 330 375 425 480 540


However, some people in the oil industry describe the flow by a Darcy-type equation, which is referred to as steady-state flow. The difference in the flow rates determined from the two equations is very small. We discuss PI by use of both the steady-state and pseudosteady-state flow equations.

Steady-State Flow For a radial system under steady-state flow, the equation giving the flow rate is

where 40 =

k= h=

Pe =

Pwf =

;I I

r, = r, =

S=

oil production rate, STB/D, permeability of formation, md, thickness of formation, ft, pressure at the effective drainage radius re

normally approximated by PR, average reservoir pressure in drainage area,

psi, flowing BHP, psi, oil viscosity, cp, oil formation volume factor, RB/STB, effective drainage radius, ft, wellbore radius, ft, and skin effect (zone of reduced or improved

permeability), dimensionless

The term equivalent to the PI is

JLL 7.08x10-3kh

Ap /1,B,[ln(r,/r,)+s] ’ . ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ (2)

IO3 PERMEABILITY, md

Fig. 32.2-PI-permeability correlation.

where J is the PI, STBID-psi, and AJJ is the pressure difference between p e and p wf, psi.

In analyzing the PI, it can be seen that it is a function of the formation characteristics, k and h, the fluid characteristics, pLo and B,, and the system characteristics, h, re, r,,,, and s.

Specific PI

The term “specific PI” is frequently used and usually means the PI per foot of pay. When the term “specific” is used, it is necessary to state why. The productivity could just as well have been made specific to any other variable in Eq. 2.

Well systems do not operate at any time under steady- state conditions, but they do under pseudosteady-state conditions. Oil, water, and gas are compressible fluids; therefore, only pseudosteady-state occurs. Thus, we cannot expect Eq. 2 to yield exact correlation. The primary correlation sought has been with permeability so that the PI could be predicted from core analysis. An example of an early correlation is given by Fig. 32.2. 4

Oil flowing into a wellbore will practically always seem to enter the wellbore from a formation of lower permeability than the homogeneous fluid value determined in the laboratory. In many cases the relative permeability to oil at interstitial water saturation is one. What actually happens is that the permeability measured in the laboratory is too high because the confining pressure is lower than in the reservoir.

Muskat states that the PI should not be used to predict production of high differential pressures by simply multiplying the PI by the pressure drop of interest. He states that it is doubtful that calculated potential tests would agree with actual tests. The relative comparison should reflect the comparative production capacity with fair approximation. The PI times reservoir pressure equals the open flow potential.

Muskat also states that the productivity index is an excellent tool to determine well problems such as:

1. Comparison before and after well treatments IO evaluate these treatments. J should increase.

2. Stable GOR, R, with a declining J indicates plugging of wellbore.

3. R increasing markedly without decline in J indicates entry of extraneous gas. This would be the same if R changes with various production rates and J stays constant.

4. Rapid increase in water production should bring a decline in J if water is entering through typical strata within oil pay. If 1 is maintained, this should indicate the water is not coming through the oil-producing strata.

5, Decline of J should take place during normal reservoir depletion and parallel the normal growth of GOR or water/oil ratio (WOR). If not, plugging of the wellbore should be considered.

These are guidelines for further investigation.

Theoretical PI Muskat and Evinger6 first showed that a theoretical PI could be worked out using the steady-state formula as developed for a radial system flowing oil and gas. By

POTENTIAL TESTS OF OIL WELLS 32-5

such a system it can be shown that the J for a given well system can be expressed in terms of three parameters: (1) the producing GOR, (2) the pressure gradient in the well system, and (3) the absolute reservoir pressure.

It can be shown that for the steady-state flow of oil and gas in a radial system, the following equation expresses the rate of oil flow.

7.08~10-~ kh 40=

In re/rw +s s

PR k,/k -dp, . . . . . . . . (3)

pi PoBo

where k, is effective permeability to oil. The integraI

0 Pw l.OC+JPe 2,000 Pw Pe 3.m

PRESSURE. psia

s PR k,/k -4

py hobo

Fig. 32.3-Plot for determining PI for different GOR’s.

can be evaluated using Fig. 32.3. The PI is, therefore,

J=40= 7.08~10-~ khA,

pe -pwf (p, -p,fHW,~~,)+4 ’

for a non-circular drainage area. ’ From Eq. 6 the actual PI is

7.08x 10 -3 kh J=

fi,B,(ln X-0.75+s) ’

. . . . . . . . . . . . . . . . . . . . . . . . . (4)

where A, is the area under the curve. By using Fig. 32.3 and the definition of the PI, it can

be seen that I will not double if (p, -p,,,& is doubled because the area under the curve will not double. Also pe is determined by reservoir conditions and cannot be varied. Note that for a definite value of (p, -pwf) taken at a high absolute pressure, J will be greater than for the same (p, -pg) taken at a lower pressure because the area under the curve will be greater.

It is not readily apparent, but can be shown, that J depends on the producing GOR, R. A simple explanation is that an increase in R means that the oil saturation is less, thus k, is smaller. In Fig. 32.3, the curves labeled R t , RI, and R3 are for different GOR’s with R, > R2 > R3.

Pseudosteady-State Flow The steady-state equation is used frequently; however, this would only apply if the pressure at the outer radius stayed constant, which would only happen if a complete pressure maintenance program were maintained. If the well has a closed boundary or is operating with an established drainage radius, then pseudosteady-state flow occurs. The pseudosteady-state equation is

40= 7.08~10-~ kh (PR-p,,,,)

. . . ’ ’ ’ ’ ’ .(5)

p$,[ln(r,/r,)-0.75+s]

for a circular drainage area and

pOB,(ln x-O.75 +s) . .@I

where x is a factor for noncircular drainage area and well location.

Most reservoir engineering flow equations assume radial geometry. This assumes the drainage area of the well is circular and the well is located in the center. Ex- perience has shown that in many cases the drainage area of the well is rectangular, triangular, or other shapes. As stated previously, the PI, J, is a function of the system characteristics, which can be applied to the productivity index. Sha functions can be determined by reservoir limit tests. r

Van Everdingen originally defined the skin effects as the additional resistance concentrated around the wellbore that result from the drilling and completion techniques employed. 9 This skin effect detracts considerably from a well’s capacity to produce. More recently the skin effect is also used to indicate improved permeability around the wellbore that results from acidizing and/or fracturing. The skin effect can be defined as

) . . . . . . . . . . . . . . . (7)

where r, = radius of area around the wellbore affected

by skin effect, ft, k = formation permeability, md, and

k, = permeability of area around the wellbore affected by skin effect, md.

The skin effect, s, normally is determined from pressure transient analysis. The reader is referred to Chap. 35, Well Performance Equations, for a detailed treatment of skin effect.


The aim of the production engineer is to make the PI, J, as high as possible; the equation for J indicates this may be done by several ways that include”:

1, Remove the skin effect through acid treatment or the use of various completion or drilling fluids, depending on the formation.

2. Increase the effective permeability by fracturing or propping.

3. Reduce the viscosity by formation heating. 4. Reduce formation volume factor, B, , by production

techniques and surface separation system. 5. Increase the well penetration, h, by completing

across the entire producing formation. Care should be taken not to complete across a zone of excessive gas or water production.

6. Reduce the ratio re/rw. Since it appears as a logarithmic tey4 this has little influence. Underreaming is seldom considered as a means of well stimulation.

The above equations should indicate that the most important step in determining and analyzing the performance of any well, especially flowing wells, is to determine the well production rate for any given flowing BHP.

It is now readily apparent that to compare a PI of a well it is necessary to know what is being compared, which includes the permeability, sand thickness, well radius, drainage radius, fluid characteristics, and flow relations. A comparison should also be made on reservoir pressure and pressure drawdown for a similar GOR.

The standard procedure for conducting PI tests mainly consists of following the directions that have been set forth in the procedures for conducting static and flowing reservoir pressures and gauged-rate production tests. The most popular wireline pressure gauge is the Amerada recording pressure gauge.

In some cases, the use of artificial-lift equipment prevents the passage of subsurface gauges; therefore, other means must be found for determining these pressures. It is possible with the use of sounding devices-i.e., Echometer or Sonolog - to determine the liquid level. Knowing the liquid level, the static or flowing pressures can be approximated by gradient and depth calculations.

Care should be exercised in determining the static and flowing pressures to be sure they are the equilibrium pressures. If there is any doubt regarding the equilibrium conditions, two or more pressure readings should be made several hours apart to be sure they are the same. Some formations stabilize in one hour but most take four to 24 hours. Tight formation could take several days. In determining the actual J, the flowing rates should have wide enough variation to compensate for any errors in measurement.

When artificial-lift equipment is used, the gauged production tests for determining the J must be lower than the production limitations of the lift equipment.

Methods of determining production rates are: (1) stock-tank measurement; (2) portable well testers, including batch-type meters, positive-displacement meters, turbine meters, and flow meters; and (3) sta- tionaty test equipment.

Stock-Tank Measurement The oldest and most widely accepted means of determin-

ing the amount of liquid produced by an oil or gas well is the manual gauging of the production in stock tanks. A single well producing into a tank battery presents no testing problems, as it is a simple process to measure the liquid in the stock tanks at the start of the test and the liquid in the stock tanks at the end of the test. Most tank batteries are arranged so that one well may be tested at the battery while the other wells are being produced. This requires, of course, the addition of a test separator in addition to the production separator and also sufficient stock-tank volume so that no commingling of the production is required. A separate gas run and meter would also be required for measurement of the gas produced while the well is on test. If this meter run is not available, a portable orifice well tester could be used.

If testing facilities are not available at the lease, it is necessary to shut in the entire lease while individual wells are being tested into the tank battery. In the latter case, it is usually better to use portable test equipment to determine the production rate.

Before the production test is started, with stock tanks as a means of measurement, it is necessary to determine the amount of basic sediment and water (BSSrW) at the bottom of the tank, in addition to the liquid level at the start of the test. If at all possible, stock tanks should be clean, since errors may be introduced in determining BS&W. Dirty stock tanks can cause the tank tables to be in error. If possible, produced water should be produced and gauged in separate stock tanks.

After gauging the test tank or gun barrel, the usual pm- cedure would be to proceed to the separator, check and record the operating pressure, and on large-volume separators, if the well being tested has a low productivity, record the liquid level in the separator. The choke size at the wellhead should be carefully determined and if there is a question, the choke should be checked and calibrated.

If a treater or heater is used, its operating characteristics should be noted so that any conditions not uniform may be considered on the gauged production test. All tests should be made after the production has stabilized and under conditions that are as uniform as possible. No change should be made at the wellhead or tank battery during the duration of the test.

Standard tests should range from 24 to 168 hours in length, depending on the well and reservoir characteristics. All data should be observed and recorded at less frequent intervals. The time between intervals will vary depending on the length of test. In cases where short tests (6 to 8 hours’ duration) are necessary, consecutive data recordings should be made hourly.

Tests should be for 24 to 168 hours’ duration so that fluctuations in the GOR, as a result of heading tendencies and temperature variations, may be considered and the test results averaged. It is not uncommon to observe a 40 to 50°F temperature variation between night and day atmosphere and to observe a 10 to 20% variation in the gas/liquid ratio. Recognizing these facts, it becomes necessary to measure the temperature of either the liquid or vapor section of the separator.

The preferred location to obtain the temperature would be in the flow line immediately before the separator. This latter temperature would more nearly reflect the ac-


FLOATE 77+&i/ r 20 r WATER OUTLET

1 ET

OIL LLC WAT

Z&WELL FLUID

WATER OUTLET &$#$~OIL;UTLET

FRONT ELEVATION SIDE ELEVATION

(II Degassing element

(2) Mist extractor (vane-type)

(3) Relief valve

(4) Safely head (optional)

(5) Elkpt~cal manway

(6) 011.dump valve

(7) Water-dump valve

(6) 011 meter

(9) Water meter

(IO) Check valves

(11) Strainers (optional)

(12) Plug Yalws

(13) Pressure gauge

(14) 011 outlet-wew nipple (removable)

(15) Interface LLC pIlot

(16) 011 LLC pIlot

(17) Water outlet (from separator)

(18) Gas outlet (from separator)

(19) Orifice fittmg (optmnal)

(20) Gas back-pressure valve

(21) Liquid-level sight glasses

(22) Trailer assembly

Fig. 32.4-Trailer-mounted three-phase well tester with PD meters.

tual liquid-phase temperature prior to the flash liberation process.

The production should be sampled each time the data are recorded during the production test. This interval sampling is very necessary if storage facilities are such that the water produced must be disposed of as it is produced. Refer to Chap. 17 for sampling information. Wells that produce with a high WOR should always be tested at length because of the usual uneven oil- producing rate.

Depending on the separation pressure and the characteristics of the crude for shrinkage, some consideration should be given to determining the amount of gas produced that is not measured by the gas meter but is vented from the stock tanks.

Points to check to ensure the accuracy of stock-tank gauges include:

1. Correct and accurate strapping table is used with the test tank.

2. No dents or damage has occurred to the stock tank since strapping table was made.

3. Tank is clean with no encrustations or deposits on the walls.

4. If foamy crude is being produced the liquid level will be almost impossible to determine correctly with a gauge tape. Chemical addition or settling time may be required to minimize the foam.

5. BS&W at bottom of tank is determined as accurately as possible before and after the test.

6. Gauge tape must not be kinked and plumb bob must be carefully touched at the bottom of tank.

7. Temperature of oil in the stock tank must be considered.

8. The oil level must be steady and undisturbed while a gauge reading is taken.

Portable Well Testers The trend toward unitization and centralization of tank batteries has increased the demand for a means of determining production rates without requiring the installation of additional expensive stock tanks and test separators. The requirements are being solved by the use of well testers.

The well tester is a combination separating and measuring unit for oil, water, and gas. The well tester can be either two or three phase, can be used for penna- nent installation, or can be skid or trailer mounted for portable operation (see Figs. 32.4 through 32.8). The well tester may utilize several types of meters for both liquid and gas measurement. Note that the two-phase testers (Figs. 32.5 and 32.8) are not fitted with liquid level controllers (LLC’s), but are blanked so LLC’s can be added in the field for three-phase testing.

Each established class of metering equipment has sur- vived and advanced in the petroleum industry today because it fits a definite need in the metering field. Each type has won its place in the petroleum industry by fulfilling the requirements of certain applications better than any other type. Selection of the type of meter used on a well tester may be determined by the user, based on the application of the well tester and the limitations and capabilities of the meters available (see Table 32.4 for various sizes and working pressures of standard well testers). Remember that it is better to have a unit that has the capacity to test (pressure and flow capacity) so that modifications to the test can be minimized.

Capacities are based on steady continuous flow for a 24-hour period. Fluid retention time is as follows.

0 to 600 psi = 1 minute. 600 to 1,000 psi = 50 seconds.

More than 1,000 psi = 30 seconds.


-8”

FLUID \T

U U , - FRONT ELEVATION SIDE ELEVATION

Fig. 32.5-Trailer-mounted two-phase well tester with PD meter

NOTE. INTERFACE FLOAT MUST BE WEIG SINK IN OIL ANU tMU

PLAN -

WELL FLUID

INLET

-5

FRONT ELEVATION SIDE ELEVATION

(1) B?gasswlg element


(3) Relief valve

(4) Safety head (optional)

(5) Elliptical manway

(6) OIldump valve

(7) Oil meter

(6) Check valves

(9) Strainer (optional)

(10) Plug valves

(11) Pressure gauge

(12) Oil outlet (from separator)

(13) Gas outlet (from separator)

(14) Orifice fittmg (optional)

(15) LLC pilot


(17) Liquid-level sight glass


(19) Auxiliary float nozzle

(I) Degassmg element


(3) Relief valve

(4) Safety head (optIonal)

(5) EllIptical manway


(7) Water meter

(8) 0114nlet motor

(9) 0~1.outlet motor valve

(lo) 011 meter

(11) Pressure gauge

(12) Oil-outlet wer nipple (removable)

(t 3) Water outlet (from separator)

(14) Gas outlet (horn separator)

(I 5) Orlflce iittmg (optional)

(1.5) Interface LLC Plkx


(18) Liqwd-level slght glasses

(19) Gas.sq”alIzi”g llne

(20) Plug valves

(2,) Gas back-presSure YalYe

(22) Check valve

(23) Check valves

(24) Siram?r (+WXMt)

Fig. 32.6-Trailer-mounted three-phase well tester with oil-volume meter and PD meter.


NOTE. ,Ll!?l < “3

INTERFACE FLOAT MUST BE WEIGHTED

SECTION’%B’

TO SINK IN OIL AND EMULSION AND FLOAT ONLY IN FREE WATER

PLAN I’----‘] -

DRAINSM

FRONT ELEVATION

FRONT ELEVATION

SIDE ELEVATION

Fig. 32.7-Trailer-mounted three-phase well tester with batch-type

Ii----l/L17

PLAN -

-ET

.ET

SIDE ELEVPTION

(1) oegassmg element

(2) Misl extractor (vane-type)

(3) Relief valve

(4) Safety head (optmal)

(5) Elliptical manway


(7) Water-inlet molar valve

(6) Water-outlet motor valve

(9) Water meter

(10) Oil-Inlet motor valve

(11) Oil-outlet motor valve

(12) Oil meter

(13) Pressure gauge

(14) Oil-outlet war mpple (removable)

(15) Water outlet (irom separator)

(16) Gas outlet (horn separator)

(17) Orifice fitting (optlonal)

(18) Interface LLC pilot


(20) Llquld-level slght glasses

(21) Gas-equahzlng llne

(22) Plug valves


(24) Check valves (optional)

(1) DegassIng element


(3) Gas outlet [from separator)

(4) Orifice fItring (optional)

(5) 011 outlet (from separator)

(6) 011 meter

(7) Oil-Inlet mOtOr Valve

(6) Oil-outlet motor valve

(9) Relief valve

(lo] Safety head (optional)

(11) Pressure gauge

(12) Gas-equalizing line


(14) Llquld-level sight glass

(151 Elllptlcal manway

(161 Plug valve

(17) Check valve (apt~onal)


Fig. 32.8-Trailer-mounted two-phase well tester with volume meters.

32-10

Separator Size

Shell Length

Shell Seam to OD Seam (in.) (fi)

16 6 24 6 30 6 36 7 48 7 16 6 24 6 30 6 36 7 16 7 20 7 24 7 30 7 14 7 16 7 20 7 24 7 12 7 14 7 16 7 20 7 12 7 14 7 16 7 20 7

Maximum Working Pressure

(Psi)

125 125 125 125 125 300 300 300 300 600 600 600 600

1,200 1,200 1,200 1,200 1,800 1,800 1,800 1,800 2,400 2,400 2,400 2,400


TABLE 32.4-WELL-TESTER SPECIFICATIONS

Rated Separator Capacities Two-Phase Separation

Oil Plus Water

(B/D)

500 1,200 1,800 2,800 4,800 500

1,200 1,800 2,800 500 850

1,200 1,800 400 500 850

1,200 300 400 500 850 300 400 500 850

Gas Oil Water (M Mscf/D) (B/D) (B/D)

1.6 500- 250 3.6 1,200 600 5.5 1,800 900 8.0 2,800 1,400 14.0 4,800 2,400 3.5 500 250 7.7 1,200 600 12.5 1,800 900 17.0 2,800 1,400 5.5 500 250 8.3 850 425 12.5 1,200 600 19.0 1,800 900 6.1 400 200 7.7 500 250 11.4 850 425 16.5 1,200 600 5.5 300 150 6.8 400 200 8.0 500 250

12.2 850 425 5.3 300 150 6.5 400 200 8.0 500 250

12.4 850 425

The type of fluid to be tested must be considered in determining the retention time. If the crude foams, the necessary retention time for the gas to break out of solution may be 5 minutes or longer. For three-phase separation, additional retention time may be required for the oil and water separation depending on the type of emulsion produced. Many times the addition of heat and/or chemicals is required to produce proper separation of the oil and water or gas and oil. Well testers are available in low working pressures that utilize either electric or gas- fired heaters to heat the well fluid and improve the separation processes. The meter used must be of sufficient metering capacity not to limit the capacity of the well tester. Working pressures are available up to 4,000 psi.

The listing in Table 32.4 of sizes and capacities of standard well testers is not complete but may be used as a guide to determine the approximate size and capacity of the unit required for your specific testing purpose.

The types of meter available for use on well testers are (1) batch-type meters, (2) positive-displacement meters, and (3) flow meters, including standard and mass flow meters.

Batch-Type Meters The batch-type meter works by means of cyclic accumulation, isolation, and discharge of predetermined volumes. Each dump volume is registered on a counter. The counter reading is then multiplied by the dump volume to determine the total measured volume.

When metering vessels such as batch meters are used to measure liquid hydrocarbons, four factors must be ob-

Three-Phase Separation

Total Liquid Oil Plus Water

W) 500

1,200 1,800 2,800 4,800 500

1,200 1,800 2,800 500 850

1,200 1,800 400 500 850

1,200 300 400 500 850 300 400 500 850

Gas (MMscflD)

1 .o 2.2 3.5 5.1 8.7 2.1 4.9 7.5 11 .o 3.3 5.0 7.5

12.0 3.8 5.0 6.5 9.1 3.5 4.3 5.5 7.0 3.4 4.2 5.3 7.0

Approximate Weight (Ibr?$

1,200 1,500 1,700 2,300 41600 1,900 2,200 2,400 2,800 2,600 2,800 3,000 3,200 2,900 3.100 31400 3,600 3,000 3,400 3,800 4,100 3,500 4,000 4,500 4,800

tained and maintained: 1. An unchanging volume in the metering vessel must

be maintained consistently. This means that there can be no foreign material deposited in the vessel and that the vessel itself must not change shape or size.

2. Exact upper and lower dumping levels must be obtained and maintained in the metering vessel. These dumping levels must be the same for each cycle.

3. Proper valve arrangement must be maintained so that no liquid may slip through the vessel without being metered. The valve or valves should be arranged so that there is a period of time at the beginning and end of each cycle during which both the inlet and outlet to the metering vessel are closed at the same time. This assures that no unmetered fluid will slip through the metering vessel.

4. An appropriate and accurate “meter factor” must be used to compensate for temperature change of the liquid, shrinkage (volume reduction) of the liquid resulting from pressure reduction, mechanical metering error of the metering vessel, and BS&W content of the liquid.

These various factors are usually combined into one factor known as the “meter factor” or “meter multiplier.” These meter factors are usually less than

1.0. In other words, the meter normally reads higher than the net stock-tank volume.

Advantages and Disadvantages of Batch-Type Meters

1. A metering vessel can be used as its own meter proving tank if the vessel is inspected for encrustation, the dumping levels are observed during operations, and valves are checked for leakage.


TABLE 32.5-NOMINAL RATED CAPACITY OF VOLUME-TYPE DUMP METERS

Barrels per discharge Metering capacity, bbl/24-hr day

0.25 0.5 1 .o

300 500 720

2. A metering vessel will handle more sand and other foreign material without causing trouble than the positive-displacement (PD) meter.

3. A metering vessel will meter from zero flow to maximum rated rate of flow with the same degree of accuracy.

4. Weight-type (hydrostatic-head) metering controls may be used to meter foaming oil.

5. The unit may be adjusted while in operation. 6. Free gas will not register as liquid if the controls

should fail to function. 7. Initial and installation cost is slightly higher than

with the PD meter. 8. The meter delivers an intermittent discharge of

liquid. 9. Gas is requited to displace the liquid from the

vessel. 10. Paraffin buildup on the vessel wall will cause

inaccuracies. 11. The meter requires more space and is heavier than

a PD meter. 12. With heavy viscous crudes a larger inlet or dif-

ferential pressure arrangement between the separator and metering vessel may be required to maintain the rated capacity.

Nominal rated metering capacity of various sizes of volume-type dump meters under normal field conditions is given in Table 32.5. Pressure ratings are up to 3,ooO psi. Volume meters are not used for gas measurement.

PD Meters

PD meters are quantitative instruments. They are termed “positive-displacement” because some sensing element is forcibly or positively displaced through a measuring cycle by the hydraulic action of the fluid on the element. l1 For a completed measuring cycle a known quantity is displaced by the sensing element. It is necessary to count the number of cycles and multiply them by the displacement volume to get the total liquid quantity that has passed through the meter. This latter function is carried out by the meter’s gear train and register.

Fig. 32.9 shows the basic types of PD meters: nutating disk, oscillating piston, oval gear, rotary vane, reciprocating piston. and bi-rotor.

Probably 80 to 90% of all PD meters in service today are of the nutating-disk type. They are most popular because of the relative simplicity of the construction, ruggedness, accuracy over a wide range, and low cost. The accuracy of the nutating-disk type meter is not as high as that of the PD meters of the other types.

Advantages and Disadvantages of PD Meters 1. Discharge of the metered liquid is continuous. 2. PD meters can be used to meter exceptionally

viscous liquids.

2.0 5.0 10.0 20.0 30.0

1,440 2,000 4,000 8,000 15,000

3. PD meters do not require gas to displace the fluid through the meters.

4. Initial and installation cost is lower. 5. Temperature compensation can be applied with cer-

tain types of PD meters less expensively than with batch- type meters.

6. Paraffin may not reduce metering accuracy. 7. Liquids metered must be free of gas, since slugs of

gas may damage or wreck the meter. Gas will register as fluid when passing through a PD meter.

8. Sand, mud, salt, or other foreign particles will cause wear on the PD meter and cause inaccurate meter readings.

9. Some type of meter-proving process is required to prove PD meters periodically. Actual stock-tank gauges are used in many cases to determine the accuracy of the meter.

10. Meters must be operated between a minimum and maximum specified rate of flow. High or low rates of flow may affect the accuracy of the PD meter.

PD meters are available in pressure ratings to 5,000 psi. Capacities of PD meters depend on the size and type of meter. If possible the manufacturer of the PD meter should be requested to furnish information regarding the

NUTATING DISK OSCILLATING PISTON

OVAL GEAR

RECIPROCATING PISTON

- EL 0’

ROTARY VANE

Bl-ROTOR

Fig. 32.9-Basic types of PD meters.


TABLE 32.6-AVERAGE CAPACITY FOR NUTATING-DISK-TYPE PD

METERS

Capacity

Size (B/D) (in.) Minimum Maximum

5/B to J/i 68 340 Yi 102 510 1 170 850 1% 342 1,710 2 548 2,740

Average Capacity for Nutating-Disk Type PD Meters. The average rates shown in Table 32.6 are based on oil as the fluid being metered. The manufacturer should always furnish information about recommended capacity. When PD meters are used downstream of separators or vessels that arc not continually dumping, it is necessary to size the meter on the maximum “rate” of discharge while the vessel is dumping.

PD meters are used in some cases for gas measurement The types used are the bellows and birotor. High cost and size have held the use of PD meters for gas measurement to a minimum.

Turbine Meter

Today most liquid measurement is done by the use of turbine meters. A turbine meter is a flow rate measuring device which has a rotating element that senses the velocity of the flowing liquid. t2 This liquid causes the rotating device to rotate at a velocity proportional to the volumetric flow. The movement of the rotating device is sensed either mechanically or electrically and is registered. The actual volume is then compared to the registered readout to arrive at a meter or register factor (see Figs. 32.10 and 32.11).

The turbine meter is used because of its simplicity and costs. Each meter application will require different meter or register factors.

Considerations in the selection of turbine meters include (1) properties of the liquid to be metered-viscosity, density, vapor pressure, corrosiveness, and lubricating ability; (2) operating conditions, including pressure, flow rates and whether continuous or intermittent, temperatures (some meters have temperature compensators), and quantity and size of abrasive particles in the fluid; and (3) space availability (see Fig. 32.12). Items or conditions that normally affect the meter factor are shown in Table 32.7. Both turbine and PD meters should be connected so that meter factors may be periodically determined.

(I) Upsiream stator

(2) Upstream stator supports

(3) Bearings

(4) Shaft

(5) Rotor hub

(6) Rotor blade

(7) Downstream stator

(6) Oownstrearn *tator supports

(9) Meter housing

(10) Pickup

(11) End connectlorw

Fig. 32.10-Names of typical turbine meter parts.

(2) Prsssure gauge (optional)

(3) Filter, au eliminator and/or strainer as required

9

( 1

,‘j 7i Ii *.1ew .

I

+q +

I?’

e+ ;<I t Mfp&.Tl; y

(4) Straight pipe

(5) Straightening vane (as required)

(6) Turbtne meter

I=

(7) Straight pipe (with straghtening vane as required) - <“> :. + ’ , (8) Pressure gauge

,h sl 6 $ hgf ‘4 (9) Thermometer

(IOJ Proving connections (should be downstream of meter run)

(IIJ Valve with double-block and bleed or valves wth a telltale bleed

(12) Control valve (as required)

(131 Check valve (as required)

Fig. 32.11-Turbine meter system schematic.


fxF= -

Fig. 32.12--Schematic operation diagram of oilwell production meter installation with stock tank or open prover.

Flowmeters

The standard-type flowmeters are: orifice plate, Venturi tubes, flow nozzle, Pitot tube, drag body, and lift surface. These meters or devices are used to create a flowing differential pressure. This flowing differential pressure is used to solve the flow equation for the rate of flow.

Orifice plate, Venturi tube, flow nozzle, and Pitot tube are commonly used. Drag body and lift surface arc not as familiar. The net force resulting from a pressure difference is measured. This pressure difference is used to solve the flow equation. If the force is parallel to the flow direction, the force is called “drag body.” If the force is perpendicular to the flow direction, the force is called a “lifting surface.”

In addition to differential pressure drop, six other factors must be considered and included in the integration to determine a basic flow rate or quantity. They are (1) static pressure, (2) flowing temperature, (3) specific gravity of the flowing quantity, (4) size of orifice run, (5) size of the orifice plate if orifice plate is used to create the differential pressure, and (6) supercompressibility, if applicable.

These factors may be considered by the solving of the flow equation or they may be applied as a multiplying factor applied to the meter reading.

Mass Flowmeter. In about 1942, W.J.D. VanDijik of The Netherlands constructed and evaluated the first mass flowmeter, as such. The mass flowmeter measures the quantity of matter passed through the meter. This mass is independent of all ambient conditions, which is not true of volumetric meters discussed previously. If any type of flowmeter mentioned above is compensated in any way (electrically, mechanically, or a combination of both) for fluid density, it is a mass flowmeter. As early as 1930, pressure and temperature compensators could be attached to a standard orifice meter. They were mass flowmeters, in a true definition of mass flowmetering, although they were not called by that name.

On well testers, and for measurement of produced

water, oil, and gas, it is most common to use turbine, PD, and batch meters for liquid measurement and the standard orifice meter for gas measurement. Mass flowmeters may be used for both gas and liquid measurement. Because of the cost and special requirements for technicians to operate and maintain these meters, they are seldom used in field operations.

Automation and remote readout requirements can be accomplished with the use of well testers in much the same way as with automatic custody units. The liquid measurement may be relayed by pneumatic or electrical impulses to a transmitter. These impulses in turn may ac- tuate some type of recording unit at a central location. The gas measurement would require some type of pressure transducer to convert the differential pressure to an electrical signal. More often, when remote recording of gas flow is required, an integrating flowmeter is used and the transmitted signal will read in volumetric units.

Fig. 32.13 shows a well tester installed at a tank battery for permanent test or lease automation.

Stationary Metering Installation

Stationary metering installations are those that include metering separators, metering treaters, and any other

TABLE 32.7-CONDITIONS AFFECTING THE METER FACTOR

1. Mechanics of meter as to tolerances. 2. Change in clearance due to wear or damage. 3. Flow rates and variations in flow. 4. Temperatures of liquids. 5. Viscosity of liquids. 6. Pressure of liquids. 7. Pressure drop across the meter as a resistance to flow. 8. Foreign material lodged or deposited in the meter or

connecting piping. 9. Inlet condition changes, such as changes in the

entrance to the meter, which change the flowing fluid profile.

10. Lubricating properties of the liquid. 11. Accuracy and conditions of meter-proving system and

meter-factor test.


Fig. 32.13-Unitized or automatic tank battery.

type of meter used in conjunction with test separators or emulsion treaters. These units are installed as an integral part of the tank battery.

The metering separator combines two functions of separating and metering the produced fluid (see Figs. 32.14 and 32.15). The metering separation is divided in- to one compartment for separating the liquid and the gas and into one or two other compartments for metering the

RELIEF VALVE

MIST EXTRACTOR

SEPARATING CHAMBER GAS EQUALIZING LINE

INLET SEPARATING ELEMENT GAS BOIL INLET -

BAFFLE PLATE- PRESSUREGAUGE

INTERFACE LLC WITH WEIGHTED

OIL-WATER INTERFACE

ERT

I,., II I OIL-METERING CHAMBER

COUNTER,

oil and water. PD meters may be used for metering all produced fluids.

Pressure ratings range to 3,000 psi. Capacities will be the same as shown for standard oil and gas separators in Chapter 12. The metering capacity will be as shown for the type of meter used.

GOR The GOR may be defined as the rate of gas production divided by the rate of oil production. It is usually expressed as standard cubic feet of gas per barrel of stock- tank oil produced under stabilized flowing conditions for a 24-hour period.

The term “cubic feet of gas” or “standard cubic feet of gas” means the volume of gas contained in one cubic foot of space at a standard pressure base and standard temperature base. This standard base is normally 14.65 psia and 60°F. Most tables published for orifice well testers, Pitot tubes, flow provers, and other gas measurement means are referred to a base pressure of 14.65 psia and 60°F temperature. Whenever the conditions of pressure and temperature vary they may be converted to a standard or base condition by the use of the real gas law.

The volume of gas used should be the total gas produced from the reservoir through either the casing or tubing. Any gas that is injected back into the reservoir for artificial lifting purposes such as gas lift should be subtracted from this total gas produced.

(j p &;$j&; OLJTLET YTr_,

‘SAFETY HEAD RELIEF VALVE

SIDE VIEW OF METERING COMPARTMENT

(OIL OR WATER) GAS EOUALIZING LINE

MIST EXTRACTOR GAS EOUALIZING LINE SEPARATING C

WELL FLUID IN

BAFFLE PLATE

PIPING - COPPER TUBING -- OPTIONAL ITEMS l

COMPARTMENTS

lNTERFC’= ( r

WATER t WATER- METER11

FOR -s

PRESSUREGAUGE

~~~~~~~~~~~

COUNTER COUNTER ACTUATOR

Flg. 32.14-Metering separator with free water knockout. Flg. 32.15-Three-phase metering separator with integral metering compartments. Gauge glasses and valves are furnished for separating chamber and both metering chambers. Automatic BS&W samples can be furnished as an option.


The volume of oil produced should be determined by any of the means discussed in the first part of this chapter.

Procedures for Well Testing

Flowing Wells. The oil flow should be stabilized during the 24-hour period immediately preceding the test. This stabilized flow should be very close to the assigned allowable or the daily producing rate. If the well being tested is a discovery well, the producing rate should be as close to the assigned discovery allowable as possible. Any adjustments should be made during the first 12 hours of the stabilization period and no adjustment made during the last 12 hours or during the time the well is on test. All gas withdrawn from the reservoir must be included as produced gas. If the oil has a great deal of shrinkage after it is placed in the stock tanks, some means should be considered for measurement of the gas that breaks out of solution. Any gas used for operation of machinery or for any other purpose must be considered as produced gas. Tests should range from 24 to 168 hours’ duration to consider any uneven flow.

Intermittent Flowing Wells (Stopcocked). The procedure for testing should be as outlined for flowing wells, except the shut-in casing and tubing pressures should be approximately equal to the pressures recorded at the beginning of the test. The Texas Railroad Com- mission states, “The closed-in casing pressure at the end of the 24-hour test period shall not exceed the closed-in casing pressure at the beginning of the test by more than six-tenths (0.6) pounds per square inch per barrel of oil produced during the test.” This rule also applies to flowing wells. This is true because of the “loading” characteristic of some wells while shut-in. Before an accurate test can be made the flow must be stabilized and stabilization cannot occur while producing from a loaded annulus or tubing.

Gas-Lift or Jetting Wells. The volume of gas used should be the net produced gas or formation gas. Forma- tion gas will be equal to the total gas produced minus the injection gas.

Pumping Wells. In computing the GOR for pumping wells, the total volume of gas produced during the 24-hour period, ending with the closing in of the well at the conclusion of the tests, and the total barrels of oil that are produced in order to obtain the daily allowable must be used regardless of the actual pumping time in the 24-hour period. If the gas produced is not enough to measure accurately, this should be indicated on the test report as gas “too low to measure.”

In some states the regulatory agencies will lower the assigned allowable of the well if the daily or producing allowable is not produced while making GOR tests.

Average GOR To obtain an average GOR for several wells or for all the wells in a field, one cannot take the arithmetic average value of the ratios. For example, two wells with GOR’s of 2,000 and 4,000 would not necessarily have an

STOCK TANK CUMULATIVE+

Flg. 32.16-Typical performance curve for an internal gas-driven reservoir.

average ratio of 3,000. For the average ratio to be 3,000 the wells would have to produce the same amounts of oil. The average GOR of several wells must be obtained by dividing the total gas production of all wells involved. For example, if the 2,000-ratio well produced 50 B/D oil and the 4,000-ratio well produced 200 B/D oil, the average GOR for the two wells would be

R=(2,000X50)+(4,0tXlx200)

50+200 =3,600 cu ftibbl.

For a large number of wells, the average ratio can be figured as

& wiw Xqhv) . . . . . . . . . . . . . . . . . . . . . . . . . . cqi, (8)

where

i? = average GOR, cu ftlbbl, R 1w = individual well GOR, cu ft/bbl, and 4iw = individual well daily production, STBID.

Cumulative GOR The cumulative GOR is defined as the total amount of gas produced and kept from the reservoir up to a ceflain time divided by the cumulative oil produced up to the same time. Therefore,

Rp= G,-G -, . ..I....I....................

NP '(9)

where R, = cumulative GOR, cu ft/bbl, G, = total gas produced, cu ft,

G = gas reinjected, cu ft, and NP = total oil produced, bbl.

GOR as a Criterion of Reservoir Performance The producing GOR is often used as an indication of the efficiency of a producing well, and the increase in the ratio is looked on as a danger signal in the control of the reservoir performance. The GOR should be kept as low as possible (see Fig. 32.16). The area under the curve, shown as the surface ratio, will be the total amount of produced gas. This is by the previous definition of


GOR.This shows that maintaining the GOR as low as possible will increase the cumulative production for the same amount of produced gas.

Consider the internal-gas-drive reservoir. As oil is produced from the reservoir the space is taken over by gas volume. The presence of gas within the reservoir decreases the ability of oil to flow and increases the ability of gas to flow. After a certain minimum gas saturation (about 5 to 10%) is exceeded, the ease with which gas flows increases to such an extent that it flows concurrent- ly with the oil. This process continues until finally the only flow is almost all gas. This allows the reservoir energy to escape and causes the reservoir to cease production by natural means. Fig. 32.16 shows how the stock-tank cumulative production almost ceases as the reservoir/GOR increases.


40 = 5.427~IO-~kh(p,-p,,~)

’ . . . . @,[ln(r,lr,,,)+s]

J2!?= 5.427x 10-4kh

Ap ~oB,[ln(r,/r,,)+.~]’ ..“““t.‘.” (2)

where q. = oil production rate, m3/d

k = permeability of formation, m2 h = thickness of formation, m

pe = pressure at the effective drainage radius I,, normally approximated by PR , kPa

p,+,f = flowing bottomhole pressure, kPa

B, = 011 formation volume factor, res mJiSTm+ t, = effective drainage radius, m r, = wellbore radius, m

s = skin effect (zone of reduced or improved pwmeability), dimensionless

J = productivity index (PI), m3 I(d.kPa)

References

I. Moore, T.V.: “Definitions of Potential Productions of Wells Without Open Flow Tests,” Bull.. API, Dallas (1930) 20.5.

2. Harder, M:L.: “Productivity Index,” API, Dallas (May 1936).

3. API Recommended Practice fir Determining Productivity Indices, API RP 36, first edition, API, Dallas (June 1958).

4. Calhoun. J.C. Jr.: Fundamentals of Reservoir Engineering, E- vised edition, U. of Oklahoma Press, Norman (19.53).

5. Muskat, M.: “Physical Principles of Oil Production,” Intl. Human Resources Development Corp., Boston (1981).

6. Muskat. M. and Evinger, H.H.: “Calculation of Theoretical Pro- ductivity Factor,” Trans., AIME (1942) 146, 126-39.

7. Odeh, A.%: “Pseudosteady-State Flow Equation and Productivity Index for a Well With Noncircular Drainage Area,” .I. Pet. Tech. (Nov. 1978) 1630-32.

8. Earlougher, R.C. Jr.: “Estimating Drainage Shapes From Reser- voir Limit Tests,” J. Pet. Tech. (Oct. 1971) 1266-75; Trans.. AIME, 251.

9. van Everdingen, A.F.: “The Skin Effect and Its Influence on the Productive Capacity of a Well,” J. Pet. Tech. (June 1953) 171-76; Trans., AIME, 198.

IO. Dake, L.P.: Fundamentals of Reservoir fkgineering, Elsevier Scientific Publishing Co.. New York Cite (1978). -

I I. Measurement of Petroleum Liquid Hy~rocarbotu by Positive Displacement Meter, API Standard 1101, first edition, API, Dallas (Aug. 1960).

12. Manual of Petroleum Measurement Standards, API, Dallas (1961)

PO = oil viscosity, Pa 1 s Chap. 5.”

Chapter 33 Open Flow of Gas Wells R.V. Smith, Petroleum Consuitant*

Introduction The gauging or testing of gas wells arose from the need to measure the productive capacity of a well. The earliest response to this need was to open the well to flow to the atmosphere and then to measure the flow rate. However, it soon became apparent that such practices were wasteful of gas, dangerous for personnel and well equipment, and frequently damaging to the reservoir. In addition, such tests provided very little information for estimating production rates into a pipeline. As a result, the practice of gauging gas wells by opening the well to flow to the atmosphere decreased and now is almost completely confined to stripper gas areas where pressures are very low and the rates of flow are small.

Pitot-Tube Gauging of Low-Pressure Wells The pitot tube is one of the simplest instruments for measuring the rate of flow of gas. As such, the pitot has been used extensively to obtain an approximate gauge of the open-flow capacity of low-pressure gas wells. The well is opened to flow to the atmosphere through a flow nipple, and the producing rate is measured with a pitot tube. The producing rate is influenced by the hydrostatic head of the column of flowing gas and the friction between the flowing gas and the walls of the flow string. Thus the observed rate of flow to the atmosphere may be a very close measure of the ability of shallow low- capacity reservoirs to deliver gas into the wellbore. However, it may be more nearly a measure of the flow capacity of the flow string in the case of a well producing from a high-capacity reservoir. This is especially true where the flow is through a small-diameter flow string.

Historically, gauging of wells with pitot-tube measurements has been useful in the drilling and completion of low-pressure gas wells. During the drilling of many wells in the Hugoton field of Kansas, Oklahoma, and Texas, it was the practice to take pitot gauges after

‘The author also wrote the original chapter on this topc fn the 1962 edItIon

every bailer run or at the end of each 5 ft of formation drilled. Upon completion, data were available to con- sttuct a chart showing a relationship between the rate of flow and depth. The chart is useful in determining the depth of the major gas-producing zones. Such data were valuable in planning remedial work that may be necessary during the life of the well. Pitot-tube gauges were useful in determining rate-of-flow increases resulting from each stage of acid treatment. In many cases the pitot-tube gauge after acid treatment provided data from which the desired flow rates for a backpressure test could be selected.

Fig. 33.1 shows a pitot-tube and flow nipple arrangement that is suitable for gas measurement. The pitot tube should be made of %-in-ID pipe shaped to measure impact pressure at the center and in the plane of the opening of the flow nipple. The flow nipple should be at least eight pipe diameters long, free from burrs or other obstructions, and must be round. The impact pressures are measured with water or mercury manometers or a pressure gauge, depending on the pressure to be measured.

The impact pressure is converted to rate of flow by suitable equations or tables such as those published by Reid. ’ Subsequent experimental work by the USBM* is in reasonable agreement with the Reid data. The equations published by Reid were investigated by Binckley, 3 who concluded that they were based on sound theoretical principles. Reid’s equations and tables have been adjusted to a pressure base of 14.65 psia for the purposes of this handbook. The adjusted equations for impact pressures less than 15 psig are

~/,~=34.81~&* K, . . . . . . (1)

qa =1284d; Jh, , . . . . (2)

and

y,C=183.2dt &, .___ _. _____. _. ___.. (3)


TO MANOMETER ORPRESSURE GAUGE CONNECTION

L=8di

Fig.33.1-Typical flow nipple and pitot tube for gas measurement.

where

qx = rate of gas flow, Mcf/D (14.65 psia and fjo”F),

dj = ID of flow nipple, in., h,. = height (manometer reading), in. water, h,, = height (manometer reading), in. mercury, and pi = impact pressure, psig.

For impact pressures more than 15 psig, the adjusted Reid equation is

q&, =23.89d?p, , . . . . . . . . . . . . . . . . . . . . . . . . . . (4)

where p, is impact pressure, psia. Values of rates of flow for various impact pressures are given in Table 33.1 for a flow nipple with an ID of 1.000 in. Rates of flow in Table 33.1 were computed by Eqs. 1 through 3. The range of impact pressures is from 0.1 in. of water to 15 psig. Rates of flow for impact pressures from 15 to 200 psig were computed by Eq. 4 and are given in Table 33.2 for a flow nipple with an ID of 1.000 in. Impact pressures measured on larger flow nipples can be converted to rates of flow by multiplying the rate of flow from the table corresponding to the impact pressure by the square of the ID (in.) of the larger nipple.

Rates of flow taken from Tables 33.1 and 33.2 or computed by Eqs. 1, 2, 3, and 4 are for gases with a specific gravity of 0.600 (air = 1 .OOO), flowing temperatures of

60”F, and for discharge into an atmospheric pressure of 14.65 psia. Corrections can be made when desirable by multiplying values from the equations or tables by the following factors.

J 0.600 F,= -

YR and

J 520 FT=

(460+ Tf) ’

where

F, = specific gravity correction factor,

YY = specific gravity of gas being measured, air= 1.000,

FT = flowing-temperature correction factor, and Tf = temperature of flowing gas, “F.

The atmospheric-pressure correction factor for values from Table 33.1 and Eqs. 1, 2, and 3 is

Fbar = J Pa - 14.65 ’

where Fbar is barometric correction factor and pa is atmospheric pressure, psia. The value of pressure used for p, in Eq. 4 is the absolute pressure and is computed by adding the barometric pressure to the gauge pressure. The correction factor for barometric pressure for Table 33.2 is

Fbar = Pi +Pa

pi + 14.65 ’

In ordinary usage, rates of flow are taken from pitot tables or formulas without correction.

Example Problem 1. Given an impact pressure of 27.2 in. of water on a flow nipple with ID~2.441 in., determine the rate of flow.

Rate of flow from Table 33.1 for ID = 1 .OOO = 182 Mcf/D.

Rate of flow for ID = 2.441 in. is

q,=182(2.441)2=182x5.958=1,080Mcf/D.

Or, by Eq. 1, the rate of flow is

=(34.81)(5.958)(5.215) = 1,080 McfiD.

Example Problem 2. Given an impact pressure of 65 psig on a flow nipple with ID=4.082 in. with discharge into a barometric pressure of 13.2 psia, determine the rate of flow.

Rate of flow from Table 33.2 for ID of 1 .OOO and atmospheric pressure of 14.65 psia is 1,904 Mcf/D.

For ID of 4.082 in. and barometric pressure of 13.2 psia, the rate of flow is

qg = 1,904(4.082)*(65+13.2)/(65+14.7)

=(1,904)(16.663)(0.9812)=31,100 Mcf/D.

OPEN FLOWOFGASWELLS

Or by Eq. 4.

qs =23X9(4.082)*(65+ 13.2)

=31,100 McfiD.

Backpressure Testing Before the development of the backpressure method for testing gas wells, the open-flow capacities of gas wells were determined by actual “open-flow” tests. The flowing of wells at their wide-open rate results in waste and possible damage to the well. In addition, the open-flow

33-3

test yields very little information regarding the capacity of a well to deliver gas into a pipeline system.

The backpressure method of testin gas wells was developed by Rawlins and Schellhardt. 9 Results of tests on 582 wells as reported in their study and other work on many wells reported elsewhere show that when the rates of flow are plotted on logarithmic coordinates against corresponding values of (pi -p,,,,)-the difference of squares of the shut-in pressure FR and the flowing sandface (bottomhole) pressure (BHP) p,f-the relationship may be represented empirically by a straight line.

TABLE 33.1-RATES OF FLOW FOR IMPACT PRESSURES LESS THAN 15 PSIG MEASURED WITH A PITOT TUBE FOR FLOW NIPPLE WITH ID = 1 .OOO in. *

Impact Pressure qg, IO3 cu ft/D Impact Pressure

Water Mercury (14.65 psia Water Mercury q,,103 cu ft/D

(14.65 psia (in.) (in.) psig and 60°F) (in.) On.) (Psig) and60°F) -~- 0.1 0.2 0.3 0.4 0.5

- - - - - - - - - -

11 .o 10.9 15.6 12.0 19.1 12.2 22.0 13.9 24.6 15.0

0.6 - - 0.7 - - 0.6 - - 0.9 - - 1.0 - -

27.0 29.1 31.1 33.0 34.6

1.25 - - 1.36 0.10 - 1.6 0.12 - 1.6 0.13 - 2.0 0.15 -

38.9 40.6 44.0 46.7 49.2

2.2 0.16 - 51.6 2.4 0.18 - 53.9 2.7 0.20 - 57.2 3.0 0.22 - 60.3 3.5 0.26 - 65.1

4.1 0.30 - 70.5 4.5 0.33 - 73.6 5.0 0.37 - 77.6 5.4 0.40 - 60.9 6.0 0.44 - 65.2

6.6 0.50 - 90.6 6.2 0.60 - 99.7 9.0 0.66 - 104.4 9.5 0.70 - 107.3

10.0 0.74 - 110.1

5.6 - 309 6.0 3.0 314 6.5 - 327 7.0 3.5 340 7.5 - 352

6.0 4.0 363 6.5 - 374 9.0 4.5 365 9.5 - 396

10.0 - 406

10.2 5.0 410 11.2 5.5 430 12.2 6.0 446 13.2 6.5 466 14.3 7.0 466

16.3 17.7 19.0 20.4 21.6

24.5 27.2 29.9 32.6

-

-

- -

- - - -

- - - -

- - - - -

- - - - -

-

0.60 - 0.66 - 0.90 - 1.02 0.5 1.1 -

115 121 122 130 135

1.2 - 140 1.3 - 146 1.4 - 152 1.5 - 157 1.6 - 162

1.8 - 172 2.0 1.0 182 2.2 - 190 2.4 - 199 2.6 - 207

2.6 3.0 3.2 3.4 3.6

-

1.5

- -

215 222 230 237 244

3.6 4.0 4.2 4.4 4.6

2.0

-

250 257 263 269 275

4.8 5.0 5.2 5.4 5.6

2.5 - - -

261 267 293 296 304

15.3 16.3 17.3 16.3 19.3

7.5 6.0 6.5 9.0 9.5

10 11 12 13 14

15

502 516 522 549 564

20.4 22.4 24.4 26.5 26.5

560 606 634 661 677

710

‘Multiply rate of flow from fable by the square of the diameter for flow nipples with ID’s mm than 1,DDO ,n


TABLE 33.2-RATES OF FLOW FOR IMPACT PRESSURES. 15 TO 200 PSIG, MEASURED WITH A PITOT TUBE

FOR FLOW NIPPLE WITH ID = 1 .OOO in.’

Impact Pressure

Wg) 15 16 17 18 19

qg, lo3 cu ft/D impact (14.65 psia Pressure

qg, 103 cu ft/D (14.65 psia

and 6OOF) Wg) and 60°F)

710 40 1,307 733

z: 1,426

757 1,546 781 55 1,665 805 60 1,785

20 829 65 1,904 21 853 70 2,023 22 877 75 2,143 23 901 80 2,262 24 925 90 2,501

25 948 100 2,740 26 972 110 2,979 27 996 120 3,218 28 1,020 130 3,457 29 1,044 140 3,697

30 1,068 150 3,935 32 1,116 160 4,174 34 1,163 170 4,412 36 1,211 180 4,651 38 1,259 190 4,890

200 5,129

‘Multiply rate of tlow from table by the square 01 the diameter for Row nipples with ID’s mere than I.000 in

The backpressure method of testing wells requires that a series of flow rates and corresponding pressure measurements be obtained under stabilized conditions or at certain fixed time intervals. Testing under stabilized pressure and rate-of-flow conditions or according to a fixed time interval has become known as multipoint or “flow-after-flow” backpressure testing.

As the original backpressure or multipoint method came into general use, it became evident that the method of testing was applicable to those wells that approached stabilized producing conditions within a relatively short time. However, performance characteristics could not be determined by this method for wells that approached stabilized producing conditions slowly over a considerable period. This characteristic of slow stabilization has been associated generally with wells producing from reservoirs with low permeability and resulted in the development of the isochronal method of backpressure testing by Cullender. 4

The procedure used to obtain the necessary performance data for the isochronal testing method is to open the well from a shut-in condition and allow the well to flow without disturbing the rate by changing the mechanical adjustment of chokes or valves for a specific period of time. The well is then shut in and allowed to return to a shut-in pressure comparable with that existing before the well was first opened, after which the well is again opened at a different rate of flow. In isochronal testing, each rate of flow starts from a comparable shut- in condition, which provides a means of maintaining a simple pressure gradient throughout the drainage area of the well during testing. The isochronal method of testing

99, lo3 cu ft/D

Fig. 33.2-Multipoint test showing bottomhole performance for Well 0.

is especially suitable for determining the performance characteristics of wells producing from reservoirs with low permeability.

High-Pressure Gas and Gas-Condensate Wells All the instructions for testing wells in this chapter apply to gas wells that produce a single-phase gas into the wellbore or to wells that are predominantly gas wells and the fluid flowing in the reservoir has a high in-place gas/liquid ratio (GLR). However, these methods for testing gas wells have been applied to high-ratio oil wells with some degree of success.

The chief difference between testing methods for high- pressure gas and gas-condensate wells and low-pressure wells is the care used in taking the data and methods used in computing the results. The effect of liquids is usually more pronounced in high-pressure than in low-pressure wells. Consequently, special care should be used to

measure GLR’s in high-pressure wells. Often it is necessary to determine the GLR at each rate of flow during a backpressure test. If the ratio was not constant during testing, the well probably was accumulating liquid in the wellbore during testing or unloading liquid. In either case the test is probably not acceptable and the well should be cleaned by flowing at a high rate and retested at rates of flow high enough to keep the well free of liquid.

Temperature effects during testing of high-pressure wells may be troublesome in interpreting test results. For example, Well B (Fig. 33.2) has a shut-in wellhead pressure of 4,173 psia at a wellhead temperature of 117°F. Maximum wellhead pressure was observed 3 minutes after the well was shut in. If wellhead pressure has been observed for an extended period of time, the wellhead pressure would have decreased to about 4,140 psia. The decrease in wellhead pressure is caused by the cooling of the gas in the well. In general, better tests can be obtained on such large-capacity wells if the testing is done after a preflow period. The preflow period should be run long enough to bring wellhead temperatures to a normal operating range of temperature. Wellhead

OPEN FLOW OF GAS WELLS

temperatures should be recorded during testing at periodic intervals so that actual measured temperatures can be used in computing subsurface pressures by methods outlined under Example 3 in the section on computing subsurface pressures.

Official Testing Official testing of gas wells for state regulatory bodies is usually a multipoint test of short duration. In addition to the multipoint test, a single rate of flow for a period of 24 to 72 hours is required in some cases. The tester is referred to the test manuals of the various states, provinces of Canada, or appropriate countries for exact procedures, and no attempt is made here to outline official testing.

Backpressure Equations In either multipoint or isoehronal backpressure testing, the rates of flow and the corresponding values of the difference of squares of the average formation (reservoir) pressure pR and the sandface pressure [bottomhole flowing pressure (BHFP)] p,,f are plotted on logarithmic coordinates and a straight line is drawn through the points. The equation for the relationship is

qg =C(F,2 -p,J)“, . . I . , . . . . . . . . . . . . . . . (5)

where the performance coefficient is represented by C and the exponent of the backpressure curve by n. The industry by common usage has referred ton as the “slope” of the backpressure curve, even though n is the reciprocal of the mathematical slope of the line. Here n is referred to as the “exponent” of the backpressure curve. Eq. 5 is an empirical relationship for both the multipoint test and the isochronal test and has resulted from the study of results of many tests. Values of the exponent vary for individual wells in the range of 0.5 to 1 .O. Tests that result in exponents less than 0.5 or more than 1 .O should be rerun. Exponents of less than 0.5 resulting from multipoint tests may be caused by the slow- stabilization characteristics of the reservoir or by the accumulation of liquids in the wellbore. Exponents greater than 1 .O may be caused by the removal of liquid from the well during testing or by a cleaning of the formation around the well, such as the removal of drilling mud or stimulation fluids. Also, a multipoint test run in decreasing rate sequence may have an exponent of more than 1 .O for wells in slow-stabilizing reservoirs. Erratic exponents in isochronal testing are caused by either accumulation or cleaning of liquids from around the well. Erratic alignment of data points from multipoint or isochronal testing is usually caused by changes in actual well capacity during testing. Such changes may be caused by accumulation of liquids or the cleaning of the wells. The effects of the liquids in the well on multipoint testing have been given in detail by Rawlins and Schellhardt.’

Eq. 5 represents the capacity of a well to deliver gas into the wellbore, and it is useful especially in evaluating reservoir conditions. The capacity of a well to deliver gas at the wellhead may be represented by

qy =c(p,\? -pl,2)‘i, . . (6)

33-5

where C, the performance coefficient, and n, the exponent, are different from those in Eq. 5 for a given well. prs and ptf represent wellhead shut-in (static tubing) pressure and working (flowing tubing) pressure on the flowing-gas column at the wellhead, respectively. Eq. 6 is useful especially in estimating the capacity of a well to deliver gas into a pipeline under specified conditions.

Gas Well Inflow Equation, Pseudosteady State Reservoir engineers have realized for many years that interpretation of multipoint and isochronal tests by means of Eq. 5 gave no insight into the effect of reservoir or gas properties on the rate of flow into a well. Thus, Eq. 5 proved inadequate for reservoir engineering purposes. An equation that describes the pseudosteady-state flow of gas into a well has been presented in the literature. 5-8 It is

qe= 703 x 10-6k,h(& -pwf2)

CL8 t TRZ(lIl reh, -0.75+s+FnDq,) ’ . . (7)

where qg = k, =

h=

PR =

pWf= Pg = TR =

z= re = rw =

s= F nD =

If we let

gas-production rate, lo3 cu ft/D, permeability, effective to gas, md, formation thickness, ft, average reservoir pressure, psia, flowing bottomhole pressure, psia, gas viscosity, cp, reservoir temperature, “R, compressibility factor of gas, effective drainage radius, ft, wellbore radius, ft, skin factor, and non-Damy flow factor.

703 x 10 +kgh(&$ -p,‘) =

PgTZ Cl,

and

In r,lr,-0.75+s=C2,

Eq. 7 becomes

q#= c1 C2 +F,,q, ’

or

F,,Dq; +CzqR -C, =O.

From this we get

-C2 +dC,2 +4F,,,C, 9g= . .

2Fn1, (8)

The maximum rate of flow [open-flow potential (OFP)] is given when Ct is a maximum-that is, whenp,f = 0. Eq. 7 incorporates the properties of the reservoir and the gas and can be extended to noncircular areas as given in Ref. 5.


Determination of Absolute Open Flow (AOF) The terms “calculated absolute open flow” (CAOF) and OFF’ are the rate of flow in thousands of cubic feet of gas per 24 hours that would be produced by a well if the pressure against the face of the producing formation in the wellbore were zero. The value of the OFP is usually determined graphically by plotting rates of flow qg against the corresponding values of a,$ -p wf2. The straight-line relationship between qg and jji -pwf2 is extended so the rate of flow qg corresponding to the value ofp,$ can be read by extrapolation. Then qs is the AOFP of the well in cubic feet per 24 hours. The AOF can be computed from Eq. 5 or read directly from plotted relationships.

In wells producing from reservoirs with low permeability, the reported AOF must be identified further by the time involved in the test and the type of test. For example, the OFP of such a well as determined by a 3-hour multipoint test (each rate of flow lasting 3 hours) would be less than that determined by a 2-hour multipoint test. The open flow determined by an isochronal test of 3 hours would be different from that determined by a multipoint test. A good example of the relationship between AOF and type of test is given by Cullender.4 Reported OFP’s on wells in low-permeability reservoirs are more or less meaningless without an indication of the type of test involved.

Determination of the Exponent n The calculation of the exponent n is based on Eq. 5 and the relationship

II= 1% qg2 -1% 481

log@j -p& -log(J,If -p&, . . .

Values of qg and corresponding values of pi -p,,f* , either actual experimental points or values read from the straight-line relationship, are substituted in Eq. 9. Usual- ly the data points do not fall exactly on a straight line; so the best practice is to read values of qg and jji -pwf2 directly from the straight line.

Determination of the Performance Coefficient C After the value of the exponent n has been determined, the value of the performance coefficient C may be determined by substitution of a corresponding set of values for qg and a,$ -pwf2 and the value of n into Eq. 5. The value of C is found by solution of the resulting equation. Graphically the value of C may be determined by extension of the straight-line relationship to jj,$ -t,“f2 = 1 and reading the corresponding q!. When jr~ -pwf2 is unity, C is equal to qg. In practtce, a determination of the value of C is seldom necessary for routine analysis of backpressure tests.

Preparation of Well for Testing The wellbore should be cleaned of liquids by flowing at a high rate to a pipeline for a period of 24 hours. If the well does not have a pipeline connection, it may be blown to the air for a short period of time, provided blowing is considered safe. Extra precautions should be taken on new wells to remove drilling mud, solids, and stimulation fluids from the wellbore. The well should be shut in

for 24 hours or longer to equalize the reservoir pressure in the vicinity of the well. Wells with slow pressure- buildup characteristics should be shut in 48 to 72 hours, if possible.

While the well is shut in, the gas-measurement equipment should be prepared for use. If the gas is to be measured with an orifice meter, the meter should be calibrated, the diameters and condition of the run and plate verified, and the differential pen should be zeroed in accordance with good meter practice. If a critical-flow prover (see later section on gas measurement) is used, it should be placed in a vertical position at the wellhead or downstream from the separator so that the gas will flow up and away from the test area. If a separator is used, control the rate of flow with a production choke and maintain pressure on the separator with a critical-flow prover or backptessure regulator when an orifice meter is used. If a separator is not used, control rate of flow and pressure at the wellhead with the critical-flow prover. Always install thermometer wells at the wellhead and at gas-measuring equipment so that temperatures may be measured with a thermometer or calibrated recording device. The thermometer wells should be filled with water or oil to obtain accurate temperature measurement.

Shut-In Pressure All shut-in or flowing pressures should be measured with a dead-weight or piston gauge, because spring gauges are usually not accurate enough for backpressure tests. Determine and record the pressure at the end of the shut- in period, prepare the well for testing, and redetermine the shut-in pressure as a check on the first measurement and to obtain the rate of pressure buildup. Report each pressure and time the well was shut in prior to each pressure measurement. After the second pressure measurement, either the isochronal or multipoint test may be started.

Subsurface pressures in gas wells may be measured directly with pressure gauges or computed from wellhead pressures. Subsurface-pressure gauges are very useful in wells where liquids accumulate in the wellbore during shut-in. However, the use of subsurface gauges limits the rates of flow during the backpressure test to velocities that will not lift the gauge in the flow string. The use of subsurface gauges is limited to rather low rates of flow in 2%-in. OD tubing, but there is practically no limitation on their use in 7-in. casing. The use of subsurface gauges in the annular spaces of dual completions is practically impossible. In cases where large- capacity wells are being tested, correction must be made for the effect of hysteresis on gauge readings, or the BHP must be measured at each rate of flow by a separate run of the gauge.

The accumulation of liquid in the wellbore is probably the most serious cause of erroneous calculated BHP’s. Other sources of error are uncertainties in temperature gradients and specific gravities of the fluids flowing in the well. Before a backpressure test is begun, special care should be taken to remove the liquids from the wellbore by flowing at rates large enough to lift the liquid. If possible, each rate of flow used in the backpressurc test should be large enough to lift continuously any liquid that may move into the wellbore during production. Temperature gradients can be

OPEN FLOW OF GAS WELLS 33-7

established for a new area only by actual measurement. Usually a flowing-temperature gradient can be estimated by assuming a straight-line gradient between flowing wellhead temperature and bottomhole temperature. Uncertainty in the specific gravity of the fluid flowing in the well can be eliminated to a large degree by careful measurement of gas/hydrocarbon liquid ratio and determination of the specific gravity of the separator gas, separator liquid. and stock-tank liquid.

Multipoint Test and Example A four-point multipoint test of constant duration for each rate taken in increasing rate sequence is normally satisfactory for establishing the performance of a well. In the case of high-liquid-ratio wells or high-flowing- temperature conditions, a decreasing-rate-sequence test may be used if an increasing-rate-sequence test would not result in alignment of points. In the case of high- liquid-ratio wells, the low flow rates will not clean the wellbore of liquids that accumulate during production. In the case of wells with exceptionally high flowing temperature, it may be desirable to start the test at the highest rate of flow that will result in more nearly constant wellhead temperatures during the test rather than starting at the lowest rate of flow. However, a test in decreasing-rate sequence should not be run unless it is known that an increasing-rate-sequence test will not give a satisfactory test.

The four rates of flow for the test should be evenly distributed over the test range. For average- to low- capacity gas wells, the first rate of flow should lower the pressure at the wellhead about 5%) and the pressure reduction for the fourth rate should be 25 %. The rate of flow required to reduce the working pressure to 5% for the first test rate can be approximated from pressure readings obtained while the well is being cleaned before the well is shut in. These recommended pressure reductions may not be possible for large-capacity wells with large flow strings.

After the well is opened for the first rate of flow, the test rate should be continued for 3 hours but no more than 4 hours. Each succeeding flow rate should be for the same period of time. During each flow rate, the wellhead working pressure and temperature, meter or prover pressure and differential, and temperature should be reported at the end of each I5-minute period, If separator and tanks are used during testing, the rate of liquid accumulation, both hydrocarbon and water, should be reported. If a critical-flow prover alone is used, the presence or absence of liquids in the gas stream should be noted and reported. The specific gravity of the separator gas or the specific gravity of the gas flowing from the critical-flow prover should be measured and reported, or a gas sample should be taken for analysis and calculation of the specific gravity. More representative gas specific gravities can be obtained after the well has been flowing at least an hour.

Table 33.3 is an actual copy of the field data sheet for a multipoint backpressure test for Well A in the Guymon Hugoton gas field in Texas County, OK.* The form on which the data are reported has proved convenient for recording test data. The times at which each plate was

‘Thus test, used m the 1962 edlfion of the handbook was run many years ago It still stands as a clawc multlpoint test example today

changed and when the well opened on each rate of flow were carefully reported. The “remarks” column gives the results of the specific-gravity measurement and the condition of the flow with regard to whether the well was producing water. All the observations recorded in Table 33.3 are necessary for accurate analysis of test results.

Computation of the results of a backpressure test on a gas well involves the following steps.

I. Compute rates of flow and pressures at the face of the producing formation from pressure and volume observations made at the wellhead.

2. Determine values of p,: -prf2 and p,$ -p,+f* and rates of flow corresponding to these pressure factors. Then, PR and pwf are calculated at the midpoint of the sandface in wells without tubing. If the well has tubing, they are determined at the entrance to the tubing, provided the entry to the tubing is no more than 100 ft from the midpoint of the sandface.

3. Plot values of q8 and corresponding values of PR’ -pwf2 and pt: -pti2 on logarithmic coordinates.

4. Determine values of the exponent n and the performance coefficient C of the flow equations

qg =C(Pl? -Pwf2Y and

4x =c(P,.? -Pff2Y*.

For most routine analyses of backpressure tests. determination of the value of C is not necessary.

5. Determine the CAOF. Computations for rate of flow and pressures at the producing formation are explained in separate sections.

A convenient form for reporting the results of a multipoint test is illustrated in Table 33.4 for the test data taken on Well A and reported in Table 33.3. Table 33.4 shows general well information, a summary of test data, calculation of rates of flow, data for determining compressibility, and the difference of squares of pressures for wellhead and bottomhole conditions. The calculated OFP of 25,000~10~ cu ft/D was determined in Fig. 33.3 where the rate of flow is the abscissa and PJ -p w,2 (in thousands) is the ordinate on logarithmic coordinates. The data points were connected by a straight line and extrapolated to a value of PJ -p,,,f2, where p&f2 is zero. In this case, the value is j~i = 230.9 (thousands). The corresponding rate of flow is 25,000 x lo3 cu ft/D. The AOF of 25,000~ lo3 cu ft/D for Well A is for a 3-hour four-point test. If the test were for a lesser-time four- point test, the resulting AOF would have been more than 25,000 x lo3 cu ft/D.

The exponent n was determined by taking values of qs andpd -pwf2 from the straight line in Fig. 33.3 and Eq. 7 as follows.

qs, lo3 cu ft/D p,$ -p wf2 (thousands)

20,000 168 4,ooo 16.8

log 20,000-log 4,000 log 5.00 0.699 n= =-=-

log 168-log 16.8 log 10.0 I .ooo

=0.699.

33-a PETROLEUM ENGINEERING HANDBOOK

TABLE 33.3-FIELD DATA SHEET FOR MULTIPOINT TEST (WELL A)

Company Lease Well No.-

Location rema carnty. okuha

2”Prover n”Meter Run P Taps

DhTE WELLHEAD WORKING PRESSURE METER OR PROVER REMARKS

6-IW? Tbg. Csiq. An;&us Tey. Tim IHrr, Psi0 W

p*iq Dif‘. “,“” Orifice

I u*ll hut lo fo a dam I I I I /

L I I I I I

PAGEL OF JDATA BY J. it. J.

The performance coefficient C was determined from the exponent n=0.699, Eq. 5, and one of the corresponding

33.4 where qg and corresponding pt: -ptf* values ate

values of qg and j12 -pd* as follows. plotted on logarithmic coordinates. The straight line has been extended to show a wellhead OFP of 22,000 X lo3

20,000 = C(168)0.699 cu ft/D. The exponent is 0.672 and C is 621. The backpressure relationship corresponding to Eq. 6 is

C = 20,000/(168)“~699 log C = log 20,000-0.699 log 168 log c = 4.3010-1.5555

c = 557.

The value of 557 may be checked b straight line on Fig. 33.3 top2 -p,,,, z-

extrapolating the - 1 and reading

the corresponding value of qs. Note that the value of C=557 is for qg in units of lo3 cu ft/D and for jr2 -pg* in units of thousands.

The backpressure equation for the results of the multipoint test on Well A given in Table 33.4 and illustrated in Fig. 33.3 is

The wellhead Performance of Well A as determined by the test results given in Table 33.4 is illustrated in Fig.

qR =627(pr,2 -P~~)O.~‘*.

This wellhead performance equation for Well A, illustrated in Fig. 33.4, is a measure of the ability of Well A to deliver gas at the wellhead through 5 %-in. casing as indicated by the multipoint test given in Table 33.4. The relationship is influenced by the size of the flow string and hydrostatic head of the gas column as well as the productive capacity of the well.

An example of the bottomhole performance as indicated by a multipoint test is given in Fig. 33.2 for an extremely large-capacity well. Well B (Fig. 33.4) had a shut-in pressure~R of 5,169 psia at a depth of 10,658 ft and a wellhead pressure of 4,173 psia. The calculated OFP was 280,000x103 cu ft/D. The corresponding wellhead performance for Well B producing through 2X-in.-OD, 6.5-lbm/ft tubing is illustrated in Fig. 33.5 where the data points for the test are plotted as circles.


TABLE 33.4--RESULTS OF MULTIPOINT BACKPRESSURE TEST (WELL A)

COMPANY LEASE - WELL N0.I

ADDRESS DATE 6-17 19k

DISTRICT FIELD ~goton RESERVOIR Uwota

LOCATION Tens CmmtJ, Okldwm

CASING SIZE5 WT.x I D 5.012 SET Al 269 PERF 2665-2620

TUBING SIZE- WT.--- ~ - I.0 SET AT PERF. PRODUCING BOTTOMHOLE SECTION FROM 2Lb5 TO 2620 Ii 2542 TEMPERATURE 90 Ca 25fQ

DATE OF PRODUCING ELEVATION - COMPLETION A THROUGH TBG.: CASING I

F, o.wl6105 BAROMETER 13.2 p*I ACRES -

REMARKS:

P,. uB.5 DrioP,’ 201 15x10’ j- Pa Le3.5 Pb230.92xlO’

Potmtbl 25.m IO’ C” fm CommItdon n 0.699 company

Others

qg, lo3 cu ft/D

Fig. 33.3-Multipoint test showing bottomhole performance for Well A.

3001------

I01 1 II,,,, I 1 1000 10,000 30,cQo

qg, IO3 cu ft/D

Fig. 33.4-Multipoint test showing wellhead performance for Well A.

3-

3-

3-

:0 I

0 10,000 IOC q9, lo3 cu ft/D

Fig. 33.5-Multipoint test showing wellhead performance for Well 0.

Data points represented as squares (Fig. 33.5) are flow tests of several days’ duration with Point 1 taken shortly after production started and Point 3 taken over a year later. The position of the data points in Fig. 33.5 indicated that the performance of Well B improved after the well was placed on production, which was probably caused by the removal of drilling fluids from the area around the wellbore.

The wellhead OFP of Well B was 41,000~ IO3 cu ND, which was the approximate capacity of the tubing. A different wellhead performance curve would result if the tubing were changed in Well B. The wellhead performance for a different string of tubing can be calculated by starting with the bottomhole performance curve in Fig. 33.2 and calculating the pressure drop caused by friction for the different string of tubing.

Isochronal Test and Example The isochronal method of backpressure testing as defined by Cullender4 considers the performance coeff- cient C in Eqs. 5 and 6 to be a variable with respect to time until the well stabilizes but a constant with respect to a specific time. Thus the backpressure performance of a well producing from a reservoir with low permeability is a series of parallel curves. Each curve represents the performance of the well at the end of a given time interval. Isochronal performance curves for wells producing from reservoirs with relatively higher permeability arc closely spaced. For example, the isochronal curves for various times for Well B (Fig. 33.5) are for all practical purposes one curve, and Well B is said to stabilize rapidly.

The isochronal method of testing permits the determination of the true exponent n of the performance curve for a given gas well. This is accomplished by the


establishment of a simple pressure gradient around a producing well during the test period, which prevents the variation of the performance coefficient with time from obscuring the true value of the exponent. The determination of the relationship between performance coefficient and time permits the estimation of the rate of flow of a given well into a pipeline over long periods of time.

The term “isochronal” was adopted as being descrip- tive of the method, because only those conditions existing as a result of a single disturbance of constant duration are considered as being related to each other by Eqs. 5 and 6. The expression “single disturbance of constant duration” is defined as those conditions existing around a well as a result of a constant flow rate for a specific period of time from shut-in conditions. Under actual test conditions this requirement is rarely satisfied. However, this condition may be approximated by starting a well on production and allowing the well to produce without further outside or mechanical adjustments in rate of flow. Thus a simple pressure gradient is established around the wellbore as opposed to a complex pressure gradient resulting from a multipoint backpressure test.

The presentation of isochronal test data as a series of parallel curves with a constant exponent n and a constant performance coefficient C for a specific time interval involves certain assumptions. The exponent of the performance curves for a gas well is assumed independent of the drainage area. It is established immediately after the well is opened. The variations of the performance coeff- cient with respect to time are believed to be independent of the rate of flow and the pressure level under simple gradient conditions.

The procedure employed to obtain the necessary performance data for an isochronal test is to open a well from shut-in conditions and obtain rate-of-flow and pressure data at specific time intervals during the flow period without disturbing the rate of flow. After sufficient data have been obtained, the well is shut in and allowed to return to a shut-in condition comparable with that existing at the time the well was first opened. The well is again opened at a different rate of flow with data being obtained at the same time intervals as before. The procedure may be repeated as many times as necessary to obtain the desired number of data points.

With the exception of starting each rate of flow from shut-in conditions, the procedure for running isochmnal tests is the same as that for the multipoint test. The necessity for cleaning the well, calibrating the gas- measuring equipment, and accurately measuring pressures and temperatures remains the same. At least four rates of flow should be taken; the lowest rate should reduce the pressure at the wellhead about 5% and the highest rate of flow should reduce the pressure about 25%.

The results of an isochronal test are computed in the same manner as those for a multipoint test. The data points are plotted on logarithmic coordinates as illustrated in Figs. 33.6 and 33.7. The isochronal curves are drawn so that the points taken at a constant time for the various rates of flow are joined by a straight line. For example, all the points on the line labeled “Time, 3 hr” in Fig. 33.6 represent the performance of Well A after flowing at the various rates of flow for 3 hours from shut-in conditions.


IO I III 1000 l0,000 60,000

qg. IO3 cu WD

3oor--, 0

; loo-

.P zi

N^

ct I

N

:

IO_ * I II 1000 10,000 50,000

qg. lo3 cu ft/D

Fig. 33.6~lsochronal test showing bottomhole performance for Fig. 33.7~lsochronal test showing wellhead performance for Well A. Well A.

The results of isochronal tests can be analyzed in two ways. One way is to use Eqs. 7 and 8 and the properties of the gas to determine the properties of the reservoir and the skin factor. The second way is to use the results as a basis for comparison of well performance at the time of the test with performance as measured previously or to set a base against which future performance is to be compared.

The isochronal type curves shown on Fig. 33.6 can be used to estimate the pressures that would have been observed if the test had been a constant-rate drawdown test. Test periods longer than the 3-hour periods on Fig. 33.6 are much more desirable for this purpose. With this information the k,h value for the reservoir and the total skin value (s,=s+F,~q~) are calculated as given in Chap. 35. This results in several values for the total skin, s,, as a function of the rate of flow, qg, from which s and F,D can be obtained for use in Eq. 7.6 The multipoint test can be analyzed to obtain k,h, s, and F,JJ as indicated by Ref. 7. A discussion of the performance- comparison method follows.

A copy of actual field data for an isochronal test is given in Table 33.5 for Well A, which is the same well used in the example of a multipoint test.* Four rates of flow of 3 hours’ duration were used with each flow starting from shut-in conditions. Shut-in pressures reported varied from 359.6 psig after 48 hours for the first rate of flow to 357.6 psig, which was just previous to the fourth rate of flow. The results of the isochronal test are summarized in Table 33.6. Bottomhole and wellhead performance curves are illustrated on Figs. 33.6 and 33.7, respectively.

The isochronal test on Well A (Fig. 33.6) shows that the calculated OFP for a BHP of 399.1 psia was 5 1,500, 41,500, 35,ooO, and 31,500~ lo3 cu ft/D at the end of 0.5, 1 .O, 2.0, and 3.0 hours, respectively. The calculated potential after 3 hours’ flow was only 61% of the potential after 0.5 hour of flow, A similar figure for the wellhead performance of Well A is 66% (Fig. 33 -7) If Well A were opened into a pipeline with a constant

‘This test, used I” the 1962 edltlan, was run many years ago. It still stands as a classtc tsochronal test example today.

pressure, the rate of flow at the end of 3 hours would be 66% of the rate of flow at 0.5 hour. Experimental data not given here show that the production at the end of 72 hours has decreased to about 48% of that at 0.5 hour. The figures showing change-of-performance characteristics with time illustrate the need for isochronal test data for estimating the delivery from a particular well into a pipeline. Accurate estimation of pipeline deliveries from wells producing from reservoirs with low permeability is practically impossible without isochronal test data.

Examination of the field notes under the “Remarks” column in Table 33.5 indicates that Well A started to produce water during the flow test taken on Dec. 20, 195 1, which was the largest rate of flow. The effect of water production on well performance is illustrated by the irregularities in the corresponding data in Figs. 33.6 and 33.7. Water production and accumulation of water or liquids in the wellbore cause the performance characteristics of a well to deteriorate.

The data represented as squares in Fig. 33.5 are isochronal points taken after Well B has been flowing from 5 to 30 days. Their close agreement with the data from the multipoint test indicates that the performance of Well B does not vary appreciably with time. Well B produces from a reservoir with high permeability and the radius of drainage is established quickly after the well is opened to flow.

Comparison of Multipoint With Isochronal Test Either the multipoint or the isochronal test is suitable for wells producing from reservoirs with high permeability. The isochronal method of testing is especially suitable for testing wells in low-permeability reservoirs. However, for wells producing from extremely low- permeability reservoirs where the unsteady-state effects last for days or even weeks, economic considerations may limit the testing to only one point of the isochronal type (starting flow from a shut-in condition). Multipoint tests should be limited to reservoirs where the unsteady- state effects are of very short duration. Otherwise the results of the multipoint test are difficult to analyze.


TABLE 33.5-FIELD DATA SHEET FOR ISOCHRONAL TEST (WELL A)

company L.30S0 Well No.&- Location Tmaa CounW. LKUba 2”Prover n*t&1er Run a Tops

I I I I I I I I I I I I

I

PAGEA OFAOATA BY J. If. J.

TABLE 33.6--RESULTS OF ISOCHRONAL TEST ON WELL A The results of the 3-hour multipoint test and the 3-hour isochronal test on Well A are shown together in Fig.

Flow Duration

33.8 as wellhead performance curves. The exponent Pts

Date (psi4 (hr) (M%D) $ -P,,$ PrsZ - Pn2 (0.672) for the multipoint test is less than the exponent (0.848) of the isochronal test. In general, exponents of

Dec. 17, 1951 372.6 0.5 1 .o 2.0 3.0

4,159 4,120 4,078 4,047

Dec. 18, 1951 372.0 0.5 1 .o 2.0 3.0

Dec. 19, 1951 372.0 0.5 1 .o 2.0 3.0

Dec. 20, 1951 370.8 0.5 1 .o 2.0 3.0

5,552 5,485 5,461 5,423

multipoint curves run in increasing rate sequence are less than those for isochronal curves for the same well. The first data point on the multipoint test ( qn =4,928 Mcf/D) is on the isochronal curve (Fig. 33.8) because the first rate of flow for the multipoint curve was started from shut-in conditions. Thereafter, the position of each succeeding point of the multipoint test is influenced not only by the rate of flow but also by each preceding point.

7,019 6,982 6,847 6,777

8,599

8,153 8,048

10.60 10.60 13.19 12.82 15.79 15.08 17.63 16.55

14.85 15.18 18.10 17.97 21.58 20.87 23.56 22.58

17.93 20.59 22.17 24.14 26.48 27.76 26.80 29.81

24.96 27.93

34.10 35.22 37.00 37.63

The initial points of each multipoint test on wells producing from reservoirs with low permeability represent the formation characteristics, while other points represent complex conditions that are almost impossible to interpret. The characteristic exponent of the isochronal curve still applies to the complex points, with the only difference in performance being in the performance coefficient C. If the exponent of 0.848 is applied to the complex points of the multipoint test (Fig. 33.8). it can be

OPEN FLOW OF GAS WELLS

qg. IO3 cu ft/D

Fig. 33.6-Comparison of multipoint with isochronal test for Well A.

seen that the coefficient obtained in each case can be considered the result of an “effective” time, which has no permanent significance because it is not equal to the elapsed time or to the elapsed time since the last change in flow rate.

An examination of the multipoint and isochronal data presented in Fig. 33.5 for Well B shows that there are certain gas wells that stabilize so rapidly that there is no necessity for obtaining isochronal performance data. As the time required for stabilization increases, the differences between data obtained by the isochronal test and the multipoint test increase.

Gas Measurement Orifice Meters The recommended specifications for orifice meters and methods for computing rates of flow are those published by the American Gas Assn. 9 It should be noted that the basic orifice factors are for a pressure base of 14.73 psia. Multiplying the basic orifice factors in Ref. 9 by 1.0055 changes volumes to a pressure base of 14.65 psia. Basic orifice factors,for a pressure base of 14.65 psia have been published in the test manual of the Corporation Commission of the State of Kansas lo and the Interstate Oil Compact Commission. ”

Critical-Flow Provers The following method for measurement and computation of rates of flow for critical-flow provers is a modification of the method published by Rawlins and Schellhardt.* The equation computing rates of flow from measurements with a critical-flow prover is

qg=psFpFgFTFpv, . . . . . . . . . . . . . . . . . .(lO)

where p,, is static pressure on critical-flow prover, psia. Basic orifice factors, F,, , for 2- and 4-in. critical-flow provers are given in Table 33.7. These factors apply only to plates designed according to USBM specifications.

The adjustment factor (Table 33.8) to correct for an assumed specific gravity of 1.000 to the actual specific gravity of the gas flowing through the prover may be computed by

33-13

TABLE 33.7-BASIC ORIFICE FACTORS FOR CRITICAL-FLOW PROVER (USBM plate design) F, - McflD

Base temperature, OF 60 Base pressure, psia 14.65 Flowing temperature, OF 60 Specific gravity 1.000

2-in. Prover 4-k Prover

Orifice Diameter Factor Orifice Diameter Factor (in.) (F,) (in.) (FP)

0.06569 0.1446 0.2716 0.6237 0.8608

1.115 1.714 2.439 3.495 4.388

6.638 9.694

13.33 17.53 22.45

28.34 34.82 43.19

2% 136.9 3 168.3

1.074 2.414 4.319 6.729 9.643

13.11 17.08 21.52 26.57 31.99

38.12 52.07 68.80 88.19

110.6

F,= i, . . . . . . . . . . . . . . . . . . . . . . . . . . ...(n) 7s

where yg is specific gravity of the flowing gas, air = l.COO.

Factors to correct for an assumed flowing temperature of 60°F to the actual flowing temperature of the gas at the point of measurement are given in Table 33.9 and may be computed by

520 FT= -, __. _. . . . . . . . . . . . . . . . . (12)

Tf where Tf is actual flowing temperature of the gas, (“F +460).

The supercompressibility factor to correct for the effect of gas compressibility is computed from the compressibility by

F,,\,= r i, . . . . . . . . . . . . . . . . . . . . . . (13) z

where z is compressibility of the gas at ps and Tf or the pressure and temperature at point of measurement.

Methods for estimating gas compressibilities are given in Chap. 20.

Calculation of Subsurface Pressures Specific Gravity of Flowing Fluid Calculation of either shut-in or flowing pressures in gas wells requires a knowledge of the specific gravity of the fluid in the wellbore. In the case of a gas-condensate well, the specific gravity of the separator gas and the gravity of the stock-tank liquid are measured, and it is

33-14 PETROLEUM ENGINEERINGHANDBOOK

TABLE 33.8--SPECIFIC-GRAVITY ADJUSTMENT FACTOR

Specific Gravity

0.550 0.560 0.570 0.580 0.590

0.000

1.348 1.336 1.325 1.313 1.302

0.001 0.002

1.3471.346 1.335 1.334 1.323 1.322 1.312 1.311 1.301 1.300

0.003

1.345 1.333 1.321

0.006

1.341 1.329 1.318

1.310 1.299

0.004 0.005

1.344 1.342 1.332 1.330 1.320 1.319 1.309 1.307 1.298 1.296

1.306 1.295

0.007

1.340 1.328 1.316 1.305 1.294

0.600 1.291 1.290 1.289 1.288 1.287 1.286 1.285 1.284 0.610 1.280 1.279 1.278 1.277 1.276 1.275 1.274 1.273 0.620 1.270 1.269 1.268 1.267 1.266 1.265 1.264 1.263 0.630 1.260 1.259 1.258 1.257 1.256 1.255 1.254 1.253 0.640 1.250 1.249 1.248 1.247 1.246 1.245 1.244 1.243

0.650 1.240 1.239 1.238 1.237 0.660 1.231 1.230 1.229 1.228 0.670 1.222 1.221 1.220 1.219 0.660 1.213 1.212 1.211 1.210 0.690 1.204 1.203 1.202 1.201

1.237 1.236 1.227 1.226 1.218 1.217 1.209 1.208

1.235 1.225 1.216 1.207 1.199

1.234 1.224 1.215 1.206

1.200 1.200 1.198

0.700 1.195 1.194 1.194 1.193 1.192 1.191 1.190 0.710 1.187 1.186 1.185 1.184 1.183 1.183 1.182 0.720 1.179 1.178 1.177 1.176 1.175 1.174 1.174 0.730 1.170 1.170 1.169 1.168 1.167 1.166 1.166 0.740 1.162 1.162 1.161 1.160 1.159 1.159 1.158

0.006

1.339

0.009

1.338 1.326 1.314

1.327 1.315 1.304 1.293

1.282 1.272 1.262 1.252 1.242

1.303 1.292

1.281 1.271 1.261 1.251 1.241

1.233 1.232 1.224 1.223 1.214 1.214 1.206 1.205 1.197 1.196

1.188 1.188 1.180 1.179 1.172 1.171 1.164 1.163 1.156 1.155

1.189 1.181 1.173 1.165 1.157

0.750 1.155 0.760 1.147 0.770 1.140

1.154 1.153 1.146 1.146 1.139 1.138 1.132 1.131 1.124 1.124

1.152 1.145 1.137 1.130 1.123

1.152 1.144 1.137

1.151 1.143 1.136 1.129 1.122

1.150 1.149 1.143 1.142 1.135 1.134

1.149 1.148 1.141 1.140 1.134 1.133 1.127 1.126 1.119 1.119

0.780 1.132 0.790 1.125

1.129 1.122

1.128 1.127 1.121 1.120

0.800 ,118 1.117 1.117 1.116 0.810 ,111 1.110 1.110 1.109 0.820 ,104 1.104 1.103 1.102 0.830 .098 1.097 1.096 1.096 0.840 ,091 1.090 1.090 1.089

,115 1.115 1.114 1.113 1.112 1.112 ,108 1.108 1.107 1.106 1.106 1.105 ,102 1.101 1.100 1.100 1.099 1.098 ,095 1.094 1.094 1.093 1.092 1.092 ,089 0.088 1.087 1.087 1.086 1.085

0.850 0.860 0.870 0.880 0.890

,085 1.084 ,078 1.078 ,072 1.072

1.083 1.077 I.071 1.065 1.059

,082 1.081 1.081 1.080 1.080 1.079

1.066 1.065 1.060 1.059

1.083 1.076 1.070 1.064 1.064 1.058 1.058

,076 1.075 1.075 1.074 1.073 1.073 ,070 1.069 1.068 1.068 1.067 1.067

1.063 1.062 1.062 1.061 1.061 1.057 1.056 1.056 1.055 1.055

0.900 1.054 1.054 1.053 1.052 1.052 1.051 1.051 1.050 1.049 1.049 0.910 1.048 1.048 1.047 1.047 1.046 1.045 1.045 1.044 1.044 1.043 0.920 1.043 1.042 1.041 1.041 1.040 1.040 1.039 1.039 1.038 1.038 0.930 1.037 1.036 1.036 1.035 1.035 1.034 1.034 1.033 1.033 1.032 0.940 1.031 1.031 1.030 1.030 1.029 1.029 1.028 1.028 1.027 1.027

0.950 1.026 1.025 1.025 1.024 1.024 1.023 1.023 1.022 1.022 1.021 0.960 1.021 1.020 1.020 1.019 1.019 1.018 1.017 1.017 1.016 1.016 0.970 1.015 1.015 1.014 1.014 1.013 1.013 1.012 1.012 1.011 1.011 0.980 1.010 1.010 1.009 1.009 1.008 1.008 1.007 1.007 1.006 1.006 0.990 1.005 1.005 1.004 1004 1.003 1.003 1.002 1.002 1.001 1.001

yL = specific gravity of hydrocarbon liquid referred to water, and

VL = vapor volume equivalent of 1 bbl (60°F) of hydrocarbon liquid, cu ftibbl.

The specific gravity and the approximate vapor volume of the hydrocarbon liquid can be calculated from the API gravity by

usually necessary to compute the specific gravity of the fluid flowing in the wellbore. The shrinkage of the liquid between the separator and the stock tank is usually unknown and apparently can be neglected. The equation for computing the specific gravity of the flowing fluid, ysJ, is:

R ‘&Yg +4m3 YL -rff= ) . . . . . R,L~“L

where R h’L = gas to hydrocarbon liquid ratio, cu ft/bbl, and

(14b)

OPEN FLOWOF GAS WELLS

TABLE 33.9-FLOWING-TEMPERATURE ADJUSTMENT FACTOR

33-15

5 6 7 8 9

Observed Temperature

lOFl 0 1 2 3 4

1.063 1.062 1.061 1.060 1.059 1.057 1.056 1.055 1.054 1.053 1.052 1.051 1.050 1.049 1.047 1.046 1.045 1.044 1.043 1.042

1.039 1.038 1.037 1.035 1.034 1.033 1.032 1.031 1.028 1.027 1.026 1.025 1.024 1.023 1.022 1.021 1.018 1.017 1.016 1.015 1.014 1.013 1.012 1.011

50 60 70 80 so

0.9905 0.9896 0.9813 0.9804 0.9723 0.9715

1.008 1.007 1.006 1.005 1.004 1.003 1.002 1.001 0.9981 0.9971 0.9962 0.9952 0.9943 0.9933 0.9924 0.9915 0.9887 0.9877 0.9868 0.9859 0.9850 0.9840 0.9831 0.9822 0.9795 0.9786 0.9777 0.9768 0.9759 0.9750 0.9741 0.9732 0.9706 0.9697 0.9888 0.9680 0.9671 0.9662 0.9653 0.9645

100 110 120 130 140

0.9636 0.9628 0.9619 0.9610 0.9602 0.9594 0.9585 0.9577 0.9568 0.9560 0.9551 0.9543 0.9535 0.9526 0.9518 0.9510 0.9501 0.9493 0.9485 0.9477 0.9469 0.9460 0.9452 0.9444 0.9436 0.9428 0.9420 0.9412 0.9404 0.9396 0.9388 0.9380 0.9372 0.9364 0.9356 0.9349 0.9341 0.9333 0.9325 0.9317 0.9309 0.9302 0.9294 0.9286 0.9279 0.9271 0.9263 0.9256 0.9248 0.9240

150 0.9233 0.9225 0.9217 0.9210 0.9202 0.9195 0.9187 0.9180 0.9173 0.9165 160 0.9158 0.9150 0.9143 0.9135 0.9128 0.9121 0.9112 0.9106 0.9099 0.9092 170 0.9085 0.9077 0.9069 0.9063 0.9055 0.9048 0.9042 0.9035 0.9028 0.9020 180 0.9014 0.9007 0.9000 0.8992 0.8985 0.8979 0.8972 0.8965 0.8958 0.8951 190 0.8944 0.8937 0.8931 0.8923 0.8916 0.8910 0.8903 0.8896 0.8889 0.8882

200 210 220 230 240

0.8876 0.8870 0.8863 0.8856 0.8849 0.8843 0.8836 0.8830 0.8823 0.8816 0.8810 0.8803 0.8797 0.8790 0.8784 0.8777 0.8770 0.8764 0.8758 0.8751 0.8745 0.8738 0.8732 0.8725 0.8719 0.8713 0.8706 0.8700 0.8694 0.8687 0.8681 0.8675 0.8668 0.8662 0.8656 0.8650 0.8644 0.8637 0.8631 0.8625 0.8619 0.8613 0.8606 0.8600 0.8594 0.8588 0.8582 0.8576 0.8570 0.8564

VL=369+5yAP, +O.O4(y Apr)2, . . . .(14c) where L = length of flowstring in well corresponding to

H, fit H = vertical depth in well, ft, and

98 = rate of gas flow at 14.65 psia and 60”F, lo6 scf/D.

where yAPr is stock-tank oil gravity, “API. The derivations of Eqs. 14a and 14c were given by Smith. I2

Equations for Computing Subsurface Pressures

Pressures at the sandface or at the inlet to the tubing in shut-in or flowing gas wells may be measured with BHP gauges or computed from wellhead pressures. However, most subsurface pressures in gas wells are calculated by equations. The most usable and realistic equations available are those of Cullender and Smith, I3 which have been adopted by the Kansas Corp. Commission, the Interstate Oil Compact Commission, and the New Mex- ico Conservation Commission, and by the Railroad Commission of Texas for cettain fields. The equations were revised’* recently for use with programmable calculators and small computers.

The revised flow equation for gas wells is

F*= 2-6665-fq,2 di

=(F q )* . . . . . r 1 Wa)

and

J 1 4 log 7.4ri -72 , . . . . . . . . . . f K (16b)

where

f = coefficient of friction (friction factor), ri = internal radius of pipe, in., K = absolute roughness characteristic = 0.0006

in., and r/K = relative roughness.

Refer to Ref. 12 for the background of Eqs. 15, 16a, and 16b. The second term in the numerator on the right side of Eq. 15 is the kinetic energy term that heretofore has been set at zero because the computations were made manually. Although the kinetic energy term can be neglected without appreciable error in the majority of cases, there is no need to do so when programmable

u yg qg *dp 1,ooo Y,L _

s PI

p Tz-2.082- d,% >

53.356 -pz H (~/Tz)~ I

F*+-- L 1,000

. . . . . . . . . . . . . . . . . . . . . . (15)


TABLE 33.10- F, VALUES FOR VARIOUS FLOW STRING (K = 0.0006 in.)

Nominal Size d, d, Minimum (in.] (in.) (Ibmlft) (in.) N Rs f=,

Tubing

1.315 1.80 1.049 139,000 0.09505 1% 1% 2 2’/2

3 3% 4 4%

4%

Nominal Size

(2) d,

(in.) (Ibmlft) (in.) ~- - ~

Minimum N Fe Fr

696,000 0.002146 681,000 0.002257 784,000 0.001617

778,000 0.001647 773.000 0.001670

Casing

5.000 13.00 4.494 5.000 15.00 4.408

5% 5.500 14.00 5.012

5.500 15.00 4.976 5.500 15.50 4.950 5.500 17.00 4.892 764;OOO 0.001722 5.500 20.00 4.778 744,000 0.001830 5.500 23.00 4.670 726,000 0.001942

5.500 25.00 4.580 710,000 0.002043 5% 6.000 15.00 5.524 872,000 0.001256

6.000 17.00 5.450 860.000 0.001301 6.000 20.00 5.352 843;OO0 0 001363 6.000 23.00 5.240 823,000 0.001440

6.000 26.00 5.140 806,000 0.001514 6% 6.625 20.00 6.049 964,000 0.0009922

6.625 22.00 5.989 953,000 0.001018 6.625 24.00 5.921 941,000 0.001049 6.625 26.00 5.855 930,000 0.001080

6.625 28.00 5.791 919,000 0.001111 6.625 31.80 5.675 899,000 0.001171 6.625 34.00 5.595 885,000 0.001215

6% 7.000 20.00 6.456 1.035.000 0.0008380 7.000 22.00 6.398 1;025;000 0.0008579 7.000 23.00 6.366 1,019,OOO 0.0008691 7.000 24.00 6.336 1,014,OOO 0.0008798 7.000 26.00 6.276 1.003.000 0.0009018 7.000 28.00 6.214 .992;000 0.0009253 7.000 30.00 6.154 982,000 0.0009489

7.000 40.00 5.836 926,000 0.001089 7’h 7.626 26.40 6.969 1,125,OOO 0.0006872

7.625 29.70 6.875 1,108,OOO 0.0007119 7.625 33.70 6.765 1,089,OOO 0.0007423 7.625 38.70 6.625 1,064,OOO 0.0007837

1.660 2.40 1.380 189,000 0.04643 1.990 2.75 1.610 224,000 0.03105 2.375 4.70 1.995 284,000 0.01776 2.875 6.50 2.441 355,000 0.01050

3.500 9.30 2.992 445,000 0.006180 4.000 11.00 3.476 525,000 0.004184 4.500 12.70 3.958 605,000 0.002985 4.750 16.25 4.082 626,000 0.002755 4.750 18.00 4.000 612,000 0.002905

5.000 18.00 4.276 659,000 0.002442 5.000 21 .oo 4.154 638,000 0.002633

calculators or computers are used. Eq. 15 is based on the assumptions that the flow is completely turbulent, the coefficient of friction, f, is a constant, the compressibility of the gas at base pressure and temperature conditions (14.65 psia and 60’F) is 1 .OOO, and only a gas phase is flowing.

Eq. 15 has a subtle but important concept in the value of the quantity H/L at the wellhead, where both Hand L are zero. For a vertical wellbore, H = L and

Nominal Size d, d, Minimum (in.) (in.) (Ibmlft) (in.) N fle F,

Casmg

7=/a

7.625 45.00 6.445 8.000 26.00 7.386 8.125 28.00 7.485 8.125 32.00 7.385 8.125 35.50 7.285

1,033,OOO 0.0008417 1,199,ooo 0.0005911 1,216,OOO 0.0005710 1,199,ooo 0.0005913 1,181,000 0.0006126

8% 8.125 39.50 7.185 1 ,I 63,000 0.0006349 8.625 17.50 8.249 1,353,OOO 0.0004438 8.625 20.00 8.191 1,342,OOO 0.0004520 8.625 24.00 8.097 1,326,OOO 0.0004658 8.625 28.00 8.003 1,309,OOO 0.0004801

8.625 32.00 7.907 1,292,ooo 0.0004953 8.625 36.00 7.825 1,277.OOO 0.0005089 8.625 38.00 7.775 1,268,OOO 0.0005174 8.625 43.00 7.651 1,246,OOO 0.0005394

9.000 34.00 8.290 1,360,OOO 0.0004382 9.000 38.00 8.196 1,343,ooo 0.0004513 9.000 40.00 8.150 1,335,ooo 0.0004579 9.000 45.00 8.032 1,314,OOO 0.0004756

9 9.625 36.00 8.921 1,473,OOO 0.0003623 9.625 40.00 8.835 1,458,OOO 0.0003715 9.625 43.50 a.755 1,444,OOO 0.0003804 9.625 47.00 8.681 1,430,OOO 0.0003888 9.625 53.50 a.535 1,404,OOO 0.0004063 9.625 58.00 8.435 1,386,OOO 0.0004189

9% 10.000 10.000 10.000

10.750 10.750 10.750 10.750 10.750 10.750

33.00 9.384 55.50 8.908 61.20 8.790

10 32.75 10.192 35.75 10.136 40.00 10.050 45.50 9.950 48.00 9.902 54.00 9.784

1,557,OOO 0.0003178 1,47l,OOO 0.0003637 1,450,OOO 0.0003764

1,704,OOO 0.0002566 1,694,OOO 0.0002602 1,678,OOO 0.0002660 1,660,OOO 0.0002730 1,651,OOO 0.0002765 1,830,OOO 0.0002852

H/L=~l&(~/L)=l.ooO. +

In a deviated wellbore, H is less than L, and for a horizontal pipeline, H = 0, and as a result the term for the head of gas drops out of Eq. 15. For a complete guide to the algebraic convention for H and L, refer to Ref. 12.

OPEN FLOWOF GAS WELLS 33-17

TABLE33.11-F,VALUESFORVARlOUSANNULl (K= O.OOlin.)

Casing ID

(in.) 1.900

4.154 0.005082 4.276 0.004576 4.408 0.004107 4.494 0.003838 4.580 0.003593

4.670 0.003361 4.778 0.003109 4.892 0.002872 4.950 0.002761 4.976 0.002713

5.012 0.002649 0.003235 0.004251 0.006883 0.01245 5.140 0.002438 0.002946 0.003809 0.005947 0.01012 5.240 0.002289 0.002746 0.003509 0.005343 0.008738 5.352 0.002137 0.002545 0.003213 0.004770 0.007506 5.450 0.002016 0.002385 0.002983 0.004342 0.006634

5.524 0.001931 0.002274 0.002825 0.004055 0.006074 0.01098 5.595 0.001854 0.002175 0.002684 0.003806 0.005601 0.009783 5.675 0.001773 0.002070 0.002538 0.003552 0.005133 0.008658 5.791 0.001883 0.001930 0.002346 0.003226 0.004552 0.007351 0.01017 5.836 0.001623 0.001880 0.002277 0.003111 0.004354 0.006924 0.009455

Tubino OD (in.1

2.375

0.008901 0.006oa7 0.005356 0.004948 0.004583

2.875 3.500 4.000 4.500 4.750 5.000

0.01093 0.009268 0.007867 0.007119 0.006473 0.01250

0.004242 0.005886 0.01086 0.003880 0.005281 0.009289 0.003544 0.004738 0.007980 0.003390 0.004492 0.007419 0.003324 0.004389 0.007187

5.855 0.001607 O.OOla59 0.002249 0.003065 0.004274 0.006755 0.009176 5.921 0.001551 0.001790 0.002155 0.002911 0.004012 0.006215 0.008301 5.989 0.001497 0.001722 0.002064 0.002764 0.003768 0.005726 0.007528 6.049 0.001452 0.001665 0.001988 0.002643 0.003570 0.005341 0.006935 0.009582 6.154 0.001376 0.001572 0.001865 0.002450 0.003260 0.004757 0.006057 O.OOa132

6.214 0.001336 0.001522 0.001799 0.002349 0.003100 0.004466 0.005630 0.007451 6.276 0.001296 0.001472 0.001735 0.002251 0.002947 0.004193 0.005235 0.006837 6.336 0.001259 0.001427 0.001676 0.002161 0.002810 0.003952 0.004892 0.006313 6.366 0.001241 0.001405 0.001647 0.002119 0.002745 0.003839 0.004734 0.006074 8.398 0.001222 0.001382 0.001618 0.002074 0.002878 0.003724 0.004573 0.005835

6.445 0.001195 0.001349 0.001576 0.002012 0.002584 0.003565 0.004352 0.005508 6.456 0.001189 0.001342 0.001566 0.001998 0.002583 0.003529 0.004302 0.005436 6.625 0.001099 0.001234 0.001429 0.001796 0.002266 0.003041 0.003639 0.004486 6.765 0.001032 0.001153 0.001327 0.001651 0.002057 0.002710 0.003201 0.003879 6.875 0.0009830 0.001095 0.001255 0.001549 0.001912 0.002486 0.002910 0.003486

6.969 0.0009439 0.001049 0.001198 0.001469 0.001800 0.002316 0.002692 0.003196 7.185 0.0008619 0.0009524 0.001079 0.001306 0.001577 0.001987 0.002276 0.002655 7.285 0.0008273 0.0009120 0.001030 0.001240 0.001487 0.001857 0.002116 0.002450 7.385 0.0007946 0.0008739 0.0009839 0.001178 0.001405 0.001740 0.001972 0.002268 7.386 0.0007943 0.0008736 0.0009834 0.001177 0.001404 0.001739 0.001970 0.002266

Eq. 15 does not lend itself to mathematical integration without making assumptions regarding T and z, but it may be integrated over definite limits by the trapezoidal mle.

If we let I

[ yk?qsL s Pn p/Tz-2.082-

di4 P 1 Q = pnz(jp= s

l,ooo Y&J PI H (P/Tz)* p,

FZ+-- 53.356

L 1,000

+...+(pn-pn-,)(I,+Z,-*)], . . . . . . . (17)

then

‘(~3+~2)+...+(pn-pn-l)(zn+zn-1)], . . . (18)

whereZt,Z2,Z3 . . . I, is the trapezoidal rule interval corresponding to the respective pressure. If we make the assumptions that the kinetic energy term is zero or that the temperature, T, and the gas compressibility factor, z, are constant, the equations given in Chap. 30 of this handbook can be derived. However, the numerical examples that follow will make use of Eqs. 15 through 18.

The details of computations of a BHFP and a shut-in BHP by Eqs. 16a, 16b, 17, and 18 are illustrated by Ex- ample Problem 3 on Page 33-18. To utilize the equations, it is necessary to evaluate the factor F, for various flow strings. The value may be determined by several correlations; however, the values given in Tables 33.10 and


TABLE 33.12-WORK SHEET FOR CALCULATION OF SUBSURFACE FLOWING PRESSURE BY EQS. 15,16a, AND 16b

Company Lease Well No. B Dateof Test

- ^lg 0.615 %CO, 2.5 % N 2 PPC

679 T 361 EquationsUsed 15,16a,16b PC

49 11.29s H 10,658 , 10,490 d. 2.441 in. Temperature Gradient 5°F/1,000 ft

10,658 ' 1.995

H L d P” T

-02.4413,913.0117

2 I AP 0 0.8776 104.719 0

1,000 1,000 2.441 4,023.l 122 0.8894 104.346 110.1 1,000 1,000 2.441 4,023.3 122 0.8894 104.343 110.3 2,000 2,000 2.441 4.134.0 127 0.9012 103.992 110.7 3,000 3,000 2.441 4,245.0 132 0.9129 103.659 111.0 4,000 4,000 2.441 4,3X3 137 0.9244 103.337 111.3 5,000 5,000 2.441 4,468.0 142 0.9359 103.036 111.7 6,000 6,000 2.441 4580.0 147 0.9472 102.743 112.0 7,000 7,000 2.441 4,692.3 152 0.9584 102.464 112.3 8.000 8.000 2.441 4.805.0 157 0.9695 102.196 112.7 9,000 9,000 2.441 4,917,s 162 0.9805 101.943 112.9

10,000 10,000 2.441 5,031.l 167 0.9913 101.693 113.2 10,490 10,490 2.441 5,086.7 169.5 0.9966 101.583 55.6 10.490 10,490 1.995 5,086.7 169.5 0.9966 76.546 0 10,658 10,658 1.995 5,112.0 170.3 0.9989 76.446 25.3

33.11 were calculated by the methods published by Smith. ‘*

To compute subsurface pressures where the well is equipped with tubing set without a packer, the preferred practice is to calculate the flowing subsurface pressure from the wellhead pressure measured on the static gas column by means of the static column equations. If the well has a packer, it is necessary to calculate the flowing subsurface pressure by means of the equations for flowing gas columns.

Depths for calculating or measuring subsurface pressures in wells are determined in practice by the equipment installed in the well. Where a well is equipped without tubing or with tubing set without a packer, the proper depth for pressure determinations is the distance to the midpoint of the productive sandface. If the well has tubing set with a packer, the pressures are determined at the entrance to the tubing provided the entry to the tubing is no more than 100 ft from the midpoint of the productive sandface. Otherwise, appropriate corrections would be made to determine the pressure at the midpoint of the sandface.

An explanation of the computational procedures used in Tables 33.12 and 33.13 will be helpful before going into the details of the calculations. The recent advances in computing equipment or, more realistically, the dramatic decrease in the cost of computations have given the average engineer access at least to a handheld programmable calculator or mom likely a microcomputer. Therefore, the emphasis in the past has been to simplify equations by making assumptions regarding pressure, temperature, and gas compressibility, but that has not been done here. Now the factor F, and compressibility factor, z, become subroutines, the results of which are never seen by the user. In this case, Tables 33.10 and 33.11 may seem redundant. The compressibility factors given in Tables 33.12 and 33.13 were calculated by the equation of state published by Hall and Yarborough t4 and Yarborough and Hall. l* The results of the computations in Tables 33.10 through 33.13 have been rounded,

- 23,018 23,059 23,063 23,049 23,039 23,052 23.047 231045 23.065 23,047 23,052 11,302

-

3,871

- 23,018 23,059 46,121 69,170 92,209

115,261 138,308 161,352 184.417 207,464 207,473 230,516 230,526 241,818 241,822 241,616 241.822 245,689 245,695

Y,L 0

23,053

46,105 69,158 92,211

115,263 138,316 161,369 184,421

Line

1 2 3 4 5 6 7 8 9

IO II 12 13 14 15

and the rules for rounding vary from one piece of computing equipment to another. The algorithm used for solving Eqs. 15, 17, and 18 seems to work for all cases, but users may wish to devise their own algorithm.

Example Problem 3-Flowing Well. Details of the method for calculating a flowing subsurface pressure for Well B are given in Table 33.12.

The wellhead flowing pressure for Well B was 3,913 psia at a flow rate of 11.299 x lo6 cu ft/D. The annular space between the tubing and casing was packed off and filled with mud so that it is necessary to calculate the flowing subsurface pressure at a depth of 10,658 ft down the flowing column of gas. Gas properties are those given in Table 33.12.

The flow string measures 10,490 ft of 27/s-in.-OD, 6.50-lbm/ft tubing with 168 ft of 2%-in.-OD, 4.70-lbm/ft tubing at bottom of flow string. Also, H = L, or the flow string is vertical.

Computation of the required pressure is done in two major steps because of the change in size of the flow string at a depth of 10,490 ft. Computations are given in the following steps.

Step 1. Obtain the ID’s from Table 33.10 and enter at top of Table 33.12

2% in. 0%ID = 2.441 in.

2% in. OD-ID = 1.995 in.

Step 2. Determine the temperature gradient applicable to the problem. In this example, the flowing temperature of the gas at the wellhead was 117”F, and the subsurface temperature at 10,658 ft was 170°F. The temperature was assumed to be a straight-line relationship between 117°F at H = 0 and 170°F at H = 10,658 ft for a temperature gradient of 5°F per 1,000 ft.


TABLE 33.13-WORK SHEET FOR CALCULATION OF SUBSURFACE SHUT-IN PRESSURE BY EQS. 15,16a, AND 16b

Company Lease Well No. 0 Date of Test

yg 0.615 %CO, 2.5 - 679 %N, PPC T 361 Equations Used 15,16a, 16b PC

99 0 H 10,656 , 10,656 d N.A. Temperature Gradient 5°Fll,000 ft

(4J)x WP) x 37.464 x H T Z I AP (1” +/n-l) u, +/n-1) Y,L Line

- L d, PO

0 ---ii 4,173.o 117 123.931 N.A. 0.6963 0 - - 0 1 1,000 1,000 N.A. 4,266.0 122 0.9071 123.753 93.0 23,036 23,036 23,053 2 1,000 1,000 N.A. 4,266.l 122 0.9071 123.751 93.1 23,059 23,059 3 2,000 2,000 N.A. 4,359.3 127 0.9177 123.573 93.2 23,051 46,i 10 46,105 4 3,000 3,000 N.A. 4,452.6 132 0.9262 123.410 93.3 23,043 69,153 69,156 5 4,000 4,000 N.A. 4,546.1 137 0.9365 123.245 93.5 23,062 92,215 92,211 6 5,000 5,000 N.A. 4,639.7 142 0.9486 123.061 93.6 23,056 115,271 115,263 7 6,000 6,000 N.A. 4,733.4 147 0.9566 122.929 93.7 23,051 136,322 136,316 6 7,000 7,000 N.A. 4,627.2 152 0.9665 122.766 93.6 23,046 161,370 161,369 9 6,000 6,000 N.A. 4,921.l 157 0.9762 122.645 93.9 23,046 164,416 184,421 IO 9,000 9,000 N.A. 5,015.l 162 0.9677 122.500 94.0 23,044 207,460 207,474 11

10,000 10,000 N.A. 5,109.3 167 0.9971 122.362 94.2 23,066 230,526 230,526 12 10.658 10,656 N.A. 5,171.3 170.3 1.0033 122.266 62.0 15,166 245,694 245,695 13

Step 3. Enter wellhead data on Line 1 where Hand L are zero. Calculate f t from definition of I in Eq. 17.

From Eq. 17. I is:

;-2.082(g)

F2 + H (P& .

L 1,000

;=(3913)/(577)(0.8776)=7.72747.

Note that z was calculated by methods given in Refs. 14 and 15 (see also Chap. 20).

2.082(ygq,2/dpp>= 2.082(0.615)( 11.299)*

(2~l41)~(3913)

=0.00118.

[p/~z-2.082(y,q,2/dpp)]=7.72629.

Using Eqs. 16a and 16b:

=2.6665(11.299)2/~(2.441)5

. [4 log(2.441/O.ooO6) +2.27281] ‘)

=340.425/24,200=0.014067,

or, from Table 33.10:

F*=(F,qs)*=(0.01050~11.299)*=0.014075.

This value of F* will be used later for comparison.

(p/Tz)*/1,CKIO=(7.72747)*/1,000=0.059714.

At the wellhead, where H=O and L=O for a vertical wellbore. H=L, then

H/L=lim (H/L)=l.OOO. H&L+0

For a deviated wellbore, H is less than L, and for a horizontal pipeline, H = 0, and the term for the head of gas drops out of the term for 1.

FZ+~(plTz)‘/l,OOO

=0.014067+(1.000)(0.059714)

=0.073781.

Then

Z=(7.72629)/(0.073781)=104.719.

If the F2 value determined from F, (taken from Table 33.10) is substituted above, I becomes 104.708, which compares well with 104.719.

Step 4. Determine trial Ap (Line 2) for a depth of 1.000 ft by

Ml= 37.484~7, XL 37.484(0.615)(1,000)

21, = 2( 104.719)

=llO.l psi.

Step 5. Complete calculation of first trial 12 (104.346) on Line 2 where the temperature is 122”F, and the first trial pressure is 3913.0+ 110.1=4023.1 psia. At these conditions, the compressibility factor, Z, is 0.8g94. Esti- mate the second trial Ap by:

&2= 37.484(0.615)(1,000) = 1 1o 3

104.719+104.346 ’ ’


Step 6. Complete calculation of second trial 12 (104.343) on Line 3 where the temperature remains at 122”F, and the second trial pressure is 39 13 .O+ 110.3 = 4023.3 psia. Under these conditions, the compressibility factor, Z, remains at 0.8894. Estimate the third trial Ap by

*~3= 37.484(0.615)( 1,000)

= 110.3. 104.719-t 104.343

Since the third trial Ap is the same to within 0.04 psi, the pressure at a depth of 1,000 ft was determined by trial and error to be 3,913.0+110.3 = 4,023.3 psia. (Note that the third trial was not entered in Table 33.12.)

Step 7. Repeat Steps 4 through 6 to calculate the pressure at a depth of2,OOO ft. Only the final step was given in Table 33.12.

Table 33.13 illustrates the calculation of subsurface shut-in pressures in a gas well by Eqs. 15, 16a, and 16b by the same procedure used in Example 1. The only difference is that for the shut-in well the rate of flow, qg , is zero and, as a result, the pressure loss caused by friction is zero. Therefore, the inside diameter of the pipe has no effect on the calculations.

Size of Integration Interval The integration interval was 1,000 ft in Tables 33.12 and 33.13 for a moderately high-pressure well and, for the flowing example (Table 33.12), the rate of 11.299 x lo3 cu ft/D gave an effective or average velocity of 14.7 ft/sec near the wellhead. Also, the compressibility factor, z, of the gas at wellhead conditions is in that portion of the z vs. pressure curve where z is very nearly a linear function of pressure. At this low velocity and the nearly linear relationship of z with pressure, an integration interval of 1,000 ft is probably more than enough. Likewise, at low pressures where z is again almost a straight-line function of pressure and at low velocities, the integration interval could be extended to 3,000 ft without undue error. However, even moderate computation facilities eliminate the necessity for expanding the integration interval to more than 1,000 ft.

Application of Backpressure Tests to Producing Problems Backpressure tests taken properly are useful in predicting delivery rates into a pipeline and in reconditioning studies. For these purposes, either the multipoint or the isochronal test is suitable for wells producing from reservoirs with high permeability such as Well B (Fig. 33.5). The isochronal-type test is necessary for an accurate analysis of producing problems for wells producing from low-permeability reservoirs such as Well A (Fig. 33.7). Although multipoint tests can be used, such analyses are much more difficult.

Well performance at the bottom of the well is a measure of the capacity of the reservoir to deliver gas in- to the wellbore and is useful in analysis of reservoir problems. A wellhead performance curve is a measure of the capacity of the well to deliver gas into a pipeline and is useful in equipment and reconditioning problems. Usually, an analysis of producing problems can be completed with wellhead backpressure data.

Production Rate Estimation of the steady production rate of a well into a pipeline operating at a relatively constant pressure requires both test data and a general knowledge of the producing characteristics of the well. For example, an estimate is required of the capacity of Well A (Fig. 33.7) to deliver gas into a pipeline operating at a pressure so that pts * -ptf * in thousands equals 20. Starting from shut-in conditions, the delivery rates would be 6,950, 6,000, 5,150, and 4,730x103 cu ft/D. The rate at 72 hours would be 3,340 x lo3 cu ft/D from data given in the text. The steady reduction rate would be about 2,000 to P 2,400x10 cu ft/D. Although theoretical methods have been published for estimation of stabilized production rates, they would require more data than is available for the well.

Well B (Fig. 33.5) would produce about 4,300~ lo3 cu ft/D into a pipeline when

PlS 2 -prf* =500

as long as the well remained in good condition. Actually, the performance of Well B increased during production and the rate of flow would have increased. The performance of Well B did not deteriorate with time.

Estimation of the sustained production rate of a particular well against fixed pipeline conditions requires a general knowledge of well performance and a definite knowledge of the performance characteristics of the particular well. The accuracy of such estimations is dependent to a large extent on the amount of proper test data available for study.

Causes of Deterioration in Performance The principal causes of deterioration in gas-well performance are hydrates, liquids, cavings, deposition of salts, equipment leaks, foreign objects, and damage to the producing formation. Any one or a combination of these causes may result in loss of productive capacity and in decreased income. The determination of the cause of deterioration in performance and the recommendation of remedial measures require a history of the performance of the particular well.

The tests illustrated in Fig. 33.8 for Well A give a history of the performance between the date (June 17, 1947) of the multipoint test and the date (Dec. 17, 1951) of the isochronal test. The performance indicated by the first point of the multipoint test (q8 =4,928x lo3 cu ft/D) is the same as that of the isochronal test. Thus it is concluded that the performance of Well A was maintained for about 4% years. Nothing occurred that harmed the well. Similar conclusions regarding Well B are indicated for the time interval represented by the data on Fig. 33.5.

A regular program of testing gas wells is essential to planning remedial action.

Hydrates The formation of gas hydrates in the flow string or in the reservoir may cause a well to cease flowing. The author knows of no remedial action to remove hydrates from the producing formation except that of allowing the natural heat of the reservoir to melt the hydrates. The formation of hydrates in the flow string may be prevented by use of


qg, IO3 cu ft/D

Fig. 33.9-Effect of tubing installation on performance of Well C; Points 1 through 4 are before tubing installation, Point 5 is after.

qg, lo3 cu fVD

Fig. 33.10-Effect of obstruction in tubing on performance of Well D; Points 1 through 6 are before removal, Point 7 is after.

bottomhole chokes, injection of chemicals such as the alcohols or glycols into the flow string, or by the installation of downhole heating equipment. The accumulation of hydrates in the flow strings may be alleviated to some extent by elimination of obstructions in the flow string, use of proper valve sizes at the surface, elimination of sharp bends in surface lines, and proper placement of chokes in surface lines. Remedial action consists in lowering of hydrate-formation temperatures by chemicals or by maintaining the temperature of the flowing gas above the hydrate-formation temperature. Heating of the flow string in a well is usually accomplished by the circulation of hot oil in the casing around the tubing of the well. However, it must be em- phasized that hydrate troubles are very easily confused with liquid troubles in low-temperature wells. A careful study should be made of flowing temperatures in a well before recommendations are made for hydrate prevention.

Liquids Most performance difficulties in gas wells are caused by the accumulation of liquids in the wellbore. Liquid troubles may be caused by hydrocarbons (condensate and etude oil), salt water, or brines coming into the wellbore from the producing formation, brines from foreign sources through casing leaks, or fresh water. Oc- casionally, the production of formation water or crude oil may be eliminated by plugback operations. Liquids in wellbores may be removed by tubing strings of proper design, siphon strings (tubing with jet holes or gas-lift valves), and plunger lifts. Periodic flowing of the well at high rates to the pipeline may eliminate liquid troubles.

Remedial action for water troubles requires an identification of the source of the water. This is done by water analyses. If it is decided from analyses that the water is native to the formation, there is a choice between plugback work and water removal by various means. Salt water that is foreign to the producing forma-

tion or fresh water in excessive amounts indicates a casing leak that should be repaired. However, moderate amounts of fresh water usually condense in the flow strings of gas wells. Fresh water that occurs naturally should not be confused with fresh water from a foreign source.

Cavings

Cavings that consist of shale and pieces of the formation are usually most troublesome in openhole completions. The presence of cavings in wells without tubing can be determined easily by comparison of measured depth with drilled depth. Remedial action consists of cleaning out, installation of liners in openhole, and acid washes where the formation is soluble in acid.

Unconsolidated sand is troublesome in many Gulf Coast wells. Sand may damage the performance of a well in addition to causing severe damage to equipment. Remedial action consists of cleaning out, installation of special liners, or consolidation treatment for the formation.

Deposition of Salts Salts (sodium chloride or other chemical compounds) may be. deposited in the flow strings or wellbores of gas wells. Sodium chloride and water-soluble salts often may be removed by water or light acid washes. Occa- sionally it is necessary to replace the flow string with clean pipe. Heavy crude oil (not a salt) may be removed From the flow string and to a limited extent from the face of the wellbore by washing with kerosene.

Casing and Tubing Leaks Casing leaks usually permit the migration of gas into another formation, but occasionally in low-pressure areas water may come into the wellbore through leaks. The migration of gas into another formation is wasteful. Casing leaks, depending on their size in relation to well

33-22

capacity, cause deterioration in well performance. Positive identification usually can be made with subsurface temperature surveys or special techniques supplied by service companies.

Tubing leaks, where there is no packer, tend to defeat the purpose of the tubing. Liquid removal becomes difficult if the hole in the tubing is large. Small leaks in tubing are usually the result of corrosion. In wells where the annular space is packed off, tubing leaks may allow casing pressures to build up to dangerous levels.

Foreign Objects Foreign objects such as swab rubbers, stud bolts, or pieces of metal may remain in the flow string of a well after completion. Such objects should be removed from the flow string because they can seriously affect the delivery capacity of a well. The removal of foreign objects ftom the upstream side of chokes is common.

Examples of Remedial Operations The effect of water production and the installation of tubing on the performance of Well C in the Texas Hugoton field is illustrated in Fig. 33.9. The curve (n=0.860) shows the 3-hour isochronal test results taken immediately after completion. Numbered points are 72-hour isochronal tests taken at yearly intervals, except for Points 4 and 5, which were immediately before and after installation of tubing. Point 1, taken after completion, and Point 2, taken about a year after completion, represent good performance. Points 3 and 4 show poor performance with the result that Well C was producing about 30% of its assigned allowable. A study of Well C indicated that salt water was causing the poor performance. A string of 1 g-in. tubing with a X,-in. jet hole 100 ft from the bottom of the tubing was installed. The well was then produced continuously through the tubing string. At the time Point 5 was taken, the performance of the well had not only been restored but it had been improved over what it had been originally, which is shown by the relative positions of Points 1, 2, and 5 with respect to the 3-hour isochronal curve. Conclusions regarding Well C are that there was a minor water problem from completion through the time that performance data were taken for Points 1 and 2 (Fig. 33.9). Water movement into the wellbore had seriously damaged the performance of the well at the times Points 3 and 4 were taken. The installation of tubing after Point 4 permitted the removal of water from the well and even allowed the water saturation to be reduced in the formation around the wellbore. The position of Point 5 indicates better 72-hour performance than the well had originally as it is closer to the 3-hour isochronal curve than Points 1 and 2.

An example of the effect of a tubing obstruction on the performance of a well is illustrated in Fig. 33.10 for Well D, where the performance points (indicated by circles with and without numbers) were taken at intervals of a month after start of production. Well D was an extremely high-capacity well as indicated by the position of the original multipoint test. As the numbered points were of long-time-flow duration, it was thought that position of Points 1, 2, and 3 indicated some sort of liquid blockage in the reservoir. However, the tubing appeared to be free of liquids when the well was shut in and pressures were normal. Water-gas and condensate-gas


ratios were normal. Thus it was concluded that liquids were not the source of trouble. After Points 4, 5, and 6 were taken, it was decided to blow the well. Shortly after the well was opened, a swab rubber and several pieces of metal were blown from the well. Afterward, the performance of Well D returned to normal, as indicated by the positions of Point 7 and later performance points that are not numbered on Fig. 33.10.

Space does not permit a complete description of reconditioning procedures. However, it is hoped that this brief outline does illustrate the importance of adequate performance tests in the maintenance of well productivity and planning reconditioning procedures.

Nomenclature C = performance coefficient

di = internal diameter, in.

f= F=

F, = F =

;; =

Fpu = F, = FT = h, = h, =

H=

I=

K=

L=

n=

P’

Pi =

PI =

Ppc =

PR =

Ps =

Ptf =

Pts =

Pwf =

qg =

ri =

R gL =

coefficient of friction (friction factor) term in Eq. 16a specific-gravity adjustment factor non-Darcy flow factor basic orifice factor for critical-flow prover,

lo3 cu ft/D at 14.65 psia, 60”F, specific gravity = 1.000

supercompressibility adjustment factor factor defined by Eq. 16a flowing-temperature adjustment factor height (manometer reading), in. mercury height (manometer reading), in. water vertical depth in a well, ft (in untubed wells

H is the vertical depth to the midpoint of the productive formation; in tubed wells H is the vertical depth to the entrance to the tubing)

terms in Eq. 17 absolute roughness characteristic, in. length of flow string in well corresponding

to H, ft

exponent of the backpressure equation or slope of the backpressure curve

pressure, psia impact pressure on a pitot tube, psig impact pressure on a pitot tube, psia pressure, pseudocritical, psia average pressure in the reservoir at vertical

depth H

static pressure on critical flow prover, psia flowing pressure at wellhead measured on a

flowing column of gas, psia shut-in pressure at wellhead, psia subsurface (bottomhole) flowing pressure in

the wellbore at vertical depth H, psia rate of flow, lo3 cu ft/D or lo6 cu ft/D

(14.65 psia and 60°F) internal radius of pipe, in. gas to hydrocarbon liquid ratio, cu ft/bbl

T = temperature, OF+460 Tf = temperature of flowing gas, OF+460


Tpc = temperature, pseudocritical, OF+460 TR = reservoir temperature I’, = vapor volume equivalent of 1 bbl (60°F) of

hydrocarbon liquid, cu ft/bbl z = compressibility factor for gas

A = difference between two values

78 = specific gravity of separator gas or gas being measured, air = 1.000

yg = specific gravity of the flowing fluid, air = 1.000

-ye = specific gravity of hydrocarbon liquid referred to water

Key Equations in SI Metric Units qn =o. 1533 d?p, . . . . . . . . . . . . . . (4)

ztgLYn +g19.g YL -rff= . . . . .

RgL+vL

141.5 YL= 131.5+yAPl . . . . . . . . . (14b)

vLy65.7+0.89 -fApI+0.~7(YApI)2. (14C)

H (p/Tz)’ ’ “’ . (15)

F2+-p L 1,000

F== 5.328Ofq;

di5 . . . . . . . . . . . (16a)

Al- l 7.4 Ti - =4 log-. . . . . . f K

(16b)

~~.~~~Y,L=[(P~PI)(IZ+~)+(P~PZ)

. (1.3 +12) f... (Pn -pn-1) (‘n +4-l)]

. . . . . . . (18)

where qn is in m3/d, d; is in mm, p is in kPa, VL is in m/m, L is in m, T is in K, H is in m, T; is in mm, and K is in mm.

References 1. Reid, W. : “Open Flow Measurement of Gas Well, ” Western Gas

(Nov. 1929) 32. 2. Rawlins, E.L. and Schellhardt, M.A.: “Back-pressure Data on

Natural Gas Wells and Their Application to Production Prac- tices,” USBM Monograph (1935) Washington, DC.

3. Binckley, C.W.: “Methods of Approximating Open Flow of Gas,” Proc., Southwestern Gas Measurement Short Course (1954) 304

4. Cullender, M.H.: “The Isochronal Performance Method of Deter- mining the Flow Characteristics of Gas Wells,” J. Pet. Tech. (Sept. 1955) 13742; Trans., AIME, 204.

5. Odeh, A.S.: ‘ ‘Pseudosteady-State Flow Equation and Productivity Index for a Well With Noncircular Drainage Area,” J. Per. Tech. (Nov. 1978) 1630-32.

6. Ramey, H.J. Jr.: “Non-Darcy Flow and Wellbore Storage Effects in Pressure Build-Up and Drawdown of Gas Wells,” J. Per. Tech. (Feb. 1965) 223-33; Trans., AIME, 234.

7. Odeh, A.S., Moreland, E.E., and Schueler, S.: “Characterization of a Gas Well From One Flow-Test Sequence,” J. Per. Tech. (Dec. 1975) 1500-04; Trans., AIME, 259.

8. Smith, R.V.: “Unsteady-State Gas Flow into Gas Wells,” J. Pet. Tech. (Nov. 1961) 1151-59; Trans., AIME, 222.

9. “Orifice Metering of Natural Gas,” Gas Measurement Commitfee Report 3, American Gas Ass”., New York City (April 1955).

10. Manual of Back Pressure Testing of Gas Wells, State of Kansas, Topeka (1959).

Il. Manual of Back Pressure Testing of Gas Wells, Interstate Oil Compact Commission, Oklahoma City (1962).

12. Smith, R.V.: Practical Natural Gas Engineering, Pennwell Publishing Co., Tulsa (1983).

13. Cullender, M.H. and Smith, R.V.: “Practical Solution of Gas- Flow Equations for Wells and Pipelines with Large Temperature Gmdients,” J. Pet. Tech. (Dec. 1956) 281-87; Trans., AIME, 207.

14. Hall, K.R. and Yatirough, L.: “A New Equation of State for Z- Factor Calculations,” Oiland GasJ. (June 18, 1973) 71, No. 2.5, 82-85.

15. Yarborough, L. and Hall, K.R.: “How to Solve Equation of State for Z-Factors,” Oil and Gus J. (Feb. 18, 1974) 72, 86-88.

howard b. - petroleum engineers handbook, part 3

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