a?

SPE 26668

Compressibility Factors for Naturally Occurring Petroleum GasesL.D. Piper, Texas A&M U.; W.D. McCain Jr., S,A, Holditch & Assocs. Inc.; and J.H, (lorredor,Inters Petroleum Production Div.

SPEMembers

Sooietyof Pddwll a’fgirlec?rs

COpyrighl 1993, Sc@efyof Petroleum Englneam Inc.

Thta paper was prepared for presentation at the 66fh Annual Technical Conferenw and Exhibition of the $ocie!y of Petroleum Engineers held In Houston, Texas, 3-6 October 1993.

Thle paper was selected for presentation by an SPE Program Committee following review of information contelnad In an abstrect submitted by the author(a). Contents ot the paper.as praaantad, have not been ravlewad by the Soclafy of Petroleum En@eara and are eublect to C-Jrrecfionby the author(a). The material. as Preee~ted. doee not necessarily reflectMY poaitlon of the SocIefy of Petroleum Engineere. IISoffiwra, or members. Pepara preeonled al SPE maatin?lsare eub]act to publication review by Editorial Commlftaos of the Soclatyof Petroleum Enginaare. Permieelonto coPy lareetricfed to an abstract of not more than 3@ worde. Illuslratione may not be copied. The absfrdcf should contsln conspicuous acknowledgmentof where and by whom tha paper is praeantad. Write Librarian, SPE, P.O. Box S33836, Richardson, TX 76083-3S36. U.S.A. Talex, 1S3246 SPEUT.

The Sutton gas specific gravity correlation gives values ofpseudocritical properties which, when used with the Dranchukand Abou-Kassem (DAK) representation of the Standing andKak (SK) chtW currentiy provide the most accurateestimatesofcompressibility factors for naturally occurring petroleum gases.However, other correlations must be used to account for thepresenceof acid gases. A new gas specific gravity correlation ispresented which takes into account the effects of the acid gasesand nitrogen. The new correlation provides more accurateestimates of the compressibility factor than can be obtained bycurrent methods and also elimimtes the need for involvingadditional correlations to comet for the presence of acid gasesand nitrogen. The new correlation was developed using a set of1482data points, ranging in composition flom lean sweet to richacid gases.

Knowledgeof the pressure-volume-tempemture(PVT) behaviorof natural gases is necessary to solve many petroleumengineeringproblems. Gas reserves, gas metering, gas pressuregradients, pipeline flow and compression of gases are some ofthe problemsrequiring the gas compressibtity factor, or z factor.Typically, the z factor is determinedby laboratorymeasurement.Howevex,laboratorydata is only applicable for the compositionsand conditions investigated. When conditions of interest aredifferent from those of the laboratory studies or data is notavailable,correlationsmust be used.

The basic methods for esthnating the gas compressibility factorare relatively simple and well known] The principle of

Referencesand illustrationsat end of ~aper.

correspondingstates, Kay’spseudocriticalpointi and the SK chartare commonly used. If the composition of the gas is known, thepseudocriticaltemperatureand pressure may be calculated usingKay’s rules--molar averages of the critical properties of themixture’scomponents. Otherwise, the pseudocriticaltemperatureand pressure may be estimated using correlations based on gas;pecific gravity. Then, the reduced temperature and pressurenay be calculated and the SK chart or its representation by theMK equationof state maybe used to determinethe z factor.

3utton2 presented more accurate methods for both cases, Hisnethod for calculating the pseudocritical temperature andpressurewhen the composition of the gas is known is based ontheStewti Burkhard4and Voo (SBV) equationsgiven by

‘w . . . . . . . . . . ..(la)TP=+nd~=r

where,

His gas specitic gravity correlation for estimating the pseudct-critkal temperatureand pressure when the compositionof the gasis known, based on 634 compositions from 275 PVT reports, isgivenby

TP = 169.2-t 349,5ys - 74.Oy;,and

~,=756.8 - 131.0yg - 3.6y;. . “o “ o (z)

661

* R

2 COMPRESSIBILITYFACTORSFOR NATURALLYOCCURRINGPETROLEUMGASES SPE 26668If the gas contains hydrogen suikde or carbon dioxid;, theWichert and &iz correlation:

‘rpc = TP -e,where,

d]120”[(yms+ ymf - (Yms+ Yc.6

& =

[ 1+15“(Msr - (yIt?sf,and,

ppcl-’pc . . . . . . . ...6....(3)

“PC = Tp + y~l - )@’

should be used to adjust the pseudocritical constants.2-3However, Ref. 2 is unclear on how Eqs. 3 should be applied toEqs. 2.

In an earlier pape~, we discussed Sutton’smodification to theSW rules in detail and presented a new modification whichtakes into account the effects of the heprane plus fraction, acidgases and nitrogen. TM correlation,having a form simii to theSBV equations, was based on 896 data points from 134 PVTreportsand is givenby

and,

‘=’o+$fi’’k%),+”wdH)]+’P~Y’#j +P6Yc#f@ .,,...(4)

+ MYc@fc&

where yIG {~, yma YN2}J y] = {Ye],Yc2#o.*YDC6}sad *e a:and pi were shown in Table 3 of Ref. 4. E@. 4, usti with Eqsla and the DAK representation of the SK chrul provided mor~accurate estimates of the compressibtity factor, simplified thtprocedures,and included the effectsof nitrogen.

This paper reportson further studies using a largerdatabase. Wtpresent an update for the coefficients of Eqs. 4, based on UNexpanded data base, and anew gas spec~lc gravity correlationBoth Eqs. 4 and the new correlation elhnhm the need for E@3 and include the effects of nitrogev and can be used with Eqsla to calculate more accurate estimates of the compressibilityfactor.

Our previous work on gas compressibdity cormdations used Idata base with a limited number of high specific gravity gaseand gases with high impurities content. The data set has bee]expanded by about 60 %, with emphasis on adding gases u

mrect these deficiencies. For this study, we added 586 datamints from 37 PVT reports from the literature5-13 and other)ources14-15.Table 1 shows the range of composition,physical)roperties, and conditions of the resulting data base. Our;xpanded data basu contains signitkrmtly more gases withipeciilc gravities ranging from 1.3 to 1.8. Additionally, it:ontains significantly more gases with impurities than the dataMM used by Sutton. While the maximum concentrations of~y&ogen sulilde and carbon dioxide are quite large, only tenxment of the sampleshad an acid gas concentmtiongreater than,welvepercent.

Updated Coefficients for Eqs. 4. Our previous arnlysis wasrepeated using the expanded data base to develop the newwefficients for Eqs. 4 shown in Table 2. We then evaluated theWV rules, Sutton’smodilkation to the SBV rules (SSBV) andEqs. la and 4 using the expandeddatabase. The averageabsolutewrors of the calculated compressibility factors were 2.23, 1.53,md 1.07percentirespectively. These results were consistentwithhose in Ref. 4 and are shown in Table 3, for four differentwbsets of the data ranging from lean sweet gases to rich acidBases,and Figs. 1 through 4. Figs. 2 and 4 show the distribution~f the errors with the experimental z factor. Higher emorsmwrred at lower z factors. Even though the gases in Sutton’sdatabase containedno hydogen sultlde and only limited amountsof carbon dioxide and nitrogen, Uwz factors calculatedusing hismodificationfitted the expanded data base very well. This factgives a great deal of confidence in the theoretical basis of theformof the SBV equations.

~v~

To evaluate the current gas specific gravity correlations, we firstassumedthat the amount of impurites in the mixture was known.The technique given by Standing3 for applying the Wichert andAziz correlation, Eqs. 3, was used to correct for the presence ofacidgases. We evaluated !Mnding’sreservoirgas correlationandSutton’s comelation, Eqs. 2. The results of these calculationsusing our data base are shown in Table 3 and Fig. 5. Theaverage absolute error was 1.99 and 1.42 percent respectively.We then assumed that the amount of impurites in the mixture wasunknown. As maybe seen in Fig. 6, the error was as large as 27percent and the maximum error varied linearly with the amountof impuritiesin the rjxture.

~

Our objective was a method for estimating the pseudocxiticalconstants when composition is not known which, if used with theDAK representationof the SK cM@ more accuratelyreproducesthe experimental compressibility factors. The data discussedabove was used with the DAK equation of state and aminimization procedure to detexminethe inferred paeudocritkalconstants. TLis set of inferred pseudocritical values was thenused with multiple regression analysis to develop a newcorrelation for J and K to be used with Eqs. lain calculatingvalues for the pseudocritical point, We later refer to the newmethod as the proposedgas specificgravity correlation.

Procedure. A muhidimensional conjugate gradient algorithm16

was used to find the point on the ~r-Tw sW= giv~ by the

SPE 26668 L. D. PIPER, W. D. MCCAIN,JR. ANDJ. H. CORREDOR 3

DAK representation of the SK chart which minimized thedifference between experimental and calculated z factors. Theexperimental compressibility factor, pressure and temperature,and pseudocritical constants calculated using Sutton’smodification to SBV rules were used as initial guesses. Thealgorithm converged for all the data points and returned valuesfor the inferred pseudociitical temperature and pressure. Basedon our previous finding, that much of the scatter in compmingcalculated to inferred values of pseudodtical temperamre andpressure,ocurred at the last steps of a depletion study--adtificultlaboratory procedure, 121 data points were not used in ourcorrelations. We attempted but were unable to correlate theinfersedpseudocritkal tempemttureand pressurewith gas speciticgravity because of the large amount of impurities in the gases ofOLU data base.

Inferred Values of J and K. The 1482 remaining pairs of theinferred pseudocritkal constants and Eqs. la were used to findthe inferred valuesfor the SBV parameters 1 and K, as shownbelow:

After finding that the inferred values of J and K were stronglyrelated to the specific gravity of the gas mixture as can beobserved in Flge. 7 and 8, we decided to use a regression modelsimilar to Eqs. 4, which was originallydevelopedby Corredor17.Notice the data points in the lower right half of both figures,These two samples, which contain very high concentrations 01carbon dioxide, obviously are omliers with respect to therelationships between J and K and specific gravity. Thecorrelationscan be improved by omitting them; however, theywere retained in the database because they were correlatablebythe mcdel discussedbelow.

Proposed Specific Gravity Correlation. Multiple regressiontechniques were used with the 1482 pairs of inferred J and K asdependent variables to empirically find a correlationincorporating the fmt four terms of Eqs. 4 and the gas specificgravity. The new cordations are given by E+. 6.

‘~re YiE {ysf$,yc~ yN2}, ad the Ui axldpi are shown inTabIc 4. Eqs. 6 directly account for the effects of hydrogemsulfide, carbon dioxide, and nitrogen, eliuinatiug the need folEqs. 3. The new method for calculating the z factor uses onl~Eqs. 1a and 6 and the DAK representationof the SK chart. Nottthat the new method is simplier than current methods. WhikEqs. 6 contains terms similar to those in Eqs. lb, the introductionof terms for nonhydmcarbongases is a departurefrom the currenlmelhod.

lkulte. To evaluate Eqs. la and 6, we again assumed that theunount of hnpurites in the mixture was known, Figs. 9 and 10:ompare values of the pseudocritical constants calculated usingZqs. la and 6 with the inferred values. The results of z factorxdculations are shown in Table 3 and Fig. 11. The averageibsolute error of the calculated z factor was 1.30 percent usinghe proposed correlation. We then assumed that the amount ofmpurites in the mixture was unknown. As indkated in Fig. 12,he error was again as large as 27 percent and the maximumerrorwied linearly with the amount of impurities in the mixture.rable 5 shows a comparison of emors made in using the gas;peciflc gravity correlations when the amount of impurities aremknown. Notice that the errors am relatively small if the gas islean and sweet. However, the errors can be laxge if the gasxxttainsmore than five percent acid gas and is at a high pressure.I%eright half of Fjg, 12 shows results from several sampleswntaining a large amount of impurities. The large errors areattributableto high concentrations of acid gas alone. The largeange in errorat a constantcompositionis attributableto variation[npressure, Generally, the larger errors occurred at the Wtgherpressures.

n

1.

2.

3.

4.

A set of z factors, temperatures, pressures, and gascompositions covering a very wide range of naturallyoccurring petroleum gases and nonhydrocarbon impuritieshas been used to develop two new pseudocritical propertycorrelations for use in calculating z factors. Thesecorrelations may be used with confidence for any naturallyoccumingpetroleum gas with an acid gas content as high as50 percentand ni$rogencontent as high as ten percent.

One proposed correlation, based on gas composition, is amodification of the SBV mixing rules, which does notrequire the use of other correlations for the propertiesof theheptanes plus fraction or the effect of acid gas and nitrogen.This correlation resulted in z factors which fitted the database with an average absolute error of 1.1 percent and amaximumerror of 5.8 percent.

The other proposed correlation,based on gas speci!lcgravityand the amounts of nonhydrocarbon impurities in the gas,also does not require the use of other correlations for theeffect of acid gas and nitrogen. This correlationresulted in zfactors which fitted the data base with an average absoluteemorof 1.3percentand a maximumerror of 7.3 percent.

The presenceof nonhydrocarbonimpurities in a gas must beaccounted for when using a gas specific gravity~orrelation.Errors in z factors as high as 27 percent occurredwhen highconcentrationsof acid gas were ignored.

J = SBV parameter,OR/psiaK = SBV parameter,OR/psiaO’S

= molar mass, lb-moleMC: = molarmass of heptaneplus fraction,lb-mole

P = pressure,psiaPG = aitical pressure,psia

663

4 COMPRESSIBILITYFACTORSFOR NATI

% = pseudocriticalpreSSIW,pSiZPpr = pseudoredwed pressure

= correlationeoeffieierit1 = tempemtum, ‘R

Te = critical temperature, ‘R

Tpc = psemkwrkicaltemwfi !ure, ‘RTW = pseudoreducedtemperature

YC7+ = mole fnwtionof heptaneplus fraction

Yi = mole fractionof the i-th componentz = gas compressibilityfactor

ai = cuftieients of the chelations for J

B, = coefficientsof the correlationsfor K

7* = qwciftc gravityof the gas mixtureE = Wichert and Aziupseudocriticaltemperature

adjustmentparameter, ‘R

We thank Core Laboratories Inc. and S. A. Holditch &Associates,Inc. for providing data.

1.

2.

3.

4.

MeCain, William D., Jr; ThePropertiesofPetroleumFluids,2ndcd., PennWellBooks, Tulsa(1990) 104-22,510-12.Sutton, R. P; “CompressibdityFactors for HighMolecularWeight ReservoirGases,” paper SPE 14265presentedat the SPE AnnualTechnicalMeeting andExhibition,l-as Vegas,Sept. 22-25,1985.Standing,M. B.: VolumetricandPhaseBehavwrof OilFieidH@rocarbonSystems,9thRiming, SocietyofPetroleumengineersof AIME, Dallas(1977)122.Corredor, J.H., Piper, L.D., and McCain, W.D. Jr.:“CompressibilityFactors for NaturallyOceuming

Variable

HydrogenSulfideCarbon DioxideN~trogenMethaneEthanePropaneiso-Butanen-Butaneiso-Pentanen-PentaneHmaneHeptanePlus

MC7+

7c3#+

zT, ‘Tp, psia7*(air= 1)

ALLYOCCURRINGPETROLEUMGASES SPE 2666

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.15.16.

17.

PetroleumGases: paper SPE 24864 presentedat the SPBAnnualTechnicalMeeting and Exhibition, WashingtmD. C., Oct. 4-7,1992.Wiche%E.: “CompressibilityFactor of Sour Natural~7~” MEng Thesis, The Universityof Calgary,Alberta

Metcalfe,R. S. and Raby, W. J.: “PhaseEquilibriafw aRich Gas Condensate-NitrogenSystem,”FluidPhaseEquilibria29 (1986) 563-73.Fimozabadi,A., Hem Y. and Katz,D. L.: “ResewoirDepletionCalculationsfor Gas CondensatesUsingExtendedAnalyses in the Peng-RobmsonEquationofState,”&M. Per.Tech, (Get.,1978)610-15.Coats, K. H. and SmarLG. T.: “Applicationof aRegression-BasedEOS PVT Program to LaboratoryDataSPERE(MZy,1986)277-99.KenyonD.E. and Behie, A.: ““lldrdSPE ComparativeSolutionProjeec Gas Cycling of RetrogradeCondensateResxvoirs: JPT (Aug., 1987)981-97.Whiison,C. H. and Torp, S. B.: “EvaluatingConstantVolumeDepletionData: JPT (Ma@ 1983) 610-620.Moses,P. L.: “EngineeringApplicationsof PhaseBehaviorof Cfude 011and CondensateSystems,”JPT(July, 1986)715-23.Coats, IL H; “Simulationof Gas CondensateReservoirPerformance: paper SPE 10512presentedat the SixthSPE Symposiumon ReservoirSimulation,New Orleans,Jan. 31-Feb.3,1982.Kilgren,K. H..: “PhaseBehaviorof a High-i%essureCondensateReservoirFluid; JPT (Aug, 1966) 1001-’7.Vrla,F.: personalcommunication,May 29,1992.Holditch,S. A,: personal communication,June 7,1993Press, W. H., FJannery,B. P., Teukolsky,S. A. andVetterling,W. T.: NumericalRecipes,1stcd., CambrklgeUniversityPress,New York (1986) 301-7.Corredor, J. H.: “Compressibtity Factors for RetrogradGases: A New Correlation,” MS Thesis, Texas A&lIJniversity,College Station (191).

TABLE 1--RANGE OF DATA

Mean

2.453.381.87

71.158.214.040.901.550.640.880.654,28

135,2

0.779

0.989243.8

3758.60.972

Minimum

0.000.OO0,00

19.372.300.06

i%0.000.00

w

98.0

0.710

0.69878.0

514.00.613

Maximum

51.3767.1615.6894.7318.4012.742,606.042,24

:%14.94

29;.0

0.884

2.099326.0

12814.01.821

684

L. D. PIPER,W. D, MCCASN,JR, ANDJ. H, CORREDOR

TABLE 2-WPDATED COEFFICIENTS FOR EQS. 4

J K

~ standard Pi standardi Error I&or

o 5.2073E-02 8.8370E-03 -3.9741E-01 2.2271E-011 1.0160E@0 2,3018E-02 1,0503E+O0 1.5428E-02

8,6961E-01 2.1985E-02 9.6592E-01 1,6132E-02: 7.2646E-01 4.1292E-02 7.8569E411 4.2227E-024 8.5101E-O1 1.5402E-02 9.8211E-01 1,S134E-02

~2 I 0,981 I 0,979

TABLE 3--ACCURACY OF COMPRESSIBILITY FACTOR CALCULATIONS

Psmdocritlcal Property Correlation

SEYSSBY~ (0.61< ‘ygc 0.99)-628 datapoints@C7,<4% & yH$+y~<5%)AvemgeErru -0.023 -:ol;M@mum Absolute13m3r 0.065AverageAbsoluteError,% 2,508 1:577MaximumAbsoluteError,% 6,668 4,582

~ (0.63c y~< 1,42)-369 datapoints

@c7+<4% & YH2S+Y~>5%)Average13rm -:,;: -0,002MaximumAbsoluteError :04;AverageAbsolute Error,% 1:627Maximurn AbsoluteFaor, % 6.467 6:518

BkkWWMM (0.84 c ‘ygc 1.82)-439 data points(Yc7+Z4% ~ YIi2s+Yco2<5%)AverageBra -:.:;; 0.008MaximumAlmoluteError :05;Awage AbsoluteError,% 2:556MaximumAbsoluteWor, % 7.571 5:816

~ (0.84< Yge 1.82)-167 datapointsti~~+~4% & yn#+yC0225%)AverageErnx -:ol; 0,011MaxirmunAbsoluteEmor 0.057AverageAbsoluteWor, m 1:656 1.689MaximumAbsoluteEmoL,m 5.789 7.719

~m~l~hta points-::;: -0.003

MaximurnAbsoluteEaror 0,067AverageAbsoluteEmor,% 2:230 1.526MaximumAbsoluteError,% 7.5’.. 7.719

665

0.0010.0541.0405.831

-Wlol(/:();

3:647

0,0030,0531,1734,410

0.0010.0481.0693.674

0.001(/.()):

5:831

SmdinL?

-:jloo

1:2935.882

-;:;;

1:2956.356

-0.0340.1623,0709,795

-;.;;;

3:3079.829

-:.:::

1:9909.829

0.0010,0791.3046.371

-:.:;;

1:1636.450

0.009p));

7:856

-:00;

1:7156.786

0.002::;;

7:856

-g.::;

1:1764.386

0.0010.0611.3564.709

-0,0020.0431.2355.350

0.0010.0761.3047.230

o

4

●

COMPRESSIBXLITYFACIXIRSFORNATUW4LLYOCCURRINGPETROLEUMGASES SPE 26668

TABLE 4==PROPOSED GAS SPECIFIC GRAVITY CORRELATION

:

1

5

1.1582E-01-4,582QE-01-9.0348E-01-6.6026E=-017.0729E-01-9.9397E-02

StandardError

7.4SOE-031,3616E-021.5387E-023.9664E-021.3878E-026.055E-03

0,979

3.8216E+O0-6.5340E-02-4,21 13E-01-9.1249E-011.7438E+-01

-3.2191E+O0

Sta&rcd

\:\\,XE-O:

1.0812Ek24,I073E-023.1914E-011.3925E-01

0.975

TABLE 5--ACCURACY OF GAS SPECIFIC GRAVITYCORRELATIONS WHEN IMPURITIES ARE UNKNOWN

I YH*S+ YcO~<$ % I yH2S+ YC02~ 5 %I

Is utton I MS. 6 1 Sutton I ~S. 6i

YC7+<4 %

YC7+24%

1 I 1 1 1—

666

WE 26668 L. D. PIPER, IV. D. MCCAIN, JR AND J. H. CORREDOR 7

2.0-

1.8- i

I1.6- ...... .... ......... ...

kl 1

~ 1.4- ...........*..... ...................+........t

!:

i:!~

1*2 t I...........T..+ .......1

1.0

0.13-.......

0.6

0.6 0.S 1.0 1.2 1.4 1.6 1.8 2.0

Eapsrimcntal z Factor

Fig. I=-Calculated z Factor using Sutton’sModification to SBV Rules

2.0-

1~

!5 1.6-- 1..................................+.....................

gj

N 1.4-......................+........... .......

!

............................................+....

l.o-- .................................... ...

0.8=

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Expcrimentsl z Factor

Fig. 3-.Calculated z Factor using ProposedModification to SBV Rules

........................ ......................... ............ .........i;;

+1+j 1

t

I l!~

+l~i i-..*..I.. 1;.............................................{.........+~+~~+1

?*! : : !,.

+........

t... ...

0:6 0:8 1:0 1:2 1:4 1:6Espcrimsntal z Factor

++:I 1

1

+

@. . . .

0:6 0:8 1:0 1:2 1:4 1:6 :Expcdmental z Factor

Fig. 2--Error ID Calculated z Factor using Sutton’s Fig. 4-.Error in Calculated z Factor using ProposedModification to SBV Ruka Modification to SBV RUISS

●

8 COMPRESSIBIIII’Y FACTGRSFOR NATURALLYOCCURRINGPETROLEUMGASES SPE266S8

P ‘r-l ! I W(’2.0 ................o....o..\...........i..............""....."..““”””””””””i””””””””*;““”’

1la-t ...........i........................L............j............\......+..F ...........i.....i

!%l-l~#i-i’.......................................4..*......... ............!.....Tj 1.2-

81.o-...........

o.s-.......

0.6

0.6 0.8 S.0 1.2 1.4 1.6 1.s 2.0

Experimental z Factor

Fig. S--Calculated z Factor using Sutton’s SpecificGravity Correlation with Impurities Known

.-.....l.....\.....j.....j.....i.....j.....\.....!.....j.....l.....i...~...~...........~

l~i:{;i;1:?!

24’ {~:..... .....+............j............y ...~.................. .....f.....

~1; ~ ;: j..:”+”j

‘“”””""'""\"."""~""""{"".""~".."""i""-"";"""""i""""'!"""4".".';"""[.*"~""'"j"""""!20 !~ I.......................................................................... .............}:: {1::: ;+1:+::@ I j;:..................................................................:.......+.?....y....t.

Ei :::: : i: I!! i:;.....................................’,....;...fl.....~....................... ............16!wi: i!:\ ~*!*: : :

n3

ILL:‘ ‘

\.....~....~..l~ ....l.~ ....y" . ...... ...f ....~...j.$ .. ....*...~

a12i [~.:::;

31...........................................+.............................................[i:+::~;.....1...........+..... ............. ............ ...... ..... ............ ...... ...... ..;

4 ~iil;ilit~+~~: i8 . .... .... . ... .. .. ... ..... ................................. ..... ...... ....+.....

1.... ,. . ....+..... ..\ ......r .....~....J .....j .....f ....t ....\ ..........j ......

4..+F+;f ~Ji ‘i!’;-r.. ..... .......... ...... .................. ...... ............

h

+~l~j::: ::~:.........!..... ...... .... ........... \...................

:+,:~~i i;5,..’..?............1............... ...........“............”.....i

1 I 1 1- 1 [ I B I

0:0 0:1 9:2 0:3 0;4 0:S 0:6 0:7YSM+ Y- + YNJ

Fig. 6--Error in Calculated z Factor using SUttdsSpecific Gravity Correlation with Impurities Unknown

/............ ............................

: !

1 I

II

+

4

............ .......... .

} :4*

++

;;...:! .........,+ I

I+

*1+

r

............ ...........

4+:

i

1.2 3.4 1

(%s Specific Gravity

-

[$

....+..+.iiiI............ ....~i}~~

...........*.....

~!i

--i-1.6 1.S

Fig. 7--Variation of the Inferred Value of J withthe Specific Gravity of the Gas Mixture

26i

24- 1I i I .............l*...........~............................................................,1 ii I h.$k $ i1i I

22-1.............!......................................

~ tj

,4

20- .............I..............!........*4

‘+R&.!...........+....P#)IM..i.. .......... .............!.....q. ........t..~ \.-.;...:.. .-...-.’&””

‘:-q4 ........j. ......$... +.... ““f”””””““’”””;”””’”P~:~i

?.

14. I.::.....+...........................L............. .............~.....i i !

12 ...2...*.4. ..........j.............i.............!L............l.............i.....

i~~1 11

10 I i ? 1i 1

I !

I I

Gs8 Sedtlc Gravity

Fig. 8--Variation of the Inferred Value ofthe SpecMic Gravity of the Gas Mixture

K with

4,,

SPE 2666J L. D. PIPER,W,D,MCCAIN,JR,AND J, H. CORREDOR

I I

I 1 i I I

3oa 3io 4Q0 4s0 Soo 550 t

Inferred Pscudocritlcal Temperature, ‘R

foo

Fig. 9.=Calculated Pseudocritical Temperature usingI%opoeed Specific Gravity Correlation

................. 1/\.........................................!............".."""""~““””””””

fi !

+* :

I.................].........................................*.4...........!.........I

ti~ ;

\ ;+* + \

.................. ............. “ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .tii

+

........... ..j i.

$

I;I!

$-................L..................................................

Soo 600 7tio 800 900

InkrrcdPseodocrMcalPressure, psla

Fig. 10--Ctdcu1ated Pseudocriticai Pressure usingProposed Specific Gravity Correlation

E . . . . . . ..+ . . . . . . . ..+ . . . . . . . . ..j . . . . . . . . . ..{ . . . . . . . . . ..+ . . . . . . . . ...*.....

iyj j ; : ; ~ : I!: I

0.6! j ~: II

I I I 1 I I I I0:6 0:8 1:0 1:2 1:4 1.6 1.8

Experimental z Factor

Fig. n--Calculated z Factor using ProposedGravity Correlation with Impurities Known

2.0

Specific

:-

*; .....&.........&.................i....

0:0 0:1 0:2 0:3 0:4 0:5 0.6 0.7YIW + h: + yNa

Fig, 12--Error in Calculated z Factor using ProposedSpecific Gravity Correlation with Impurities Unknown

.

SPE266i8~ as a ~Unction of Gas Specific Gravity and Amount of Impurities

~iH~:H~:=.,,...................................

o 10 20 0 10 20 0 10 20Mol % H2S Mol % COa Mo1 % A’,

1.1 , :: : ;

1.o-

! o.9-9g:

1!g .z

......f ....... ........}.......i............. :.......

~

-

006 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.S 1.6 1.7 1.8 l.~

Gas Specific Gravity

Burkharcit and Voo equations,

K2‘=to estimate TpcTpC=~dkppC= J & Ppc*

See Piper, McCain, & Corredor, “Compressibility Factors for NaturallyOccurring Petroleum Gases”, SPE 26668, presented at the 1993 WE AnnualTechnical Conference and Exhibition in Houston, Texas, October 345, 1993.

670

,,W

SPE26668K as a Function of Gas Specific G~avity and Amount of Impurities

,;H ,8= ,:M,...........................0 10 20 0 10 20 0 10

Mol % IIJ? Mol % C03 Mo] % Na

26 ii

24

I9

I

&

II

12

0.6 0.7 0.8 0.9 1.0 l-l ~02 l-s 104 I*5 1*6 1*7 108 1*9Gas Spcclfh! Gravity