appraisal of analytical steamflood modeis

7/24/2019 Appraisal of Analytical Steamflood ModeIs

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SPE

SPE 200;3

Appraisal of Analytical Steamflood ModeIs

H-L. Chen, Texas A&M U., and N,D. Sylvester, U. of Akron

SPE Members

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$teamflooding in heavy oil reservoirs is one of the

principal thermal oil recovery methods. This paper evaluates

the existing analytical steamflood models with respect to their

mechanisms and predk ive capabilities and compares them

with field data. The three steamflood models selected were: a

frontal advance model [Jones (1981)], a modified frontal

advance model [Farouq Ali (1982)], and a vertical gravity

override model [Miller and Leung (1985)]. Each model was

somewhat modified to improve its abil ity for the prediction of

production rate and/or history match of typical field

production data.

The Jones steamdrive model, with its empirically

determined scaling factors, was found to give a reasonable

history match of oil production for the Kern River field.

Fields with different characteristics will require an

adjustment of these scaling factors artdlor f ield property data

to achieve an acceptable history match. The modified Farouq

Ali steamdrive model gives a good history match without need

for empirical factors or adjustable parameters. It is thus

recommended for the prediction of steamdrive oil recovery

when fisld production data are unavailable. The Miller-Leung

gravity override steamflood model, which contains two

adjustable parameters, was found to posses the best W3rail

history matching capabili ties and is recommended for this

purpose.

ANDI ITFRATLW.BUUW

The injection of steam into heavy or pressure depleted oil

reservoirs has been a successful enhanced oii recovery

process for more than three dsoedes. A principat application

of the steam injection is steamflooding which is also termed

steam drive or steam displacement. In this process, steam is

continuously injected into

a

number of injection wells, and the

dispiaced fluids are produced from the production wells.

Ideally, the injected steam forms a steam saturation zone

around the vkinity of the injection welL The temperature in

the steam zone is nearly equal to that of the injected steam.

References and figures at end of paper.

Moving away from the injection well, the steam temperature

drops graduaily as the steam expands in response to the

pressure drop and heat losses to base formations. At a certain

distance, the steam condenses and forms a hot-oil bank. In the

steam zone, oil is displaced by the steam. In the hot oil zone

several changes take place which result in oil recovery. They

include heat losses the formation, thermat expansion of the oil,

and reduction of oil viscosity. In addition, residual saturation

may decrease and changm in relative permeability may occur

due to the variations of temperature and saturation.

There are three major options available in literature for

predicting the reservoir response to steamflocding. These

include: empirical correlations 2) , Simple analytical

models(l 13-7),and muit icomponent, multiphase numeri~al

simulators(8-11 ). Empirical correlations can be useful for

correlating data within

field and for predicting performance

of new wells in that or similar fields, However, use of such

correlations for situations much different from the ones that

led to their development can result in large discrepancies for

hist~. ~ matching.

Numerical simulators yield rigorous

solutions to the material and energy balances, However, their

results are sensitiva to the rock and fluid property input data

and other geological information, some of which may be

unattainable. In addition, large computation time is required

and numerical convergence, and stability problems suggest

that thermai simulators are not appropriate for short-cut

design and/or preliminary evaluation for steamflooding

projects. Thus, the incentive to develop simple analytical

models which account for the important mechanisms invotved

and for routine or approximate engineering prediction is

obvious. The existing analytical steamflood models can be

divided into two categories:

1. Frurrta/advance models: The steam-drive mechanism is

2.

modeled as a horizontal frontal displacement [Figure

1(a)]. The steam zone ISassumed to gmw horizontally

and the tendency of the steam to finger beyond the front

is suppressed by condensation.

Verlikal displacemet?t or gravity overz lemodels:

The

problem of gravity overr ide of the steam due to its low

la

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2

APPRAISALOF ANALWICAL STEAMFLOODMODELS

SPE 20023

density assumes that the principal direction of steam

zone propagation is vertically downward [figure

2(b)].

An early frontal advance model was that of Marx and

Langenheim(l 2) who applied an energy balance of a radially

growing steam zone In which one-dimensional conduction heat

losses, uniform steam zone and reservoir temperature were

assumed. Willman el al.(13) presented a model similar to

that of Marx and Langenheims but included the Buckley-

Leverett equation to estimate oil production from a hot water

zone ahead of the steam zone. Mandle and Volek(l $)extended

the concepts of Marx-Langenheim by including convective heat

transfer from the steam zone into the region ahead of the

condensation front at times greater than a cri tical time. The

model was modified by Myhill and Stegemeier(l 5) to calculate

the thermal efficiency after tha cri tical time to account for the

disparity observed in physical models versus theory.

Jones(l) noted that the Myhill and Stegemeier model often

overestimates the oil production, especially in the early phase

of a project because of the assumption that the oil displaced by

the steam zone is immediately produced. Thus, there was no

lag in oil production due to fi ll-up of any gas volume, or due to

the development of an oil bank. Jones(l) thus developed a

modified predictive model including the results of van

Lookeren(l 6) for taking into account the extent of steam

override, and introduced three empirical factors to account for

the dominant mechanisms during the three stages of

production.

Neuman (2S17, and Rhee and Doscher(3) proposed that

the principal direction of steam zone growth is vertically

downward In the horizontal reservoirs. Neumans(17) model

requires the data of relative permeabil ity to oil and water as

functions of temperature. Also, oil production from the

condensate zone was determined semi-empirically. Aydelotte

and Pope(4) used fractional flow theory and overal l energy

and material balances to account for changes in oil cut, gas

production, etc.. Also volumetric sweep eff iciency was taken

into account by using van Lookerens( 16) vertical sweep

efficiency and an empirical correlation given by Farouq

All( 18) for areal sweep efficiency {EA). This model is

restricted to horizontal, homogeneous, isotropic, and

incompressible reservoirs and only five spot sweep

corrections were included.

Doscher and Ghassemi(f 9)

proposed that he steamflood process consists of the heated oil

displaced by a gas drive mecharrism. Their model showed an

insensitivity of oil recovery to formation thickness, especially

during the early stage of production. Their experimental

results indicated that the oil/steam ratio increases with a

decrease of oil viscosity.

Unlike previous models, Vogel(20) proposed that oil

production was not driven by the growing steam zone, but vice

versa, He pointed out the general weakness of predictive

models based on simple energy balances of a growing steam

zone. With a predominantly overriding steam zone, the heat

balance calculations require that the steam produced In

production be accounted for as well as the steam that migrated

out of pattern, Vogel suggested that the total underground heat

requirement was equal to the heat in the steam chest plus the

heat flow upward and downward from the steam chest. He

concluded ;hat oil production must be determined from some

way other than steam zone growth,

Miller and Leung(6)

utilized the concepts of VogeI(20) and Neuman( 17, to

determine tka oil production rate by conductive heating of the

oil below the steam zone.

The purpose of this paper is to evaluate existing analytical

steamflood models with respect to their mechanisms and

predictive features. Three typical steam flooding models were

studied and modified by Chen(21): Jones(l) frontal advanced

model, Farouq Alis(5) modified frontal advance model, and

Miller and Leungs(6) vertical gravity ovarride model.

History-matching of field data were carried out for each model

to test its applicability.

Table 1 summarizes the characteristics and the

parameters for three steamflood models. Complete parameter

sensitivity analyses for each model are available in

Chens(21) dissertation.

The major modifications for each

model are presented in the Appendix section.

Jones(l) applied van Lookerens(l 6, method for the

optimal steam injection rate for a given set of steam and

reservoir parameters, and utilized the Myhill and

Stegemeier(l 5) method to predict oil production. In the

Myhill and Stegemeier model, the average thermal efficiency

of the steam zone was calculated by the Marx and

Langenheim(l 2) solution at early times while the Mandl and

Volek(l 4, method was used to account for heat transfer

through the condensation front after the critical t ime. Jones

model contains a number of empirical factors

(ACD, VODt VPD)

which were obtained through history matching for specific

sets of field production data. Thus, the adjustment of field data

may be necessary (TR, ht,hn ,t.toI) to achieve reasonable

history matching for some projects as shown in Jones Table 1.

In the original Jones model, the steam injection pressure was

calculated assuming a geometric relationship between

pressure and injection rate. The optimum steam injection rate

is taken to be the steam injection rate which gives the

maximum value for the vertical conformance factor (ARD)

Unfortunately, steam Injectivity test data is often not available

in the field.

Therefore, the computer program written to

evaluate the Jones model was modified to allow input of steam

injection rate and pressure, This modification was necessary

to permit comparison of model predictions with actual field

data.

Farouq Atis(5) model is a modif ied fontal advar ]d model

which considers the effect of steam gravity override using van

Lookerens( 16) method. At any instant of time during the

production, the model predicts both oil and water production-

displacement rates, the steam zone volume-thickness, the

heated zone average temperature and the water and oil

saturations. An advantage of the model is that It simulates the

dominant mechanistic features by material and energy

balances and does not employ empirical factors. However, this

produces the modets primary disadvantage in that several

parameters such as Sorst, Sor, Sst

and

Swir are required

which, unfortunately, are normally unknown and need to be

assumed or defaulted by using acceptable values. Also, it has

been shown by Chen(21 ) that the water saturation during

production affects the relative permeabilities and the

production rate, and the model predictions are very sensitive

to the accuracy of the Krw and Kro versus SW* which are

difficult to obtain through experiments. Even though the

experimental difficulties can be overcome, the data may not

represent the actual relative permeability versus saturation

I

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3

H. L. Chen and N. D. Sylvester

SPE 20023

relations due to the effect ot temperature and reservoir

heterogeneity. ,.I .}

relative permeabllities versus saturations

equations presented by Farouq Ali were based on the curves

presented by Gomma(22), These normalized curves were

obtained through history matching of the Kem River field data

reported by Chu and Trimble (23), The prediction of the

original Farouq Ati model for the Kern River A field production

data indicates it to be totally inadequate at long times (>1.5

years). Several important modifications were able to take into

account heat losses [Figure 2(a)] and displacement mechanism

[Figure 2(b)] to improve its deficiencies. These are discussed

in Appendix (b).

Miller and Leung(6) developed a simple gravity override

model which assumed a complete vertical overlaying steam

zone with a steam-condensate zone between the steam zone and

the oil zone below. They used one-dimensional, unsteady state

heat conduction to calculate the temperature distribution

inside the

COIIdWISate

and oil zones, and employed tha

Neuman(l 7) method to determine condensate zone thickness as

a function of fract;on of condensed steam that is produced from

the reservoir (fcp: 0.7-O.95).

They ciaimed that the modei

overrxedicts the oi l twoduction rate for fieid cases with iarge

patterns (> 10 acres)because the steam override may not be

fully developed in those cases. Therefore, another trmPirical

factor, the areal sweep efficiency (EA: 0.4-1,0) presented by

Aydelotte and Pope(4) was introduced for the field cases with

Iar9e

pattern area.

Chen(21) has shown that both values of

fcp and EA have substantial effects on the predicted oil

production rate.

in addition, the heat baiance which

determines the optimum steam injection rate was modified by

Chan(21) to take into account the fact that the steam injection

rate should be based orI cold water fed to a steam generator not

on saturated steam.

The five of fieid projects l isted in Table 2 were chosen for

history matching.

They represent smail [Kern-A(23), Kern-

Canfield(24), and Kern-San Joaquin(24)], medium [Kern-

Ten Pattern], and large pattern areas [Tia Juan].

The field production history data for each fieid case was

adapted from the Enhanced 011Recovery Fiei6 Report (27). A

time ir?crement of 1.2 month was used for the prediction of

Kern River A project, and 1.5 month for Kern-Canfield and

Kern-San Joaquin matches.

The time increment us d in

medals for Kern-Ten Pattern and Tia Juana was chosen ~~be

one month because the production history data was reported

monthly. it is noted that the Kern River A field data was the

oniy used to test the performance prediction for the modif ied

Farouq Alimodel because of the availability of reiati~e

permeability versus saturation relations which are required

by this model. The other four field production histories were

used to compare the predictive performance of the Jones and

Miiler-Leung models.

Figure 3(a) shows, the performance prediction for the

Kern River A field using the modiflad Farouq Ali model. Also

shown are the predictions obtained using the Myhill and

Wegemeier (15) model, the numerical simulation results of

Chu and Trimbie(2~), and the actual field data. Figure 3(b)

compares the calculated cumulative production versus time

results to

the field data. The agreement Is good with a

difference after 5 years of only 5.5% for cumulative oil

production. It is

apparent in

Figure 3(a) that the modified

Farouq All model gives superior predictions to those of

Myhill-Stegemeler and Chu-Trimble.

Figure 4(a) shows that the Jones model predicts a lower

oi l production rate at the beginning and a highar production

rate for the longer times for Kern-Canfieid project. Figure

4(b) shows that aithough the Jones modei underpredicts the

cumulative oi l production, the prediction improves as time

increasp. As shown in Table 3, at the eyf of the 7.5 years, the

Jones modei overestimates the cumulative production by

2.1 EYO.

it

is seen in Figure 4 that the prediction of the

Miiier-Leung model is superior to the Jones model for this

fieN case.

The comparison between the Jones model and Kern-San

Joaqukt f ield is similar to the Kern-Canfield case. That 1s,the

oil production rate is underestimated at short times and

overestimated at long time as shown in Figure 5(a)t while the

prediction of the Miller-Leung model is just the reverse. The

Miller-Leung model with a iag time (z) of 61 days is capable

of predicting the production up to about 1.75 years. The

computer run was terminated after two years bacause the

thickness of the condensate and steam zones became iarger that

the net thickness of the reservoir. Table 3 shows that the

Jones model overestimates the cumulative production by

8.1770 at the end of the third y~ar, and the Miller-Leung

model overestimates the cumulative production by 3.39 % at

the end of the second year.

Figure 6(a) shows that both the Jones and Mii ler-Leung

modeis underestimate the oii production rate for Kern-Teil

Pattern field for the first two years. it also can be observed

from Figure 8(a) that the Milier-Leung prediction is

superior to Jones modei during this time.

Aithough the

predicted production rate of the Miller-Leung model decreases

sharpiy after 5.5 years, the MiIler-Leung model gives a more

accurate cumulative oil production up to about 5 years as

shown in Figure 6(a) and Tabie 3.

Figure 7(a) shows that neither model does weli in

predicting the measured oii production rates for the large

pattern case of the Tia Juana field aithough Figure 7(b) shows

that both models do reasonably well in predicting the

cumulative oil production. It should be noted that the Tia

Juana case is a poor candidate for triatory matching because the

less productive wells were steam stimulated, there were a

large number of unrepaired welis in the pattern, and the two

productive

zones

had oils of different viscosity. This may

explain the observed decline of oil production rate.

The following conclusions can be drawn form the

resuits of the steamflood model modification and evaluation:

1, The Jones modei with input of steam injectivity data

can be used to predict oil production for steamflooding projects

with properties similar to the Kern River field. For other

cases, the empirical factors or input data may require

adjustment to achieve better history-matching.

2. The modified Faro~q Ali model is the most realistic

steamflood modei because it simulates both 011and water phase

dominant mechanisms (such as the combination 6f frontal

advanoa and steam override) by matedal and energy baiances.

In addition, this model gives reasonably good prediction and

history-matching results without requiring any empirical

factors or adjustable parameters.

However, retatlve

permeablilty versus water saturation data is needed for fields

otker than Kern River A to obtain reasonable history-

matching.

101


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4

APWWSAL OF A?lALvrloAl STEAMFLOODMODELS

SPE 20023

3. For history-matchingof field data, the modified Miller

and Leung model is better than the Jones model. Careful

adjustment of the parameters fcp and EA yields accurate

history-matching.

4. Use of the modif ied Farouq All model is recommended

for predicting steamflood production when field production

history is not available. The Miller and Leung model is

recommended for trtstory matching of steamflood performance.

%4)

= dimensionless steam zone size

API

c1

q,

&

fc p

fsdh

hfs

= specific gravity of oi l at 60 F, dimensionless

= specif ic heat of phase i, Btu/lbm-F

= areal sweep efficiency

x vertical sweep efficiency

= tondensed steam produced, fraction

= cownhole steam quality, fraction

= enthalpy of saturated steam at steam temperature,

Btu/lbm

hn

= net zone tl~ickness,ff

hs = steam zone thickness, ft

ht

-

grosszonethickness, ft

ist

= steam injection rate, cold water equivalent BWp O

Kh = thermal oonductfvity of cap rock and base rock,

Kro

Krw

Lvdh

b

%

N

N

P

%

qoi

qw

Btu/ft-hr-F

x relative permeabil ity to oi l, fraction

= relative permeability to water, fraction

= latent heat of steam, Btu/lb

= heat capacity of cap rock and base rock, Btu/ft3-F

9

heat capacity of steam zone, Btu/ft3-F

= oil originally in place, bbl

= cumulated oil displacement, bbl

= cumulative oil production, bbl

= oil productionrate, BOpD

= pre-steamoil productionrate, BOPD

= water production rate, BWPD

6

= heat Injection rate, Btu/hr

QI

- heat bsses to cap rock andsteam zone, Btu

G>

= oil displacement rate,BOpD

Qw

= waterdisplacementrate, BWPD

so

= oil saturation, fraction

%c

= condensate zone oil saturation, fraction

Soi =

initial oil saturation, fraction

Sor

= residual oil saturation, fraction

Scrst = steamflood residual oil saturation, fraction

%s

= steam zone oil saturation, fraction

Sq =

steam saturation in the steam zone, fraction

SW

=water saturation, fraction

s~

- (~-swir) (-Swir-Sorw). dimensionless

Sw/r

= irreducible water saturation, fraction

t

= time, hr

tc

= critical time, hr

c D

= dimensionless critical time

At

- t ime increment, hr

tB T

= steam breakthrough time, hr

T1,2 =

temperature at condit ions 1 and 2, F

Ts

= steam temperature, F

TR

= initial formation temperature, F

v~

= bulk volume of the pattern, ft3

B

= VB -s(rr+l), fti

oD

= dimensionless displaced oil prtiucad

vpD

=

Initial pore void fil led with steam as water,

dimensionless

Vs(t) = steam zone volume at time t, f@

VsBT = steam zone volume at breakthrough, ft3

a

= reservoir thermal diffusivity, ft2/day

@

= porosity, dimensionless

z = constant (=3.14159)

P

= density of phase i, lbm/ft3

s = lag time, days

v

= viscosity , cp

Voi

= oil viscosity at ini tkd reservoir condition, cp

(n)

= at time step n, dimensionless

avg = average temperature condition

sdh

= steam at downhole condition

o = oil phase

s

= steam phase

R

= rock phase

w

= water phase

1. Jones, J.:

Steam Drive Model for Hand-Held

~~~~~;able Calculators, J. Pet. Tech. (Sept. 1981)

.,

2.

Neurnan, C.H, A Mathematical Mo ,el of Steam Drive

Process-Application; paper SPE 47.,7, presented at the

California Regional Meeting of the SPE, Ventura,April 2-

4, 1975.

3. Rhee, S.W., Doscher, T.M.: A Method for Predicting 011

Recovery hy Steamflooding Including the Effects of

Dlstillatkm and Gravity Overrlde~ Sot.

Pet. Eng. J Aug.

1980) 249-66.

mm


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H. L. Chen and N. D. Syfvester SPE 20023

4,

5.

6.

7.

8.

9.

10.

lf.

12.

13,

Aydelotte, S.R, and Pope, G.A.: A Simplified Predictive

Model for Steamdrive Performance: J. Pet. Tech. (May

1983) 991-1002.

Farouq All , S.M.: Steam Injection Theories - A Unified

Approacht paper SF2 10746, presented at California

Regional Meeting of the SPE, San Francisco, March 24-

26, 1982.

Miller, M.A. and Leung, W.K.: A Simple Gravity Override

Model of Steamdrive paper SPE 14241, presented at the

60th Annual Technkal Conference and Exhibition of the

Society of Petroleum Engineers held in Las Vagas, Sept.

22-25, 1985.

Wingard, J.S. and Orr, F.M. Jr.: An Analytical Solution

for Steam/Oil/Water Displacement; paper SPE 19667,

presented at the 64th Annual Technical Conference in San

Antonio, TX, Oct. 8-11, 1989.

Coats, K.H., George W.D., Chu, C. and Marcum, B.E.:

Three-Dimensional Simulation of Steamflooding: Sot.

Pet. Eng. J. (Dec. 1974), 573-92.

Crookston, R.B., Culham, W.E., anfi Chen, W.H.: A

Numerical Simulation Model For Thermal Recovery

processes,- Sot. Pet. Eng. J. (1979) 19, 37s58.

Vinsome, P.K.W., and Westeweld, J.: *A Simple Method

for Predicting Cap and Base Rock Heat Losses in Thermal

Reservoir Simulators,

J. Can, ~e?. Tech.,

19,

No. 3

(1980) 87-90.

Barry, R.: A General Thermal Model: paper SPE 11713,

presented at the California Regional Meeting in Ventura,

March 23-25, 1983.

Marx, J.W. and Langenheim, R.H.: Resewoir Heating by

Hot Fluid Injections Trans., AlME (1959) 216, 312-

15.

Willman, B.T., Vallerory, V.V, Runberg, G.W. Cornelius.

A.J., and Powers, L~W.:

Laboratory Studies of Oil

Recovery by Steam Injection; J. Pet. Tech. (July 1961j

681-90.

14. Mandl, G. and Volek. C.W.: Heat and Mass Transport In

Steam-Drive Processes, Sot. Pet. Eng. J. (March 1969)

46, 59-79; Trans., AIME.

15. Myhlll, N.A. and Stegemeier, G. A.: Steam-Drive

Correlation and Prediction, J, Pet. Tech. (Feb.

1978)173-182.

16. van Lookeren, J.: Calculation Methods for Linear and

Radial Steam Flow in Oil Resewolr; paper SPE 6788

presented at the 52th Technical Conference and

Exhibit ion, Denver, Colo. Oct. 9-12, 1977.

17. Neurmn, C.H,: A Gravity Override Model of Steamdrive,

J,. F . Tech.

(Jan. 1985) 163-6%

18. Farouq All, S.M.: Graphical determination of 011Recovery

in a Five-Spot Steamflood paper SPE 2900, presented at

the Rocky Mountain Regional Meeting of SPE, Casper, WY.,

June 8-9, 1970.

19. Doscher, T.M, and Gh&ssemi, F.: The Influence of Oil

Viscosity and Thickness on the Steam Drive; J. Pet. Tech.

(Feb. 19S3) 291-98.

20, Vogel, J.V.:

Simplified Heat Calculations for

Steamflood, J. Pet, Tech (July 1984) 1127-35.

21. Chen, H.-L.: Analytical Modeling of Thermal Oil Recovety

by Steam Simulation and Steamflooding,- Ph.D.

Dissertation, The University of Tulsa, Tulsa, Oklahoma

(1987),

22. Gomma, E.E,: Correlation for Predicting Oil RecoveV by

Steamflood; J.

Pet. Tech.

(Feb. 1980) 325-32.

23. Chu, C. and Trimble, A.E.: Numerical Simulation of Steam

Displacement-Field Performance Applications, J. Pet.

Tech. (June 1975) 765-76.

24. Greaser- G.R. and Shore. R.A.: Steamffocd Performance in

25.

26.

27.

28.

----., ... .

the Kern River Field, paper SPE 8834, presented at the

1s Joint SPE/DOE Symposium on Enhanced Oil Recovery,

Tulsa, OK, April 20-23, 1980.

Oglesby, K.D., Belvins, T.R., Rogers.E.% and Johnson*

W.M.: Status of the Ten-Pattern Steamflood Kern River

Field, California J. Pet. Tech. Oct.1982 2251-57.

de Harm, H.J. and van Lookeren: Early Results of the

First Large-Scale Steam Soak Project in the Tia Juana

Field, West Venezuela J. Pet Tech. (Jan. 1969) 101-

10.

Enhanced 011 Recovery Field Report, 11, 2, Society of

Petroleum Engineers (1986).

Somerton, W.H., Keese, J.A., and Chu, S.L.: Thermal

Behavior of Unconsolidated Oil Sandst Sm. Pet. Eng. J.

(oct. 1974) 513-21.

29. Leung, W.K.: A Simple Gravity Override Predictive

Model, M.S. Thesis, The University of Texas, Austin

(1986)

APpFNW

The changes made to the Jones model permit direct input

of steam injection rate and pressure, and dimensionless

volume of displaced oil produced as:

NPSoi

VO 3= [-~(~oi.sor)l

1

where Np is used insiead of Nd in the original Jones paper(l)

[Eq(A-25)] since VODIs a function of the amount of displaced

oil which equals the total amount of mobile oil less the

cumulative oil production.

Several modif ications have been made to the Farouq Ali

model to improve its predictive capability.

I Tim

The critical time calculation recommended by Mand19and

Volek(14) was used :

t.= [ -xqtcD

4 Kh MA

(2)

I


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..

7 H. L. Chen and N. D. Syfvester

SPE 20023

In Figure 2(b), the solid line indicates the extent of

displacement by steam, The displaced volume Is the volume

~

between the dashed and sol id lines. The material baiance for

the displacement element is given below.

The only modification made for the Miller-Leung model

is m the calculation of optimum steam injection rate whkh

The oil displacement rate, ~o, is given by:

was originally presented by Leung (29) as:

Qi

Q.= Av~ S~)-SOr t)

(19)

ist=

(27)

5.6146 PWLvdhAt

The water displacement rate, Qw, is given by: To account for the fact that the sleam injection rate should be

based on cold water fed to a steam generator,

Eq (27) becomes

C)w = AVS@[St)- l -Sst -S.rst)]

is t-

Qi

(28)

= AVS$(S$)- 1+Sst -+Sor$t)

20)

5.6146 p~[hfs+fsdhLvdh-& (TR-32)]

Then, the overail material balance on oil-water zone between

where the amount of heat injected, Q i is calculated by

t(n) and t(n+f ) is as follows:

Vogel(20) as:

For oil :

Qj=4K~A(Ts-TR)@+ AhsMs(Ts-TR) (29 )

Qo - qoAt =

[VB-VY)]I$[S$+)- S$)] (21 )

Assume that VB - @+)= v;, then

for wate~

Qw -

qwAt =

V:@[s$+ )- s ?] .

= V:o[(l -s +)- Sg)-(1-swsg)]

= v@@lw+)]

(22)

From Eqs (21) and (22) we have

*=

W&[sy+wq

(23)

w

Qw-v@o

(n)- - s +l ) l

From the fractional f iow eqution, we can write

fw=~=~

(24)

qo+q~

1+Kro~w

Krwpo

Let,

qo Kro~w c

= . .

(25)

qw K~oVo

(n+ )

Substituting Eq (25) into (23) and solving for So

gives

Sy (1+C)+

Qo-CQw

Sy+l) =

t$v;

(26)

1+C

-..

111


8/12

Wb ~qp~g~

Me

1

Summary of Steamflooding Models

Jones (1981)

Farouq Ali (1982)

Miller and Leung (1985)

rype

of the Modal

FrontalAdvanoe

Modified Frontal Advance

Vertbal Advanoe Gravity Override

Cftaracteristios

1. Predkts ~,~, Ehs,and

Fos.

1,

Prediits

~,~,qw,So,~, and

1. Pradiote~ and ist.

andTaW

2. Adjustment of fW SW,%s. ~,ad

2. Empirkal coefficientssuchas

2. Requires defaulted values for

and EAv lu s

maybe

nacaasaryor

AcDtVOD, Vpo areused.Data

Sorst,Sor,%irl ad %t.

for reasonablehistory-rnafohiftg.

suchas TR,hn,~i mayneed

3. Km, Kmvs.&data needed

3. Tuningof f ield data for history=

to be adjustedto obtaingood

when a ffefd0sss other than

matching is notnecessary.

history matching for some

Kern Riier-A field is evaluated.

field cases.

Tuningof hn may needed for

reasonable history-matching.

Comparison d

Underpradots ~ at short t imes

Was notevaluated for field cases Setter pradktbn than Jones model

Predictive Ability

and

over-shoots

he measured

other than Kern River-A project.

especially for large ~atterrt area fieftf

values at bnger time for large

cases (see Tabte 3).

., pattern area oases.

[see Figures 6(a) and 7(a)]

Sensitive

isto Soit sdh

ist~sdh$orst

fcP EA, ~i, hi, S~, ~c

Parameters

lBbles Z

Data Used

for History Matching

Field T~ TR

kaI(TI ) WOI(T2) ~01

qoi

f~dh API Soi ht hn

(:F) (~) [cp(F)j [GP(F)] (CP) (BOPD)

(ft) (ft)

Kern River A

380 95 1380(100) 47(200)

1380 25 0.7 15 0.5 75 9rJ

iChu.Trlmble(23)]

Kern-Canfield

300

100 1700(100) 10[230)

f700 15 0.7

13.5 0.51 125 80

iQreaaar-Shoro(24)]

Kern.SanJoaquin

300 90 1000(100) 10(250) 1000 10

0.75 14.5 0.52 33 29

iGraaaar-Shoro(24)]

Kern-1O Pattern

400 SO 2710(85) 4(350)

2710 230 0.7 14

0.50 97 97

iO@aabyet 4J2S)]

(acres)

(BWPD) {tt2/D) (BTU/tt3

2.5

2.7

2.7

60.7

137

0.345

225

0.31

300

0.2s 300

0.33

6000

0.33

5s000

0.96

1.097

1.097

0.870

0.9s

35.0

3s.4

38.4

35.7

35,0

laJuana

400 113 27S0(1 13) S{350)

2780 1S40 0.6 15 0.71 250 200

[da Haan6

m Lookardq

-112


9/12

Fmb$aNp

m

Kem.Canfield

132677

(7.5)

Kern.San

28928(2.0)

Joaquln

37507(3.0)

Kern-Ten 334346a

Pauorn

(6.0)

TiaJuana

10414373

(5.5)

Comparisonof \hs History Match Roaultafor

Ulllmato Cumulative 011 Production

%%

NP %

udU@@Qcs

Lkl?lsl~

124053 -6.50

136531

2.t5

(7.5)

(7. s)

42912

1s.21

40571

8.17

(3.0)

(3.0)

3131158

-9.35

3572606

6.84

(6.0)

(6.0)

110800s4

6.39

---- ----

(5.5)

Np

136198

(7.5)

30943

(2.0)

3313459

(6.0)

10073073

(5.5)

%

2.65

3.39

-0.90

.3.28

1. Thenumbernaldaheparentfwalsrdkatestheuitimateoilpmdwtbnyearby thefielddataorpredkfivemdal.

2. % difference [(Np,model.

NpMd)1fJP.f~~x1~

Heat condid lon to cap

rock

4

Stec.rn ZO= 011zone

+

+

Heatcanductlon ta base rack

(a) Frontal AdVCWICedDisplacement

Heat ccmductkrn to caD rack

Steam zone

4

Haofnowto

undeftyfngzone

Condenwte

011zone

= 20023

----- -- --

1-T*

ASEOCK

(a) Heai Losses

x

,a

n

--

,/

R,H

0 0:

*71W

,+

INITIAL (1)

%.$:

SW*8W

fkal

(1+1

so swat

$WI-seidor.t

(b) Dlsplaoement Meohanism

Figure 2. Control Volumo for

Energy

end Material Eralencee

(b) Vertical or Gravity Overrtde Dtsptacement

(Modified Farouq Ali Model]

Note: ~ k the dkectlon of heat transfer

~ k thedkecflonofsteam@owth

Ffguro1. lhe Mechonf$rnof St-m Displocemonf


10/12

1- 1

I

I

I

I

I

t

Otn

I

S V

Tk[YCARM

(a) oil Production Ratevs. Time(At= 0.1 year)

(b) Cumulat ive Oil Productionve. Time (At.= 0.1 year)

Figure 3, History Match of Kern River - A

Data

I

.a

TIK

IWRIr

(a) Oil Production Rate vs. Time (At -0.125 year)

d

m

I .m

m.m

. . .

S.n

.

Tna

w

(b) Cumulat ive Oil Production vs. Time (At = 0.125 year)

B

FigUre

4. HietorY Matoh ot Kern - Cenfed at a

m


11/12

*E 20023

d

1

i

1

:euklo mr-w~

rmlmalws -

d,

,4aKerlaa

I

I.*

1.40

mm

.40

a

aw

1.40

TM -

(a) 011

Production Rate vs. Time (At -0.125 year)

(b) Cumulative 011 Production vs. Time (At -0.125 year)

Figure 5. History

Matoh of Karn - San Joaquin

Data

am

.

b

-s

4rn .

/

,$

r :

*

Ira

:Mr4 .

9

~om .

I

/

iia.

s

F:a.m W O PA-

ml lm nM s

,maammm.

l.a

9.41

4.*

s.o

4.U

Tin? m

(a) Oil Product ion Rate vs. Time (At -1 Month)

+

i d .

a

Ii :

Xsl,m Wm4-lo Mm

i

. ~*-

i

4QEa -

*4

n.m

S.U

4.n

s.n

- .m

.a

1.48

11= -

b) Cumulat ive 011Production vs. Time (At -1 Month)

Figure 6. History Match of Kern . Ten Pattern Data


12/12

sPE

20029

3

h=88

S417

-t

=~

8-

-L

8

8

8

8

F - TIA _

m87

/

,

Mw.utuwss

.

SOW

, J@ES

@

TIME (YSAM)

(a) Oil Production Rate vs. Time (At = 1 Month)

L

_ FIEIG 71A JWJU

.

WSF1-mMs -

8 , J- MOOSL

TX= -

(b) Cumulative Oil Production vs. Time (At = 1 Month)

Figure 7. History

Match of Tia Juana

Data

116

appraisal of analytical steamflood modeis

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