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Correlations for Predicting Oil Recoveryby SteamfloodEzzat E. Gomaa, SPE-AIME, Stan dard Oil Co. of California

IntroductionHeavy-oil properties that classify as candidates forsteam flooding often need to be screened for priorityranking due to budget, manpower, development, andpermitting limitations. Also, sensitivity studies oftenare run on steam flood projects to determine theeffects of various operating strategies on projectperformance and economic feasibility. Steam floodperformance predictions required in such screeningand sensitivity studies certainly can be made usingone or more of the analytical and empirical modelsavailable in the literature. I-4 Numerical reservoirmodels that simulate the process of steamflooding 5-9also can be used to make the required predictions.While these analytical and/or numerical modelscould suffice, they generally require somewhatlengthy computations and necessitate the use of acomputer.There is a need for a simplified easy-to-use methodfor predicting steam flood performance. This paperdescribes the development of such a method and itsbasis, procedures, and limitations of applicability.Basic Concept and AssumptionsThe basic concept of the method is to define theminimum set of parameters that have the most influence on steam flood oil recovery and are easy to

01492136180100026169$00.25 1980Society of Petroleum Engineers of AIME

determine for any given project. Oil recovery then isdetermined as a function of these parameters usingfield data and/or numerical simulation. Generalizedcorrelations or charts are prepared from these resultsand used for prediction purposes.In a steam flood, oil recovery should be dependenton (1) rock properties such as permeability, porosity,compressibility, relative permeability, capillarypressure, and net/gross ratio; (2) fluid propertiessuch as specific gravity, viscosity, compressibility,and PVT relationships; (3) flood geometry such aspattern shape, spacing, and sand thickness; (4)thermal properties such as thermal conductivity, heatcapacity, and thermal expansion; (5) reservoirconditions such as initial oil saturation, temperature,pressure, and residual oil saturation after steamflood; and (6) injection conditions such as rate,pressure, and steam quality.Because most steamflood applications are focusedon shallow heavy-oil-bearing sands, typical unconsolidated sand characteristics were used in thiswork. This meant that parameters such as absolutepermeability, capillary pressure, compressibility,thermal properties, and fluid properties were notconsidered as variables in the development of thesecorrelations. Instead, these parameters were fixed atacceptable typical values.In most projects, reservoir temperature andpressure prior to steam flooding generally are low.Low temperature is because of the shallow depths

Reservoir simulation was used to develop a set of correlation charts for predictingsteamflood oil recovery and oil/steam ratio as functions of reservoir characteristicsand operating conditions. The correlations emphasize the effects of steam quality,mobile oil saturation, reservoir thickness, and net/gross ratio.FEBRUARY 1980 325

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IINJECTOR

2 3 4

J

2

35

PROOUCER

Fig. 1 - Simulation grid for oneeighth of fivespot pattern.

involved in such projects, and low pressure primarilyis a result of reservoir depletion that takes placeduring primary and/or stimulated production priorto steamflooding. With low initial reservoir temperature and pressure, any variations in their valuesfrom one area to another would be insignificantcompared with injected steam temperatures andpressures. Therefore, typical values also could beassumed and kept unchanged for those twoparameters.The relative permeability for heavy-oil sands andtheir variation with temperature probably are themost difficult to measure or predict among theparameters mentioned above. Even whenmeasurements are available from a few core samples,they may not be representative of the whole reservoir. Thus, considerable uncertainty almost alwaysexists in any set of relative permeability values usedin a study. Therefore, it was considered practical inthis work to use a set of curves typical of unconsolidated heavy-oil sands. Normalizing thesaturation axes of such curves would allow the use ofdifferent residual oil saturations.Fixing the above parameters at their typical valuesreduced the independent parameters that influenceoil recovery to porosity, net/gross ratio, reservoirthickness, initial oil saturation, residual oilsaturation after steamflood, pattern shape, spacing,injection rate, and steam quality. Coats et al.'sBnumerical steam flood simulator then was used in a

TABLE 1 - ROCK AND FLUID PROPERTIESHorizontal permeability, mdVertical permeability, mdSolution gasTank oil gravity, APIFormation compressibility, psi -1Water compressibility, psi- 1Oil compressibility, psi- 1Specific heat of rock, Btulcu ttoFSpecific heat of oil, BtullbmoFSpecific heat of overburden, Btulcu ftoFSpecific heat of underburden, Btulcu ttoFThermal conductivity of formation,

Btu/tt day FThermal conductivity of overburden,Btulft day FThermal conductivity of underburden,Btulft day F

Thermal expansion coeffic ient of oil,F- 1326

1,900950o140.000080.00000310.000005350.48547.047.043.017.017.00.00041

Vr /

IINJECTOR

/~/

3 4

\ \ \1\ 4~PROOUCER

Fig. 2 - Simulation grid for onetwelfth of sevenspotpattern.

sensitivity study to determine the effect of each ofthese parameters on oil recovery and to supply theresults necessary for developing the correlations.Simulation DataTwo simulation grids were used. A 5 x 3 gridrepresented one-eighth of a five-spot pattern (Fig. 1)and a 5 x 4 grid represented one-twelfth of a sevenspot pattern (Fig. 2). These grids were consideredadequate for this study because the interest is inoverall project performance rather than individualwells. Four reservoir layers were used with each gridand were found to be adequate for representing thegravity override effects.As mentioned earlier, several reservoir rock andfluid properties were fixed at their typical valuesthroughout the present study. Table 1 shows asummary of the assumed values. Table 2 shows theviscosities of oil, water, and steam as functions oftemperature.A typical set of oil/water and gas/oil relativepermeability curves was obtained through historymatching of an actual Kern River field steamflood byChu and Trimble. 1O This set of curves was used inthis study after normalizing their saturation axes tovary the residual oil saturation. The normalizedcurves for the oil/water and gas/oil systems areshown in Figs. 3 and 4, respectively.A reservoir temperature of 90F and reservoirpressure of 60 psi a were assumed prior to steam

TABLE 2 - VISCOSITY AND TEMPERATURE DATATemperaturerF )

75100150200250300350500

Oil4200.01100.0130.033.012.56.43.81.6

Viscosity (cp)Water0.9200.6810.4350.3050.2350.1870.1560.118

Steam0.00950.01020.01140.01270.01380.01490.01580.0174

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k row

1.0

0. 8

0. 6

0. 4

0.2

o o 0.2

~ \\ \ II\k row I

\1*rw ------K0. 4 0. 6 O.B

0.04

krw0.02

o1.0

Fig. 3 - Normalized oil/water relative permeabilitycurves.

injection. Injected steam pressure at the sand-facewas fixed at 200 psia. Producing wells were assumedto be skin free and pumped off to a 40-psia bottomhole pressure at all times.Analysis of Simulation ResultsEffect of Various Parameters on Oil RecoveryThe effect of each parameter on oil recovery wasinvestigated by varying its value over a reasonablerange while fixing others at their typical values. Ingeneral, the observed qualitative effects were inagreement with conclusions made by previous investigators. However, this analysis was extended toquantify these effects and to develop a method topredict oil recovery. The results are summarized asfollows.Porosity. High-porosity reservoirs produced more oil

100 I I IINJECTION RATE = 1.7 B/O/Acr. Ft.

80 - STEAM QUALITY = 0.6RESERVOIR THICKNESS =100 Ft.MOBILE OIL SATURATION =0.42 ~ ~

/ - ~f ,- POROSITY-0.21 r--III --- 0.35

.--?- Io 2 3 4 6TIME, YEARS

Fig. 5 - Effect of porosity on steamflood oil recovery.

FEBRUARY 1980

1.0 r-----,----,-----,----,----,

0 . 8 r - - - - + - - - + - - - ~ - - - ~ - - ~

0 . 6 r - - - - + - - - - + - - - ~ - - - ~ - ~ ~krog8kr g

0 . 4 r - - ~ - + - - - + _ - - _ 1 - - - ~ - - _ _ 1

0 . 2 r - - - - + - - ~ ~ - - ~ ~ - - ~ - - _ _ 1

0.4 0.6SL - Sw.i- - Sorqf - Sw.i- - Sorg

0.8 1.0

Fig. 4 - Normalized gas/oil relative permeability curves.

per barrel of steam injected than low-porosityreservoirs due to the larger fraction of heat used inthe latter for heating solid rock. But on a fractionalrecovery basis, the effect of porosity becomes insignificant as long as the steam injection rate per unitof reservoir volume is fixed (Fig. 5).Reservoir Thickness. Fig. 6 shows the effect ofreservoir thickness on oil recovery for a fixed steaminjection rate per unit of reservoir volume. Thethicker the reservoir, the higher the recovery at anygiven time. This is basically because the heat lossfrom thin reservoirs to overlying and underlyingstrata is more significant relative to the total heatinput. Therefore, it was determined that the net heatinjected would give a better correlation. Net heatinjected equals the total enthalpy of the injectedsteam less the heat lost to overlying and underlying

100,- - - , - - - - , - - - - , - - - - , - - - - , - - - . - - .

INJECTION RATE =1.7 B/O/Acr. FtSTEAM QUALITY = 0. 680 MOBILE OIL SATURATION = 0.42

I RESERVOIR-+--- -+ THICKNESS,FI,__ 30 0,_---,100

6 0 r - - - r - - ~ . - - ~ - ~ ~ ~ ~ ~ - - ~ 4 0

0 0 L - ~ ~ ~ ~ ~ 2 = = = = ~ 3 - - ~ 4 - - - J 5 - - - J 6 ~TIME, YEARS

Fig. 6 - Effect of reservoir thickness on steamflood oilrecovery.

327

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100 I I IINJECTION RATE = 1.7 B/D/Acr. Ft.STEAM QUAU TV = 0. 6

80 _ MOBilE Oi l SATURATION = 0.42

oo

XX0xO0

.,.

.410I AX RESERVOIRo THICKNESS,Ft.X 30 0AJL 0 -i a - A 20 10A."oX

200 400 600 80 0 1000 1200NET HEAT INJECTED MMBfu./Acre FI.

Fig. 7 - Effect of reservoir thickness on steamflood oilrecovery.

100 I I IINJECTION RATE: 1.7 B/D/Gro Acr.Ft.STEAM QUALITY = 0. 6

80 f- MOBilE OIL SATURATION = 0 .42

I ---- ~/ / // -/ ""V// GROSS THICK. NET/GROSS/ / FI. RATIO} / I

- 10 0 0. 6 -- -- 60 1. 0~ / I I I Io o 4 6

TIME, YEARSFig. 8 - Effect of net/gross ratio on steamflood oilrecovery.

1 0 0 r - - - - - r - - - - . - - - - - , - - - - ~ - - - - _ , - - - - _ , _ .

328

INJECTION RATE = I. 5 B/D/Acr. Ft.RESERVOIR THICKNESS = 70 Ft.MOBilE OIL SATURATION 0.42

oO ~ ~ ~ ~ _ _ _ _ _ _ _ _ _ __L_____L____ ~o 2 3 4 5 6

TIME, YEARS

Fig. 9 - Effect of steam quality on oil recovery.

strata. When oil recovery was plotted vs net heatinjected per unit of reservoir volume (Fig. 7), allcurves became nearly identical.Net/Gross Ratio. A reservoir may contain somediscontinuous shale streaks so that its net productivethickness is less than the gross interval withoutdiminishing vertical communication. This situationwas modeled by using effective porosity and permeability equal to the product of net/gross ratio andthe sand porosity and permeability, respectively. Thereservoir thickness then was taken as the gross interval. The oil recovery of this case was comparedwith that of a clean sand with a thickness equal to thenet productive interval. Fig. 8 shows this comparison, which indicates that for a fixed injectionrate per unit of gross reservoir volume, the shaly sandapparently has a slightly better recovery. This wasmostly the result of lower heat loss to overlying andunderlying strata from the shaly reservoir because ofits greater thickness. When the fractional oil recoveryof the two cases was plotted vs net heat injected, asdiscussed before, the differences disappeared. Thissuggested that in steam flooding shaly sands, theinjection rate should be based on gross interval andthe oil production on net interval. As a result, theshaly sands would require higher steam/oil ratiosthan clean sands.Mobile Oil Saturation. In this work, mobile oilsaturation was defined as

Sam = So;-Sors , ............. " ...... (1)where Sam = initial mobile oil saturation, So;initial oil saturation prior to steamflood, and Sors =residual oil saturation after steamflood.It was found that steamflood oil recovery (expressed as fraction of mobile oil in place) correlatesvery well with Sam' An increase in the value of Samcauses an increase in both ultimate recovery and rateof recovery.Pattern Shape, Spacing, and Injection Rate. Asmentioned earlier, two pattern shapes were modeledin this work: five-spot and seven-spot. I t was foundthat neither pattern shape nor spacing influenced theoil recovery curve as long as the injection rate perunit of reservoir volume was fixed. The result alsowas conditional upon the absence of any limitationon well productivity in the simulator. Therefore, thebasic difference between the five- and seven-spotpatterns - producer-to-injector ratio - becomesmeaningless. In actual field projects, wherelimitations on well productivity could exist,preference may be given to patterns with higherproducer-to-injector ratios. Caution, however,should be exercised when considering a pattern withnonuniform locations of producers with respect tothe injectors - e.g., the nine-spot. This may causeearlier steam breakthrough, lower sweep efficiency,and, perhaps, a loss in ultimate oil recovery.

I t was found that the steam injection rate is bestexpressed per unit of reservoir volume, whicheliminates the effect of several geometricalJOURNAL OF PETROLEUM TECHNOLOGY

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parameters. However, even in this form the injectionrate was found to have a slight effect on oil recovery.This effect was not considered in this work.Steam Quality. Fig. 9 shows the effect of injectedsteam quality on oil recovery at a fixed injection rate.As would be expected, higher steam quality resultedin higher and faster oil recovery. However, when thedata were converted to a net heat injected basis, thedifferences did not disappear (Fig. 10). In otherwords, at any fixed value for the net heat injected,the oil recovery was dependent on steam quality. AsFig. 10 indicates, the effect of quality is somewhatcomplex. Oil recovery increased with quality up to apoint and then decreased, indicating an optimumsteam quality in the range of 40070. This is believed tobe caused by at least two factors: (1) the combinedeffects of steam volume and viscosity and (2) vaporoverride and liquid underrunning in the reservoir.High-quality steam has larger volume but lowerviscosity than low-quality steam; thus, countereffectscould occur and result in an optimum quality range.The effect of vapor override and liquid underrunningis illustrated in Fig. 11, which shows the influence ofsteam quality on various displacement parameters.The displaced oil bank (zone of So ~ Soi) and thetemperature front reach the producing wellbore mostuniformly for the 40% injected steam quality. Thisallows optimum utilization of the heat and minimizesbypassing regions of high oil saturation. For steamqualities higher or lower than 40%, nonuniformity ofdisplacement and bypassing regions of high oilsaturation do occur. The vapor saturation profilesshown in Fig. 11 indicate earlier breakthrough for thehigher injected steam qualities. This, of course, willresult in premature higher heat losses to bothoverburden strata and producing wells. Similarly, thelower injected steam qualities will give rise to earlierhot-water breakthrough at the bottom of thereservoir and bypassing of oil at the top.Heat Utilization FactorIt is clear that steam quality has a pronounced effecton steamflood oil recovery. Besides being a necessaryfactor in determining the total heat injected, thequality also has an effect on displacement characteristics. To quantify the latter effect, the quantity"effective heat injected" is introduced and definedas the fraction of the net heat injected that is utilizedeffectively in the reservoir. In other words, it is theminimum required net heat to achieve a given oilrecovery. The ratio between the effective heat injected and net heat injected is defined as the "heatutilization factor":

Qe = YQinj' ......................... (2)where Qe = effective heat injected (MMBtu/acreft), Qinj = net heat injected (MMBtu/acre-ft), and Y= heat utilization factor.The heat utilization factor could be viewed as ameasure of how efficiently the wet steam heats anddisplaces oil in the reservoir. In other words, itrepresents some sort of an overall sweep efficiencyand accounts, at least in part, for the heat lost withFEBRUARY 1980

the produced fluids, especially after breakthrough.From the data in Fig. 10 and other similar plots fordifferent Sam' a correlation was obtained for the Yfactor as a function of steam quality. The followingprocedure was used.1. At a fixed oil recovery value on Fig. 10, thevalues of net heat injected corresponding to thedifferent steam qualities were read.2. The net heat injected values were plotted vsquality to determine the minimum net heat requiredfor that recovery value. This minimum, of course, isthe effective heat defined earlier.3. The heat utilization factors (Y) then werecalculated as the ratio between the effective and netheat injected values for each steam quality.4. Steps 1, 2, and 3 were repeated for several oil

100r-----,-----,-----,-----,-----,----.

MOBILE OIL SATIIRATION = 0.42

1.00.80.60.40.2

O ~ ~ ~ L _ ____L -__ L - _ _ L _ __ ____o 200 40 0 600 80 0 1000 1200NE T HEAT INJECTED. MMBtu / AcrfJ Ft.

Fig. 10 - Effect of steam quality on oil recovery.

QUALITY,%o--- 20+ + + + 40 600000 80~ I O O

INJECTOR (A): 50"10 OIL SATURATION PROFILES(DISPLACED OIL BANK)

QUALITY, %o Sol = 500/0- -- 20 Qinj: 395 MMBlu/Acre Ft.++++ 40

. . . . . . . 600000 80""*"""* 100

INJECTOR (B): 150F ISOTHERMS(UNIFORMITY OF WELLBORE HEATING)

(C): 10"10 VAPOR SATURATION PROFILES(STEAM ZONE GROWTH a BREAKTHROUGH)Fig. 11 - Effect of steam quality on displacement

parameters.329

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recovery values and for several mobile oil saturation(Sam) values.5. The results then were correlated to give theaverage relationship between Y and steam quality.This correlation is shown in Fig. 12.The correlation in Fig. 12 shows an optimumsteam quality of slightly less than 40070. At thisoptimum steam quality value, the heat utilizationfactor is 1.0 and the required net heat is a minimum.Vertical Heat LossThe simulation results were used to correlate vertical

.., /"" .......... r---....../ ", ......... "'-"'

o Q2 Q4 Q6 Q8 1.0INJECTED STEAM QUALITY

Fig. 12 - Heat utilization factor as a function of steamquality.100

oo

~ ~\ ~ 10..1\\\f\:"\

40

~ HEAr INJECrJON RArE~ t'-.05 . -V MMBtu./O/Acr. Ft.f'..- 1'.1 ~ t - -.2..""'-.. ]'.4h:' ;:::: ::::::-.6 r-- ~ t- -

80 120 160 200 240 280 320RESERVOIR rHICKNESS, FEErFig. 13 - Heat loss to overlying and underlying strata.

I I I I ~ ; ; : : . - ..-80 INlriAL MOBILEOIL SArI/HArlaN, 111 ~ V /"" VI - -"'-sgtV/V I "" '" _I-- ,--I--so ~ + - - - + - - - + ~ ! i ' 40 V ...-c..hv 30 V V t-V/V V20,0 ...V40 hVIV V + - + - + - t - I - - - - t I - - - - - - - + - = ~ ; : : ; I - 1

~ 2 0 ~ + - A ~ ~ ~ J ~ V ~ ; f r ~ _ + ~ ~ v r _ 5 ~ ~ _ + ~ ~ r _ r _ T _ 1:l] hVl'ir/ vV

O ~ ~ ~ ~ ~ V ~ V ~ ~ ~ ~ ~ ~ _ L _ L ~ ~ ~ ~ ~o 20 0 40 0 SOO 80 0 1000 1200 1400EFFECTIVE HEAr INJECTED, MMBfu./Gro$$ Aero Ff.Fig. 14 - Steam lood oil recovery as a function of effective

heat injected and mobile oil saturation.330

heat loss to overlying and underlying strata withsome independent variables; thus, the net heat injected could be calculated for any given system. Ofthe variables discussed earlier, only reservoirthickness, injection rate, and steam quality showedconsistent effects on heat loss. Large reservoirthickness, high injection rate, and high steam qualityresult in low heat loss as a fraction of input and viceversa. The effects of injection rate and steam qualitywere combined by lumping the two variables as theheat injection rate. The variation of heat loss withtime was neglected in this study. Fig. 13 shows thepercent of heat loss as a function of thickness andheat injection rate per unit of reservoir volume. Thecorrelation indicated that for reservoirs thicker than180 ft, heat loss is on the order of 15070 of input and isalmost independent of thickness.Prediction of Steamflood Oil RecoveryAs discussed, simulation results indicated goodcorrelations between steam flood oil recovery andboth effective heat injected per unit of reservoirvolume and initial mobile oil saturation. Thus, allavailable results were used to construct a group ofcurves relating these three parameters (Fig. 14).The procedure to use Fig. 14 to predict oil recoveryfor a given steam flood could be summarized asfollows.1. Read the vertical heat loss (fhv) as fraction ofinput from Fig. 13.2. Read the heat utilization factor (Y ) from Fig.12.3. Calculate the net heat injected (Qinj) inMMBtu/gross acre-ft from

Qinj = 0.128 1:[/ h (1 -h v ) .::It]i J (3)where / = injection rate (B/D/gross acre-ft), h =enthalpy (Btu/Ibm) from Fig. 15, .::It = time increment (years), and i = index of time increments .4. Calculate the effective heat injected (Qe) inMMBtu/gross acre-ft from Eq. 2.5. Read the oil recovery from Fig. 14.6. Repeat Steps 3, 4, and 5 as many times asnecessary until the ultimate recovery is reached.The oil recovery predicted from Fig. 14 should beconsidered only as the combined steam flood andprimary response. Net response due to cyclic steamstimulation should be estimated from field performance and added to the predicted recovery tomake up the total. In this regard, the oil saturationused in the above procedure should be adjusted toreflect the net cyclic stimulation recovery.Oil/Steam RatioThe ultimate oil/steam ratio (Pas) was calculatedfrom Figs. 13, 14, and 15 for a case of constantinjection rate of 1.5 B/D/acre-ft and steam qualityof 0.6. The oil/steam ratio is plotted in Fig. 16 as afunction of reservoir thickness, net!gross ratio, andinitial mobile oil saturation. As expected, increasingany of these three variables resulted in a significantincrease in the oil/steam ratio. Plots similar to Fig.16 could be obtained for other conditions and should

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be helpful in designing and determining economics ofsteam flood projects.Limitations of ApplicabilityThe correlations should be useful in predicting oilrecovery and oil/steam ratio for steamflood projectsthat have reservoir characteristics similar to or nearthe range of those outlined above. Caution should beexercised when using the method for reservoirs withcharacteristics outside that range. This is especiallyimportant if precise values of oil recovery andoil/s team ratio are required. In addition, if details ofsaturation, temperature, and pressure distributionsare required, use of numerical reservoir simulators isrecommended. I f the oil recovery and oil/steam ratiopredictions are required for property screening andsensitivity analysis, this method should besatisfactory in most cases.Application to a Field CaseData and performance of a steam flood project in theKern River field in California were given by Blevinsand Billingsley.1I The basic data required for theapplication of the method is summarized in Table 3.Calculations of predicted oil recovery for thisexample and actual observed values are shown inTable 4. Comparison of observed and predictedrecoveries indicates reasonable agreement. Thecalculated recoveries do not include any adjustmentsdue to cyclic steam stimulation. Field performancedictated that stimulation response was insignificantwith respect to flood response.Note that in calculating the effective heat injectedat any time for a project, only the portion of theinjected steam that is confined to the project areashould be used. Steam quality used should be that atthe sand-face - i.e., at bottom hole conditions.Conclusions

1. Average vertical heat loss as a fraction of inputis correlated with reservoir thickness and heat inputrate.

2. Above 180 ft, reservoir thickness has littleeffect on vertical heat loss.3. Pattern shape and spacing have insignificanteffect on steam flood oil recovery if injection rate perunit of reservoir volume is fixed, well productivity is

not a limiting factor, and producers are at uniformdistance from injectors.4. In designing steam flood projects, injection rateshould be based on gross reservoir thickness.5. Steamflood oil recovery is dependent on steamquality, even on a fixed total heat injected basis. Aheat utilization factor is introduced to account forthis effect. Maximum heat utilization appears at asteam quality of about 40070.6. Steam flood oil recovery is correlated witheffective heat injected per gross acre-foot and initialmobile oil saturation.7. Cumulative oil/steam ratio depends strongly oninitial mobile oil saturation, reservoir thickness, and

net/gross ratio.FEBRUARY 1980

TABLE 3 - BASIC PROJECT DATA FOR THE FIELD CASE,KERN RIVER FIELDArea (acres)Sand thickness (gross ft)(net ft)PorosityOil saturation prior to steamfloodingResidual oil saturation after steamfloodInjected steam quality

61100700.350.520.100.6

Injection rate Year1BIDof Cold WaterEquivalent

40 00

2000

100080 0

60 0

40 0

20 0

10080'". 6040

il:20

23456

6,6009,1006,6006,0006,1006,100

/ :/f0/ II / \ \/ // / / I/ / I

/ / I I ISTEAM' / i / / I il

100UALITY," - 0 20 40 60I I I I/ I I I/ I I II ,/ I IIII II I, 'I I Ioo 200 400 600 800 1000 1200 1400

ENTHALPY, Blu./LIJ.

Fig. 15 - Enthalpy of wet steam as a function of qualityand pressure.

0.5,----,--,-----r---,----r---.-'ZOO

04

STEAM QUALITY" 60%INJECTION RATE" 1.5 BIDIGROSS ACRE FT.NET IGROSS-1.00-- - 0.75

100

zoo03 1 - - - - + - - + - - - - - + - - - + . ' 1 ' - + 1 - 7 ' - - + 100

'"::!c ozi:: '"30

30

01 I - - - - + - - ~ ....-TC7''''''--:...t-'''-'----+- THICKNESS, Ft.

0 ~ - - = ' 0 - - ~ Z O ~ - ~ 3 0 ~ - ~ 4 ~ 0 - ~ 5 L O - - ~ 6 0 - - ~INITIAL MOBILE OIL SATURATION, "

Fig. 16 - Effect of oil saturation, reservoir thickness, andnet/gross ratio on cumulative oil/steam ratio.331

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TABLE 4 - PREDICTEDAND OBSERVED OIL RECOVERY FOR THE FIELD CASE, KERN RIVER FIELDIncremental Cumulative Predicted ObservedIncremental Effective Effective Cumulative CumulativeSteam Injected Heat Injected Heat Injected Oil Recovery Oil Recovery Oil RecoveryYear (bbl/gross acre-ft) (MMBtu/gross acre-ft) (MMBtu/gross acre-ft) (% of mobile oil) (bbl) (bbl)

1 395 852 544 1223 395 854 359 755 365 776 365 77

Nomenclaturefhv = vertical heat loss, fraction of inputFosh

Ikrg

krogk rowk rwQe

=======

cumulative oil/steam ratiosteam enthalpy, Btu/Ibmindex of time incrementssteam injection rate, B/D/gross acre-ftrelative permeability to gasrelative permeability to oil in presence ofgasrelative permeability to oil in presence ofwaterrelative permeability to watereffective heat injected, MMBtu/grossacre-ft

Qinj net heat injected, MMBtu/gross acre-ftSL = liquid saturation

SLn = normalized liquid saturationSo oil saturationSo i = initial oil saturat ion

Som initial mobile oil saturat ionSorg = residual oil satura tion after gas floodSors = residual oil saturation af ter steam floodSorw residual oil saturation after water flood

SVi = initial vapor saturationSw = water saturationSwi = irreducible water saturationSwn = normalized water saturation

!::.t = time increments, yearsY = heat utilization factor

AcknowledgmentsI thank the management of Standard Oil Co_ ofCalifornia for permission to publish this paper. I alsoexpress my appreciation to P.T. Woo and J.H.Duerksen of Chevron Oil Field Research Co. fortheir helpful and constructive discussions.References

I. Marx, J.W. and Langenheim, R.N.: "Reservoir Heating byHot Fluid Injection," Trans., AI ME (1959) 216, 312-315.

332

85207292367444521

1.0 46,000 40,00016 756,000 820,00029 1,372,000 1,350,00043 2,034,000 2,000,00057 2,696,000 2,550,00065 3,075,000 3,000,000

2. Mandl, G. and Volek, C.W.: "Heat and Mass Transport inSteam Drive Processes," Soc. Pet. Eng. J. (March 1969) 59-79; Trans., AIME, 246.3. Neuman, C.H.: "A Mathematical Model of the Steam DriveProcess - Applications," paper SPE 4757 presented at theSPE 45th Annual California Regional Meeting, Ventura,April 2-4, 1975.4. Myhill, N.A. and Stegemeier, G.L. : "Steam-DriveCorrelation and Prediction," J. Pet. Tech. (Feb. 1978) 173-182.5. Shutler, N.D.: "Numerical, Three-Phase Model of the LinearSteamflood Process," Soc. Pet. Eng. J. (June 1969) 232-246;Trans., AIME, 246.6. Shutler, N.D.: "Numerical Three-Phase Model of the TwoDimensional Steamflood Process," Soc. Pet. Eng. J. (Dec.1970)405-417; Trans., AIME, 249.7. Vinsome, P.K.W.: "A Numerical Description of Hot-Waterand Steam Drives by the Finite Difference Method," paperSPE 5248 presented at the SPE 49th Annual Fall Meeting,Houston, Oct. 6-9,1974.8. Coats, K.H., George, W.D., and Marcum, B.E.: "ThreeDimensional S imulation of Steamflooding," Soc. Pet. Eng. J.(Dec. 1974) 573-592; Trans., AIME, 257.9. Coats, K.H.: "Simulation of Steamflooding With Distillationand Solution Gas," Soc. Pet. Eng. J. (Oct. 1976) 235-247.10. Chu, C. and Trimble, A.E.: "Numerical Simulation of SteamDisplacement - Field Performance Applications," J. Pet.Tech. (June 1975)765-776.

II . Blevins, T.R. and Billingsley, R.H.: "The Ten-PatternSteamflood - Kern River Field, California ," J. Pet. Tech.(Dec. 1975) 1505-1514; Trans., AI ME, 259.SI Metric Conversion Factors

acre-ft x 1.233482 E+03 m3bbl x 1.589873 E-Ol m3Btu x 1.055056 E+03 Jcp x 1.0* E-03 Paoscu ft x 2.831 685 E-02 m3degreeAPI 141.5/(131.5 + .API) g/cm3degree F CF-32)/1.8 Cft x 3.048* E-Ol mIbm x 4.535924 E-Ol kgpsi, psia x 6.894757 E+OO kPa

Conversion factor is exact. JPTOriginal manuscript received in Society of Petroleum Engineers office July29, 1976. Revised manuscript received April 4, 1979. Paper accepted for

publication Oct. 22, 1979. Paper (SPE 6169) first presented at the SPE 51stAnnual Fall Technical Conference and Exhibition, held in New Orleans, Oct. 36,1976.

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