43 - Gas-Injection Pressure Maintenance in Oil Reservoirs

7/22/2019 43 - Gas-Injection Pressure Maintenance in Oil Reservoirs

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43-2 PETROLEUM ENGINEERING HANDBOOK

maintain individual well productivities, and producingwells are generally more able to maintain their desiredproducing rates or allowables. Further advantages can beobtained by elimination of penalties imp osed byregulatory agencies for excessive net gas productionwhere produc ed gas is not reinjected. Thus, many timesit is possible to maintain full-field allowables over mostof the producing life of the project, thereby reducing thedepletion time of the reservoir, with attendant savings inoperating costs and increased presen t value of futurerevenues.Since 1978 and the passage of the Natural Gas PolicyAct. the increasing value of sales gas has resulted in adecline in the numbers of new gas-injection projects.Howe ver, some opportunities still exist in remote areaswhere recovery considerations are augmen ted by thestorage aspects of such projects and by specialized ap-plications in connection with gravity drainage systemsand attic oil recovery projects.Concurrent with this, CO2 and nitrogen injection formiscible displacement of crude oil have been of increas-ing interest and application. On the basis of botheconomic and technical considerations, it is notunreasonable to expe ct that immiscible nitrogen-injection projects will see increasing application in manyoil reservoirs that in the past would have been subjectedto hydrocarbo n-gas injection. In general, calculationtechniques previously d evelop ed for hydrocarbo n-gas in-

jection and displacement can be used for the design andapplication o f nitrogen-injection projects under condi-tions of immiscible displacement.It is the purpose of this chapter to point out thephysical criteria for successful gas-injection operations,to describe the variables that must be defined andevaluated, and to demonstrate some of the techniquesavailable for the prediction and evaluation of field per-formance under immiscible gas-injection operations.Mo st of the calculations described are now ac-comp lished with hand calculators o r digital computers;many of them can be applied with relatively basicvarieties of todays generation of microcom puters. Atthe same time, the physical and mathematical relation-ships described have been incorporated into a wide varie-ty of mathem atical reservoir simulation mode ls. The for-mulation and application of such models is beyond theintended scope of this chapter, but a few selectedreferences to technical articles describing models forgas-injection process es are included in Appendix B.The calculation techniques described h ere are theclassical meth ods for describing immiscible displace-ment with comp lete pre-equilibrium between the injectedand displaced phase s, gas and oil, while accounting forthe effects of reservoir heteroge neities, injectioniproduc-tion well configurations, and differing physicalcharacteristics of the fluids. Th e reservoir is treated interms of the average properties of a unit volume of rock,and production performanc e is described on the basis ofan average well.The simplest types of so-called reservoir simulationmode ls employ essentially these same techniques but, bymeans of one-, two-, or three-dimensional cell arrays,account for area1 and vertical variations in rock and fluidproperties, well-to-well gravity effects, and individualwell characteristics.

More complex component or compositional modelsallow also for nonequilibrium conditions between in-jected and displaced fluids and can be used to describeindividual well streams in terms of the compositions ofthe produced fluids.

The accuracy and reliability of the results obtainedgenerally increase with each of these methods, ormodels, in the order described , depending on the quanti-ty and quality of the reservoir and fluid data available,the internal variations in reservoir p roperties, the fluidcharacteristics, and the ability to describe the overallphysical system. The time and work er requirements, andhence the cost of the study, also increase in the sameorder.Therefore, the choice of a method for describing proj-ect performan ce is a matter of judgment, consideringeconom ics, the time available, and the requirements foraccuracy in a practical sense. Obv iously, these re-quirements will vary with the phase of work undertakenand the overall purpose of the study at hand. Certainly,early feasibility studies usually can and should be madewith nothing more than the simple, classical techniques.Such is also the case for many detailed studies where theeffects of gravity and phase equilibrium are negligible orwhen the quantity and quality of data are inadequate tosuppo rt more comp lex full-scale simulation studies.Types of Gas-Injection OperationsGas-injection pressure-maintenance operations aregenerally c lassified into two distinct types depending onwhere in the reservoir, relative to the oil zone, the gas isintroduced. Basically, the same physical principles of oildisplacement apply to either type of operation; howe ver,the analytical procedu res for predicting reservoir perfor-mance, the overall objectives, and the field applicationsof each type of operation may vary considerably.Dispersed Gas InjectionDispersed gas-injection operations, frequently referredto as internal or pattern injection, normally use somegeom etric arrangement of injection wells for the purposeof uniformly distributing the injected gas througho ut theoil-productive portions o f the reservoir. In practice,injection-well/production-well arrays vary from the con-ventional regular pattern configurations (e.g., five-spot,seven-spot, nine-spot) to patterns seemingly haph azardin arrangement with relatively little uniformity over theinjection area. The selection of an injection arrangementis usually based on considerations of reservoir con figura-tion with respect to structure, sand continuity,permeability and porosity variations, and the number andrelative positions of existing wells.This metho d of injection has been found adaptable toreservoirs having low structural relief and to relativelyhomo geneou s reservoirs having low specific permeabil-ities. Becau se of greater injection-well density, dispersedgas injection provides rapid pressure and productionresponse-thereby reducing the time necessary to depletethe reservoir. Dispersed injection can be used where anentire reservoir is not under one ownership, particularlyif the reservoir cannot b e conveniently unitized.

Som e limitations to dispersed-typ e gas injection are:(1) little or no improvement in recovery efficiency isderived from structural position or gravity drainage, (2)


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GAS-INJECTION PRESSURE MAINTENANCE IN OIL RESERVOIRS 43-3

area1 swee p efficiencies are generally lower than for ex-ternal gas-injection operations, (3) gas lingeringcaused by high flow velocities generally tends to reducethe recovery efficiency over that which could be ex-pected from external injection, and (4) higher injection-well density contributes to greater installation andoperating costs.External Gas InjectionExternal gas-injection operations, frequently referred toas crestal or gas-cap injection, use injection wells in thethe structurally higher positions of the reservoir-usuallyin the primary or secondary gas cap. This manner of in-jection is generally employ ed in reservoirs havingsignificant structural relief and average to high specificpermeabilities. Injection wells are positioned to providegood area1 distribution of the injected gas and to obtainmaximum benefit of gravity drainage . The number of in-jection wells required for a specific reserv oir willgenerally depend on the injectivity of each well and thenumber of wells necessary to obtain adequ ate area 1distribution.External injection is generally con sidered superior todispersed-type injection, since full advantage can usuallybe obtained from gravity drainag e benefits. In addition,external injection ordinarily will result in greater area1sweep and conformance efficiencies than will similardispersed injection operations.Optimal Time to Initiate Gas Pressure-Maintenance OperationsGeneralizations as to the optimal time to initiate gaspressure m aintenance are of limited practical valuebecause of the exceedingly large number of variablesthat must be considered from an economic and reservoirmechanics standpoint. Obviously, there is no metho d ofcalculating directly th e optimal time from an economicstandpoint: instead, sev eral calculations of future perfor-mance, assuming initiation of injection at various stagesof reservoir depletion, must be made and compared onan economic basis.Considering only hydrocarbon recovery and im-provemen ts in producing characteristics, it can be statedthat generally more favorable reservoir conditions forgas-injection operations are present when the reservoir isat or slightly below the reservoir fluid saturationpressure. Within this range of reservoir pressu res, the in-itial free-gas saturation in the oil zone is at aminimum-a condition favorable to obtaining maximumrecovery efficiency from the gas displacement proces s.Efficiencies of Oil Recovery byGas DisplacementIt is convenient to analyze and evaluate the recovery effi-ciency obtainable by gas displacement operations interms of three efficiency factors, generally referred to as(1) unit-displacement efficiency, (2) conformance efti-ciency, and (3) area1 swee p efficiency. Each recovery ef-ficiency may be considered as one componen t elementthat accounts for the influence of certain para meters onthe overall reco very efficiency of the displacement proc-ess. The produc t of the three efficiency factors providesan estimate of the percentag e oil recovery that can be ex-pected with this recovery proces s in a particular reservoir

under specified conditions. Analytical proced ures areavailable for evaluating each efficiency factor in-dividually. In certain instances, such analytical p ro-cedures are combined to determine two or more of thefactors as a unit; for examp le, the term volumetric efti-ciency is sometimes employed where the conformanceand area1 sweep efficiencies are combined into one fac-tor. Similarly, the term displacement efficiency issometim es used where the unit displacement and confor-mance efficiencies are evaluated in combination. For thepurpo se of this chapte r, the three components describingthe overall recovery proces s are defined as follows.1. Unit displacement eficiency is the percenta ge of oilin place within a totally swep t reservoir-rock volume thatis recovere d as a result of the displacement process .

2. Conformance eficiency is the percentage of thetotal rock or pore volume within the swept area that iscontacted by the displacing fluid.3. Areal sweep e$iciency is the percentage of the totalreservoir or pore volume that is within the swept area,the area contacted by the displacing fluid.Each of the three efficiencies increases with continueddisplacement; therefore, each is a function of the numberof displacement volumes injected. The rate of increase inrecovery efficiency in a given p ortion of a reservoirdiminishes as gas breakthrou gh occurs. Therefore , themaximum value of each compone nt efficiency an d, con-sequently, the ultimate reco very efficiency is limited byeconomic considerations.Methods of EvaluatingUnit-Displacement EfficiencyEquationsUnit-displacement efficiency is normally determined byanalytical procedures developed from the two fundamen-tal equations reported by Buckley and Leverett. * Theseequations essentially ch aracterize th e mechanics o fsteady-state, two-ph ase fluid flow encountered in oildisplacement by an immiscible fluid. These equationswere develop ed by means of relative-permeability con-cepts and are based on Darcys law describing steady-state fluid flow through porous media.

The so-calledfi-ucrional-flow equation describes quan-titatively the fraction of gas flowing in terms of thephysical characteristics of a unit element o f porou smedia. In customary units, using a unit area, this equa-tion is as follows.f g =

1 + l.l27[k,A/(~,q,)][(aP,./aL)-0.433(p ,, -p,


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-c---------- TERSTITIAL WATER

DISTANCE, L

Fig. 43.1-Schemat ic representat ion ofsa tu ra t i on d i s t r i bu t i on du r i nggas-d i sp l acemen t p rocess.

PETROLEUM ENGINEERING HANDBOOK

tia 50%L840

NOTE:V =VOL UME OF GAS (MEASURED UNDERRkERVOIR CONDITIONS) WHICH HASINVADED UNIT CROSS SECTION OF OILSAND.

OO I I I I I I100 200 300 40 0 500 600 700 800 900 1000DISTANCE, FTF ig .43 .2-F l u i d sa tu ra t i on d i s t r i bu t i on a t f ou r t ime pe r i ods du r i ng gas d i sp l acemen tp rocess.

PO = oil density, g/cm,P,q = gas density, g/cm,

CY= angle of dip, positive dow n-dip, degree s,Ii,, = effective perm eability to oil, darcies,

k n, = relative permeability to oil, fraction,k,, = relative permeability to gas, fraction,PC = oil viscosity. cp, andPC S = gas viscosity, cp.

To relate the fraction of gas flowing to time, Buckleyand Leverett dev eloped the following material-balanceequation.

L= 5.615 y,t aj-&~A (-1 , . .s,s 2)

wheret = time, days,

4 = porosity, fraction, andS, = gas saturation, fraction.

The value of the derivative d(f,)/&S,) may be ob-tained for any value of gas saturation by plotting j, fromEq. 1 vs. S, and determining slopes at various points onthe resulting curve. 3*4 This graphical procedure isgenerally considered to be sufficiently precise for mostreservoir engineering calculations. It is especially suitedwhere the calculations are to be made by handcalculators. A more precise mathematical procedu re forevaluating the function a& ,)/a(S,) was presented byKern5 and is particularly adaptable for use with digitalcomputers.

Figs. 43.1 and 43.2 illustrate the displacement processdescribed by Eqs. 1 and 2. Calculated oil- and gas-saturation distributions for a hypoth etical examp le of gasdisplacement after successive periods of injection areshown in Fig. 43.2. The area beneath any curverepresents the gas-invaded zone, w hereas the area to theright of the gas front at any time represents the unin-vaded zone.Modifications of Displacement EquationsEqs. 1 and 2 were developed on the basis of the follow-ing simplifying assumptions.1. Steady-state flow conditions prevail.2. Displacemen t takes place at constant pre ssure.3. The displacing and displaced phase s are in com-positional equilibrium.

4. None of the injected g as is dissolved in the oil.5. There is no production of fluids from behind thegas front.6. The advancing gas moves parallel to the beddingplanes of the formation.7. The gas front moves uniformly through laminatedsands.8. Th e interstitial water present is immobile.The applicability of the basic displacement equationsto a given reservoir is, of course, governed to a large ex-tent by the restrictions imposed by the basic assump-tions. Several authors have reported modifications to thedisplacement equations that eliminate the need for mak-ing certain of the assumptions. Modifications that takeinto consideration the swelling effects experience d frominjection into an undersaturated reservoir and productionof fluids from behind the gas front have been presentedby Welge,3 Kern, Shreve and Welch,6 and others.Jacoby and Berry, Attra,8 and others have presentedequations and analytical proced ures fo r calculating per-


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GAS-INJECTION PRESSURE MAINTENANCE IN OIL RESERVOIRS

formance where there is significant co mpositional inter-change of components between the displacing gas phaseand the reservoir oil. The influence of deviations fromthe conditions described in Assumptions 6 and 7 isgenerally taken into consideration in the determination ofconformance efficiencies.

Influencing FactorsEqs. 1 and 2 provide a means for investigating therelative influence o f the various param eters affectingunit-displacement efficiency. These factors are (1) initialsaturation conditions, (2) fluid viscosity ratios, (3)relative-permeability ratios, (4) rate and formation dip,(5) capillary pressure, and (6) reservoir pressure andfluid properties.

Initial Saturation Conditions. Frequently, gas-injection operations are initiated after reservoir pressureshave declined to such an extent as to permit the ac-cumu la t i on of free gas released from solution in the oil.If the free-gas saturation excee ds the breakthro ugh orcritical saturation determ ined from the fractional-flowcurve, an oil bank ahead of the front will not be formed;consequently, oil production will be accomp anied by im-mediate and continually increasing free-gas production. 2This influence of initial mobile gas saturation on gasdisplacement performance has been demonstrated bylaboratory investigations and mathem atical analyses. 9Fig. 43.3 shows a comparison of calculated and ex-perimentally determined g as displacement performan ce.It will be noted that approximately 10% oil recovery wasattained prior to gas breakthrou gh where the initial gassaturation was zero, where as w ith an initial g as satura-tion of 18.1% PV, a pe r i od of gas-free production wasnot observed.The magnitude of the interstitial water saturation pres-ent in a reservoir, of course, influences the quantity ofoil subject to gas displacement. It apparently does nothave an influence on the breakthro ugh unit-displacementefficiency as determined by the fractional-flow equa-tions, howe ver. lo If the interstitial water saturation is amobile ph ase, the displacement equations are not direct-ly applicable since they were developed from concepts oftwo-phase flow. Approximations of gas displacementperformance can usually be made where three phases aremobile by treating the water and oil phase s as a singleliquid phase. Displacement calculations can then bemade with k,/k, data determined from core samplescontaining interstitial w ater saturation. Oil recovery canb e differentiated from total liquid recove ry on the basisof k,/k, data or by material-balance calculations incor-porating an estimated minimum interstitial watersaturation.Fluid Viscosity Ratios. The effects o f variations in oilviscosity on calculated unit-displacement efficiency canbe seen from an examination of the curves p resented inFig. 43.4. Note that the oil recovery is significantly im-proved as the viscosity of the oil approaches that of thedisplacing gas. This indicates that the most efficientdisplacement will occur where the oil-to-gas viscosityratio is unity or less.

EXPERIMENTAL DATA -PREDICTED PERFORMANCEIO-

10 -

o-

O-

/

0IITIF ig . 43.3-Comp ar ison of ca lcu la ted and exper imenta l gas-i n j ec t i on pe r fo rmance fo r two cond i t i ons o f i n i t i a l

gas saturat ion.

Rate and Formation Dip. Note from Eq. 1 that severalfactors influence the magnitude of the gravity term.Since the fractional flow of gas decreases as themagnitude of the gravity term increases, maximumbene f i t s f rom gravity segregation are obtained when thefollowing occur.1. Specific permeabilities and relative permeabilitiesto oil are high.

2. Reservoir oil viscosities are low and densities arehigh.3. T he cross-sectional area to flow is large.4. The ang le of dip is high (Fig. 43.5).5. Injection and production rates are low.Frequently, the design of a gas-injection program can

have an appreciable effect on whether maximum advan-tage is obtained from gravi ty drainage in a given reser-voir. For examp le, prope r location and distribution of in-jection wells along the structurally high portions of thereservoir may in some cases increase the cross-sectionalarea to flow and take full advantag e of maximum reser-voir dip. C ap oil viscosities and relative oilpermeabilities are favorable when pressures are highest.In addition, injection and production rates, in terms ofreservoir withdraw als, are generally lowest at high reser-voir pressures, indicating that maximum benefits fromgravity drainage can be achieved by initiating gas-injection operations early in the life of a reservoir.Relative-Permeability Ratios. It has been shown thatthe concepts of relative permeability can be appliedequally well to comp lete or partial pressure-maintenanceoperations. t Since relative-permeability ratio, along


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o-

5-

80 -

15 -

OO 110 20 30 40 50 60 70 80 90 tooGAS SATURA TION-PER CENTFig. 43.4-Ef fect o f o i l visco si ty on f ract ional f low of gas.

with viscosity ratio, fixes the relative portions of gas andoil flowing at any given saturation condition, it is one ofthe more important factors influencing unit-displacementefficiency. Relative permeab ility is a characteristic of thereservoir rock and is a function of fluid-saturation condi-tions; there fore, an operat or has no control over therelative-permeability characteristics of a given reservoir.How ever, because of the significant influence th at thisfactor has on the performanc e of gas-displacementoperations, it is important that calculations be based ondependab le data obtained from laboratory analyses o fcore samples. If possible, th e laboratory-determined datashould be supplemen ted by relative permeabilitiescalculated from field performance data.Capillary Pressure. Capillary-pressure forces tend tooppo se the forces of gravity drainage and, as a result,tend to decreas e unit gas displacement efficiency. At ex-tremely low rates of displacement whe re frictional fac-tors becom e negligible, the saturation distribution maybe controlled to a large extent by the balance betweencapillary and gravitational forces. How ever, at the ratesof displacement normally employ ed in practice, it isgenerally considered that in most cases capillary forces,or capillary-pressure gradients, can be neglected withoutseriously detracting from the utility of the analysis.Reservoir Pressures and Fluid Properties. In certainhighly undersaturated reservoirs, particularly those con-taining high -gravity crude oils that are to some deg reevolatile, the unit-displacement efficiency can be in-creased by initiating pressure-maintenance operations atthe highest pressure possible. Under the prope r condi-tions of pressure and fluid composition and at the properdegre e of undersaturation, a miscible-fluid displacementcan be achieved by use of relatively dry injection gas.The mechanics of this process, which reportedlyachieves unit-displacement efficiencies approach ing

SA;:RA T::N - P6: 80 90Fig. 43.5-Ef fect o f form at ion d ip on f ract ional f low of gas.

lOO% , will be considered more in detail in Chap . 45 .Recov ery efficiency often can be improved by gas injec-tion at high reservoir pres sures even though m iscibility isnot achieved . This improvement in recovery may be aresult of (1) swelling or expansion of the undersaturatedreservoir oil resulting from addition of dissolved gas, (2)reduction of the oil viscosity from addition of dissolvedgas, and (3) vaporization of the residual oil and subse-quent recovery from the produced gas. I2Laboratory data obtained from tests using samples ofreservoir fluid and injection gas are necessary to evaluatequantitatively the degree of swelling and vaporizationthat will take place under specified reservoir conditions.These data may be used in conjunction with conventionalmaterial-balance, compositional-balance, and displace-ment equation s to arrive at an estimate of unit-displacement efficiency.

Calculation ProceduresExam ple procedure s for calculating displacement effi-ciency are included in Appendix A for the cases ofhorizontal and vertical (downd ip) flow of displacing gas.Methods of EvaluatingConformance EfficiencySeveral methods have been advanced for evaluating theconformance efficiency for a given reservoir. Generally,all the methods are somewhat empirical and are based oneither comparison s of calculated and observed pastdisplacement performanc e or statistical analyses of core-analysis data.If a displacement proces s such as gas-cap exp ansion orpilot injection operations has been operative in a reser-voir long enough to yield sufficient and reliable d ata con-cerning the position of the gas front and recovery as afunction of time, pas t reservoir performance can be usedto calculate conforman ce efficiency. The basic premise


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for this type of analysis is that the conformance efficien-cy is the predominant factor responsible for deviationsbetween actual displacement performan ce and the idealor theoretical. On this basis, the conformance efficiencyis calculated by dividing the observed recovery at vari-ous time intervals by theoretical recovery for correspond-ing time periods. Theo retical recovery may be determinedfrom unit-displacement-efficiency calculations includingan approp riate areal sweep efficiency. The conformanceefficiencies thus determined may then be empirically cor-related with either rate of production or percent recov-ery to determine an average value or trend for use inmaking future performanc e predictions.

Several autho rs have presented metho ds fo r determin-ing conformance efficiencies based on statisticaltreatments of core-analysis data. Perhap s the most fre-quently used is an adaptation of the method presented byStiles I3 for evaluating the effect of permeability varia-tions on waterflood performance (see Chap. 44).Conformance-efficiency calculations for miscible-fluiddisplacement using this analytical technique arepresented in Chap . 45. The same calculation proced uresmay be used when immiscible gas displacement is con-sidered, except that the relative-permeability ratiok,/k, must be considered for immiscible gas displace-ment, where as it is not applicable to miscible displace-ment. The relative-permeability ratio used in suchcalculations is considered to be constant and is generallytaken to be the relative pe rmeability to gas at residual oilsaturation divided by the relative permeability to oil atinitial gas saturation.

Influencing FactorsThe conformance efficiency for a given reservoir islargely con trolled by the influence of (1) variations inrock properties, (2) mobility ratios, and (3) gravitysegregation.Variations in Rock Properties. Reservoir-rock porosityand permeability vary from one pore channel to the next.In addition, reservoir rock almost universally is formedin layers-stratified-either to a small extent or overlarge distances. Stratification can be merely differencesin porosity and permeability of layers in capillaryequilibrium or can be separations caused by im-permeable shale or other rock streaks. Variations inporosity and permeability can be both vertical andhorizontal. All these rock heterogene ities tend todecrea se the effective size of the reservoir a s far asdisplacement operations are concerned. Therefore , thedegre e of heterogeneity controls to a large extent theconformance efficiency attainable from gas-injectionoperations in a given reservoir.Mobility Ratios. The mobility of a fluid is an index o fthe ease with which the fluid will flow under specifiedconditions. Herein, mobility is defined as the relativepermeability to a fluid at a given saturation divided bythe fluid viscosity. Mobility ratio, M, is an index of theease with which one fluid will flow relative to anotherfluid. It is defined herein as the ratio of the gas mobilityto the oil mobility or, in equation form,

A4 =p 0, . . . . . . . . . . . . . . . . ..I...... (3)m Fgwith permeabilities and viscosities as before.If the mobility ratio is equal to unity, it indicates that,for a given pressure differential, oil and gas will flowwith equal ease; values greater than unity indicate thatgas will be the more mobile fluid, etc. During the gasdisplacement process, mobility ratio can vary fromessentially zero during p eriods of low gas saturation tovalues approachin g infinity during th e periods of highgas saturation.In heterogen eous reservoir-rock systems, relati


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PETROLEUM ENGINEERING HANDBOOK

REClkOCAL MOBILITY RATIO I/MFig. 43.6-Sweep ef f iciency as a func t ion of mob i l i ty ra t io .

6.0 80 IO c

Applied mathem atical techniques have been used toinvestigate the influence of these factors on regulargeometrical reservoir units of constant thickness. On theother hand, various types of laboratory and numericalmodels have been used to study the effects on area1sweep efficiencies of irregular reservoir boundaries, ir-regular well arrangements, variable formation thick-nesses, and variable mobility ratios. From these in-vestigations, it generally can be concluded that the arealsweep efficiency at gas breakthrough will bc a maximumin a given reservoir when the mobility ratio is low andwhen the distance from injection to production well islarge. After gas breakthro ugh, areal swee p efficienciesare improved as the number of injected displacem entvolumes increase. The influence of mobility ratio anddisplacement volumes injected on the area1 sweep effi-ciency of a regular five-spot reservoir unit may be seenin Fig. 43.6. The data presented in this illustration wereobtained from model studies th at used miscible fluids ofva r i ous viscosities to study the influence of variousmobility ratios. These data are generally considered to beapplicable to reservoir an alyses for either w ater or gasdisplacement when actual model studies for a givenreservoir are not available.

Areal sweep efficiencies, calculated at gasbreakthro ugh and at successive periods thereafter untilthe econom ic limit is reached , a re required for estimatingreservoir performance under pressure-maintenanceoperations. If the injection/production well arrangementsand the fluid mobility ratios for a given reservoir closelyapproximate those that have been studied in thelaboratory, the data on this subject reported in theliterature may be used as a basis for estimating the arealsweep efficiencies. Data reported by Dyes et al. havebeen found particularly useful since consideration wasgiven t o t he i n f l uence of production after gasbreakthro ugh. Note that the quantitative applicability oflaboratory da ta is inherently questionable because ofuncertainties in model scaling, laboratory techniques,and associated simplifying assum ptions. Neverthe less,laboratory-model studies still offer the most convenientmeans of determining quantitative data concerning areal

DISPLACEMENT VOLUMEFig. 43.7-Areal sweep ef f iciency as a func t ion o f i n j ec t i onf l u i d vo l ume fo r a mob i l i t y ra t l o o f un i t y .

swee p efficiencies. For this reason, if mathem aticalmodel studies are not practical for the particular reservoirunder consideration, published data (tempe red by ex-perience) must generally be resorted to as a basis forpredicting areal sweep efficiencies even though the wellarrangements being investigated do not duplicate th osereported in the literature.For application to performanc e predictions, it is fre-quently desirable to construct a curve showing the arealsweep efficiency for a given mobility ratio as a functionof the fractional gas flow, fK, or the displacementvolumes injected. For examp le, Fig. 43.7 shows a replotof the data presented in Fig. 43 .6 for a mobility ratio ofunity. If necessary, the trend established from these datamay be adjusted up or down depending on the judgmentof the engineer as to the applicability of the model to thereservoir under consideration.As was discussed in a previous section of this chapter,during gas displacement operations there is a significantgradient in mobility ratios behind the gas front.Therefo re, an average mobility ratio must be selected todetermine areal sweep efficiencies from published data.Probably the most representative, and certainly th e mostconservative, value for this purpo se is the mobility ratiodetermined at the average gas saturation behind the frontaccording to the metho ds presented in connection withunit-displacement efficiencies.Calculation of Gas Pressure-MaintenancePerformanceEstimates o f gas-injection performance are generallybased on the simultaneous solution of one or more formsof the conventional material-balance equations and thedisplacement equations previously discu ssed. The man-ner in which these equations are applied will vary de-pending on the scope of the investigation. the type ofreservoir under consideration, and wheth er dispersed orexternal injection is to be used for comple te or for partialpressure maintenance. Rigorou s treatment of all factorsinfluencing production performanc e and the displace-ment proce sses in a given reservoir can result in thedevelopme nt of calculation proced ures th at are quite


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GAS-INJECTION PRESSURE MAINTENA NCE IN OIL RESERVOIRS 43-9

comp lex. Sp ecific analytical techniques and proced uresas applied to various types of reservoirs hav e been thesubject of numerous articles in the technical literatureand several reservoir engineering textbook s. A selectedbibliography of technical articles dealing w ith specificanalytical techniques and procedures that can be used forestimating reservoir performance under gas-injectionoperations is included in Appendix B. Note that thesereferences are indexed acco rding to the type of reservoirunder consideration, the major influencing factors, andthe type of injection-well arrangement. These referencescan be used as a basis for developing suitable analyticaltechniques to estimate future pressure-maintenance per-formance in any given reservoir. How ever, since eachpetroleum reservoir is unique, in the final analysisengineers must rely upon imagination and experience todevelop techniques, based on fundamental theory, forthe particular reservoir under consideration.

Although the equation forms and specific details ofestimating reservoir performance will vary some what foreach reservoir considered, certain general analytical pro-cedures are comm on to most investigations and can beused as a basis for developing specific calculation tech-niques. A complete engineering analysis of a reservoirfor the purpose of evaluating gas-injection operationswill usually consist of four major phases: (1) assembly,preparation, and analysis of basic data; (2) analysis ofpast performan ce; (3) projection of future performanceof current operations; and (4) estimation of gas pressure-maintenance performance.Basic DataThe need for adequate and comprehensive basic data hasbeen emph asized in other chapte rs o f this book and is ap-parent when it is realized that the validity and thereforethe utility of any engineering analysis is determinedprimarily by the quality and quantity of basic data. Thedata requirements for analysis of gas-injection operationsare, with few exceptions, the same as the requirementsfor analysis of other types of fluid-injection operations.Appendix C includes an outline of the usual data re-quirements for engineering analyses as presented by Pat-ton, I5 with certain ad ditions and modifications.Analysis of Past PerformanceThe methods used to evaluate past reservoir performancewill. of course, vary depending on the active reservoirdrive mechanisms present, the quantity of suitable basicdata available, and the amount of detail or scope of theinvestigation. Proced ures fo r analyzing p ast reservoirperform ance are discussed in detail in other chapters.The results of such analyses will determine to a large ex-tent the method s used fo r predicting gas-injectionpressure-maintenance performance and will provide thecurrent reservoir pressure and saturation distributionconditions for use in such predictions. Further, prope ranalysis o f past performa nce will aid in supplementingand establishing the reliability of data required for theprojection of reservoir perform ance under injectionoperations.Projection of Future Performance ofCurrent OperationsDecisions regarding the installation of gas-injection

operations must be made on the basis of the relativebenefits to be derived from such operations comp aredwith competitive recovery techniques. Therefo re, anycomp lete analysis of gas-injection operations would in-clude the projection of future reservoir p erforman ceunder the current production operations. Meth ods of pro-jecting future primary production perform ance and othertypes of injection operations are discussed in detail inother chapters.Estimation of Gas Pressure-MaintenancePerformanceGenerally, projections of partial pressure-maintenanceperform ance, for either external or dispersed-type gas in-jection, can be made by use of conventional material-and volumetric-balance techniques in combination withrecovery efficiency determinations previously discussed.On the other hand, if comp lete p ressure maintenance isbeing considered, the project performance can beestimated by only the displacement equations and otheranalytical p rocedu res presen ted previously in connectionwith the discussions of unit displacement, conforman ce,and are a1 sweep efficiency.Proced ures for calculating the future performance ofboth external and dispersed-type gas-injection operationsare included in Appendix A. These example calculationsinclude the determination of displacement efficiency andpressure, producing gas/oil ratio, and recovery perfor-mance fo r primary operations and for various deg rees ofgas-injection pressure maintenance for two idealizedreservoirs.Performance-Time Predictions. Predictions of futuregas-injection perform ance are necessary for makingeconomic comparison s of various types of future opera-tions. Such predictions will usually include estimates offunctions of time such as (1) reservoir pr essures; (2) oil-,gas-, and water-production rates; (3) gas- and water-injection rates; (4) GOR s; ( 5) cumulative oil, gas, andwater recovery; (6) cumulative gas and water injected;(7) number o f producing, injecting, and shut-in wells;and (8) recoverable plant products, if applicable.To estimate th ese quantities, it is necessary to developrelationships between the hydrocarbon distribution of thesubject reservoir and the positions of injection and pro-duction wells. Once this is done and w ith a given injec-tion rate, Eq. 2 can be used to calculate the timenecessary for the gas front to reach incrementallyselected points in the reservoir.In gas-cap-drive reservoirs and whe re external injec-tion is being considered for reservoirs having significantstructural relief, it is frequently convenient to relatehydrocarbon PV, cross-sectional area, and well comple-tion intervals to subsea dep th within the reservoir. Ifsuch relationships are used and if the advancing gas frontis assumed to conform to structural depth, displacementequations and fluid inventory equations can be used topredict the rate of advance of the gas front, taking intoconsideration changes in cross-sectional area and reser-voir productivity.Until the gas front reaches the top of the perforationsin the structurally highest well, oil and gas production iscontrolled by the productivities or allowables of the pro-ducing wells ahead of the front: and producing GO Rs


10/19

43.10 PETROLEUM ENGINEERING HANDBOOK

TABLE 4X1-BASIC RESERVOIR DATAOi l rese rvo i r hav i ng no o r i g i na l gas cap

In i t ia l o i l vo lum e, /V. STBAverage poros i ty, 6 ,Average rock permeabi l i ty. k, m dAverage in terst i t ia l w ater saturat ion, S w,In i t i al bubb lepo in t p ressu re ,p , , ps i g

Oi l reservo i r w i t h o r i g i na l gas capIn i t ia l o i l vo lum e, N, STBIn i t ia l gas-cap gas vo lum e, McfArea o f gas/o i l contact A, acresRat io o f gas-cap to o i l -zone vo lum e, m,f rac t i onAverage poros i ty, 6 ,Average rock permeabi l i ty, k, m dAverage o i l -zone w aler saturat ion , S w. ,Average gas-cap water saturation, S wg %Bubb lepo in t p ressu re a t gas/o i l l e ve l pb , ps i g

30,650,35129.5300.030.0

1,37530,650,35112,716,OOO842

0.61029.5300.030.025.01,375

are controlled by gas-saturation conditions ahead of thefront. If it is assumed that each produ cing well is shut inas gas breakthrough occurs, the producing GOR will re-main a function of oil-zone gas saturation, and the totalOilLproducing rate and gas-injection rate will decline asthe front reaches each successively lower-producingwell. Th e oil-producing rate at any position of the gasfront can be determined from the productivities orallowables of the wells in the uninvaded portions of thereservoir. If it is assumed that each well is produ ced toan economically limiting GOR prior to being shut in,production from behind the front must be accounted forby use of the modified displacement equations referredto previously. In such cases, a comprehen sive fluid in-ventory is required to account for the portion o f the in-jected gas being p roduced at any time and the portionthat is advancing down struc ture. If partial-pressure-maintenance operations are being considered, it isnecessary to introduce material-balance equations tocalculate, by trial-and-error metho ds, the pressuredecline and relative positions of the advancing gas front.

The basic reservoir rock and fluid data used through outare presented in Tables 4 3.1 and 43.2 and in Figs. 43.8and 43.9.

II. Unit DisplacementA. Horizontal Gas Flow1. Equation

1fg =

wheref K = fractional gas flow,

k, = relative permeability to oil at S,,k,, = relative permeability to gas at S,,PO = oil viscosity at p, cp , andpx = gas viscosity at p, c p.2. Procedure

With complete pressure maintenance in reservoirs hav- a. Calculate and construct a fractional-flow curveing low structural relief or where the gas front is likely toadvance parallel to the bedding planes of the formation,

for selected increments of gas saturation, S,, as in-dicated in Table 43.3 and Fig. 43.10.

the cumulative hydrocarbon distribution, cross-sectionalarea, and reservoir productivity can be related to distancefrom injection to production wells. Where dispersed ga sinjection is being considered, calculations can be madefor a typical pattern element of the reservoir and theresults applied to the total number of patterns presen t.Care should be taken to select a method of reservoirrepresentation that will conform as nearly as possible tothe anticipated frontal advance in a given reservo ir.

APPENDIX AExample Calculations of FuturePerformanceI. Basic Data

Pressure(Psg)

pb = 1 3751.3001;2001,1001,000

900800700600500400300200100

0

TABLE 43.2-SUMMARY OF RESERVOIR-FLUID PROPERTIESOi l -Vo lume So lu t i on Gas-Vo lume Oi l Gas Oil Gas

Factor GOR Facto r V i scos i t y V i scos i t y Dens i t y Density

1.210 430.1 0.00178 0.480 0.0148 0.7651.200 414.9 0.00194 0.490 0.0146 0.7661.186 397.0 0.00211 0.508 0.0143 0.7671.173 379.0 0.00233 0.527 0.0140 0.7691.160 361 .O 0.00258 0.544 0.0137 0.7711.1471.1341.1201.1061.091

342.0321.7301 .o277.9254.9

0.002900.003290.003ao0.004470.00540

0.5640.5870.6090.6330.661

0.01340.01320.01290.01260.0124

0.7730.7750.7790.7030.788

1.076 230.2 0.00677 0.692 0.0121 0.7941.060 202.1 0.00904 0.729 0.0119 0.8011.043 167.9 0.01339 0.773 0.0117 0.8091.024 125.2 0.02545 0.832 0.0116 0.819

(gGl3)0.0840.0820.0790.0760.0730.0680.0620.0560.0500.0430.0350.0270.0180.0090.001.001 0.0 0.19802 0.910 0.0114 0.835


11/19

GAS-INJECTION PRESSURE MAINTENANCE IN OIL RESERVOIRS 43-l 1

b. Construct the tangent to the& curve from theequilibrium gas saturation, S,(equal to zero in this case),and read the average gas saturation behind the front atbreakthrough from the intercept w here f 1 O. Thisaverage gas saturation S R corresponds to the oilrecovery as a fraction of total pore volume behind thefront. c. Construct other tangents as required to obtainthe average gas saturations and oil recoveries at va r i ousother values of f R or frontal gas saturations S,.

B. Downdip Gas Flow1. Equation

f g = 1+0.489[k,b, -p,)sin dq, k,)l1 k r J k r ~ ) P L g h 4where& = fractional g as flow,

k,, = effective permeability to oil, darcies,P&S= g as density at p, g/cm ,P 0 = oil density at p, g/cm 3,01 = angle of gas flow (-90 ).q, = rate of frontal gas movemen t, B/D-sq ft.

k, = relative permeability to oil at S,,k % = relative permeability to gas at S,,P II = oil viscosity at p, cp, andfi, = gas viscosity at p, cp.2. Procedurea. By using a unit flow, calculate and construct afractional-flow curve for selected increments of gas

saturation, S,, as indicated in Table 43.4 and in Fig.43.11.b. Construct the tangent to thef, curve from theequilibrium gas saturation, S,,, (equal to zero in thiscase), and read the average gas saturation behind thefront at breakthrough from the- intercept where & = 1 O.This averag e gas saturation S fi correspond s to the oil

recovery as a fraction of the total swe pt pore volum e.c. Construct the tangent to the fs curve wh ere fxbecomes asymptotic to 1 O and read the ultimate or max-imum value for S R .III. Dispersed Gas-InjectionPressure MaintenanceA. Partial Pressure Maintenance1. Equations

AN,= 1 -N,;) A[ B,IB,)-R,,]-B~,bA liB,)[(B,IB,)-R,] +R(I -AG;)

I I I I I I I I10080

-1-II- L\ 4

Fig. 43.8-Reservo i r vo lum e and area as func t ions of he ight .

T

iG/

Flg. 43.9-Relat ive-permeabi l i ty data

R = instantaneous GOR , scf/STB,R = average GOR, scf/STB,

R, = solution GOR, scf/STB,SL = total liquid saturation, fraction,S,, = interstitial water saturation, fraction,k 1 = relative permeability to gas at S1,,kz = relative permeability to oil at SL,pfi = g as viscosity at p, cp ,PLO= oil viscosity at p, cp ,B, = oil FVF, RBISTB,

B = oil FVF at Pb, RB/STB,ii = gas FVF, bbllscf, andAC, = incremental gas injection, fraction of prc-

duced gas.

- I.1

-0

-0

-0

-0

AN,, = incremental oil production, fraction of OIP.N, = cumulative oil production, fraction of OIP,

N,, = cumulative oil produ ced from previous ste p,fraction of OIP,


12/19

43-l 2 PETROLEUM ENGINEERING HANDB OOK

TABLE 43.3-FRONTAL-ADVANCE CALCULATION,HORIZONTAL FLOW

s(13

k,/k,, W~ ,/lo) l+(3) f, =1/(4)2) (4) (5)-0.000l 00.02 0.004 7.725 a.725 0.11460.05 0.025 1.236 2.236 0.44720.10 0.088 0.351 1.351 0.74020.15 0.265 0.117 1.117 0.89530.20 0.770 0.0400 1.0400 0.96140.25 2.300 0.0134 1 .0134 0.98680.30 7.35 0.00420 1.00420 0.99580.35 25.15 0.00122 1.00122 0.99880.40 117.0 0.00026 1.00026 0.99970.45 755.0 0.00004 1.00004 1 .oooo

Fig. 43.10-Fronta l -advance perform ance, hor izon ta l 9as f low .

1.0 lg=O983 Ilg = 0.961

0.9 - S13=0285s , 3=0255

0.C

-m 't I/ 1

FRACTIONAL GAS SATURATION, SgRACTIONAL GAS SATURATION, Sg

so(1)0.200.250.300.350.400.450.500.550.600.65

2. Procedurea. Select pressure increments such that any onemcrement I 1 0% of the initial or bubble-point pressureand obtain fluid properties as indicated in Table 43.2.b. Perform material-balance calcu la t ion as shown

in Table 43.5 , with no gas injection, by assuming an in-cremental oil production AhJ, and verifying this value bythe trial-and-error proced ure indicated. This proced urecan be shortened by use of previous calculated ANN p orthe second and third trials at each pressure. (Note thatsubscript i in Cal. 13 refers to previous step.)c. Repea t this procedu re for various values of gasinjection as shown in Table 43 .6.d. Construct performance cu rves as indicated inFig. 43.12.

Fig. 43.1 l -Fronta l -advance performanc e, g as-cap expan-s i on .

TABLE 43.4-FRONTAL-ADVANCE CALCULATION, GAS-CAP EXPANSION

k,/k,o (k,Jk,,b ,) 1 +(3) l/(4) k C, x 6)f , =

I1 - (7)1(5)2) (3) (4) (5) 4 (7) (4

0.770 0.04000 1.04000 0.9615 0.1320 366.6 -351.52.300 0.01340 1.01340 0.9868 0.0680 188.8 - 185.37.35 0.00420 1.00420 0.9956 0.0320 88.9 -87.525.15 0.00122 1.00122 0.9988 0.0130 36.1 -35.06117.0 0.00026 1.00026 0.9997 0.0048 13.3 -12.30755.0 0.00004 1.00004 0.99996 0.0116 4.44 -3.40- 0 1 .ooooo 1 . oooo 0.0005 1.39 -0.400- 0 1 .ooooo 1 . oooo 0.00015 0.417 0.583

- 0 1.00000 1.0000 0.00004 0.111 0.889- 0 1 .oooo o 1.0000 0.00000 0.000 1.000

C, =21,306 [ k ( Pg ~~ ) s m i r l ( q , r r o ) ] ,here k I S bsolute permeability


13/19


TABLE 43.5--DEPLETION DRIVE CALCULATION, FINITE-DIFFERENCE METHOD WITH NO REINJECTION OF PRODUCE D GASAN,(assumed)

2)P,=l,375 0

1,300 0.01601,200 0.01701,100 0.01551,000 0.0147

900 0.0142800 0.0132700 0.0114600 0.0110500 0.0097400 0.0093300 0.0098200 0.0112100 0.0150

0 0.0590

N, =X(2)13)

00.01600.03300.04850.0632

1 -N, t3,1Bob(4) (5)

-1.0.00.9840 0.9920.9670 0.9800.9515 0.9690.9368 0.959

0.7000.6830.6630.6450.6289

0.0774 0.9226 0.948 0.6122'0.0906 0.9094 0.937 0.59650.1020 0.8980 0.9256 0.58180.1130 0.8870 0.9140 0.56750.1227 0.8773 0.9017 0.5537:0.1320 0.8680 0.8893 0.54030.1418 0.8582 0.8760 0.52620.1530 0.8470 0.8620 0.51110.1680 0.8320 0.8463 0.49290.2270 0.7730 0.8264 0.4472

s, =(1 - S,)(4)(5)(6) ,

1.000 22,0350.983 20,8290.963 19,9510.945 18,9690.9289 17,8410.9122 16,6510.8965 15,3570.8818 13,9190.8675 12,4090.8537 10,7770.8403 9,0890.8262. 7,1840.8111 5,1490.7929 2,882017432. 403

A0

0.00010.01600.02750.0431

8)x 9)10)02.1319.2

521.6768.9

430.1414.9397.0379.0361.0

0.0653 1.087.3 342.00.0960 1,474.3 321.70.1350 1,879.l 301.00.1890 2,345.3 377.90.2575 2,775.1 254.90.3420 3,108.4 230.20.4700 3,376.5 202.10.6560 3,377.7 167.90.9600 2,766.7 125.22.580 1,039.7 0.0

R= /q= AN, =(11)+(10) IV, +~,+,W (5,/B,)-R, (13)+(14) A[(6,/B,)-/?,I (4i)(l6)* A(118,) /3,,A(l/Bg) (17)-(19) (20/15)(12) (13) (14) (15) (16) (17) 18) (19) 20) 21)430.1 - 250.0417.0 423.6 205.0716.2 566.6 165.0900.6 808.4 125.5

1.129.9 1.015.2 86.41,429.3 1,279.6 53.5 1,333.l - 34.9 -32.7 -42.6 -51.5 18.8 0.01411,796.0 1,612.6 23.4 1,636.0 -30.1 -27.8 -40.5 -49.0 21.2 0.01302,180.l 1,988.0 -6.1 1,981.g - 29.5 -26.8 : -41.0 -49.6 22.6 0.01152,623.2 2,401.6 -30.7 2,370.g - 24.6 -22.1 - 39.8 -48.2 26.1 0.01103.030.0 2,826.6 - 52.7 2,773.g - 22.0 -19.5 -38.2 -46.2 26.7 0.00963,338.6 3,184.3 -71.3 3,113.o -18.6 -16.3 -37.6 -45.5 29.2 0.00943,578.6 3,458.6 - 84.9 3,37 3.7 -13.6 -11.8' -37.1 -44.9 33.1 0.00983,545.6 3,562.1 - 90.0 3,472.l -5.1 -4.4 - 35.9 -43.4 39.0 0.01122,891.g 3,218.8 -85.0 3,133.8 + 5.0 +4.2 -35.4 -42.8 47.0 0.01501,039.7 1,965.8 - 5.05 1,960.8 +80.0 +66.6 -34.2 -41.4 108.0 0.0551

- - - -628.6 -45.0 -45.0 -45.5731.6 -40.0 -39.4 -42.7933.9 - 39.5 -38.2 -43.8

1.103.6 - 37.1 -35.3 -42.7

-55.1-51.7-53.0-51.7

Hand calculated values rounded ofl and will vary slightly from the computer-gen erated values given here.I = previous slep

OEPLETION DRIVE, AG = 0DEPLETION DRIVE. AG, = 0 5DEPLETION DRIVE, AG, = I 0PRESS. MAIN. , AG,=l 581

I I I0.10 0.20 0.30 0.40 0.58OIL PRODUCED, N, FRACTION OF ORIGINAI OIL IN PLACE

Fig.43.12-Dispersed gas- in ject io n pressur e-maintenance perform ance.

- 010.1 0.016112.3 0.016814.8 0.015816.4 0.0149


14/19

43- 14 PETROLEUM ENGI NEERI NG HANDBOOK

JNPP (assumed)2)v

-\ G,=0. 5pb =1, 375

1,3001. 2001,1001, 000

0 00. 0230 0.02300. 0240 0. 04700. 0245 0.07150.0215 0.0930

TABLE 43.6-DEPLETION DRIVE CALCULATION, FINITE-DIFFERENCE METHODWITH DISPERSED GAS INJECTION

900800700600500

400 0. 0110 0. 1810 06190 08893 0.510 0610 9, 089 0623 5.662.4 230. 2300 0. 0114 0.1924 0.8076 08760 0.495 0795 7, 184 0860 6. 178. 2 202 1200 0. 0126 0.2050 0. 7950 08620 0. 480 0760 5,149 1 180 6.075.6 167. 9100 0. 0167 0.2217 0. 7783 08463 0. 461 0761 2, 882 1790 5,156.a 125.2

0 0. 0573 0 2790 07210 0.8264 0. 417 0717 403 4850 1. 954.5 0 0AG. =l . Op. =1.375

1,3001.2001,1001,000

R= R= (14)+ U@- AN, =(l l )+(l O) i( R, ; &; , )/ 21 (1 AG, )R (B, / B, )- R, (15) A[( B, B )- I ?,] 20) (21H6)12) (14) (15) (16) (4 ' 4; $7 A(lI8,) B, , A(l / E$)(19) 20) 21) 22)-___

N,=(2) l -N, BJ B,(3) (4) (5)

s, =(1 S, )( 4)( 5)

3)0.7000.6770.6540.6290.609

s, = f , =s, + s, (~,~~,)(P,~P,)(7) (8)

k r ro @)~(Ql R,(9) (10) (11)

10 1. 00. 9770 0 9920.9530 0.9800 9285 0.9690 9070 0. 959

1000 22, 035 0 0 430.10977 20, 829 0 009 1875 414. 90 954 19,951 0022 438. 9 397. 00 929 18,969 0044 834. 6 379. 00 909 17,841 0072 1.284.6 361. 0

0.0200 0.1130 0. 8870 0 948 0. 589 0 889 16, 651 0112 1,864. Q 342.00. 0170 0.1300 0.6700 0. 937 0. 571 0671 15,357 0167 2, 564. 6 321 70. 0150 0.1450 08550 09256 0. 554 0854 13.919 0240 X340.6 301. 00. 0135 0. 1585 08415 0.9140 0. 538 0838 12, 409 0345 4, 281 1 277. 90. 0115 0.1700 08300 0. 9017 0. 524 0624 10, 777 0465 5, 011.3 254.9

0 0 1.0 1.0 0.700 1000 22, 0350.051 0. 051 0 949 0. 992 0.659 0 959 20,8290.083 0134 0. 866 0.980 0.594 0 894 19, 9510.150 0. 284 0. 716 0 969 0. 486 0786 18, 9690.284 0. 568 0.432 0 959 0. 290 0 590 17, 841

0 0 430.10019 395.8 414. 90100 1.995.1 397.01030 19. 538. 1 379.0

170.0 3,032,970.0 361.0

430.1602.4835.9

1,213.61.645.6

-516.2719.2

1.024.81.429.6

258. 1359. 6512. 47148

250.02050165. 0125 5884

463.1 -45. 0 - 45. 0 - 45. 5524.6 -40. 0 - 39. 1 -427637.9 -39. 5 - 37. 6 - 43. 8803.2 -37. 1 - 34. 4 -427

-- 55. 5- 51. 7- 53. 0- 51. 7

105126154173

00.02270.02400.02410.0215

2,206,9 1,926.2 963.1 53. 5 1.016.6 - 34. 9 - 31. 7 - 42. 6 - 51. 5 19. 8 0.01952,886.3 2,546 6 1,273.3 23. 4 1.296.7 - 30. 1 - 26. 7 - 40. 5 - 49. 0 22. 3 0.01723,641.6 3,264 0 1, 632. 0 -6. 1 1,625.Q - 29. 5 - 25. 7 - 41. 0 - 49. 6 23. 9 0.01474,559 0 4, 100 3 2,050.2 - 30. 7 2,019 5 - 24. 6 - 21. 0 - 39. 8 - 48. 2 27. 2 0. 01355.266.2 4,912.6 2,456.3 - 52. 7 2.403.6 - 22. 0 - 18. 5 - 38. 2 - 46. 2 27. 7 0.01155.892.6 5.579.4 2.789.7 - 71. 3 2,718.4 - 18. 6 - 15. 4 - 37. 6 - 45. 5 30. 1 0.01106,380.3 6,136.4 3068.2 - 84.9 2,983.3 - 13. 6 - 11. 1 - 37. 1 - 44. 9 33. 8 0.01136,243.7 6,312 0 3,156.0 - 90. 0 3,066.O - 5. 1 - 4. 1 - 35. 9 - 43. 4 39. 3 0.01285,284.0 5,763 8 2,881.g - 85. 0 2,796.g +5.0 + 4.0 - 35. 4 - 42. 8 46. 8 0.01671.954.5 3.619.2 1.809.6 - 505 1,804.6 +80. 0 +62. 3 - 34. 2 - 414 1037 0.0575

430 1810.7

2.392.119. 917.1

3,033.331.0 1

- - 250. 0 - -6204 0 205. 0 205.0 - 4501,6014 0 165.0 165.0 -40. 0

11. 154.6 0 125.5 1255 - 39. 5, 526,624.0 0 88. 4 88. 4 - 37. 1

- -- 45. 0 - 45. 5- 36. 0 - 42. 7- 34. 2 - 43. 8- 26. 6 - 42. 7

- 55. 5- 51. 7- 53. 0- 51. 7

- 010. 5 0.05113. 7 0.08318. 8 0.15025. 1 0.284


15/19

GAS-I NJ ECTI ON PRESSURE MAINTENANCE I N OI L RESERVOI RS 43- 15

TABLE 43. 7- GAS-CAP EXPANSI ON CALCULATI ON, FI NI TE- DI FFERENCE METHOD WTHOUT COUNTERFLOWWe, - R, )+

ANN, N, = 6) R(l -AG,)[fromI I )] W) 1-Np A(B,/B -R, )2) (3) (4) (4 (4; ; y) A(l/B,) (I+ W,(7) (fromdep. dr. ) 2,(7) 3) (10) 01)-AGi-01.375 013QQ 0. 08941,200 0.08291,100 0.05461mQ 0. 0523

900 0. 0423800 0. 0350700 0. 0344AG, =0. 5

1,375 01.300 0.09411,200 0.09041,100 0.08481, QQQ 0. 0718AG, =l . O1,375 013QQ 0. 21271,200 0.3133

x.c694 A:Ez0. 1323 0. 66770.1669 0.61310. 2392 0. 76080.2815 0.71850. 3165 0. 68350. 3509 0. 64910 l . OoOO0.1046 0.69540.2103 0.78970.3124 0.68760.4092 0.59060 1.00000.2127 0.76730.5260 0.4740

-- 45. 0- 40. 0- 39. 5- 37. 1- 34. 9- 30. 1- 17. 3

-- 45. 0- 40. 0- 39. 5- 37. 1

-- 45. 0- 40. 0

- -- 46. 0 - 45. 5- 37. 2 - 42. 7- 34. 3 - 43. 8- 30. 2 - 42. 7

- 88.6 &6- 63. 2 46. 0- 05. 3 51. 0- 63. 2 53. 0

-626.6731.6933.9

1,013.6

00.08940.08290.05480.0523

- 26. 6 - 42. 6 - 83.0 56. 4 1, 331, l 0.0423- 21. 6 - 40. 5 - 78. 9 57. 3 1.636.0 0.0350- 11. 6 - 41. 0 - 79. 9 68. 1 1,961.9 0.0344- 45. 0- 35. 8- 31. 2- 25. 5

- - - -- 45. 5 - 68. 6 43. 6 463.1- 42. 7 - 83. 2 47. 4 524.6- 43. 8 - 85. 3 54. 1 837.9- 42. 7 - 83. 2 57. 7 603.2

00.09410.09040.08480.0710

-- 45. 0- 31. 5

- - - - 0- 45. 5 - 66. 6 43. 6 205.0 0.2127- 42. 7 - 63. 2 51. 7 165.0 0.3133s, s,(from (13)+(16)

A@ )18 ~fW4,dW) df; ' dr. ) f , VS. Sg)AN,NR AG, [17i )( l 2) (2W5) h,

(13) (14) (15)(l o6 bbl )16) ( , , ~ ~~I ) ~~)% ( l o3 bbl ) ( I $$) (P&&O; bbl )(17) (18) (19)__,

- -0. 00016 2,034,5600. 00017 2,161.7200. 00022 2,797,5200. 00025 3,179,000O. ooO32 4. 069, 120 0. 08780.00039 4. 959,240 0.1035o. Ocm51 6,465, 160 0. 1182

- -0.00016 2, 034,5600.00017 2. 181,7200.00022 2, 797,5200. 00025 3, 179, wo

- -0. 00016 2,034,5600.00017 2, 161,720

00.0170.0370.0550.0711

0.750 00.647' 00.647 00.647 00.647 00.647 00.645 00.645 0

0 0.7500.017 0. 647' 62i . 50.037 0.647 1,165.O0.055 0.647 1,603.50.0711 0.647 2, 120.60 0. 750 00.017 0.647' 3,927.20.037 0.647 15. 378

Calculated a, correspondmg ,a@ and pressu,e of 1.375 pslg (9480 3 kPa)Calculated at correspond,ng rate and ,xessure of 900 pslg (6205 3 kPa)

e. For cases w here the gas saturation, S, , exceedsthe critical gas saturation as determined from an fK vs.S, curve at the appropriate pressure, performance fromthat point to abandonment must be determined by thefrontal-advance metho d illustrated in III-B, whichfollows. Abando nment recovery to a limiting GOR canbe determined directly from thef, relationship.

B. Pressure Maintenance1. Equation is same as II-A in preceding section.2. Procedurea. Construct fs curve and tangents as shown inII-A. b. Calculate performanc e as shown in Fig. 43. IO.c. Construct performanc e curves as indicated inFig. 43.12.d. Calculate injection requirements for comple tepressure m aintenance at the bubble-point by the equation*G,=I+ @o/B,)-R.

IR.7 .

000

000

0 0827.5 1, 6xX. 41,992.5 4,204.23,596.0 09378.75,716.E 14, 749.3

0 03,927.2 7,616.E

19. 305.2 40.734.0

-0000000-00.30.92.1

01.3

- -2.034.6 3, 1452,161.7 3, 3412,797.5 4,3243,179.0 4,913

20. 017. 015. 412. 710. 0

4.069.1 6,289 6.94.959.2 7,699 3.46,485.2 10, 055 - 1.0

-3,640.o6366.211, 177.l

17, 930.4

5,626.o9839. 6179275. 3

27, 713. l

20. 016. 310. 63.7- 5. 2

-9, 65X4

42. 897.014, 920.266301.4

20. 012. 1- 1. 7

IV. External Gas-Injection PressureMaintenance

A. Partial Pressure Maintenance1. Equation

AN,=

(1 ~,,)A[(WB,)W ?,] -(I +~P,,~,Nl~B,)[cB,/B,)-R,]+R(IAC,)

whereLW,, = incremental oil production, fraction of OIP,N,,; = cumulative oil production from previous

step, fraction of OIP,R = average GOR, scf/STB,

R,Y = solution GOR, scf/STB,B, = oil FVF, RBISTB,

Bob = oil FVF at pb, RBISTB,


16/19


; * c i , - II AG =05 I

7 o o o m5.6000 c c5000 4

z4ocDg

23000~z2000 02&IO00 a

- 102 03 04 05 06 07 08 09 IO0OIL PRODUC ED, NpFRACTION OF ORIGINAL OIL IN PLACE

Fig. 43.13-Extern al gas-injection preSSure-maintenanceperformance.

B, = gas FVF, bbllscf,AG; = incremental gas injection, fraction of

produced gas, andm = ratio of gas-cap to original o il-zone volume,

fraction.(Note that subscript i refers to previous step.)

2. Procedurea. Select pressure increments such that any oneincrement I 10% of the initial or bubble-point pressureand obtain fluid properties as indicated in Table 43.2.b. Perform depletion d rive material-balance cal-culation with AG; =O, as described in III-A.c. Perform material-balance calculation as shownin Table 43 .7, using R as determined from depletiondrive calculation in Point b and S g as determined fromunit-displacement calculations.d. Determine positions of gas/oil level and aban-donment conditions, using data in Fig. 43.8 and calcula-tions in Table 43.7.e. Construct performance curves as indicated inFig. 43.13.B. Pressure Maintenance1. Equation is the same as II-B.2. Procedurea. Constructf, curve and tangents a s in II-B.

b. Calculate recovery and construct performanc ecurves as indicated in Fig. 43.13.c. Calculate injection requirements for completepressure maintenance at the bubble-point by the equation

AG,=l+ [W&-R,]R,

APPENDIX BSelected References ContainingEquations, Calculation Procedures, andExample Calculations Related to Gas-Injectlon Performance PredictionsExternal Injection-Complete PressureMaintenance

Emphasis on Gravity Drainage and Segregation1. Combs, G.D. and Knezek, R.B.: Gas Injection for Upstructure

Drainage, J. Pet. Tech. (March 1971) 361-72.2. Craig, F.F. Jr. etal.: A Laboratory Study ofGravity Segregation

in Frontal Drives, J. Pet. Tech. (Oct. 1957) 275-81: Trans.,AIME, 210.

3. Martin, J.C.: Reservoir Analysis for Pressure MaintenanceOperations Based on Complele Segregation of Mobile Fluids,Trans., AIME (1958) 213. 220-27.

4. McCord, D.R.: Performance Predictions Incorporating GravityDrainage and Gas Cap Pressure Maintenance - LL-370 Area,Bolivar Coastal Field, J. Pet. Tech . (Sept. 1953) 231-48; Trans.,AIME. 198.

5. Shreve, D.R. and Welch, L.W. Jr.: Gas Drive and GravityDrainage Analysis for Pressure Maintenance Operations, J. Pet.Tech. (June 1956) 136-43; Trams., AIME. 207.

6. Stewart, F.M., Garthwaite, D.L., and Krebill, F.K.: PressureMaintenance by Inert Gas Injection in the High Relief Elk BasinField, J. Pet. T ech. (March 1955) 49-55; Trans., AIME. 204.

7. van Wingen, N., Balton, W.C. Jr., and Case, C.H.: CoalingaNose Pressure Maintenance Projecl, J. Per. Tech. (Oct. 1973)1147-52.

General Frontal-Advance Applications1.2.

3.

4.

5.

6.7.

Buckley. S.E. and Leverett, M.C.: Mechanism of FluidDisplacement in Sands, Trans., AIME (1942) 146, 107-16.Craft, B.C. and Hawkins, M.F.: Applied Petroleum ReservoirEngineering, Prentice-Hall Inc., Englewood Cliffs, NJ (1959)361-75.Dardaganian, S.G.: The Application of the Buckley-LeverettFrontal Advance Theory to Petroleum Recovery, J. Pet. Tech.(April 1958) 49-52; Trans., AIME (1958) 213, 365-68.Justus, J.B. et al.: Pressure Maintenance by Gas Injection in theBrookhaven Field, Mississippi, J. Pet. T ech. (April 1954)43-53: Trans.. AIME (1954) 201. 97-107.Kirby, J.E. Jr., Stamm, H.E. 111.and Schnitz. L.B.: Calculationof the Depletion History and Future Peformance of a Gas-Cap-Drive Reservoir, J. Pet. T ech. (July 1957) 218-26; Trans.,AIME, 210.Pirson, S.J.: Oil Reservoir En neering, McGraw-HIII Book Co.Inc., New York City (1958) 555-605.Snyder, R.W. and Ramey, H.J. Jr.: Application of Buckley-Levereu Displacement Theory to Noncommunicating LayeredSystems, J. Pet. T ech. (Nov. 1967) 1500-06: Trans.. AIME,240.

8. Stutzman, L.F. and Thodos, G.: Frontal Drive ProductionMechanisms-A New Method for Calculatmg the DisplacingFluid Saturation at Breakthrough. J. Pet. Tech. (April 1957)67-69; Trans., AIME, 210, 36+66.

9. Welge, H.J.: A Simplified Method for Computing Oil Recoveryby Gas or Water Drive. Trans., AIME (19 52) 195, 91-98.

Gas Displacement Above the Bubble-Point ndProduction From Behind the FrontI. Kern, L.R.: Displacement Mechanisms in Multi-Well

Systems. Trans., AIME (1952) 195, 39-46.2. Shreve, D.R. and Welch, L.W. Jr.: Gas Drive and GravityDrainage Analysis for Pressure Maintenance Operations, J. Pet.

Tech. (June 1956) 136-43: Trrms., AIME, 207.Nonequilibrium Gas Displacement

I. Attra, H.D.: Nonequilibrium Gas Displacement Calculations,Ser. Pet. Eng. J. (Sept. 1961) 130-36; Trans., AIME, 222.

2. Jacoby. R.H. and Berry, V.J. Jr.: A Method for PredictingPressure Maintenance Performance for Reservoirs ProducingVolatile Crude Oil, J. Pet. Tech. (March 1958) 59-69: Trans.,AIME, 213.

Gas injection in Combina tion Drive ReservoirsBlair, E.A. et al.: A Reservoir Study of the FriendswoodField, J. Pet. Tech . (June 1971) 685-94.Cotter, W.H.: Twenty-Three Years of Gas Injection Into AHighly Undersaturated Crude Reservoir, J. Per. Tech. (April1962) 361-65.Wooddy. L.D. Jr. and Moscrip, R. III: Performance Calcula-tion& for Combination Drive Reservoirs, J. Pet. Tech. (June1956) 128-35: Trans., AIME, 207.


17/19


Dispersed Gus Injection-Complete uncl PurtiulPressure Muintenunce1.

2.

3.

4.5.

6.

7.

8.

9.

IO.Il.

12.13.

14.

Craft, B.C. and Hawkins. M.F.: Ap/)/ied Prrrolrurn RrvrrwrrEngirirrring. Prentw-Hall Inc.. Englewood Cliffs, NJ (1959)37s~90.Crttig, F.F. Jr. and Gcffen. T.M.: The Determination of PanialPressure Maintenance Performance by Laboratwy Flow Tests,J. Per. Trrh. (Feb. 1956) 42-49: ~r&s.. AIME; 207.Craig. F.F. Jr., Geffen, T.M.. and Morwz, R.A.: 01 RccovcryPerformance of Pattern Gas or Water Injection Operations fromModel Test\, J. Prr. T&I. (Jan. 19.55) 7-14: Trnnc , AIME.204.Has, R.L.: Calculated Effect of Pressure Maintenance on OilRecovety. ~ Trm.\. , AIME (1948) 174. 121-30.Kelly. P. and Kennedy, S.I..: Thirty Year5 of Effective PmawrcMaintenance By Gas Injection III the Htlbig Field. J. Per. Tdz.(March 1965) 279-X I.Last. G.J.. Craig. F.F. Jr.. and Reader. P.J.: Significance 01PAttial Pressure Maintenance hy Fluid Injectton. J Per. T~I.(Jan. 1964) 20-24.Lcihrock. R.M.. H&z. R G.. and Huzarcvich. J.E.: Results 01Ga Injection in the Cedar Lake Field, Trrrrzs.. AIME (1951)192, 357-66.McGraw, J.H. and Lohec. R.E.: The Pickton Field-Review 01a Successful Gas Injection Project. J. PC,/. Qc,/i. (April 1964)399-404: discussion, 405.Meltrer, B.D.. Hurdle. J.M., and Cassingham. R.W.: An Elft-cicnt Gas Displacement Project-Raleigh Field, Mi\aissippl. J.PH. 7id1. (Mav 1965) 509%14.Muskat, M.: P/&cd Priwiples of Oil Proc/uctior~, McGraw-HillBook Co. Inc., New York City (1949) 437-53.Patton, E.C. Jr.: Evaluatmn tit Prewure Mamtenance by InternalGas InJectmn tn Volumetrtcally Controlled Reservoirs, Trtrn.r.AIME (1947) 170, 112-52: Discussion. 154-55.Pirson, S.J .: 011 Re.c~rwir Efr~~nwn,~fi, McGrawHill Book CoInc.. New Yorh City (1958) 4X4-532.Shehahi, I A.N.: Effective Displacement ofOil by Gas ln,jectionin B Preferentially Oil-Wet, Low-DIP Rewvoir. J. Pet. Td?.(Dec. 1979~ 1605Sl3.Tracy. G.W.: Sm~pltficd Form of the Maternal Balance Equa-tion, J. Pet. Tdt. (Jan. 195.5). X-56: Tiwts.. ACME. 204.?I~-46.

Mathernaticul M odels for Reservoir Simu lationCoats. K H.: An Analysis for Stmulating Reservoir PerformaxeUnder Preawre Maintenance by Gas and/or Water Injectton.Srx PH . Eq. J (Dec. 1968) 331-40.Cook. R E.. Jacoby. R.H., and Ramesh, A.B.: A Beta-TypeReservoir Simulator for Approximating Compositional EffectsDuring Ga Injection. Sot. Pcv. &IX. J. (Oct. 1974) 471-81.McCulloch. R.C.. Langton. J.R.. and Spivak. A.: Simulation ofHigh Relief Reservoirs. RainboLc Field. Alhcrta. Canada. J. PC/.TciIr. (Nov. 1969) 1399-1408.McFarlanc. R.C.. Mueller. T.D.. and Miller. F.G.. Unsteady-State Distnbutwns of Flutd Compositions in TwovPhase OilReserwirs Lindergoing Gas In,jection. SIC,. Per. EQ. J. (March1967) 61-74: Twrx.. AIME. 240.Price. H.S. and Donohue. D.A.T.: Isothermal Di\placrmentProcese\ With Interphase Mass Transfer. .S~x. Pet. Eq. J.(June 1967) 20.5-20. Trcln.\. AIME. 240.Strickland. R.F. and Morse. R.A.: Gas Injection for Upatructurc011 Dranage. J. PC,/. 7d1. (Oct. 1979) 1323-3 I.Thomas. L.K.. Lumpkin. W.B.. and Rchcis. G.M.: Rc~crwirSlmulatton of- Varlahle Bubble-Point Prohlerm. Sock. PC, . E/Q.J. (Feb. 1976) 10-16.

APPENDIX CData Requirements for EngineeringAnalysis of Gas-Injection OperationsIAnalytical Data

1. Core analyses from a representative number ofwells

a. Porosityb. Permeabilityc. Water saturation2. Special c ore analyses on a sufficient number o fsamples to cover permeability range of the reservoira. Capillary-pressure data (for determining in-terstitial saturations)b. Gas/oil relative permeability, k,/k,c. Relative permeability to oil, k,,,3. Hydrocarb on comp ositional analysisa. Gas-cap, casing-head, and trap samplesb. Reservoir-fluid samples

4. Reservoir-fluid property analysesa. Solubility(1) Flash(2) Differentialb. Relative oil volume(1) Flash(2) Differentialc. Oil viscosityd. Oil densitye. Gas viscosityf. Gas density

Field Data1. Developm ent history2. Abandonment history, if any3. Production historya. Oilb. Water

c. Gas4. Injection history, if anya. Gasb. Water5. Pressure history6. Well productivity data7. Gas/oil and oil/water contacts (original an dpresent)

8. Well and test dataa. Drillstem testsb. Production testsc. Sample cuttingsd. Core descriptionse. Electrical and radioactivity logs

9. Average reservoir temperature10. Well completion dataInterpretive Dataprepared from preceding data)

1. Structure mapsa. Top of zoneb. Base of zone2. kopachous mapsa. Total net sandb. Net gas sandc. Net oil sand3. Reservoir volume distributiona. Volume vs. subsea depth, and/orb. Volumes by injection/production units

4. Cross-sectional areaa. Area vs. subsea depth, and/orb. Area perpendicular to bedding planes for injec-tion/production units


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43- 18 PETROLEUM ENGI NEERI NG HANDBOOK

5. Volume-weighted reservoir datum6. Averag e reserv oir fluid proper ties (as functions ofpressure)

a. Differential oil formation volume factorb. Flash relative volume factorc. Gas formation volume factord. Oil viscositye. Gas viscosityf. Oil gravityg. Gas gravityh. Gas deviation factori, Differential gas solubilityj. Averag e oil and gas compositionk. Oil and water compressibility

7. Volume-weighted average pressures8. Permeability distribution9. Average reservoir-rock propertiesa. Porosityb. Permeabilityc. Interstitial water saturationd. Gas/oil relative permeability ratio, kg/k,e. Oil relative permeability, k,/k

10. Well productivitiesa. As a function of subsea de pthb. By injection/production unitsc. Productivity indices

NomenclatureA=

B,, =B,, =

B;: 1A($;. =k,, =

k,.,s =k,.,, =

L=nl =M =

N,, =M,] =P=

Pb =

cross-sectional areagas FVFoil FVFoil FVF at P),fractional gas flowincremental gas injectioneffective permeability to oilrelative permeability to gasrelative permeability to oildistanceratio of gas-cap to original oil-zone volumemobility ratiocumulative oil productionincremental oil productionpressurebubblepoint pressurep,. = oil/gas capillary pressure ( p. -P,~)

q, = total flow ratef = instantaneous GO RR = average GOR

R, = solution GORS,, = gas saturationS,, =. total liquid saturationS,,. = interstitial water saturation

f = timecy = angle o f dip, p ositive down dip

p s = gas viscosityP ,I = oil viscositypx = gas densityPO = oil density4 = porosity, fraction

Key Equations in SI Metric Units

f

I +(8.639x 10-5)[k,,Aiipq,)] -9.795(p,,-p,)s~1 N1

where.fg =91 =A=

P,. =L=

PO =

fractional flow of gas,total flow rate, m3/d,cross-sectional area, m2,oil/gas capillary pressu re, P ,, -pg. kPa,distance, m,oil specific gravity (water = 1) or density.

g/cm3,Pg = gas specific gravity (water = 1) or density,g/cm,

Cl= angle of dip, positive downdip, degree s.kc, = effective permeability to oil,, pm,k = effective perm eability to gas, pm,PLO = oil viscosity, Pass. an dPh = gas viscosity, Pa* s.

I+ y :t). . . . . . . . . . . . . . . . . . . . . . . . . . . . . (1)

L=q,r 3~A( > . .s,s 2)where

t = time, days,C = porosity, fraction,

S,q = gas saturation, fraction,and others are as in Eq. 1.

fq = 1+0. 848x lo-[k ,,(p, -0,)) sin oll(y,p,,)]

l+(t) (2)

(A.1I.B)where

akc,k,0,POCY9/

CL,,h

= fractional gas flow,= effective perm eability to oil, pm,= effective perm eability to gas. pm.= gas specific gravity at p (water= 1).= oil specific gravity at p (water= I),= angle of gas flow (-90).= rate of frontal gas movement, m /d*m2= oil viscosity at p, Pa *s. and= gas viscosity at p. Pa.s.

Note: All other material-balance, saturation. and GO Requations that follow are correct for standard SI units,where B ,, and B,v are volume factors (in m /m3) and R.R,, and R, are GORs (in mim).


19/19

GAS-INJECTION PRESSURE MAINTENANCE IN OIL RESERVOIRS 43 19

References

5.6.

7.

8.

Muskat. M.: Ph~sica/ Prinqles os0il Pwducrion. McGraw HillBook Co. Inc.. New York City (19491 709.Bucklev. S.E. and Leverett. M.C.: Mechanism of FhxdDisplacement in Sands. Trcrrlr.. AIME (1942) 146. 107 16.Welge. H.J.: A Simplified Method for Computing Oil Recoveryby Gas or Water Drive, Trclns.. AIME (1952) 195. 91-98.Dardaganian. S-G.: The Application of the Bucklev-LeverettFrontal Advance Theory to P&leum Recovery. J. Per. Tech.(April 1958), 49-52: Trms., AIME, 213. 365-68.Kern, L.R.: Displacement Mechanism in Multi-well Systems,Truns. ( AIME ( 1952) 195. 39-46.Shreve. D.R. and Welch, L.W. Jr.: Gas Drive and GravityDrainage Analysis for Pressure Maintenance Operations, J. Per.Tech. (June 1956). 136-43: Tram.. AIME. 207.Jacoby. R.H. and Berry. V.J. Jr.: A Method for PrechctingPressure Maintenance Performance for Reservoirs ProducmgVolatde Cmde Oil, J. Per. Tech (March 19%). 59-69: Trans.,AIME, 213.Attra H.D.: Nonequilibrium Gas Displacement Calculation,Sot. PC . Eng. .I (Sept. 1961) 130-36; Trms., AIME. 222.

9. Craft, B.C. and Hawkins, M.F.: A&rd Petroleum Reserw;rEngineering, Prentice-Hall Inc., Englewood Cliffs. NJ (1959)370

10. Anders, E.L. Jr.: Mile Six Pool-An Evaluation of Recovery Ef-ficiency, J. Per. Tech. (Nov. 1953) 279-86; Truns.. AIME.198.

1 I. Craig, F.F. Jr. and Geffen, T.M.: The Determination of PartialPressure Maintenance Performance by Laboratory Flow Tests.J. Per. Tech. (Feb. 1956) 42-49; Trcms.. AIME. 207.

I?. Slobod, R.L. and Koch, H.A Jr.: High Pressure Gas Injec-tion-Mechanism of Recovery Increase, 0-i//. and Prowl. Pm-. ,API (1953) X2.

13. Stiles, W.E.: Use of Permeability Distribution in Water FloodCalculations, Trans.. AIME (1949) 186, 9-13.

14. Dyes, A.B.. Caudle, B.H.. and Erickson, R.A.: Oil ProductIonafter Breakthrough as Influenced by Mobility Ratio. J. Per.T?ch. (April 1954), 27-32; Truns., AIME (1954) 201, 81-86.

15. Patton, E.C. Jr.: Evaluation of Pressure Maintenance by InternalGas Injectcon in Volumetrically Controlled Reservoirs. Trans.,AIME (1947) 170, 112-52, Discussion 154-55.

43 - Gas-Injection Pressure Maintenance in Oil Reservoirs

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