effect of aquifer size.pdf

7/22/2019 Effect of Aquifer Size.pdf

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Iranian Petroleum Engineering Congress

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Effect of Aquifer SizeOn the

Performance of Partial Waterdrive Gas Reservoirs

Shahab Gerami,Abdollah Mohammadi , Abdolhossein Mohammadi

-R&D National Iranian Oil Company - Science and Research branch, Islamic Azad University,Tehran, Iran.

- Science and Research branch, Islamic Azad University, Tehran, Iran - Iranian Central OilField Company.

- Sepanir Oil & Gas Energy Engineering CO.

[email protected]

Summary

Predicting the advancement of a gas/water contact (GWC) in awaterdrive gas reservoir plays an important role in evaluating,forecasting, and analyzing the reservoir performance. This study wasconducted to predict the behavior and the rise of the GWC, assumingthat it remains horizontal, and to determine its effect on ultimate gasrecovery. Several factors control the rise of the GWC. Some of the mostimportant factors are the size of the aquifer, gas production rate, initialreservoir pressure, and formation permeability. These factors accountfor the abandonment of a number of gas reservoirs at extraordinarilyhigh pressure.Several methods have been developed for predicting the volume ofwater influx into a reservoir; the van Everdingen-Hurst method is used inthis study. The performance calculated in this study was based on the

material-balance equation for gas reservoirs. The gas reservoir pressurewas adjusted to the original GWC for the water-influx equation, and thetrapped gas in the water-invaded zone was accounted for in the water-invaded region. A constant reservoir permeability of md was used inall calculations. The results showed that when ra/rg , the effect of theaquifer on gas reservoir performance can be neglected. Also, the rate atwhich the GWC advances is controlled by the aquifer size when ra/rg > .Finally, regardless of the size of the reservoir, when ra/rg > , thepressure in the unsteady-state water-influx equation has to be corrected

to the original GWC. Failure to do so may result in an error of more than


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% in the cumulative water influx, which in turn could lead to thewrong conclusions regarding the performance of the gas reservoir.

Key words: gas/water contact (GWC) - size of the aquifer, gasproduction rate - initial reservoir pressure - formation permeability - vanEverdingen&Hurst method.

- Introduction

Several methods for predictingthe depletion performance ofwaterdrive gas reservoirs havebeen published in the literature. -

Bruns et al. studied the effect ofwater influx on the p/z-vs.-Cumulative-gas-productioncurves. From their Study, they

concluded that it is dangerous toextrapolate the p/z charts on astraight line without consideringthe possibility of water influx.

Agarwal et al. used a material-balance model to study the effectof water influx on natural gasrecovery. On the basis of theircalculations, they concluded thatgas recovery depends onproduction rate, residual gassaturation, aquifer strength,aquifer permeability, and thevolumetric sweep efficiency ofthe encroaching water zone.Dumor predicted the futurebehavior of a bottomwater-drivegas reservoir. In his study, heneglected the total

compressibility and assumed that

all the gas in the reservoir andthe free gas in the water-invaded

zone was at the same averagereservoir pressure and that therising of the GWC remainshorizontal all the time. On thebasis of his study, he concludedthat the straight-line relationshipbetween p/z and GP obtainedfrom reservoir pressure data inthe early life of the reservoir does

not necessarily indicate a gasdepletion-type productionmechanism but is consistent witha moderate water influx. Thecalculated p/z curve (in hisexample of a gas reservoir)deviated very little from thestraight line until more than %of the initial gas in place hadbeen produced.When the pressure dropped to

atm ( kpa), the calculatedGp was about% of the initialgas in place, and the GWC hadrisen to about % of the closureof the reservoir.In , Knapp et aL developeda two-phase, Two-dimensionalmodel to predict gas recovery

from aquifer storage fields. The


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model was used to study the

effects of heterogeneity, aquiferstrength, and gas productionrates. From the results of theirstudy, they concluded that gasrecovery is a function of gasproduction rate, aquifer strength,and heterogeneity. Their conclusions agree with those of

Agarwal et al. regarding the gas

production rate and aquiferstrength.Sbagroni studied the effect offormation compressibility andedge water on gasfieldperformance. On the basis of theresults of his study, he concludedthat it is incorrect to extrapolatethe early part of the plz-vs.-GP

curves as a straight line top/z=. to estimate the initial gasin place without considering thepossibility of water influx and theeffect of formationcompressibility, and that thesensitivity of the performancecurve (p/z vs. Gp) to formationcompressibility increases as theinitial reservoir pressureincreases.

An experimental study of residualgas saturation under waterderivewas performed by Geffen et al .in . The results of theirexperimental study indicated thatresidual gas saturation underwaterdrive varies from to %pore space, depending on the

type of sand.

pepperdine used a

mathematical model to study theperformance of the Devonian gasfields in northeastern BritishColumbia.From the results of themathematical model and theanalysis of the actual field data,he concluded that to achievemaximum gas recovery, the

depletion Process should beincreased as much as possibleby production practices, and thattie important factor in the lowefficiency of gas recovery waswater influx rather than theconing phenomenon in theportion of the Clarke Lake fieldthat was modeled.

Lutes et al. studied theperformance of a strongwaterdrive gas reservoir (Katy V-C Reservoir in the U.S. gulfcoast) with a modified materialbalance equation that accountsfor higher pressure in the water-invaded zone. They reachedconclusions similar to that ofPeppdine regarding the effect ofrapid blowdown of waterdrivegas reservoirs. They alsomonitored the advancement ofthe GWC of the Katy gasreservoir as it was put onaccelerated blowdown, and analmost vertical front wasobserved.GiWenS used a simulation

model to determine the effects of


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well density, production rates,

water influx, water coning, androck and fluid properties on thedepletion performance of dry gasreservoirs with bottomwaterdrive. On the basis of his results,he concluded that the bestperformance for reservoirs withbottomwater drive will notnecessarily be obtained by high

producing rates and that thepresence of bottomwater drive ingas reservoir lowers the ultimaterecovery and increases theproducing life of the gasreservoirs.The objective of this study is topredict the depletionperformance of partial,

waterdrive gas reservoirs;particularly to study the effect ofaquifer size, gas production rate,and initial reservoir pressure onthe rate at which the GWCadvances and on gas recovery.

- Method of CalculationThe depletion performance of thentural gas reservoir bounded byan aquifer was predicted with amaterial-balance model. Fig.shows the geometry of the flowmodel used in this study. Themodel assumes that () there isno phase change in thereservoir;( ) the residual gas saturation in

the water-invaded zone, Sgrw, isequal to %; ( ) there is nowater production;( ) the GWCremains horizontal at all times;and ( ) a fault exist at rf.The general form of the material-

balance equation for a gasreservoir is

G(Bg-Bgi) + (cwswi + cf)(pi-p) +

. we= GpBg+. WPBw.....()

Note that the gas FVFs for Eq.are in cubic feet per standardcubic foot. By writing thematerial-balance equation (Eq.)in terms of p and z and solvingfor the cumulative water influx,We, we obtain Eq. :

We={Gp(z/p)-G(z/p-zi/pi)-G[zi/pi/(-swi)] (cwswi+cf) (pi-p)}TPsc/ . Tsc ...............( )

Note that Eq. requires the initialgas in place, G, to be known tobe able to evaluate We. In thispaper, G is assumed to beknown, The initial gas in place,G, can be obtained either by avolumetric method or from thepast performance of the gasreservoir as suggested by


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Shagroni. The volumetriccalculation of the initial gas inplace for the flow model shown in

Fig. can be obtained by thefollowing equation :

GBgi=FS h(rg -rf )(-swi).......( )

Note that rfcan be expressed asa fraction of rg such that

rf=arg.( )

where a is a constant less thanone.Substituting Eq. into Eq. results in

GBgi=FShrg (- )(-Swi) .( )

Fig.- Schematic of simplified radial flowmodel.

If G, pi, Fs,,h,a, and Swi: areknown, Eq. can be solvedfor r g, and the initial pore

volume,Vpi, can be determined.The cumulative water influx, we,into the gas reservoir iscalculated from the vanEverdingen and Hurst

unsteady-state water influxequation:

Wen= [ew (tdn-tdj-)

pj] , for j=-n............................( )

Where td = .( )

pj= for j .....( )

And

p= for j=... ( )

Note that pJ in Eq. is thepressure drop at the originalGWC as a fiction of time, t. Inthis study, at t=O, the aquifer isassumed to be at staticequilibrium. For t> O, the

pressure at the original GWC


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drops with time as a result of

production, causing the water

TABLE.- RESERVOIR AND AQUIFER PROPERTIES

Fig. - Average reservoir pressure and

pressure at original GWC performance for

pj= ,

psia and various ra/rg.


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Fig. - Average reservoir pressure and

pressure at original GWC performance forpj= , psia and various ra/rg.

Of the aquifer to expand andinvade the gas reservoir acrossthe original GWC. Thecumulative PV of the water-invaded zone at time tn, Vpmn, canbe calculated by the followingequation:

VPWN= pw forj=-n.. ( )

Where

pwj=[(wej-wej-)-(wpBw)j+(wpBw)j-

+( Sgrw)]/(-Swi-Sgrw) ,fr k=(-j-).......( )

Having determined thecumulative PV of the water-

invaded zone, the remaining PVcontaining free gas, VPcn, above

the GWC canbe determined by

Vpcn=Vpi- Vpw , for j=-n......( )

The corresponding rise of theGWC ( hn) above the original

GWC can be determined by useof the following relation:

hn=(rg-rgn) ....( )

where rgn is the radius of theremaining gas PV and can becalculated with Eq..

The pressure at the originalGWC at time tn can be calculatedby the following equation:

pnoGWC = pn+. hn w+,..... ( )

Where dWe/dt is the rate of water

influx and can be evaluated from


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the previous timestep or by

iteration if it is taken at the sametimestep. In this study, dWe/dtwas evaluated from the previoustime step.For details of the calculationprocedure, Ref. should beconsulted.

- Results

Depletion performance for apartial waterdrive gas reservoirwas computed under differentreservoir and aquifer conditions.Table presents details of thereservoir and aquifer propertiesused in this study. The

performance was computed for arange of aquifer sizes, gasproduction rates, initial reservoirpressures, and two differentsizes of gas reservoirs to allowevaluation of the importance ofseveral key factors. A reservoirpermeability of md was usedin all the calculations.Figs. and show theperformance of the average gasreservoir pressure and thepressure at the original GWC fordifferent aquifer sizes. It shouldbe noted that the gas reservoirshown in Fig. is times biggerthan that shown in Fig.. Thesefigures show that the differencebetween the average gas

reservoir pressure and the

pressure at the original GWC

increases as the size of the gasReservoir increase as the aquifersize increases. This indicates theimportance of using the pressureat the original GWC to calculatethe unsteady-state cumulativewater influx.

Figs. and present the P/Z vs.cumulative gas produced, GP, fordifferent aquifer sizes andvarious gas production rates.Several important features of thecurves are noted below.

. As the aquifer size increases,the p/z-vs.-GP curves departfrom the straight-line

relationships (dashed lines onFigs. and ) for a volumetricgas reservoir and tend to be athigher levels. This indicates thedanger of extrapolating the earlypart of these curves to p/z equal

to zero to obtain tbe initial gas inplace.Not only do the curves tend to beat higher levels, but gas recoveryat a given Initial reservoir pressure and gas production ratetend to decrease as the aquifersize increases.


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. Gas recovery is found to be

rate sensitive only for largeaquifer sizes, r a/rg > . For thegiven reservoir conditions, whenra/rg increased from to , gasrecovery tended to be lower atlow gas production rates. Thisindicates the dependency of gasrecovery on the field gasproduction rate. It should also be

noted that low gas productionrates tend to keep the p/z-vs.-GPcurves at high levels, while highgas production rates permitdrawing down the gas reservoirpressure before water influxcompletely floods the reservoir.

. The effect of initial reservoir

pressure on the performance ofthe gas reservoir and on gasrecovery can be seen bycomparing the results of Figs.and. Figs. and show that fora given gas production rate,when the initial gas reservoirpressure increases

Fig. - P/Z-VS.GP curve performance for

pj= ,

psia , various ra/rg andvariousgas production rates.

Fig. - P/Z-VS.GP curve performance for

pj= , psia , various ra/rg andvariousgas production rates.

from, to , psia [ . toMPa], gas recovery was not

affected when ra/rg = . However,the level of the P/z-vs.-Gp curvestends to be at higher levels forthe high-initial-gas-reservoirpressure cases, For ra/rg > , gasrecovery is affected by the levelof the initial pressure and tendsto be lower at a given gas

production rate for the high initialgas reservoir pressure. Figs.and show that the calculatedgas recovery for a gasproduction rate of MMscf/D[ x std m /d] and r a/rg =ranges from an excess of %for initial pressure of , psia[ . MPa] to % for an initial

pressure of , psia [ MPa].


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The results of this study

regarding the performance of theP/Z-VS-Gp curves for largeaquifer sizes (ra=/rg >) and theeffects of gas production ratesand initial reservoir pressure ongas recovery agree with those of

Agarwal et al. for an initialaquifer.

Although the effect of aquifer

permeability on the gas reservoirperformance is not the target ofthis study, it is worthwhile tomention some results obtainedfrom this study regarding thesubject.

The effect of aquifer permeability

on gas reservoir performancewith water influx was studied byBruns et al. for finite aquifersand by Agarwal et al. for aninfinite aquifer. Bruns et al.showed that for ra/rg = . , theeffect of the aquifer on theperformance of the gas reservoiris negligible for the given watercompressibility of.x - Psi-[. x - kpa-l], Porosity of. , and water viscosity of l.cp [. mPa. s], regardless of thepermeability. Their result agreeswith the results obtained fromthis study ra/rg = .. Agarwal etal. showed that the aquiferpermeability has a great effect onthe gas reservoir performance

and on gas recovery for an

infinite aquifer. They also

showed the effect of gasproduction rate on gas recoveryfor various aquifer permeabilityand conclude that gas recoverydecreases as the permeabilityincreases.In this study, an aquiferpermeability of md was used,and when ra/rg increased fromto , gas recovery appeared tobe sensitive gas production rate.Fig. shows this effect forproduction rate of MMscf/D per, , and Bscf [ . std

m /d per . , I . ,and. std m ] of initialgas in place.

Fig. - Effect of gas production rate on the

GWC performance.


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Fig. - Effect of initial reservoir pressure on

the GWC performance.

Fig. - Effect of aquifer size on the GWC

performance.

Fig. - Effect of expansion of trapped gas in

the water invaded zone on the cumulativePV invaded.

To show the effect of ra/rg on the

performance of the GWC andgas recovery, one of the casespresented in Fig. is repeatedfor an initial gas reservoirpressure of , psia [ MPa]and is presented in Fig.. Notethat as the initial gas reservoirpressure increases, gas recoveryDecreases and the GWC

advances at a higher rate thanthe rate for low or moderateinitial gas reservoir pressure.Figs. and show the effect ofthe aquifer size and theexpansion of the trapped gas inthe water-invaded zone on therate at which the GWCadvances. Because of gas

production, the gas reservoirpressure declines, and inresponse to the pressure drop,the aquifer reacts to offset or toretard the pressure decline byproviding a source of water influxor encroachment by theexpansion of the water andaquifer rock compressibility.Consequently the GWCadvances, entrapping some gasbehind it.As the reservoir pressurecontinues to decline, the GWCcontinues to advance and thetrapped expands, resulting in anacceleration of the rate at whichthe GWC advances. Note thatthe rate at which the GWC

advances is controlled by the


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rate of water influx and the

expansion of the trapped gas inthe water-invaded zone, as canbe seen from Figs. through .

As ra/rg increases, the expansionof the trapped gas decreasesand can be neglected when ra/rg>., as can be seen from Fig. .

So far, field gas production rate

was assumed to be maintainedAs a constant level throughoutthe producing life of the field.

Although this might be achievedby drilling additional wells in theunflooded area, it is more likelythat it will decline. The decline inthe field gas production rate canbe attributed to many

factors.important among themare the encroachment of waterinflux and the rise of the GWC.Figs. through present thepredicted performance of apartial waterdrive gas reservoirfor a constant gas productionrate of

Fig. - Effect of decline gas production

rate on the performance of average gasreservoir pressure.

Fig. - Effect of decline gas productionrate in the P/Z-VS- GP curve performance.

MMscf/D[ * std m /d]and a declining gas productionrate. The declining rate startedwith an initial rate of MMscf/D[ * std m /d] and thendeclined in proportion to thevolume of the reservoir notinvaded by water.Fig. shows that after yearsof production, the predictedaverage gas reservoir pressureat a constant rate declined morequickly than that predicted at a

declining gas production rate.Fig. also shows that theabandonment pressure for thedeclining rate is as much astwice that for the constant rate.Figs. and show theperformance of the P/Z-vs.-GPcurves and gas recoveriespredicted by the two rates. It is

noted from these figures that thedeclining gas production rate


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tends to keep the P/z-VS.-GPcurve at high levels and giveslower gas recoveries. It is alsonoted that the declining gasproduction rate tends to increasethe producing life of thereservoir, as Can be seen fromFig. .It should be emphasized that theresults presented in this paper

regarding the effect of gasproduction rate on ultimate gasrecovery are based on theassumption that the GWC willremain horizontal all the time andthe water coning is not acontrolling factor.

- conclusions

On the basis of the results of thisstudy for a constant reservoirpermeability of md and otherreservoir and aquifer propertiesshown in Table , the followingconclusions were reached.. When ra/rg < , the effect of theaquifer on the performance of thegas reservoir can be neglected.. Regardless of the size of the

reservoir, when ra/rg > ., thepressure in the unsteady-statewater-influx equation has to becorrected to the original GWC.Failure to do so may result in anerror of more than % in thecumulative water influx, which in

turn could lead to the wrong

conclusions regarding the

predicted performance of the gasreservoir.. Gas recovery appeared to be

sensitive to initial reservoirpressure and the aquifer size(when ra/rg >.). As r a/rg and theinitial reservoir pressureincrease, gas recoverydecreases.

. Gas recovery appear to besensitive to gas production ratewhen ra/rg > .. The rate at which the GWC

advances is controlled by theaquifer size and gas productionrate when ra/rg > .., As r a/ rg increases, the

expansion of the trapped gas in

the water-invaded zonedecreases and could beneglected when ra/rg>... The declining gas production

rate should be avoided as muchas possible to increase gasrecovery.. Water production from the

flooded wells might help toreduce the activity of the aquiferand consequently might increasegas recovery.. The performance of the

waterdrive gas reservoir must beanalyzed for all the possibledevelopment and productionprograms to determine theoptimum production rate andmaximum recovery.


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Fig. - Effect of decline gas productionrate on gas recovery.

- Nomenclature

a = constant less than oneB = water FVF, RB/STS [resm /stock-tank m ]Bg = gas FVF at pressure p,ft /scf [m /std m ]

Bgi = gas FVF at pressure, pi,ft /scf [m /Stdm ]Bgj = gas FVF at pressure pJ,ft /scf [m /std m ]Ce = Cw+Cfpsi

-l [Pa-l]Cf = formation compressibility,psi - [Pa-]CW= water compressibility, psi

-

[Pa-]

ew = van Everdingen and Hurstwater influxFs = shape factorG = original gas ii place abovethe GWC, scf [std m ]GP = cumulative gas produced,scf [std m ]

h = net thickness, ft [m]

Ahn = height above original GWCat time tn, ft [m]kw = effective permeability towater in aquifer, mdp = pressure, psia [Pa]pi = initial reservoir pressure,psia[pa]Pn = reservoir pressure at time tn,psia[pa]

PnoGWC = pressure at originalGWC at time tn, psia [pa]PSC = pressure at standardcondition, . psia[ . kpa]qg = gas production rate, scf/D[std m /d]r = aquifer radius, ft [m]rf= fraction of rg (location of

fault), ft [m]rg = radius of gas reservoir atoriginal GWC, ft [m]rgn= radius of gas reservoir attime, tn, ft [m]Sgrw= residual gas saturation inwater-invaded zone,fractionSwi = initisl water saturation ingas reservoir, fractiont= time variabletD = dimensiordess time (see Eq.)

tDJ = mensiodess time attimestep J (see Eq. )tDn = dmensionless time at time tn(see Eq.)T = reservoir temperature F[c]Tsc= standard conditiontemperature, F [C]


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VPCn = PV containing free gas at

time tfl, ft [m ]Vpi = initial PV containing freegas above original GWC,Ft [m ]Vpwn= PV of water-invaded zone(see Eq. ), ft [m ]

Vpw= incremental PV of water-invaded zone (see Eq. ),fi [m ]We = cumulative water influx, RB[m ]

Wp= cumulative water produced,RB [m ]

= specific gravity of gas.

= Specific gravity of formation

water= difference

= dip angle

w = viscosity of water, cp[ pa.s] = porosity, fraction

Subscriptsi = initial conditionJ = index of loops

k = index of loopsn = number of timestepssc = standard condition

- References

.Bruin,J,R.,Fefkwich,M,J., andMeitzen,V.C.:The Effectof WaterInflux on p/z-Cumulative

GasPrcduction Curves,'

JPT(March )- .. Agarwval, R.G., A-H.ssainy,

R., and Ramey,H.J, Jr.: TheImportance of Water Influx inGas Reservoirs, JPT (Nov.

) - Tmn.s,, AIME,.

. Dumore, J.M: MaterialBalance for a Bottom-Water-

Drive Gas Reservoir, SPEj (Dec.)- .

.Knapp, R.M, et al.: Calculationof Gas Recovery upon UltimateDepletion of Aquifer storage,JPT (Oct. ) - .. Shagroni, M, A.: Eff... of

Formation Compressibility andEdge Water on Gas Field

Performance. MS thesis.Colorado School of Mines,Golden, CO ( ).. Geffen, T.M. et al.: Efficiency

of Gas Displacement fromPorous Media by LiquidFlooding, Trans., AIME ( )

,- .. Pepperdine,L.: The

Recognition Evaluation of WaterDrive Gas Reservoirs, paper-

- presented at the Petroleum Soc. Of CiM AnnualTechnical Meeting.. Lutes, J.L. et al.: Accelerated

Blowdown of a Strong Water-Drive Gas Reservoir,JPT (Dec.

) . - .. Givens,J,W.: A Practical Two-

Dimentional Model for Simulatig


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Dry Gas Reservoirs with Bottom

Water Drive ,JPT(Nov. ) - . . Van Everdingen, A.F. andHurst, W.: The Application of theLaplace Transformation to FlowProblems in Reservoirs,Trans ,

AIME( ) , - . . AI-Hashim, H.S, : The Effectof Gas Production Rate on the

Performance of Partial WaterDrive-Gas Reservoir, MS thesis,

Colorado School of Mines,

Golden, CO (I ).

SI Metric Conversion Factorscp x .* E = Pa.sdegrees x . E = radft x. * E = mft x. E =m

( - )/l. =

psi x. E+ =KPapsi - x . E =Kpa-

effect of aquifer size.pdf

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