Arps correlations

7/29/2019 Arps correlations

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SPE 19009

SPEBoundary-Dominated Flow in Solution Gas-Drive Reservoirsby R, Camacho, iMP-Mexico, and R. Raghavan, Texas A&M U.SPE Members

Copyright1989, Societyof PetroleumEngineers,Inc.Thispaperwaa preparedforpreaentafionat the SPE JointflockyMountainRegional/LowPermeabilityResarvoiraSymposiumandExhibitionheldin Denver,Colorado,MarchThispaper wes selectedfor presentationby an SPE ProgramCommitteefollowingreviewof informationCOntahW6dn an sibstracteubmittedby the author(s).Contenteofas presented,have notbwn reviewed by the Society of Patroleum Englnaera and are aubjecl to correctionby the author(s).The matarial. aa presented,does notnecaaaany positionofthe Societyof PetroleumEngineers,itaofficers,ormembers.Paparapresentedat SPE meetingsare aubjacttopublicationreviewby EditorialCommitteesofofPetroleumEngineers.Permissiono copyisreslrffitedoan abstractofnot morethenS00words.Illuslratiis maynotbecqr+ad.The abstractafroufdcontaincorraplcuouaofwhere and by whomthe paper ia preaentad. Write Publlcationa Manager, SPE, P.O. Sox 833S36, Richardson, [email protected], 730SS9SPEDAL,

ABSTRACT conat ,ant wellbore pressure production modes .In this work the performance of wells in solution gas-drive rmer- To accomplish our goala, this work is divided into three pvoirs during the boundary-dominated flow period is examined. Both the first part , the theoretical resu lts related to boundary-domin

constant wellbore pressure and constant oil rate production modes in flow given in Refs. 1 and 2 are outlined to establish a framewclosed systems are considered. the findings presented in this communication.

For the constant wellbore preeaure production mode, the condi- In part 11, the caae of a well flowing at a corretant preearrtiona under which procedures in the literature can be used to ana- ing the boundary-dominated flow period ia enalyaed. For thIyze data are diacuaaed. Specifically, Arpaa equationa for performance Fetkovieh3 ahowed that the empirical family of curvu of Arps4prediction are examined and it is shown that predictions of future combined with tbe sligh tly compr=ible l iquid flow solut ion (experformance are strong functions of well spacing, well condition, and tial decline rqmnaes) to obtain a family of curves that carsflu id propert i-. The parameters, b (the decline exponent) and di (the to pred ict fu ture per formance and estimate the reservoir poreinitial decline rate), in the Arps equationa are expressed in terlils of Refs. 1 and 6 report that during tbe boundary-dominated perphysical properti=. The conditions under which these equations can rate response plotted veraua time does not match a fixed valuebe used are specified. An empirical procedure to predict production decline exponent, b, in the type curves of Ref. 3. An explanatiratea is also presented. this observation ia presented. Refa. 3 and 7 emphaeiie that the

in the caae of constant oil rate production, an expression to cor- exponent, b, must be less than or equal to unity. They also norelate the pressure distribution in the reservoir is presented. The cor- if transient data are used, then the value of tbe decline exponenrelat ing funct ion permits us to extend the defin ition of pemrdoetcady the Arpaa solution can be greater than unity. Ueing the develostate flow to solution gas-drive aystema. Ita use also allows the simul- given in Ref. 8 for transient flow, a theoretical justificationtaneous computation of average propert ies (pressure and aatumtion) observation is provided. An empiri cal procedure to pred ict produring boundary-dominated f low from wellbore information. rat= of welle produced at a constant pressure, over ehort timeia also presented.

INTRODUCTION Part 111is devoted to the situation when tbe production isThe in tent ion of this work ia to document some theoreti cal results a constant oil rate. For this case it ie known from Mrs. 1,2, andthe reservoir does not achieve the condition of ~udoatdy-statethat are useful for predicting well performance from production data i e., the derivative of pressure with respect to time is not cin solution gas-drive reservoirs during the boundary-dominated [low and is also not independent of pcmition in the reservoir. In thiperiod. In the process of documenting these results it is also intended

to furnish a theoretical support for empirical obaervationa that exist a correlation for the preaacrre distribution in the mervoir durboundarydominated flow period is developed . Thii correlatingin this subject . tion permits ua to obtain an extension of the peeudoeteady-atateBoth constant wellbore pressure and conatarst oi l rate production cept to solution gas-drive reservoirs. Furthermore, thie timctio

modes in circular closed systems are considered. The osrteomrx pre- allows ua to compute aimul taneorieiy tbe vafuee of average presaented in this communication take as a baeia the theoretical rrw i its and average saturation, so, having wellbore information. .presented in Refs. 1 and 2.* Specifically, the result. given here follv~ The numerical reaulte presented in thie paper wero obtainefrom our ability to correlate responses of solution gas-drive systems a finite difference model described in Ftef. 1. Procedu~ followith the response of a slightly compressible liquid flow duri]lg (lieboundary-dominated flow period for botb constanl oil ram iII1d ensure the accuracy of the acdutione are given in Refa. 1 a nd 2

* References and Ilhtatraton at the end of this paper.


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A homogeneous closed cylindr ical reservoir withs ful ly penetra ti -ng well located at its center is considered. The well u capable ofproducing at either a constant oil rate or at a constant wellbore ptes-sure. An annular region that is concentric with the wellbore, with apermeabil ity di tferent from formation permeabil ity is used to includethe effect of a skin region l. The eflects of gKKWiLY, C@blY Pre~ure,and non-Darcy flow are not considered.

Figures 1 and 2 show the PVT properties of tbc fluids ussrl inthis work. Figure 3 presents the relative permeability data. The datamts shown in Figs. 1-3 are identical to the data wtr+onsidered inRefs. 1,2,8 and 11 and are used here mainly to preserve continuity.The conclusions derived in this work do not depend on the specificdata used in the simulations. Table 1 presents the information on therange of variab les examined in th is study .

UNDFollowing the development in Ref. 1, let us dcfim [he dinwwicm-

less pseudopressure sz fol lows

{/[IA ap

mD (r, t) = 141.2q. (t) , 1P, So) ~ rfr1t

/[ 1}P ~t, ,+ @(P! So) ~ - (1)o rHere the function a (p, S.) is given by

k,. (S.)@ (P, so) = (2)PO (P ) B . (P ) and F is the radius corresponding to the position iH the reservoirat which pressure p(r) is equal to the average re>,woir pressure,p . During the boundary-dominated flow period F cs 0.54928 ~~ D@0472 r. (see Fig. 5 of Ref. 2).

Dimensionless d ist ance is def ined asrD = ~.rw (3)

In Ref. 1. it is established that during boundarjf-donlinated flow, thefol lowing reeults are val id

(m~ (rtt) = fiD (i) + }nr,D -:+s )

( )[1 r4D+ ;-1 -L* 1[ 1 (l;, 1)f hrD-4 r~D r,D 3 1I(:D (4)#

fOr 1< rD < r@, and

D(r)=fiD()+( n%-:)+

( )[k 1 (r~D - 1)~_&+__El Z r~D r~D 2 r~~ 11 (r~ 1)Z r~~ (5)

for r#D ~ rD < r@. Here r#D is the dimensionless radius of the skinzone. The symbol fiD (t) in Eqs. (4) and (5) is the vohmnetric averageof the pseudopressure, which can also be obtained as folbwa

fiD (t) = ~IT VT

m ~ (r , t ) W, (6)

where VT is the vofume of the reservoi r.By using the Muskat12 materials balance equation, we show in

Ref. 1 thatkh _, -

/

D (t ) = 141.2q. (t) p(~)a (p , r) dp = 2wE, (7)

*2where ~ = iDrW/A, with the dimensiorrle.w time. %, definfollows 0.006328k

I 90(t)T(~)d ,

G = q$r$qo (t) o a(v) Here ~ and ~ represent the system mobility and system comibility corresponding to the average reservoi r pressure, j , (and avsaturation, ~o ); respectively, thus F and m are givm by~=[%+:l(,so,and

ct.-& (~)p-&j(fyj),,

()+Fo B~ (p) dl t jB. (I I dp ~

For the constant oil rate cazc, Eq. (7) can be simplified as follofiD (t) 2~~,

where ~ = ~r~/A, with ~ defined as

Eq. (11) is an extension of the materials balance equ~t.ion forphase liquid flow (production at a constant rate); similarly Emay also be considered to be a generalization of the rnnteriab bequation for production at a constant preaaure in solution gasreservoirs. In Fiefs. 1 and 2, it waz shown that Eq. (7) mayused if the production mode is changed from constant rate to copressure (or vice versa) .

For reference purposes, the defin it ion of dimensiohaz timeon initial system properti es given by the fo llowing ex]weeaion iduced

For sing le-phatw liquid flow during boundary-dominated flowthe dimensionless flow rate, qD, is given by1314:

where[141.29(t)@ = ~exp 2tiDA9D (tD) = k~ (pi - Pwj ) D D

[4AD.; In 128 .e7C,4rW

Here T is Eulers constant, and C,4 is the shape factor. Itshown that the average reservoir pressure and flow r st e ar e relathe following equation,

kh (pi -P)D tD) = 141.29 (t) B/c -D[l-exfw

In Ref. 1, it is also shown that for solution gas drive systerne trelat ion is val id=(=)-+-(%)]Note that the right-hand side of ~ (7) ie independent of r.Dresults are expressed in terme of=, whereas Eq. (1 i) u a fof r~D, where rcD = r.JrW.

Figure 4 exemplifies the use of the appropriate definitionmensiordeas average pseudopressure, ~(t), and dimeneiordeefor production at a constant wellbore preeeure and for botb dused in this study. The tilled in data pointa eorreapond to D1 with a skin factor, s, of 10 and ro = 8000. The open datacorrespond to Data Set 2 with u = 2 and r~ = 2000. h tbi


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JI? 1ql-roq R. G. Carnacho-V. and R. Ra~havan(=)=,,=.he unbroken straight line represents Eq. (7), ffiD I fJA

The circular data points represent the dimensionless average pseu-dopreeeure, fiD, versus the dimensionless time, ~, obtained fromsimulation runs. An excellent correlation with the h~prid solution isobtained for all values of producing time. Similar reau Ite are obtainedfor the case of constant rate productionlz. The triangular points rep-resent ~Lr vahcee plotted as a function of tDAJ. Agreement with Eq.(7) is good for small values of tim~ however, during the bmrndary-dominated flow period the correlation is poor. (Similar results mealso observed for constant rate production]z.) The uubroken curvesin this figure represent the right-hand side of Eq. (17) fortwovalumof reD. The square data points correspond to fi~>ahree obtsinedfrom simulation runs and plotted eeafunction of fi. The results

(=] values withhown here suggest that Eq. (17) will predict ?iiD Irr.,reasonable accuracy until tDA x 3. For larger timw Eq. (7) is abet ter representat ion of iED.

From Eqs. (7)and (17) wehavethe following rel;ltion

2E=D[exp(%1118)we obtain(19)

Expanding theexponential function intheright-hand sideof Eel. (18)G>%.

This inequality explains why thedata points in~ernwof~ ill Fig.4 fall to the left of the data points in terms of & during boundnry -dominated f low.

Theresult a presented inthissection for rn th eframeworkfor thef indings presented in this work.

As explained in the Introduction, the remrlta ot this paper arepresented in twoeections. We start by considering the ceae of con.stant wellbore preesure production mode. Inthisaectiun we intend toestabl ish condit ions under which procedurea available in the li te rutnrecan be used to analyze rate data are justified and also to furnish atheoreti cal support for empiri cal observations existing in th is subject.A procedure to predict production rates ofrszwvoirs produced at aconstant prewsure is presented.

We then examine the case of production, at a constant oil rate andpreaent acorrelation for the form of the preaaure distribution iu thereservoir. Thl smrrelation provid- anextension of thepwudosteady-s tate concept toeolut ion gee-drive reservoirs.

Constant P~ Prock$kr.n M odeAna]vsis of ArDS4eauations for OerfOrmanee Drrdictions

Beeed on the success in correlati~the average pseudopressure interms of both dimensionless timee, fi, and~, we willuee theeeresults to examine the aeeumptions involved in using the Arpa4 equa-tions for performance predictions.

Different iating Eqs. (17) and(7)~ith reapect totime, consideringthedefinitions of~(Eq. (12)) and tD (Eq. (8)), we obtain

Equation (21) can be written es followsE Z~Ah!u!2. _& @- ,lt 5. 614

where NP is the cumulative oil production. Equation (22) showrelative importance that parameters like relative permeabilityPVT data, and pore volume havein theprediction. of future pmance.

Substituting theright-hand sideeof Eqs. (17) and (21) fappropriate expremion in Eq. (20) we obtain the fo llowing exprm

Equation (23) implies that if~~/?l is approximately constanttime, then we would obtain a straight line by plotting Iogqotime. This observation may also be expected in intuitive grobsaed on single-phww flow theory .

We can relate Eq. (23) with the Decline Curve EquatioArps4 aa follows. Asiswell known the Arpsequations can rewrias follows

q. = q.i w (Edit) ,

for the exponent ial decline, andq. = qti(l + b dit)-lb ,

for hyperbol ic decline. Arpss equations are applicable onboundary-dominated flow. In these expressions t represent s t imlthe rate was qti. The parameters d and b in Eqs. (24) and (Xconsidered to be constanta and represent the nomirrrd rate atdecline takea place and decline exponent , respectively. For expondecline b = O and for harmonicdecline b = 1; in general b isrange O < b


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4 BOUNDARY DOMINATED FLOW IN SThe observations regarding di and b given above are important

and to our knowledge have not been presented before. They demon-strate the assumptions that are inherent in using the Arpe relationsto analyze data, or to predict future performance. Since both dj andb depend on relative permeability and f lu id propert ies, a s imple ma-terial s balance equat ion l ike the Muskatlz materials balance equat ioncan be used to study the variation in ~~ /Z1 for any specific situationto determine the consequences of using the Arps equations.

hfore interesting and important is the fact that these equationsclearly indicate that pred ictions of future performance are st rong func-tions of well spacing, the well condit ion , and f lu id propert ies, and thusthey also furnish a theoretical support for the concerns expreeaed inRef. 17 about the use of the production rate decline curves for flowrate predictions. For gas reservoirs, Fraim and Wattenbargerla aleoobserved that the rate plotted versus time does not match a fix valueof the decl ine exponent.

Fig. 6 presents a match of data obtained from three simulationruns for Data Set 1 with the Fetkovich type curve. Here qdo and fdDrepresen t dimensionless decl ine rate and dimensionless decline timedefined by Fetkovich (see Eqs. 19-22 of Ref.3). The ~bjective of thisplot is to show the consequences of the variation in &/A~. For solutiongas drive systems Refs. 3 and 7 sugg=t that b should be in the rmrge0.333< b < 0.667. The responses shown here tit tbe range 0.4 -5.66, which is a high negative skin factor. Thus in most ofthe cases the parameter b would be greater than one if transient dataia used.

A similar conclusion results if Eq. (34) is used. [n this case weobtain

Ifweaseume IVP-iq~, then w~obtaih~=_ [ln(4tDi/e7)+2S]2

1- hl(4tDi/t?7)% (38)Equation (38) again leads to the conclusion that the parameter 6 isa function of time and that it would be in moat of the cases greaterthan one wheh transient data are used to compute b. The abovedevelopment provides theoretical justi fication for the observations inRef. 3thatb~l forthe Arpsprocedure to reapplicable.

~te det-ation of rxodr@kxr ratesThe development g iven above also suggests a procedure to predict

flow rates over short time spans without the use of relative permwrbil-ity data or decline curves. Here we present a simple proccdurc topredict flow rates over a short time spans, which may also be usedto and is similar to the Inflow Performance Predictions of Stand ing22and Fetkovich23.

Numerical computations suggest that forconstant prcasure pro-duction d

/{ [tlp Q(P?sO)~, dt 1} dr % O,t (39)

during the boundary -dominate dflowperiod. Intuitively, atlate timesthis result could becxpected. DVferentiatingE q.(4) with respct totime, evaluating the resulting expression at rw, and considering Eqs.(7) and (39), we obtain the fo llowing expression for the case ofeon ,t .an tpressure production+%(%) [(ll++s)

(9)(%-*)1Eq. (40) can also be written Mfollows

(40)

(11)

where the subscripts f and p refer 10 future and present condit ions ,respectively.

Nofc that Eq. (41) rescn]b lc sStandings22 proccduretopwdictfuture prwformarrce,given l)ythefol lowing exprmsion%mar,J ~ p,a]qo.m.r,p

(42)j5pEp

where q~,ma~ is the maximum flow rate (rate corresponding to P,, J =O). It should be noted, howeier, that Eq. (42) can be obtained byassuming that the function o(p) varies linearly with pressure2i1a42s,but nothing has been assumed regarding the shape of the functioua(p) in thedcrivationof Eq. (41).

If we now assume that E % 0~2, where 6 is a constant, as suggestedby Fet.kovich 23, into Eq. (41) yields

Ok#)f ~F;(@/d~)/ (@3/ d0,(dqO/dt)P P; (@/dt)P = (dP3/dOp (.!3)

I Noteagain, that Eq. (43)resemblea Fetkovichs procedure23 tipredifuture performance given byqo,maz,f Z= =-90.mar,p Pp

Figure 8 presents the derivative of rate data with respect toversus average pressure for a case where Data Set 1 is used. Theubroken line represents simulator values of the function dqe/df verauThe circular and square data points correspmd to the rate derivaevaluated from Eqs. (41) and(43) reapect ive1y. The computat ionsardone by starting with the simulation value of -dqO/dt at tD~i =Toevaluate theright-hand sideofboth Eqs. (41) and(43), sir@ativalues have been used. Close agreement with actua l valueniaobtaiuewith both Eqs. (41) and (43). Thercamlta obtained byusing Eq.were slightly better than the reaults obtained by using Eq. (43)other s imulat ions , s imilar resul ts were observed.

Themain advantage of Eq. (40) isthatg ivea ccsan opportun itypredict future production rates. Eq. (40) can berewritten ss foll

=%-(%9b-:+)+(:-1)(%-39

Integrating Eq. (45) from~ito ~pandto PJ(withpi>PJ>PP >using theaseumption ti=@2, in Eq. (45) we arrive at thereeull

Eq. (46) permits us to predict flowrate at afuturevalueof~in this serrse this function is similar to Eqs. (42) and (44). Oncefuture vahreofqo,~a. isdetermined then an IPRcurve can bedevoped using the relations of Vogel*Gor Fetkovichz3. Thcsedelivembiliequations are g iven, respectively by

q.= 1- 0.2~ 0.8~,90,maz P1 forVogel, and () n90= # ? iJ ,9.zm.2 P

for Fetkovich. in Eq. (48), theexponent nisinthe range 0.5 10). I hederivative of the pseudopressure with respect to time would be imlr-pendent of r. For the case presented in Fig. 12 at ID = 100II iIII(ltDAi = fl.089, tbe ratio tDi/r& = 17.89, which expiains the con+l:mtbehavior of rx9p/r% for rD


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8 BOUNDARY DOMINATED FLOW IN SOLUTION GAS DRIVE RESERVOIRS SPEb = decline exponent in Arps equations ,

Br= gas formation volume factor (RB/SCF)Bo= oilformationvohrmefactor(RB/STB)CA = geometric shape factor

Cti = totelsystem compr-ibility at initial conditions, (psi-])~= total system compr=ibitity ataverage conditions, (Eq. (5)),(psi-l )di = nominal rate atwhich decline takwplace, parameter in f\rl~sequationsD= dimensiorrlesrr constant (Eq. (15))GP= cummulative gsaproduction, MSCFh= formation thickrress, feetk= absolute permeability, md

kr~ = relative permeability togss, fractionk,o = relative permeability tooil, fraction

rn~(r, t)= dimensionlezz paeudoprezzure(Eq. (l))fiD (t) = dimensionlezz volumet ric average pseudopressure (Eqs. (6)-

(7)).n = exponent of backpressure curve

NP = cummulative oilproduction, STBp= pressure, psipi = initial pressure, psi

p~j = wellbore f lowing prezsrrre , psiF-z average reservoir pressure, psi

qd,L) = decline curve dimensiorrless rate azdefinedin Ref. 3qf = gas flow rate (MSCF/D)q. = oil f low rate (STB/D)

fk.D,c = dimensionless rate (Eq. (53))r = radial distance, feet

rD = dimensionless radial d istancer~ = externrd drai.l age radius, feetr, = radius of altered permeability zone, feetrw = wellbore radius, feetF = radius where p(r) = F, feetR = producing gas-oil rat io, SCF/STB

. R, = anlut ion gas-oil rat io, SCF/STBs = mechanical skin factorS~ = gas saturat ionSf = volumetric average of gas saturationSg. = criti cal gas saturationSO = oil saturationSO = volumet ric average of oil saturationSo, = residual o il saturation

.%i = ini tial and inmobile water saturat iont= time , hours, days

td,f)decline curve dimensionless time as defined in fief. 3tDi = dimensionless time based on initial conditions (Eq. (13) )

t~A~ = dimensionless time based on A and initial conditions~ = dimensionless time (Eq. (12))~ = dimensionless time (Eq. (8))XD = correlating variable outside the rikin zone, during boundary-

dominated flow and constant rate production, (Eq. (52X,D = correlating variable inside the skin zone, during bounddominated flow and constant rate production, (Eq. (51

a = function of prww+ure and saturation (Eq.(2)).P = function of pressure and saturation (Eq.(59)).~ = Eulers constant, 0.57721 .. .

A~i= total mobility at initial condtilons, cp-lT = total mobility at average conditions, (Eq. (9)), cp-lp = gae viscosity, cpPO = oil viscosity, cp4 = porositySU!2@l&D = dimensionlesse = externali = in itial condit ionss = property of skin region or shut in conditions

w = wellbore

AcknowledgementsComputing ime was provided by The University of TuIaa.

REFERENCES1. CamacheV, R. G.: ~ce Un cler SQMQtI S&L?

Ph. D. Dissertation, Universi ty of Tulsa, (16S7).2. CamarJro-V., R. G. and Raghavan , R.: Some Theoret ical R

Useful in AnaIyzing Well Performance Under Solut ion Gas DPaper 16580 submitted to SPE of AIME.

3. Fetkovich, M. J.: Decline Curve Analysis Using Type CuJ. Pet. Tech. (June 1980) 1065-1077; k, AIME, 269.

4. Arps, J. J.: Analysis of DecIine Curvea~ ~, AIME (160, 228-247.

5. van Everdingen, A. F. and Hurst, W.: The ApplicationLaplace IYansformat ion to Flow Problems in Reservoirs, kAIME (1949) 186,305-324.

6. Jones, J. and Raghavan, R.: (Interpretat ion of Flowing Wesponses in Gas Condensate Wells: Paper SPE 14204 preaat the 60th Annual Teclniical conference and ExhibitionSPE of AIME, Las Vegas, Nevada, (Sept. 22-25, 1985).

7. Fetkovich ,M .J.,@ ~.: Decline Curve Analysis Using Type CCase NistoriesV SPE Forma tion Evaluat ioil, (1987), 637-65

8. Camacho-V., R. G.:Constant Pressure Production in $loGaa-Drive Wservoirs: hnsient Flow, SPE Paper 17118mitted for publication of SPE of AIME.

9. Aanorrzen, S. L: w ear Ei7ects Du r imr ll ans ient Fluid F748


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...SPE R. G. Carrtacho-V. and R. Raghavan

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.20.

21.

22.

ert!m Well-~ , Dissertation Dr. Scient., Universi ty of Bergen , Norway, (1985).

Hawkins, hf. F., Jr.: A Note on the Skin EfTeet~ ~, AIME207,356-357.

CarnachmV., R. G., and Ritghavan, R.: Performance of Wellsin %iution Gu-Drive Reservoirs, Paper 16745 presented at the62nd Annual Technical Conference and Exhibition of the SPE,(Sept. 27-30, 1987), Dallas, Tx.Muskat, M.: The Production Histories of Oil Producing GaaDrive Reservoirs, Jour. of Armlied Phvsirs (March , 1945), 147-159.

Uraiet, A. A. and Haghavan, R.: Unsteady F1OWto a ~#m-ducing at a Constant Iressure~ J . Pet. Tec h. (Oc~~O), 1803-1812. \ ,.\Ehlig-Economides, C. A. and Ramey, H. J. Jr.: l&sientRate Decline Analysis for Wells Produced at Constarx Pressure,Sot. Pet. Enc. J . (Feb. 1981) , 98-104.

Gentry, R. W. and hfcGray, A. W.: The EtTect of Ibervoir andFluid Properties on Production Decline Curves, J, Pet. Tech ,(Sept . 1978) 1327-1342.

Muskat, M.: ~ of Oil Pu&&R, Interna-tional Human Resources Develcoment corporation, (1981), 460-461.

Nind, T. E. W.: ~ of Oil Well Prnd- , McGraw-EilfBook Company, (1981 ), pages 43-44.

Fraim, M. L. and Wattenbarger, R. A.: Gaa Reservoir Dexlin~Curve Anafysis Using Type Curves with Bcal Gas Psmrdoprcasureand Normalized Tlme~ ~ Formation Evaluation, (1987), 671-682.Fel ,kovicb, M. J .: Personal Communica tion

CamarhwV., R. G., and Haghavan, R.: Inflow Performance Re-lationsh ips for Solution Gas Drive Hme.rvoira, Paper SPE 16204presmtted at the 1987 SPE Production Operations Sympmium,(March 9-11, 1987) , Oklahoma City, Oklahoma.

Chen, H. Y. and Poston, S. W.: Application of a Paeudct-Timefhrnction b Permit Better Decline Curve Anafysia, Paptw 17051presented at the SPE Eastern Regional Meeting held in Pit&burgh , Pennsylvania, (Oct. 21-23, 1987).

Standing, M. B.: Concerning the Calculation of Inflow Per-formance of Wells Producing Solution C;aa Drive R.ae.rvoir,J. Pet. Tech. (Sept . 1971), 1141-1142.

23.

24.

25.

26.

27.

28,

Fetkovich, M. J .: The Isochronal Testing of Oil WellsSPE 4529 presented at the 48th Annual Fall Meeting, LaNevada, (Sept. 30- Oct. 3, 1973). (SPE Heprint Serie265.)Handy, L. L.: Effect of Local High Gas Saturations ontivity Indiccn, ~. and P~ , API (1957) 111-1Whitson, C. S.: Reservoir Well Performance and Predicl iverab ility , Paper SPE 12518 submitt ed for publ icat ion .Vogel, J. V.: Inflow Performance Relationships for solutDrive Wells, J. Pet. Tech. (Jan. 1968), 83-92.

Kelkar, B. G. and Cox, R.: Unified Relationship to Preture IPR Curves for Solution Gas-Drive Reservoirs, Pa14239 pr=ented at the 60th Annual Technical ConfereExhibition of the SPE held in Las Vegas, NevAa, (Sept1985).Uhri, D. C. and Blount, E. M.: Pivot Point MethodPredicts Well Performance: World 0,[, (hfay 1982) 153

DrainascRadius, r., feetPorosity, A fractionPermeability, k, md\ ve ll t ad , ,, , W , f etInitial Pressure, pi, psiInitial Waler Saturation, SW;Initial Compressibility, ctl, psi-LInitial 0S Viscosity, Ma, cpThicknw, h, ft

Pressure Product ion Ratio, p.,/p;:Production rate, .?., (sTB/D):

W

2024 .67 2 ,1640 40 .31 0 .

0 . 3 2 8 0S5704 . 7 8

0 .31.0s5x10-~

0 . 2 0 ss o ., 1 5 , 55

0 .2971 -0 , s9414 0 - Im ll

t . 3

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1 1. 1Q %(*\) Ob/(l)Obs@b31W ss31t401W3wKl (ti1 gp/%p. 3Auvwm 3.WM


12/12

,.,

n

!d/(+J)d OIIW 341TSS3Ud

sPE 1 9 0 0 9

AVERAGE OIL SATURATION, ~

(w(+w~~

Arps correlations

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