Monitoring and Predicting CO 2. Flooding Using Material Balance Equations

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1 Mnitring and Predicting Flding Using Material alance Equatins. Tian China University f Petrleum G. Zha University f Regina Abstract In rder t perate a scheme successfully, it is necessary t get accurate infrmatin abut the reservir dynamic perfrmance and the fluids injected. Althugh sme numerical simulatin studies have been nducted, the mplicated drive mechanisms and actual reservir perfrmance have nt been fully understd. Thus, there is a strng industrial need t develp mdels using different perspectives t prvide valuable and mplementary insights int the reservir perfrmance during the prcess. The bjective f this study is t develp mdels using material balance equatins (ME) t analyze the field data befre and after injectin. After matching the histrical field data, the prpsed mdel can be applied t evaluate, mnitr and predict the verall reservir dynamic perfrmance during the prcess. T accurately acunt fr the mplex displacement prcess invlving mpsitinal effect and multiphase fl, the PT prperties f reservir fluids and the fur-phase fluid relative permeability relatinship are integrated int the mdel. This study has investigated the effects f a number f factrs, such as the reservir pressure, the amunt f injected, the partitin ratis in reservir fluids, the pssibility f the existence f a free gas cap, the prprtin f reservir fluids ntacted by, the il selling and the il relative permeability imprvement. The mdel has been applied t analyze the Weyburn prject. The study has shn that the prpsed ME mdel is an effective mplementary tl t analyze verall reservir perfrmance in tertiary revery prcesses. The results sh that: ) there exists a free gas cap under reservir nditins, even if the reservir pressure is larger than MMP (minimum miscible pressure) in the Weyburn Field; ) the partitin ratis in il, ater and gas phases and the prprtins f reservir fluids ntacted by largely affect the drive mechanism and prductin perfrmance; and 3) the effect f slubility in ater under actual reservir nditins cannt be neglected. The prpsed ne mdel is the first ne in develping and applying ME t evaluate the verall dynamic perfrmance fr the prcess and a valuable insight int reservir respnses during this prcess has been achieved. Intrductin is nsidered ne f the mst effective tertiary revery prcesses in light/medium il reservirs and has achieved idespread use in the petrleum industry. Hever, the mplicated displacement mechanisms and reservir perfrmance invlved in the injectin prcess have nt been mpletely understd. Mnitring reservir perfrmance and btaining accurate infrmatin regarding reservir fluid and injected fluid using field data ill help understand the mechanisms and manage the injectin prject efficiently. There are t types f methds that mnitr and evaluate reservir perfrmance: numerical simulatin and ME. ME is a classic reservir engineering tl. It is applied t analyze the reservir perfrmance based n the la f nservatin f matter. Cmpared ith ME, reservir numerical simulatin is a mre mdern technique fr mdelling reservir perfrmance. One f the limitatins f numerical simulatin fr is that a large amunt f field data are required in rder t accurately inrprate gelgical hetergeneity. Hever, in sme situatins, data are unknn, uncertain r unavailable and the mplicated drive mechanisms are nt clear. Cmpared t numerical simulatins, the ME requires less data and reservir gemetry details are nt nsidered. The verall vlumetric change and balance f a reservir system are examined in the ME mdel. One f the advantages f ME is simplicity and the rapidity ith hich indicative results uld be btained. ME is a gd mplementary tl t verify the physical realities f the reservir and validate the reliability f the simulatin mdel. ince chilthuis () first presented and applied vlumetric ME in 936, a number f ME have been presented. In 963, Havlena and Odeh () develped a ppular straight line methd t estimate the hydrcarbn reserve. Walsh et al. (3, 4) intrduced a generalized ME that is applicable t the full range f reservir fluids, including vlatile il and gas ndensates. Hever, the methd is restricted t primary and sendary revery prcesses. Penuela et al. (5) develped ME fr a dual prsity carbnate reservir t determine the riginal il-in-place (OOIP) in matrix and fractured systems. Hsieh et al. (6, 7) prpsed a hrizntal line ME t estimate the OOIP and calculate the ater influx. ills (8) presented ME t determine riginal hydrcarbn-in-place (OHIP) in aterdrive il and gas reservirs. Even thugh each f these rks mentined abve ntributes t the develpment and applicatin f ME, ME are still restricted t determine the OHIP and aquifer prperties fr primary and sendary revery prcesses. Nne is applicable t the tertiary revery prcess, and the mplicated phase behaviur and mpsitinal effects in cannt be handled in present ME mdels. As the number f tertiary revery prjects in the petrleum industry increases, there is an increasing need t address these limitatins. The bjective f this study is t extend the applicatin f classic ME t EOR tertiary revery prcesses t imprve the understanding fr verall reservir dynamic behaviur during the prcess. Peer Revieed Paper ( Revie and Publicatin Prcess can be fund n ur Website) Nvember 8, lume 47, N. 4

2 Mdel Develpment The ME fr petrleum reservirs is simply a vlumetric balance, hich states that since the vlume f a reservir is nstant, the algebraic sum f the vlume changes fr the il, free gas, ater and rck vlumes in the reservir must be zer. The ne ME mdel develped extends the applicatins f the classic ME t a injectin prcess. esides the ld functins f estimating the OHIP and determining the energy surces fr il displacement, the ne functins mainly include mnitring the verall dynamic perfrmance and predicting the behaviur f the prcess. The bjective f mnitring the actual perfrmance f the prcess can be achieved by examining the displacement efficiency, investigating the dynamic behaviur f partitin and ntact in the reservir, mnitring the subsurface strage capacity and studying the change f fluid prperties under actual reservir nditins. The future perfrmance f can be predicted based n the results f mnitring and histry matching. The factrs nsidered in the mdel mainly invlve the uneven pssibility f reservir il and brine ntacted by, the pssibility f the existence f a free cap, the selling f the -il mixture, the reductin f il vissity and density, and the change f fluid relative permeability. In the mdel, the percentage f reservir fluid (il r ater, nted as x) ntacted and saturated by is defined as α x : m x α x here m x xt,... () G ρ MW ρ 44 m x x x C, x... () flls: () ME, () change f phase behaviur and PT f fluids, (3) relative permeability relatinship, (4) prducing gas-il rati and ater-il rati, and (5) fluid saturatins. Material alance Equatins Fr, the ME can be expressed as: cumu, prd cumu, inj ater cumu, exp unnt fluids + frmatin + cumu, exp nt il + cumu, exp nt ater +cumu, free... (4) here cumu, prd Np( Rsg)+ Wp+ Gpg... (5) cumu, inj ater Wi, exp + N E + E cumu unntfluids frmatin f, exp / cumu nt il m m, exp /... (6) cumu nt ater m m ( )... (7) ( )... (8) ( )... (9) xt, x pv... (3) G cumu, free free... () In reality, the α x value ill be affected by the amunt f disslving in the reservir fluid, x, the ttal amunt f fluid presented in the reservir and the slubility in the reservir fluid, x. As time passes and the amunt f injected increases, the value f α x ill vary. There is a pssibility that the injected may have either greater ntact ith the reservir il r greater ntact ith the reservir ater. T evaluate the uneven pssibility f reservir fluids (il and ater) ntacted and saturated by, the rati f α il t α ater has been calculated and defined as the characteristic reservir factr, R CRF. E + R R i si s g E C + C f i i ( )...() f effective i P... () Fr the injected, the ME can be expressed as: Mdel Assumptins The mdel is based n the flling assumptins: The mdel is zer dimensinal and the reservir gemetry and ell lcatins are nt nsidered. The injected may exist in free gas, r in il and ater phases under reservir nditins. The injected can be prduced frm the reservir in three ays: slutin gas-in-il, slutin gas-in-ater and free. The reservir fluids ntacted by are instantaneusly saturated by. The average prperties f reservir fluids are btained by eighing the reservir fluid ntacted by and unntacted reservir fluid. The rck prsity and fluid saturatin are unifrm thrughut the reservir. The mdel develped fr mnitring and predicting dynamic perfrmance nsists f five equatins as Gi Gm + Gm + G free... (3) Gm Rs β R G R 4 Jurnal f Canadian Petrleum Technlgy m s CRF... (4) subsurface strage capacity, Re, and strage efficiency, η, can be determined as G Re i prd... (5) prd il prd Rs mix Rs il ( )+ free+ ater prd R ater... (6)

3 η G Re i... (7) g ( c ) G i N g i... (3) Phase ehaviur and PT Prperties Phase ehaviur tudy fr Weyburn Oil- Mixture When is injected int a reservir, it enters int the slutin and sells the il. The saturatin pressure fr il ill vary. In additin, the vissity f il is significantly reduced and the slutin gas-il rati f il is significantly increased. In this study, the results f the phase behaviur fr the Weyburn il- mixture ere btained frm an RC labratry test (9) and have been upled in the ME mdelling. The phase behaviur relatinships upled in the ME include the relatinship beteen the saturatin pressure and the ncentratin, pressure dependence f the frmatin vlume factr, gas-il rati and vissity f the il- mixture. Injectin f int the il ill increase the frmatin vlume factr and the gas-il rati, and ill reduce the vissity f the fluid mixture. lubility in Water The slubility f in ater is a functin f temperature, pressure and ater salinity. The change f slubility, frmatin vlume factr f ater and vissity f ater saturated by are nsidered in the mdel. Relative Permeability Equatin The mplicated phase behaviur change during the prcess leads t the mplexity f the relative permeability relatinship. It is necessary t nsider reservir fluids as fur phases: unntacted il, il- mixture, ater and gas. The relative permeability relatinship upling the difference beteen the ntacted and unntacted il is expressed as flls: ( ) + K α K α K reff il r il rm... (8) Prducing Gas-Oil Rati and Water-Oil Rati Equatins K µ WOR K r reffµ... (9) lutin f the ME The final slutin is as flls: Gm Np( R s g)+ Wp+ Gpg W i N( E+ E f) G D R m ( ) s D + ( m ) Rs RCRF i Gm Np( R s g)+ Wp+ Gpg W i N( E+ E f) G D R m ( ) s D + ( m ) Rs RCRF Rs R R s CRF i... (4).. (5) Gfree Gi Gm G m... (6) m D Np( Rsg)+ Wp+ Gpg Wi N( E+ Ef) G D ( ) R m s + D m ( ) Rs R CRF i... (7) m D Np( Rsg)+ Wp+ Gpg Wi N( E+ Ef) G i D ( m ) R + s D m ( ) Rs R CRF R s Rs R CRF... (8) here K µ GOR K rg reffµ g... () D ρ MW il ρ il 44 C, il... (9) Fluid aturatin Equatins D ρ MW C ater ρ ater 44, ater... (3) ( c ) ( c ) N N Ni p W + W W Ni... () i inj p... () Applicatins Applicatin t a Field Case: Weyburn Oil Field The Weyburn Oil Field is lcated 3 km sutheast f Regina, askatchean, Canada. The medium il is prduced frm the Nvember 8, lume 47, N. 43

4 Cumulative Amunt f (, m 3).8x 6.6x 6.4x 6.x 6.x 6 8.x 5 6.x 5 4.x 5.x 5 Injected disslved in il Flding Time (mnth) FIGURE : Amunt f disslved in il at different times. Percent f Cumulative Injected (%) disslved in il disslved in ater free Flding Time (mnth) FIGURE : distributin in reservir at different times. trage Efficiency (%) Midale beds f the Mississippian Charles Frmatin at a depth f,3 m t,5 m. The riginal reservir pressure is 4.6 MPa. The il vissity is 4.7 mpa s. The field as disvered in 954 and prduced by primary depletin until April 964, hen an inverted nine-spt ater as implemented. The mbined il revery by primary and sendary prductin as apprximately 8% OOIP by 994. In, PanCanadian (n EnCana) started t implement the prject in the Weyburn Field, hich as frecasted t add incremental il revery f t 4 millin barrels. y May 3,,73 millin standard cubic metres f has been injected int the Phase a area. Currently, there are 88 il prducers, 3 ater injectrs and 3 injectrs in this area. The il prductin per ell increased frm 6. m 3 /d t.4 m 3 /d due t. Even thugh il prductin has imprved due t the prcess, there are still sme technical prblems that need t be slved. Fr instance, after the implementatin f fr apprximately three years, prductin respnses ccurred in nly 3 ells, hich shs a relatively sl respnse. In sme ells, the prducing GOR (gas-il rati) rse significantly. The mnitring and analyzing f actual injected dynamic respnse ill help slve these prblems, understand the accurate displacement mechanisms and, finally, ptimize the fld strategies. Results and Discussin Mnitring Results Cumulative Injected (%P) FIGURE 3: subsurface strage efficiency versus cumulative injected. Figure shs the amunt f injected and disslved in the reservir il at different times. The amunt f disslved int il as less than the ttal amunt f injected. At early time, the differences beteen these t curves are small, hich indicates that almst all f the injected as disslved int the il phase. Hever, the differences beme mre and mre significant as the time prgressed. This indicates that nt all f the injected is disslved int the reservir il during the prcess, even thugh the reservir pressure as higher than MMP (3.3 MPa). This is because, at the beginning f, a relatively small amunt f as injected int the reservir, mst f hich disslved int the fresh reservir il. As the prgressed, and the amunt f injected int the reservir increased, it tk a lnger time fr the injected t ntact and disslve int the reservir il. Furthermre, reservir il and ater exist in the actual reservir envirnment. The injected ntacted and disslved, nt nly int the il, but als int the ater as ell. The tertiary revery prcess after ater ill generally pssess an increasingly higher and higher ater saturatin as time passes. As a result, the amunt f nt ntacting fresh il ill increase as the prgresses and the amunt f injected increases. Figure presents the partitin f the injected in the actual reservir as a functin f the time. It is shn that apprximately 86% f the injected can disslve int reservir il, 7% ill disslve int ater and 7% ill remain in the free gas phase. The percentage f disslved int il as mparatively higher than that in ater and in the free gas phase. With the prgressin f time, the percentage f disslved int il decreased by a small degree and the percentage f disslved int reservir ater and remaining in the free phase increased slightly. This is because, ith the advance f the revery prcess, the vlume f the il prduced frm the reservir increased. Thus, the il saturatin in the reservir decreased and the ater saturatin tended t increase. As a result, the injected had mre f a chance t ntact reservir ater than il, even thugh the slubility in il under reservir nditins as much greater than that in ater. Figure 3 exhibits a plt f the subsurface strage efficiency, η, as a functin f the cumulative amunt f injected. As shn, subsurface strage efficiency decreases ith an increase f the amunt f injected and the time. At the beginning, all f the injected is disslved and/r stred in the reservir. Hever, after 3% P is injected int the reservir, the subsurface strage efficiency ill decrease t 9.8%. The change f α il ith respect t the cumulative injected (% P) is shn in Figure 4. It shs that ith the increase in the amunt f injected, the percentage f reservir il ntacted and saturated by increases almst linearly. Figure 5 displays the mnitring results fr the variatin f the average relative permeability during the prcess. The average ater relative permeability increased ith the increase in the amunt f injected. The average il relative permeability first decreased slightly and then increased gradually. This is because the vlume f ntacted il at the early time f as very small and the average il relative permeability depended 44 Jurnal f Canadian Petrleum Technlgy

5 -il (%) Cumulative Injected (%P) FIGURE 4: Percentage f reservir il ntacted by versus cumulative injected (mnitring result). Cumulative Oil Prductin (m 3 ) 6, 5, 4, 3,,, P 6 MPa P 4.8 MPa P.6 MPa Flding Time (mnth) FIGURE 6: Cumulative il prductin at different reservir pressures. Relative Permeability K r K reff Cumulative Injected (%P) FIGURE 5: Relative permeability at different stages. n the relative permeability f unntacted il. As the il as prduced frm the reservir, il saturatin decreased gradually and the relative permeability f unntacted il decreased as ell. As a result, the average il relative permeability decreased slightly. With the prgressin f the time and the increase in the amunt f injected, mre il as ntacted by. At this time, the average il relative permeability depended n the variatin f the prprtin f ntacted il and the relative permeability f ntacted il. Therefre, the average il relative permeability increased gradually as the vlume f ntacted il increased. ensitivity Analysis Effect f Reservir Pressure Maintenance Figure 6 shs the effect f reservir pressure maintenance n cumulative il prductin. In general, the higher the reservir pressure maintained, the higher cumulative il prductin ill be reached. Hever, fr the cases ith ler reservir pressures, 4.8 MPa and.6 MPa, there is n significant difference beteen the cumulative il prductin ithin the first 4 mnths. The reasn is that at a reservir pressure f 4.8 MPa, a large amunt f disslves int the il and sells the il, hich helps t displace il frm the reservir. Fr the case f a ler reservir pressure f.6 MPa, even thugh the slubility in the il is significantly ler and the selling effect is smaller than at a higher reservir pressure f 4.8 MPa, there is a larger free cap existing in the reservir than at the higher reservir pressure. This gas cap ill ntribute t the il revery. Figure 7 shs the effects f reservir pressure maintenance n the percentage f disslved in il. The higher the reservir pressure, the higher percentage f disslved in il. The percentage f disslved in il at a reservir pressure f 6 MPa 4 5,,,,5,,,,5, is apprximately 9%. At a ler reservir pressure f.6 MPa, the percentage f disslved in il is 66%, hich is 4% ler than that at a higher pressure f 6 MPa. It indicates that higher reservir pressure maintenance ill help t disslve int slutin il and beme miscible ith il. With the increase f vlume f injected and time prgressin, the three curves sh the similar tendency fr the percentage f disslved in il t decrease slightly. Effect f Reservir Pressure and Fluid aturatin n Distributin in Oil and Water Figure 8 shs the partitin rati, β, fr the injected in the reservir il and ater phases in the Weyburn Oil Field. There are t tendencies shn in this figure. Firstly, ith the increase Nvember 8, lume 47, N. 45 Percentage f Disslved in Oil P 6 MPa P 4.8 MPa P.6 MPa Cumulative Injected, Reservir lume (m 3 ) FIGURE 7: disslved in il at different reservir pressures. Distributin Rati, (in il/in ater) % 6% 5% 45% 4% 35% 3% 5% % Reservir Pressure (MPa) FIGURE 8: distributin rati in il and ater.

6 Oil Prductin Rate (m 3 /d/ell) in reservir pressure, the partitin rati in il and ater increases. It indicates that mre can disslve in the il phase than in the ater phase. endly, ith the decrease f the il saturatin in the reservir, the partitin rati, β, decreases as ell. This figure als reveals that an earlier time injectin scheme alls mre t ntact and disslve int the il phase due t higher il saturatin in the reservir, and thus, helps t dramatically imprve final il revery. Effect f R CRF n Flding Perfrmance Figure 9 shs the sensitivity analyses fr R CRF values. injectin prcesses ith nstant and variable R CRF values ere als examined in Figure 9. It is bserved that the il prductin histry can be matched by preferably using variable R CRF values, i.e.,. fr the early stage (frm the st t the 7 th mnths) and. fr the late stage (frm the 8 th t the 33 rd mnths). Physically, the increase in R CRF during the prcess indicates mre and mre disslves int the il phase. This is because gravity tends t cause the lighter t rise inside the reservir, and the natural fracture systems and/r ther hetergeneities in the Weyburn Carbnate Reservir Frmatin ill assist this prcess. Therefre, the injected has a better chance t ntact reservir il than ater. This leads t the rising tendency f the R CRF values. Cnclusins Flding Time (mnth) FIGURE 9: Effect f R CRF n il prductin rate. R CRF.5 R CRF. R CRF. ariable R CRF Field data R CRF. R CRF.8 ased n the investigatin int the Weyburn Field perfrmance and the analysis f the mdelling results, the flling nclusins can be dran:. The tank mdel is still an irreplaceable and effective tl fr analyzing and mnitring the verall reservir perfrmance in the tertiary revery prcess.. The bjective f -ptimizatin f EOR and sub-surface strage cannt be achieved currently in the Weyburn Oil Field. 3. Even thugh the reservir pressure is currently higher than MMP, the injected is nt % disslved in the il and there exists a free cap under actual reservir nditins. 4. The characteristic reservir factr, R CRF, varies at different stages f. With the prgressin f time and the increase in the amunt f injected, the R CRF value increases frm. t arund. fr the Weyburn Phase a area. 5. With the increase f the amunt f injected, the amunt f ntacted il and the percentage f il ntacted by, α il, increases and the il relative permeability increases. 6. The vlumetric distributin rati in il and ater, β, is influenced by fluid saturatin distributin and reservir pressure. 7. Different il prductin can be btained ith different reservir pressure maintenances. The higher the pressure, the higher the il revery ill be. Hever, the reservir pressure shuld be ler than the frmatin fracturing pressure in general. 8. The selling f il hen mixed ith plays an imprtant rle in the revery prcess, hich is mainly affected by reservir pressure. The reservir fluid vlume ntacted by is affected by the reservir pressure, the vlume f fluid injected and fluid saturatin in the reservir. 9. The sub-surface strage capacity is influenced by fluid saturatin, reservir pressure and the amunt f injected and fluid prduced. With the increase in the amunt f fluid injected and fluid prduced, the sub-surface strage efficiency decreases. Acknledgements The authrs uld like t thank PTRC at the University f Regina fr financial assistance. Thanks are als given t Myrn ereda, Rb Tryer and Janice Lseth at askatchean Industry and Resurces and EnCana Petrleum fr their generus ntributin f time and resurces. Nmenclature FF (frmatin vlume factr) f, m 3 /m 3 g FF f gas, m 3 /m 3 m FF f il disslved by, m 3 /m 3 m FF f ater disslved by, m 3 /m 3 FF f il, m 3 /m 3 i initial FF f il, m 3 /m 3 FF f ater, m 3 /m 3 C, xco ncentratin in fluid x, mle fractin C feffective effective frmatin mpressibility, MPa - C ater mpressibility, MPa - expansin efficient f il 46 Jurnal f Canadian Petrleum Technlgy E E f expansin efficient f ater and pre vlume G free cumulative immiscible free vlume, m 3 G i free gas cap in reservir, m 3 G i cumulative injected vlume, m 3 G mx cumulative vlume disslved in fluid x, m 3 GOR gas-il rati G p cumulative gas prductin, m 3 K rg gas relative permeability K rm relative permeability f miscible il K r relative permeability f unntacted il K r ater relative permeability K reff il relative permeability MW x mlecular eight f the reservir fluid x N OOIP, m 3 N p cumulative il prductin, m 3 R CRF characteristic reservir factr R s slutin gas-il rati f il, m 3 /m 3 R si riginal slutin gas-il rati f il, m 3 /m 3 R s slubility f in il, m 3 / m 3 R s slubility f in ater, m 3 / m 3 R smix slutin GOR f il/ mixture, m 3 / m 3 R sil slutin GOR f il unntacted by, m 3 / m 3 R ater average slubility f in ater, m 3 / m 3 g gas saturatin il saturatin ater saturatin i initial ater saturatin c irreducible ater saturatin x average saturatin f the reservir fluid x Re vlume f stred in the reservir, m 3 free vlume f free prduced t surface, m 3 prd vlume f prduced, m 3 cumu,prd cumulative vlume f the prduced fluids, m 3 cumu,injater cumulative vlume f the injected ater, m 3

7 cumu,expunntfluids+frmatin vlume expansin f unntacted il, ater and pre vlume, m 3 cumu,expntil vlume expansin f il/ mixture, m 3 cumu,expntater vlume expansin f ater- mixture, m 3 cumu,free vlume f free, m 3 mx vlume f reservir fluid, x, ntacted by ilprd vlume f prduced reservir il, m 3 pv reservir pre vlume, m 3 aterprd vlume f prduced reservir ater, m 3 x,t ttal vlume f reservir fluid x W i riginal ater reserve, m 3 W inj cumulative injectin ater, m 3 W p cumulative ater prductin, m 3 WOR prducing ater-il rati, m 3 /m 3 P reservir pressure difference, MPa α reservir fluid ntacted/saturated by, percentage β vlume rati f disslving in il t disslving in ater, m 3 / η μ ρ x ρ m 3 strage efficiency vissity f fluid, mpa s density f the reservir fluid x, Kg/ m 3 density under reservir nditins, Kg/m 3 Prvenance Original Petrleum ciety manuscript, Mnitring and Predicting Flding Using Material alance Equatin (4-96), first presented at the 5th Canadian Internatinal Petrleum Cnference (the 55th Annual Technical Meeting f the Petrleum ciety), June 8-, 4, in Calgary, Alberta. Abstract submitted fr revie Nvember 3, 3; editrial mments sent t the authr(s) January 9, 8; revised manuscript received February 7, 8; paper apprved fr pre-press February 7, 8; final apprval Octber, 8. Authrs igraphies huba Tian is a Lecturer in the Faculty f Petrleum Engineering fr the China University f Petrleum, eijing. His research interests include reservir and hrizntal ell perfrmance analysis, numerical simulatin and EOR studies. He received a.c degree frm the University f Petrleum, East China and an M.c. degree in petrleum systems engineering frm the University f Regina, askatchean, Canada. Gang Zha is an Assciate Prfessr in the Faculty f Engineering at the University f Regina, askatchean, Canada. He received a Ph.D. degree frm the University f Tulsa, Oklahma, UA. His technical interests invlve ell testing, reservir simulatin, ell (hrizntal and lateral) perfrmance analysis, multiphase fluid fl in prus media and EOR studies. ubscripts x, il phase, ater phase References. CHILTHUI, R.J., Active Oil and Reservir Energy; Transatins AIME, l. 48, pp. 33-5, HALENA, D. and ODEH, A.., The Material alance as an Equatin f a traight Line; Jurnal f Petrleum Technlgy, l. 5, N. 8, pp , August WALH, M.P., ANAH, J. and RAGHAAN, R., The Ne, Generalized Material alance as an Equatin f a traight Line: Part - Applicatins t Undersaturated, lumetric Reservirs; paper PE 7684 presented at the Permian asin Oil and Gas Revery Cnference, Midland, TX, 6-8 March WALH, M.P., ANAH, J. and RAGHAAN, R., The Ne, Generalized Material alance as an Equatin f a traight Line: Part - Applicatins t aturated and Nn-lumetric Reservirs; paper PE 778 presented at the Permian asin Oil and Gas Revery Cnference, Midland, TX, 6-8 March PENUELA, G., IDROO, E.A., ORDONEZ, A, MEDINA, C. and MEZA, N.., A Ne Material-alance Equatin fr Naturally Fractured Reservirs Using a Dual-ystem Apprach; paper PE 6883 presented at the PE Western Reginal Meeting, akersfield, CA, 6-3 March. 6. HIEH, F.., KANDEL, P.. and EGA, C., Material-alance Methd fr Prductin Rejuvenatin With Hrizntal Wells; paper PE presented at the PE/CIM Internatinal Cnference n Hrizntal Well Technlgy, Calgary, A, 6-8 Nvember. 7. HIEH, F.., EGA, C. and EGA, L., Material alance as a Hrizntal Line fr a Gas-Cndensate Reservir; paper PE 7556 presented at the PE Gas Technlgy ympsium, Calgary, A, 3 April- May. 8. ILL,.R., Imprved Material-alance Regressin Analysis fr Waterdrive Oil and Gas Reservirs; PE Reservir Engineering, l., N., pp. 7-33, May RIATAA, R.K., HUANG,.. and DONG, M., Labratry Investigatin f Weyburn Miscible Flding; Jurnal f Canadian Petrleum Technlgy, l. 39, N., pp. 4-5, February. Nvember 8, lume 47, N. 47