The Representation of Multi-component Adsorption in Reservoir Simulation of CO 2 Sequestration in Coal and Enhanced Coalbed Methane Recovery

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The Representton of Mult-component Adsorpton n Reservor Smulton of CO 2 Sequestrton n Col nd Enhnced Colbed Methne Recovery 59 Zhejun Pn nd LD Connell CSIRO Petroleum, Prvte Bg 1, Clyton South,

1 The Representton of Mult-component Adsorpton n Reservor Smulton of CO 2 Sequestrton n Col nd Enhnced Colbed Methne Recovery 59 Zhejun Pn nd LD Connell CSIRO Petroleum, Prvte Bg 1, Clyton South, Vctor, Austrl, 3169 ABSTRACT CO 2 sequestrton n col s potentl mngement opton for greenhouse gs emssons. An ttrctve spect to ths process s tht the CO 2 s dsorbed to the col nd therefore, for sttc reservor pressure condtons, s mmoble, reducng the rsk of CO 2 mgrton to surfce. Another spect to ths s tht the njected CO 2 cn dsplce dsorbed methne ledng to regon wthn the col sem of mxed gs. Therefore, n order to understnd gs mgrton wthn the reservor mult-component dsorpton models re requred. Lngmur bsed models, such s the extended Lngmur nd Idel Adsorbed Soluton, re prt of the reservor smultors currently n use for modelng CO 2 sequestrton n col. However these models re nccurte descrptons of the dsorpton process prtculrly t the hgh pressures ssocted wth sequestrton n deep cols. Therefore new pproches re requred tht cn be mplemented n computtonl effcent mnner for reservor smulton. Ths pper presents smulton work usng severl pproches to representng mult-component dsorpton, mplemented nto the col sem gs reservor smultor SIMED II. The dsorpton models re extended Lngmur, Idel Adsorbed Soluton () nd 2D Equton of Stte (). The s shown to be more ccurte descrpton thn the other models for expermentl observtons of dsorpton on Frutlnd col. The effects of ths greter ccurcy on modelng the sequestrton process s nvestgted usng hypothetcl exmple. Whle smulton results for the extended Lngmur nd re very close, results clculted usng re sgnfcntly dfferent. The dfferences re gretest wth the CO 2 njecton rte. A concluson from ths work s tht nccurte sotherm models cn led to sgnfcnt errors n smulton results nd tht the mplementton of the model provdes greter ccurcy n the representton of the sequestrton process.

2 2 The Representton of Mult-component Adsorpton n Reservor Smulton of CO 2 Sequestrton n Col nd Enhnced Colbed Methne Recovery INTRODUCTION CO 2 sequestrton n unmnble col s potentl mngement opton for greenhouse gs emssons. The fesblty of ths process wll be determned by vrous fctors ncludng the col cpcty, the rte of njecton nd the long term behvour of the sequestered CO 2. To nvestgte these requres representtve models for the reservor behvour of the CO 2. One mportnt process n determnng the reservor behvour s dsorpton nd snce mgrton wll often nvolve the dsplcement of dsorbed methne wth CO 2 nd therefore regon of mxed gs wthn the sem, t s mult-component dsorpton tht needs to be represented. Currently, most of the reservor smultors used for sequestrton n col mplement the Lngmur nd Extended Lngmur models () for pure nd mxed gs dsorpton, respectvely. Snce s not thermodynmclly correct [1] nd subject to lrge errors for mxed gs dsorpton, Idel Adsorbed Soluton () theory ws mplemented n some smultors. However, s for mxture dsorpton only nd requres pure gs dsorpton model, nd normlly the Lngmur model s used. Thus, the nccurcy of the pure gs dsorpton propgtes to the mxed gs dsorpton clculton. Recent work hs proposed new dsorpton models for mult-component dsorpton for the full rnge of pressures, such s the Two-Dmensonl Equton of Stte () pproch. Ths pper presents smulton work usng severl pproches to representng mult-component dsorpton, mplemented nto the col sem gs reservor smultor SIMED II. The dsorpton models re extended Lngmur, Idel Adsorbed Soluton nd. The smulton studes nvestgte the sequestrton process nd compre the results usng these dfferent dsorpton pproches. ADSORPTION THEORY Lngmur nd Extended Lngmur Model The Lngmur model ssumes dsorpton occurs on flt surfce s gven by the knetc theory. At equlbrum, contnul process of bombrdment of molecules onto the surfce nd correspondng evporton of molecules from the surfce mntn zero rte of ccumulton t the surfce. The ssumptons of the Lngmur model re [1]: (1) The surfce s homogeneous; tht s, the dsorpton energy s constnt over ll stes. (2) Adsorpton on the surfce s loclzed, whch mens tht the toms or molecules re dsorbed t defnte, loclzed stes. (3) Ech ste cn ccommodte only one molecule or tom. Bsed on the ssumptons bove, the Lngmur model cn be derved s: ω BP θ = = (1) L 1+ BP Where θ s the frctonl coverge, ω s the mount dsorbed, P s the pressure, B s the Lngmur constnt, nd L s mxmum dsorpton cpcty. When extended to mxture dsorpton ssumng no ntercton mong the dsorbed molecules, the Lngmur model becomes: LBPy ω = (2) 1 B Py + j j j where subscrpt represents component, nd y s the mole frcton n the gs phse. Lngmur model s successful n modelng dsorpton t low or md pressure (typclly up to 8 MP for gs dsorpton on cols). However, the dfference between the model nd the expermentl dt s lrge t hgh pressure rnges. Moreover, the extended Lngmur model () s not thermodynmclly correct unless the mxmum cpcty L s the sme for ech component [1]. Consequently, lrge errors my occur for hgh pressure mult-component dsorpton predctons, prtculrly when the dfference of L s lrge.

3 Pn, Connell 3 Idel Adsorbed Soluton The Idel Adsorbed Soluton () model s for mxture dsorpton only, developed by Myers nd Prusntz (1965) [2]. The s n dsorpton nlog to the Roult s Lw for vpor-lqud equlbrum. The ssumptons of the model re [3]: (1) The dsorbed solutons nd the gs phse re del. (2) All ctvty coeffcents n the dsorbed phse re unty. The equlbrum condton for the dsorbed phse nd the gs phse s: ˆ g Py φ = P x φ P 1... ( ) N = where P s the gs pressure of component dsorbed t the sme spredng pressure s the mxture, g ˆφ s the prtl fugcty coeffcent of component n the gs phse, x s the dsorbed phse composton nd φ s the pure gs fugcty coeffcent. The spredng pressure π cn be determned by the Gbbs dsorpton sotherm provdng tht the dsorbed phse s del: π = RT P ω d ln P (4) A where R s the gs constnt, T s the temperture nd A s the surfce re of the dsorbent. The theory ssumes tht the spredng pressure of ech component should be equvlent to the multcomponent dsorpton. When ssumng ech component ccesses the sme surfce re, the followng relton pples: P1 ω 2 ω n ω 1 P P 2 n dp = dp =... = dp (5) P P P Menwhle, the mole frcton constrnt s: n = 1 n x = y = 1 = 1 The totl dsorpton, ω T, s gven by: n 1 x = ω P T = 1 ω ( ) The component dsorpton, ω, s gven by: ω = ω T x To perform mxed-gs dsorpton clcultons, pure-component model s needed. Any purecomponent model, for nstnce the Lngmur model, cn be utlzed n the clculton. However, for mny models, nlytcl ntegrton s unvlble. Thus numercl ntegrton my be used n Equton (5). For hgh pressure dsorpton, fugcty should be used n the gs phse. However, ssumng n del dsorbed phse my be nvld t hgh pressure ledng to lrge errors for these condtons. Two-Dmensonl Equton of Stte The generl 2D nlog cn be wrtten s follows wth n ddtonl prmeter m for dded model flexblty [4]: 2 αω m Aπ + [ 1 ( βω) ] = ωrt 2 (9) 1+ Uβω + W( βω) where A s the specfc surfce re, π s the spredng pressure, ω s the specfc mount dsorbed, nd α nd β re model prmeters. The model coeffcents, U, W, nd m must be specfed to obtn specfc form of the for pplcton. For exmple, n nlog of the vn der Wls (VDW) EOS s obtned by settng m = 1 nd U = W = ; smlrly for the Sove-Redlch-Kwong (SRK) (m = U = 1 nd W (3) (6) (7) (8)

4 4 The Representton of Mult-component Adsorpton n Reservor Smulton of CO 2 Sequestrton n Col nd Enhnced Colbed Methne Recovery = ); the Peng-Robnson (PR) (m = 1, U = 2, nd W = -1); the Eyrng (m = 1/2 nd U = W = ) EOS; nd the Zhou-Gsem-Robnson (ZGR) EOS (m = 1/3 nd U = W = ). [4] One-flud mxng rules were used n the to descrbe mult-component dsorpton: α = x x jαj nd β = x x jβj (1) j j The combnton rules below re chosen becuse they work best for dsorbed phse [4]: α = α + α C / (11) j j ( j )( 1 j ) 2 β β ( 1+ D ) β = (12) j j where C j nd D j re bnry ntercton prmeters. To predct the mxture dsorpton, C j nd D j re set to be zero. To relte the dsorbed phse wth the gs phse, t equlbrum, the chemcl potentl of speces n g the dsorbed phse, µ, s equl to tht n the gs phse, : µ Thus, π g = µ d ln fˆ = π * g nd d µ = dµ (13) P P * d ln fˆ g Integrtng Equton 14, t yelds: ln fˆ * g ( π) ln fˆ ( ) ( ) ( ) g * π = ln fˆ P ln fˆ P ˆ * * g * * ( π ) = π fˆ ( P ) = P At very low pressure, f nd * P fˆ * g ( π) = π fˆ ( P) At very low pressure, 2D del gs lw pples: * * π A = ω RT Henry s constnt s defned s: * ω k = (18) * P So, substtuton nto Equton 16, we obtn: g A fˆ = Ax πφˆ = k RTfˆ For pure-gs dsorpton, Equton 19 becomes: g ωz φ = k f The fugcty for the s: ω 1 ( A ) 1 ln ˆ π φ = dω ln Z RTω ω ω T,M s, n j where ω s the mount dsorbed, s the 2D compressblty fctor, φ s the fugcty coeffcent usng Z g the, f s the fugcty for the gs phse. The 3D PR EOS s normlly used to clculte the gs fugcty. Detled dervton of Equton 21 ws provded by Zhou [3]. µ (14) (15) (16) (17) (19) (2) (21) ADSORPTION COMPARISON Pure CH 4, CO 2 nd ther mxture dsorpton on wet Frutlnd col [5] were used to evlute the models (the CO 2 dsorpton dt up to 8 MP were used). The mesurements were performed t 46.1 C wth pressures up to 12.8 MP. The feed molr compostons for the mxture dsorpton were 8%/2%, 6%/4%, 4%/6% nd 2%/8%.

5 Pn, Connell 5 The pure gs dsorpton dt re used to regress the model prmeters. The objectve functon, S, s used to correlte dt wth the dsorpton models. The functon mnmzes the sum of the squredpercentge devtons n predcted dsorpton: 2 NPTS c e ω ω e = 1 S ω = (22) NPTS c where ω nd e ω re the clculted nd expermentl dsorpton mount, respectvely. NPTS s the number of dt ponts. The percentge verge bsolute devton (%AAD) s used to evlute the results: e 1 ω ω % AAD = (23) NPTS NPTS c e = 1 ω The model evluton results for pure gs dsorpton re summrzed n Tble 1 nd the prmeters for the models re lsted n Tble 2. The model evluton results for the mxture dsorpton re lso lsted n Tble 1. Fgure 1 shows the CH 4 dsorpton results represented wth dfferent models. The Lngmur model underestmtes the pure CH 4 dsorpton t pressures hgher thn 7 MP nd slghtly overestmtes the pure CH 4 dsorpton from 2 MP to 6 MP. As result, both nd overestmte CH 4 component dsorpton below 6 MP nd slghtly overestmte the dsorpton t hgher pressure., on the other hnd, represents the pure CH 4 dsorpton more ccurtely s well s CH 4 component dsorpton. Fgure 2 shows the CO 2 dsorpton results usng dfferent models. In smlr fshon s wth the pure CH 4 dsorpton results, the Lngmur model underestmtes the pure CO 2 dsorpton t pressure hgher thn 6 MP nd slghtly overestmtes the pure CO 2 dsorpton below 6 MP. Snce the pure CO 2 dsorpton dt up to 8 MP were used n the model evluton, the models behvor t pressures hgher thn 8 MP re not known. However, for the CO 2 component dsorpton, predcts the dsorpton better thn or, especlly n the hgh pressure regon. Fgure 3 shows the totl dsorpton results usng dfferent models. Both nd underestmte the dsorpton for pressures hgher thn 7 MP. Fgure 4 shows the compostonl results for mxture dsorpton. predcts the dsorbed phse composton better thn the other two models. SIMULATION RESULTS SIMED II s colbed methne smultor cpble of compostonl dul-porosty reservor smulton. The dsorpton models ntegrted n SIMED II were nd. In ths work, the ws mplemented nto SIMED II. A hypothetcl one-dmensonl enhnced col methne through CO 2 njecton cse ws studed to llustrte how the dfferent dsorpton models ffect the reservor smulton results usng the dsorpton dt presented bove for Frutlnd col. The descrpton of the reservor propertes s lsted n Appendx A. Fgure 5 presents the gs rte clculted wth SIMED usng the dfferent dsorpton models. The CH 4 producton rte decreses fter rechng mxmum nd the dfferent dsorpton models predct smlr rtes tll round dy 4. After tht, the CH 4 producton rte ncreses nd predcts lower rte thn the two other models. Fgure 6 presents the dsorbed concentrtons for ech gs nd sotherm model. In Fgure 6(), t the erly stges of the smulton, the two wells hve no ntercton, thus the CH 4 producton well behves s conventonl prmry colbed methne recovery, where the methne s desorbed from the col by lowerng the sem pressure. Snce the representton of pure CH 4 dsorpton t pressures less thn 5 MP s lmost dentcl for the nd Lngmur models, the ntl

6 6 The Representton of Mult-component Adsorpton n Reservor Smulton of CO 2 Sequestrton n Col nd Enhnced Colbed Methne Recovery producton rte results for the two models re lso very smlr. However for Fgure 6(b) t 1 yer the CH 4 dsplced due to CO 2 njecton hs strted to rrve t the producton well nd the producton rte ncreses. The dsorbed concentrtons of CH 4 re hgher for the thn the other two models reflectng the dsorpton sotherm dfferences t these hgh pressures. As result the free gs volumes re less nd thus producton rte lower. Fgure 5(b) shows the gs rte results for 16 yer perod. Gs producton rte ncreses shrply fter dy 41, ndctng CO 2 brekthrough. Gs produced s mnly CO 2 fter dy 5. Fgure 6(e) shows tht the dsorbed CO 2 concentrton becomes hgher ner the producton well, ndctng comng CO 2 brekthrough. Fgure 6(f) shows no CH 4 dsorbed n the reservor nd CO 2 beng produced t dy 548. Fgure 5 lso presents CO 2 njecton rte. All dsorpton models consdered hve mxmum njecton rte t round dy 1. However, the CO 2 njecton rte predcted by s sgnfcntly hgher thn by ether or tll round dy 1. Then the njecton rte predcted by s slghtly hgher thn the other models. The lower CO 2 njecton rte t erly tmes by nd s due tht both models underestmte the CO 2 dsorpton t hgh pressures. Fgure 7 shows the gs phse composton profle usng nd. The results re smlr to the dsorbed gs concentrton becuse they re closely relted to ech other. Fgure 8 shows the cumultve CH 4 produced nd CO 2 njected for 2 yer perod. The results re consstent wth the gs rte results. SUMMARY nd CONCLUSIONS Ths pper hs consdered three pproches to representng dsorpton n reservor smulton of enhnced colbed methne through CO 2 sequestrton. Two of the dsorpton sotherm models, extended Lngmur nd Idel Adsorbed Soluton, re populr choces for reservor smulton. These provde computtonlly effcent clcultons but cn nvolve nccurces prtculrly for multcomponent gs mxtures nd sngle component CO 2. The sotherm model hs been consdered by severl uthors s n pproch to representng dsorpton. The sotherm model hs been shown to provde closer mtch to expermentl observtons on Frutlnd col for wde pressure rnge nd gs component mxture thn the extended Lngmur nd Idel Adsorbed Soluton sotherms. The sotherm model ws mplemented n the compostonl dul porosty smultor SIMED. A hypothetcl cse study ws formulted to nvestgte the reltve effects of the three sotherm models on reservor smulton of CO 2 sequestrton nd enhnced colbed methne recovery. In ths cse study CO 2 njecton well s seprted from CH 4 recovery well by 1m for col sem t n ntl reservor pressure of 8.8 MP, correspondng to roughly 88 m depth. Whle the njecton well opertes t pressures sgnfcntly hgher thn the ntl reservor pressure, the producton well produces methne ntlly through pressure drwdown below the desorpton pressure. In the cse study, njected CO 2 dsplces dsorbed methne whch then mgrtes wy from the njecton well nd towrds the producton well n response to the pressure grdent wthn the sem. In terms of dsorbed gses, three regons re creted wthn the sem; towrds the njecton well there s regon of pure CO 2, round the producton well there s regon of pure CH 4. In between these two regons there s zone of mxed CO 2 -CH 4, trnston regon. The sze of ths trnston regon s determned by the rte of dffuson nto the col mtrx; chrcterzed n the modellng by the desorpton tme constnt. Wthn ths trnston regon mxed gs dsorpton sotherm s requred. Intlly the methne producton rtes re very smlr for the three dsorpton models. Ths s consstent wth the ccurcy wth whch the dsorpton behvour s represented; for ths low pressure, sngle component methne regme ll three sotherm models re good descrptons of the dsorpton behvour. However wth tme ths good greement deterortes, wth the methne rtes clculted usng the beng sgnfcntly lower thn those clculted usng the other two dsorpton models. Ths

7 Pn, Connell 7 cn be ttrbuted to the ntercton of free methne dsplced by the CO 2 njecton rrvng t the producton well. As dscussed bove the CO 2 njecton cretes mxed gs regon where multcomponent dsorpton occurs. The s more ccurte descrpton of ths process thn the nd models. In ddton, the njecton of CO 2 nvolves hgh pressures; dsorpton of CO 2 for ths sngle component hgh pressure regme s lso more ccurtely descrbed usng the. The combnton of these two effects leds to ncresng dfferences n methne producton rte wth tme s the ntercton between the two wells becomes stronger. The most sgnfcnt dfferences ssocted wth the sotherm models re seen n the CO 2 njecton rte. The rte wth bsed clcultons s sgnfcntly hgher thn wth the other two dsorpton pproches, prtculrly t erly tmes. Ths behvour reflects the dfferences n the dsorpton sotherms, where t hgh pressures the CO 2 dsorbed mount, s represented by the, s greter thn tht estmted by the nd models. Snce the pressure behvour s very smlr cross the smultons, the njecton rte s therefore hgher to compenste for the greter mount dsorbed. After rechng mxmum the njecton rte decreses wth tme, n response to the pressure behvour wthn the reservor. Ths pper hs demonstrted tht mproved models for dsorpton cn hve sgnfcnt mpcts on reservor smulton of CO 2 sequestrton nd enhnced colbed methne. The mgntude of ths mpct s functon of pressure nd the role of mult-component gs mgrton. Implementton of the dsorpton sotherm model nto SIMED hs therefore mproved the cpblty of ths smultor to represent CO 2 sequestrton n col nd enhnced colbed methne producton. Appendx A. Descrpton of reservor propertes used n smulton cse study Grd system Crtesn x drecton: see Tble 3 Reservor temperture: 46.1 C Permeblty: 2.5 md Reltve permeblty: see Tble 4 Gs desorpton pressure: 5 MP Intl reservor pressure: 8 MP Desorpton tme constnt: 1 dys for CO 2, 27.5 dys for CH 4 Well loctons: Injecton well: Grd 1 Producton well: Grd 78 Well skn fctor= Bottomhole pressure: kp Injecton pressure: 14 MP

8 8 The Representton of Mult-component Adsorpton n Reservor Smulton of CO 2 Sequestrton n Col nd Enhnced Colbed Methne Recovery References 1. Do, D. D., 1998: Adsorpton Anlyss: Equlbr nd Knetcs: London, Imperl College Press. 2. Myers, A. L., Prusntz, J. M., 1965: Thermodynmcs of Mxed-Gs Adsorpton, AIChE J., V. 11, p Zhou, C., 1994: Modelng nd Predcton of Pure nd Multcomponent Gs Adsorpton, Ph.D Dssertton: Oklhom Stte Unversty, Stllwter, Oklhom. 4. Zhou, C., Hll, F., Gsem, K. A. M., Robnson, Jr., R. L., 1994: Predctng Gs Adsorpton Usng Two-Dmensonl Equtons of Stte, I&EC Reserch, V. 33, p Hll, F., Zhou, C., Gsem, K. A. M., Robnson, Jr., R. L., 1994: Adsorpton of Pure Methne, Ntrogen, nd Crbon Doxde nd Ther Bnry Mxtures on Wet Frutlnd Col, presented t the Estern Regonl Conference & Exhbton, Chrleston.

9 Pn, Connell 9 Tbles Tble 1. Adsorpton results - %AAD Pure Gs Adsorpton Lngmur CH CO Mxture Adsorpton CH CO Totl Tble 2. Best ft prmeter vlues for dsorpton sotherms of Frutlnd col Lngmur L (m 3 /ton) B (MP -1 ) CH CO α (br cm 3 g/mmol / mol) β (mmol/g) -1 -ln(k) ln(mmol/g br -1 ) CH CO Tble 3. Grd spcng used n smulton cse study Grd x(m) Grd x(m) Grd x(m) Grd x(m) * x[grd]= x[79-grd] when grd s 4 to 78 Tble 4. Reltve permeblty of wter nd gs used n smulton cse study Wter Sturton Wter phse reltve permeblty Gs phse reltve permeblty

10 1 The Representton of Mult-component Adsorpton n Reservor Smulton of CO 2 Sequestrton n Col nd Enhnced Colbed Methne Recovery Fgures Absolute Adsorpton (m 3 /ton) CH4 Exprmentl Feed Composton: Pure CH 4 8% CH 4 6% CH 4 4% CH 4 2% CH Pressure (MP) Fgure 1. CH 4 dsorpton on wet Frutlnd col t 46.1 C Absolute Adsorpton (m 3 /ton) CO2 Expermentl Feed Composton: Pure CO 2 8% CO 2 6% CO 2 4% CO 2 2% CO Pressure (MP) Fgure 2. CO 2 dsorpton on wet Frutlnd col t 46.1 C

11 Pn, Connell Expermentl Absolute Adsorpton (m 3 /ton) Pure CO 2 8% CO 2 6% CO 2 4% CO 2 2% CO 2 Pure CH Pressure (MP) 14 Fgure 3. Totl dsorpton on wet Frutlnd col t 46.1 C 1 Expermentl.8.6 Feed Composton: 8% CH 4 x CH4 Feed Composton: 6% CH 4.4 Feed Composton: 4% CH 4.2 Feed Composton: 2% CH 4 Low Pressure Hgh Pressure y CH4 Fgure 4. Composton for dsorpton on wet Frutlnd col t 46.1 C

12 12 The Representton of Mult-component Adsorpton n Reservor Smulton of CO 2 Sequestrton n Col nd Enhnced Colbed Methne Recovery Gs (m 3 /dy) 3 CO 2 Injecton Rte 2 1 CH 4 Producton Rte Tme (dy) () 2 yer (73 dys) perod 6 5 Gs (m 3 /dy) CO 2 Injecton Rte 1 Gs Producton Rte Tme (dy) (b) 16 yer (584 dys) perod Fgure 5. Gs rtes t njecton nd producton wells for the hypothetcl smulton exmple, clculted usng SIMED, for the three dsorpton sotherms

13 Pn, Connell Gs Concentrton (m 3 /tonne) CH4 Gs Concentrton (m 3 /tonne) CH () (b) Gs Concentrton (m 3 /tonne) CH4 Gs Concentrton (m 3 /tonne) CH (c) (d) 3 3 Gs Concentrton (m 3 /tonne) CH4 Gs Concentrton (m 3 /tonne) CH (e) (f) Fgure 6. Adsorbed gs concentrtons for SIMED smulton cse study t () Dy 182, (b) Dy 365, (c) Dy 547, (d) Dy 73, (e) Dy 365, (f) Dy 548

14 14 The Representton of Mult-component Adsorpton n Reservor Smulton of CO 2 Sequestrton n Col nd Enhnced Colbed Methne Recovery Gs Phse Composton CH4 Gs Phse Composton CH () (b) Gs Phse Composton CH4 Gs Phse Composton CH (c) Fgure 7. Gs phse composton for SIMED smulton cse study t () Dy 182, (b) Dy 195, (c) Dy 365, (d) Dy 4197 (d) Gs (m 3 ) 3 2 Gs (m 3 ) Tme (dy) () Tme (dy) (b) Fgure 8. Cumultve gs producton for smulton cse study () CH 4 (b) CO 2

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