SPE Copyright 2002, Society of Petroleum Engineers Inc.

Transcription

1 PE Effect f Cmpstn n Waterblckng fr Multcmpnent Gasflds Brank R. Bjeljc, Imperal Cllege, PE, Ann H. Muggerdge, Imperal Cllege, PE, and Martn J. Blunt, Imperal Cllege, PE Cpyrght 22, cety f Petrleum Engneers Inc. Ths paper as prepared fr presentatn at the PE Annual Techncal Cnference and Exhbtn held n an Antn, Texas, 29 eptember 2 Octber 22. Ths paper as selected fr presentatn by an PE Prgram Cmmttee fllng reve f nfrmatn cntaned n an abstract submtted by the authr(s). Cntents f the paper, as presented, have nt been reveed by the cety f Petrleum Engneers and are subject t crrectn by the authr(s). The materal, as presented, des nt necessarly reflect any pstn f the cety f Petrleum Engneers, ts ffcers, r members. Papers presented at PE meetngs are subject t publcatn reve by Edtral Cmmttees f the cety f Petrleum Engneers. Electrnc reprductn, dstrbutn, r strage f any part f ths paper fr cmmercal purpses thut the rtten cnsent f the cety f Petrleum Engneers s prhbted. Permssn t reprduce n prnt s restrcted t an abstract f nt mre than 3 rds; llustratns may nt be cped. The abstract must cntan cnspcuus acknledgment f here and by hm the paper as presented. Wrte Lbraran, PE, P.O. Bx , Rchardsn, TX , U..A., fax Abstract urng tertary mscble gas njectn drect cntact beteen gas and l can be prevented by ater surrundng resdual l. The prncpal am f ur study s t assess the mprtance f ths aterblckng phenmenn n multcmpnent gas njectn. We study ths prcess usng a multcmpnent prescale mdel. Lght cmpnents n the gas dsslve n the ater and dffuse thrugh the ater t reach the l. Ths causes the l t sell. Eventually the l sells suffcently t cntact the gas drectly. Hever, cmpnents n the l can dffuse nt the gas, causng the l t shrnk and preventng the cntact. We apply ur mdel t a varety f frst-cntact and multple-cntact mscble gas/l systems frm publshed feld studes. ue t the l slublty f hydrcarbns n ater, l sellng and shrnkage can prevent drect cntact fr many days t years. We sh that ncreasng the mscblty f njected gas, by, fr nstance, mvng frm a mult-cntact mscble t a frst-cntact mscble dsplacement ncreases the tme taken t acheve drect gas/l cntact. Ths leads t an extended t-phase regn n the reservr, even fr a thermdynamcally mscble gas fld. Intrductn Mass transfer acrss ater barrers by mlecular dffusn s an mprtant prcess durng l recvery by gas njectn. -5 Mscble gas njectn s typcally appled after a aterfld n hch case sgnfcant vlumes f l may be trapped thn the pre-space n the frm f gangla surrunded by ater (Fg. ). In ths case the njected gas may nt cme nt drect cntact th the l and recvery ll be reduced, as the gas ll nt be able t dsplace the l trapped behnd the ater. Fg.. chematc f aterblckng. After secndary dsplacement by ater, a fractn f the l remans n the feld shelded by ater. In tertary recvery gas s njected t dsplace the l. Ths effect has been bserved manly n the labratry 6-9 and s termed aterblckng. ependng upn the relatve cmpstns f the l and gas, gas cmpnents ll dffuse nt the l and l cmpnents ll dffuse nt the gas. If the frst mechansm dmnates then trapped l drplets ll sell and may ultmately rupture ther retanng ater barrer, enablng them t be sept aay by the gas. If the secnd mechansm prevals then the l drplets ll shrnk and the gas ll be enrched th l, althugh nevtably sme l ll stll be trapped by the ater. Waterblckng durng carbn dxde (CO 2 ) njectn has -5, been nvestgated theretcally by a number f authrs. Ths nvlves mdelng the transfer f a sngle cmpnent (CO 2 ) dffusng thrugh the ater nt the trapped l. These studes shed that the tme-scales at the pre level ver hch CO 2 dffuses thrugh the ater, sells the trapped l and ruptures the surrundng ater s relatvely shrt (~ day fr a µm thck ater flm) manly because f the hgh slublty f CO 2 n ater. Hence t appears that aterblckng s relatvely unmprtant fr l recvery va carbn dxde njectn ver the tme-scales f typcal recvery schemes (~ years). Carbn dxde s nt alays avalable n suffcent quanttes fr gas njectn, hereas many l felds, lcated n remte parts f the rld, prduce large quanttes f hydrcarbn gas fr hch there s n market. In these crcumstances t s smetmes ecnmc t mx the prduced

2 2 B.R.Bjeljc, A.H.Muggerdge and M. J. Blunt gas th lghter cmpnents f the l t the pnt here the mxture s mscble th the l at reservr temperature and pressure. Ths enrched gas s then re-njected nt the reservr. One f the best-knn examples f ths type f recvery scheme s the Prudhe Bay feld n the Nrth slpe f Alaska. Waterblckng n hydrcarbn gas njectn s a far mre cmplex prblem because t nvlves multcmpnent mass transfer. 5 Lght cmpnents n the gas dffuse nt the l, causng the l t sell. In cntrast, heaver cmpnents frm the l dffuse nt the gas, shrnkng the l. It s pssble that the ater barrer never ruptures, meanng that mass transfer s cntrlled by the exceptnally sl dsslutn f heavy hydrcarbn cmpnents, and ver the lfe tme f the reservr thermdynamc equlbrum s never acheved. T understand the dfferent tme-scales nvlved e perfrm a smple scalng analyss t assess sgnfcance f aterblckng fr dfferent cmpnents. The tme scale fr CO 2 dffusn thrugh a ater flm f length L µm-5 µm and fr typcal reservr cndtns (P 26MPa, T 344K) s t ~ ( L ) 2 ~ 3 s- 4 s ~ mnutes/hurs, here s the dffusn ceffcent n ater and s the slublty n ater (ml f cmpnent / ml f slutn). The dffusvty f CO 2 s f the rder f -9 m 2 /s 4 and the slublty f CO 2 under these cndtns s f the rder f -2. 2,3 Typcal fl rates n a reservr settng are arund.-m/day th ell spacng beteen m and m. A tmescale f 6 mnutes t reach equlbrum s equvalent t a mxng zne length f at mst a fe centmeters, meanng that n ths case ater blckng has n sgnfcant mpact n feld-scale recvery. If the njected gas ere cmpsed f lght ntermedate hydrcarbn cmpnents (say nly f n-butane, C 4, th a slublty f rder -4 2,4, an dentcal analyss gves t ~ 5 s- 6 s ~ days. Ths gves a mxng length zne f. t several meters, hch s stll small n cmparsn th the ell spacng. Under the same cndtns, the tme scale fr dffusn f heaver hydrcarbn cmpnents e.g. ctane (C 8 ) s strkngly hgher th t ~ 7 s- 8 s ~ years, mstly due t ther much ler slublty (f the rder f -6, as estmated frm the lublty ata eres () 5 ). In ths case the mxng zne length exceeds the ell spacng. Ths mples that ver a tme-scale fr gas t mve frm njectn t prductn ells (arund a year r s), gas and l fal t reach thermdynamc equlbrum, resultng n pr recveres. In ths paper e shall descrbe a smple ne-dmensnal numercal mdel t nvestgate multcmpnent mass transfer n aterblckng at the pre-scale. We shall then study the dynamcs fr a range f synthetc gas cmpstns njected nt a reservr cntanng an Indnesan crude l, as ell as applyng ur mdel t an njected gas and crude l frm Nrth Alaska. We sh that the rate f l recvery and the ay t s recvered (ether by rupturng the ater barrer r beng vaprzed nt the dsplacng gas) s senstve t the l and gas cmpstns, the l drplet sze and the rgnal thckness f the ater barrer. We sh cases here the tme t reach equlbrum beteen gas and l s suffcently lng t affect feld-scale recveres. We dscuss fr a range f frstcntact and multple-cntact mscble gas/l systems h an ncrease n the mscblty f njected gas may lead t prlnged gas/l cntact. Mathematcal Mdel We nvestgate the prblem f a sngle l drplet trapped thn a dead-end rck pre by a ater barrer at the pre thrat. Injected gas passes thrugh a pre abve the ater barrer (Fg. 2a). We represent ths system smply as three regns cmpsed f gas, ater and l separated frm each ther by a sharp nterface (Fg. 2b). L,n L,n L (t) L (t) L(t) gas ater l (a) gas ater l () (2) (b) gas ater l cmpnent cncentratn Fg. 2a,b. (a) representatn f the ater-et prus medum at the pre scale by a unt cell cnsstng f flng (gas), barrer (ater) and stagnant (l) phase; (b) mathematcal descrptn f the unt cell: () cmpnents dffuse thrugh the ater barrer frm gas t the l phase and vce versa, (2) cncentratn prfle f a sngle cmpnent s dran n the rght. The ater/l bundary s mvng as the l gangln thckness L (t) and the ater barrer thckness L (t) vary n tme by a length L(t). We make the fllng assumptns:. The njected gas s mscble n all prprtns th the l. 2. The gas s flng suffcently fast that ts cmpstn abve the ater s nt altered by mass transfer t r frm the l. 3. The l and ater thn the pre are stagnant. 4. The cncentratn prfles thn the ater are lnear. 5. Hydrcarbn cncentratns n the ater are suffcently

3 77697 Effect f Cmpstn n Waterblckng fr Multcmpnent Gasflds 3 l that Fck s La s vald. Pressure and temperature gradents are neglgble. 6. The cncentratn gradent thn the l s neglgble. 7. The gas fl rate s cnstant. 8. The prus medum s strngly ater-et. 9. Vaprzatn f the ater nt the gas des nt affect the lcatn f the gas/ater nterface.. We gnre capllary effects and the curvature f the l/ater and gas/ater mensc n assessng hen the ater barrer ruptures.. The densty f the l s gven by the cncentratneghted mean f the denstes f ts cmpnents at reservr T and P. Assumptns (8) and (9) are very mprtant as they all us t assume that the gas-ater nterface s statnary. Assumptn (8) means that the ater cats all the pre alls and s cntnuus thrughut the prus medum, hereas assumptn (9) states that any vaprzatn f ater s cmpensated by ater spreadng t mantan the lcatn f the gas/ater nterface. The pstn f the gas-ater nterface s therefre cntrlled slely by capllary frces (hch are n turn cntrlled by pressure and njectn rate). nce frm assumptn (7) the gas fl rate s cnstant, the l-ater nterface may mve as the l drplet sells r shrnks, but the gas-ater nterface ll nt. Ths means that ur mdel can be smpler than thse f and Pnczesk and hearn and Wakeham 5, h mdel the mvement f bth the gas-ater and the l-ater nterfaces. Gvernng Equatns The mass transfer rate f cmpnent F, [ml/s] thrugh the ater barrer f length L (t) [m] s gven by Fck s frst la f dffusn: F A ( C g C ), () L here A [m 2 ] s the ater barrer area perpendcular t the drectn f mass transfer,, [m 2 /s] s the dffusn ceffcent f cmpnent n ater and [ml f cmpnent / ml f slutn] s the slublty f hydrcarbn cmpnent n ater frm the gas r l phase. Cncentratns C.g [ml/m 3 ] and C. (t) [ml/m 3 ] are the cncentratns f cmpnent n the gas and l phases respectvely. nce the slubltes f hydrcarbns n ater are very l, ther dffusn ceffcents are unlkely t sh cncentratn dependence;.e. Fck s Eq. () s vald. Assumng deal mxng f cmpnents n the l and the gas, the vlume f cmpnent n the l phase, V (t) [m 3 ], n the ttal vlume f l, V (t) [m 3 ], can be rtten as: V M C V ( ), (2) t here M [kg/ml] s the mlar mass f cmpnent and [kg/m 3 ] s the densty f pure cmpnent. The changes n the densty f cmpnents due t vlume change n mxng have nt been accunted fr n ths study. The cnstrant that must be satsfed s: n c M C, (3) here n c s the ttal number f hydrcarbn cmpnents. The rate f change f the vlume f cmpnent s: V M ( V C ) M F, (4) here the mlar mass transfer rate n the l phase, F, (t), s equal n abslute terms but ccurs n the ppste drectn t the mlar mass transfer rate suppled frm the ater phase (t): F, ( V C ) F F ellng f the l cnsstng f n c hydrcarbn cmpnents can be descrbed by the fllng equatn: V A L n c M F Eq. (6) can be cupled th Eqs. (5) and () t btan: n n M M F, A ( C, c c g L C ) Fnally, cmbnng Eqs. (6) and (7) and usng the fact that the rate f ncrease n the l gangln thckness (f sellng f l takes place) s equal t the rate f shrnkng f the ater barrer thckness: L L ( t ) e btan: L n c M ( C g L C ) Ths equatn descrbes the dynamcs f l-ater nterface as a functn f multcmpnent mass transfer. In rder t descrbe fully the dynamcs f the l-ater nterface, Eq. (5) can be expanded t btan: C V C, + V F, ( ), t (5) (6) (7) (8) (9) ()

4 4 B.R.Bjeljc, A.H.Muggerdge and M. J. Blunt The vlume f l phase n tme, V (t), s the prduct f the area f the l phase and the sum f the ntal l gangln thckness,, and the thckness that changes n tme due t L, n l sellng/shrnkng, L (t): V A L () Then nsertng Eq. (9) nt Eq. () and usng denttes frm Eqs. (5) and (8) ne btans: C L( t) ( C g C L ) + C L( t) (2) Eqs. (9) and (2) cmprse a system f Ordnary fferental Equatns (OE) hch can be slved smultaneusly usng a numercal slver. These equatns ere slved n dmensnless frm by ntrducng dmensnless varables: L( t) L ( t ), (3) L, n,2,.. n (4),,,,,,,, c,2,... n (5) C g C g C c M (6) M t) C ( ) (7) (, t here L ( t ) s the dmensnless ater barrer thckness as a functn f dmensnless tme and L, n s the ntal ater barrer thckness; dmensnless slubltes and dffusvtes f a cmpnent are nn-dmensnalsed n respect th the values fr methane (, and, ). mensnless tme s: t t ( L n ) (8),, 2, Usng the abve ntatn, Eqs. (9) and (2) rtten n dmensnless frm are: L ( t ) nc,, ( C, g L ( t ) C, ( t )) (9) and C ( t ) L, ( t ) ( C g L C ( t + L )) + C ( t ) ( t L ( t ) ) (2) here L s the dmensnless rat beteen the ntal ater barrer thckness and the ntal l gangln thckness. Flud prpertes An extensve lterature search has been cnducted t btan the values fr slublty and dffusvty fr each cmpnent at the representatve reservr cndtns fr mscble gas dsplacements nvestgated here.e. P 26MPa and T 344K. At the present tme, scarcty f the expermental data at hgh temperature-hgh pressure cndtns requres ntrductn f reference values fr slublty and dffusvty f a ell-studed cmpnent and extraplatn t the unknn values fr ther cmpnents. Recent methane data at the abve cndtns ere fund fr slublty, (CH 4 ).87-3 ml/ml and dffusvty, (CH 4 ) 5-9 m 2 /s. 4,6 Our methdlgy fr estmatng dffusvtes and slubltes fr ther cmpnents at hgh temperature-hgh pressure cndtns s descrbed n Appendx. Results We frst nvestgate pssble physcal scenars n ater blckng durng hydrcarbn mscble gas dsplacement f a synthetc l f a cmpstn nearly dentcal t the cmpstn f an Indnesan crude l 7. The nly dfference s that e assumed there as n CO 2 and N 2 n the synthetc l. Later e ll dscuss the effect f CO 2 n aterblckng behavr. The njected synthetc gases at representatve reservr cndtns (P 26MPa, T 344K) ere verfed t be mscble n all prprtns th the l (assumptn () frm the mdel s satsfed) by usng a cde based n the sthermal flash studes by Mchelsen. 8,9 ependent n cmpstns f synthetc l and njected gas, ne can encunter: () rapd l sellng hch results n shrt tmes needed t cmpletely pe ut the ater barrer sheldng the l (shrt ater barrer rupture tmes), () sl l sellng resultng n very lng ater barrer rupture tmes, () bth l sellng and l shrnkng here the ater barrer eventually ruptures. Cmpstns f the gases and the l that gve rse t the abve three scenars n ater blckng are gven n Table (see page 6). We assume that nce the ater barrer ruptures, the gas and l cmpletely mx and the lcal dsplacement effcency s %. Hence, the rupture tme s the key parameter affectng the effcency f gas njectn. The frst scenar s presented n Fg. 3 fr the l and gas cmpstn () n Table. The dmensnless rat f the ntal l gangln thckness t the ntal ater barrer thckness as.5 and the ntal ater barrer thckness L as L, n 5µm n ths and all ther cases used fr llustratn f dfferent scenars durng aterblckng.

5 77697 Effect f Cmpstn n Waterblckng fr Multcmpnent Gasflds 5 dmensnless length, L(-) l gangln thckness ater barrer thckness 2 3 tme, t (day) Fg. 3. The dmensnless ater barrer and l thckness as a functn f tme fr L.5 and L, n 5µm and the l and gas cmpstn () gven n Table. The gas has hgher cncentratns f the lghter cmpnents C t C 5 than the l and ths causes rapd rupture f the ater barrer. In Fg. 3 the njected gas cntans cmpnents C t C 5, each f hch s ntally present n hgher cncentratn n the njected gas than n the l. Ths cncentratn dfference s the drvng frce fr transfer f these cmpnents frm the gas t the l, hch causes the l t sell. The sellng f l pushes the l/ater nterface tards the gas fl n the man channels, hch results n a prprtnal decrease f the thckness f the ater barrer ver tme. Ths prcess ends hen ater s cmpletely dsplaced nt the man fl channel by the l; at ths pnt the ater barrer ll have ruptured.e. the length f the ater barrer s zer. Fr the cmpstns () n Table e fnd that the ater barrer rupture tme n the pre scale s f the rder f days (3.7 days). Ths relatvely shrt tme ndcates that ater n ths case des nt prevent gas and l reachng thermdynamc equlbrum ver tme scales typcal f gas njectn prcesses n reservrs, as dscussed n the ntrductn. Hever, f there s nsuffcent drvng frce fr mass transfer f the hydrcarbn cmpnents frm the gas nt the l, the l sellng/ater shrnkng prcess becmes s prlnged that the ater rupture tmes are much lnger than several days. Ths s llustrated n Fg. 4, hch shs the dynamcs f l sellng/ater shrnkng durng njectn f a synthetc gas cntanng cmpnents C t C 8 (gas cmpstn (2) n Table ). Methane frm the gas sells the l very rapdly but nt t the extent that the ater ruptures. Rupture nly ccurs after a lng perd f tme (.2 years) and s caused predmnantly by the l sellng due t dffusn f cmpnents C 6 t C 8 frm the gas. Fg. 4 demnstrates an mprtant scenar (scenar () n the ntrductn) n aterblckng. The fact that the ater at the pre scale prevents drect mxng f gas and l fr years results n the t-phase gas-l mxng zne length beng cmparable th the feld length-scale (ell spacng), thus leadng t pr l recveres. dmensnless ater length, L(-) very rapd l sellng by methane very sl l sellng by C 6-8 cmpnents tme, t (year) Fg. 4. The change f dmensnless ater barrer thckness ver tme fr L.5 and L, n 5µm and the l and gas cmpstn (2) gven n Table. As n Fg.4 the rupture tme s very lng n ths case and cntrlled by the mass transfer f ntermedate hydrcarbn cmpnents C6 t C 8 frm the gas nt the l. The thrd scenar l shrnkng - ll ccur hen the gas f cmpstn (3) frm Table s njected. The ntal stage f mass transfer thrugh the ater s dmnated by the methane dffusn frm the l t the gas, hch results n the l shrnkng and a prprtnal ncrease n the ater barrer thckness, as seen n Fg. 5. Hever, as the gas njectn prceeds, mass transfer f the cmpnents frm the gas t the l (n the ppste drectn t the methane mass transfer) gradually prevals and the ater barrer thckness starts t decrease. Ths decrease cntnues untl the ater ruptures. dmensnless ater length, L(-) net l shrnkng net l sellng l shrnkngl sellng tme, t (day) Fg. 5. ellng and shrnkng f the ater ver tme fr L.5 and L, n 5µm and the gas and l cmpstn (3) gven n Table. The l has hgher cncentratns f C than the gas, hch causes l shrnkng n the ntal stage f the gas njectn. The later stage s dmnated by dffusn f hydrcarbns frm the gas t the l, hch results n l sellng and the ater barrer rupture. Fg. 5 llustrates that dffusn f cmpnents frm the l t gas can result n l shrnkng n aterblckng, but des nt necessarly mply lnger rupture tmes.

6 6 B.R.Bjeljc, A.H.Muggerdge and M. J. Blunt Carbn Ol Gas cmpstn Carbn Weghtng number f cmpnent cmpstn (ml/ml, (ml/ml, %) () (2) (3) number f cmpnent lublty (-) ffusvty (-) functn Order f magntude %) C C C C n-c C n-c C C C C C C C C C C C C C C n-c C n-c C C C C E-5-5 C E E-5-5 C E E-6-6 C E E-7-7 C E E-8-8 C E E-9-9 C 36+.E-8..E-9-9 Table. Cmpstns f the l and the gases used fr llustratn f a range f scenars n ater blckng durng mscble dsplacement. The l cmpstn s smlar t an Indnesan crude l. 7 Frm the abve examples t s seen that, fr a gven temperature and pressure, the cmpstn f the gas/l system s the key determnant affectng the mvement f the ater/l bundary. Hence t s f practcal nterest t assess the cntrbutn f each hydrcarbn cmpnent t the mass transfer thrugh ater. Ths cntrbutn depends n the prduct f slublty and dffusvty f a gven cmpnent (see Eq. (9)), as ell as the cncentratn dfference f cmpnent beteen the gas and l phases. We ntrduce a eghtng functn fr each cmpnent that s the prduct f slublty and dffusvty. As seen frm Table 2 the values f the eghtng functns fr the hydrcarbn cmpnents and pseudcmpnents dffer by up t ten rders f magntude. A large cncentratn dfference f cmpnents th large values fr the eghtng functn ll cause rapd rupture f ater. Waterblckng may prevent drect gas/l cntact fr a year r mre nly f the gas cntans sgnfcant quanttes f ntermedate t heavy cmpnents C 6+. The dependence f rupture tme n the dmensnless rat f ntal l t ntal ater barrer thckness s presented n Fg. 6 fr the l and gas cmpstn (2) n Table. Table 2. The values and rder f magntude f the prducts f the slublty and dffusvty (eghtng functns) fr the hydrcarbn cmpnents and pseudcmpnents n gas and l phase. Waterblckng prevents drect gas/l cntact fr f rder years f the gas cntans sgnfcant quantttes f ntermedate t heavy cmpnents - C 6+. ater rupture tme, t (year)... µ / rat, L (-) L,n µ Fg. 6. Water rupture tmes as a functn f dmensnless rat f the ntal l gangln thckness t the ntal ater barrer thckness fr varus ntal ater barrer thcknesses. The l and gas cmpstn (2) are frm Table. 7µ 5µ 3µ 2µ

7 77697 Effect f Cmpstn n Waterblckng fr Multcmpnent Gasflds 7 As the prus medum s mre saturated n ater (ler L ) the tmes needed t break the ater ncreases. The rupture tmes als scale th the length squared f the ntal ater barrer thckness (Eq. (8)). Case tudy: Gas/Ol system frm a Nrth-Alaskan feld We studed the rle f ater blckng n an njectn gas/crude l system representatve f a feld n Nrth Alaska. We cnsdered the reservr pressure t be P 26MPa and temperature T 344K. The cmpstn f the l and the gas are gven n Table 3. Cmpnent Ol cmpstn (ml/ml %) Gas cmpstn (ml/ml %) CO N C C C C n-c C n-c C C C C C C C C C C Table 3. Cmpstns f the gas and the l currently used n a Nrth Alaska l feld fr mscble dsplacement. As can be seen frm Table 3, the mst mprtant dfference frm the gas and l cmpstns n Table s the presence f CO 2 n the gas and the l. Ths presence f CO 2 n hgher cncentratn n the gas leads t relatvely rapd CO 2 dffusn thrugh the ater and therefre rapd sellng f the l n the ntal stage. Ths prcess n turn causes fast shrnkng f the ater barrer, as seen n Fg. 7. Nte that the l sellng ccurs despte smultaneus ater flm length L(-) gas CO2 sells the l tme, t (day) C2, C3 and the remanng CO2 dmnates the C mass transfer Fg. 7. The knetcs f ater blckng durng tertary mscble gas njectn fr the cmpstns f gas and the l typcal f a Nrth Alaskan l feld. L. and L, n 5µm. cncentratn n the l, C (ml/ml) cncentratn n the l, C (ml/ml).. CO2 -C4 N2 C C2 -C5 C3 n-c5 sum f all cmpnents C4-9 C2-26 C36+ C-3 C8 C C6 C27-35 C7 tme, t (day) C9 n-c tme, t (day) Fg. 8. Changes n the cncentratn f the cmpnents n an l typcal f a Nrth Alaskan l feld durng tertary mscble gas njectn. mass transfer f methane n the drectn ppste t that f CO 2, ethane (C 2 ) and prpane (C 3 ) -.e. methane s beng extracted frm the l t the gas and hence cntrbutes nly t the l shrnkng. The later stage f the gas mscble prcess s dmnated mstly by the ethane and prpane dffusn t the l, hereas the cntrbutn f all ther cmpnents t the

8 8 B.R.Bjeljc, A.H.Muggerdge and M. J. Blunt mvement f the l/ater bundary s l. These cnsderatns are clearly seen frm the dynamcs f the cncentratn f all cmpnents n the l, as shn n Fg. 8. The ater rupture s very rapd (.2days) snce the gas cntans n cmpnents heaver than C 5. It s nterestng t nte that althugh n-c 4 and -C 4 dffuse frm the gas t the l, the cncentratns f these t cmpnents n the l decrease (Fg. 8). Ths s due t the vlume ncrease f the l, hch s asscated th the l sellng. Mass balance shs that the sum f cncentratns f all cmpnents n the l at any tme s (Fg. 8). Effect f mscblty n aterblckng: a cmparsn f multple-cntact and frst-cntact mscble gas/l systems We have already shn h aterblckng can sgnfcantly sl dn gas/l mxng at the pre scale. Naturally, ths mxng ll als depend n the gas cmpstn resultng n a dfferent mpact f aterblckng n mxng f gas/l systems f dfferent mscblty. We nvestgated the nfluence f cmpstn n aterblckng fr: (a) several rch gas cmpstns (MCMg, MCMg2 frm Table 4) knn t be multple-cntact mscble th the reservr l (.e. ther multple-cntact mscblty pressures le abve the reservr pressure P 5.5MPa at T 383K) 28 and (b) the gases (FCMg, FCMg2 frm Table 4) hch ere valdated t be frst-cntact mscble th the same reservr l. 8,9 The frstcntact mscble gases ere btaned by further enrchng the rch gas cmpstns 28 frm (a) t the pnt here ther multple-cntact mscblty pressure s bel the reservr pressure but the frst cntact mscblty pressure s abve the reservr pressure. The ater-barrer rupture tmes needed t establsh drect cntact f the multple- and frst-cntact gas and l cmpstns frm Table 4 are f the rder f days, as presented n Fg. 9. The maxmum rupture tme (.3 days) s fr the frst-cntact mscble gas FCMg2 hch has the lest cntent f methane and hghest cntent f the heavest hydrcarbn cmpnents (C 6 and C 7 ). It s nterestng t nte that an ncrease n rupture tmes s evdent hen the gas s enrched th the heaver hydrcarbn cmpnents (gases FCMg, FCMg2), s that t s frst-cntact mscble th the l. On the ther hand, snce the multple-cntact mscble gas s rcher n methane (gases MCMg, MCMg2) the l sellng s mre rapd, due t the mre rapd methane dsslutn n and dffusn thrugh the ater as cmpared t the heaver hydrcarbn cmpnents frm the gas. The cnclusn f ths sectn s that makng a gas mre mscble leads t lnger rupture tmes. Ths s because the rcher gas tends t have a ler methane cncentratn and hgher cncentratns f ntermedate cmpnents. One bjectn t ths analyss s that ur mdel assumes frstcntact mscblty and cannt be appled t a multple-cntact mscble r mmscble fld. Hever, n ths example e smply ran the cde as descrbed n the mathematcal mdel sectn. Our apprach s applcable t a mult-cntact mscble cndensng drve, here mscblty s acheved thrugh Cmpnent Ol and gas cmpstns (ml/ml, %) Ol MCMg MCMg2 FCMg FCMg2 N CO C C C C n-c C n-c C C C C C C C C C C Table 4. Cmpstns f the l and the multple- and frst-cntact mscble gases used fr llustratn f the effect f mscblty n aterblckng. 28 dmensnless ater length, L(-) MCMg2 MCMg FCMg tme, t (day) FCMg2 mscblty ncrease Fg. 9. The knetcs f ater blckng durng tertary mscble gas njectn hen the l and the multple- 28 and frst-cntact mscble gases and frm Table 4 ere used. L.5 and L, n 5µm.

9 77697 Effect f Cmpstn n Waterblckng fr Multcmpnent Gasflds 9 cntact f njectn gas th l that has been repeatedly cntacted by gas. Ths s exactly the prcess e smulate. Hever, a full treatment f all multple-cntact mscblty drves and aterblckng s beynd the scpe f ths paper. scussn and Cnclusns The dynamcs f multcmpnent mass transfer thrugh ater barrers durng tertary mscble gas dsplacement has been mdeled at the pre scale. The latest hgh pressure-hgh temperature expermental data fr slubltes and dffusvtes f a number f cmpnents have been ncluded n the analyss. A range f physcal scenars arsng frm the effect f gas and l cmpstn n the mvement f the ater/l nterface has been presented fr synthetc hydrcarbn gas/l systems and ther practcal sgnfcance crtcally assessed. These scenars are: () rapd l sellng hch results n shrt tmes needed t cmpletely pe ut the ater barrer sheldng the l, () sl l sellng resultng n very lng ater barrer rupture tmes and () bth l sellng and l shrnkng. The cntrbutn f hydrcarbn cmpnents t the shrnkng/rupture f ater barrer s evaluated by assgnng t each f them eghtng functns frmed by the prduct f slublty and dffusvty. Water barrer rupture tmes f rder years are fund fr cases here l sellng s lmted by the dffusn f cmpnents C 6+. The rupture tmes ncrease th a decrease n the rat beteen the ntal l t the ntal ater barrer thcknesses and ncrease as the square ntal ater barrer thckness. A study n a gas/l system representatve f a Nrth Alaskan feld has shn the dynamcs f aterblckng t be strngly nfluenced by the presence f CO 2 n the gas and l phases. A hgh cncentratn f CO 2 n the njected gas leads t rapd l sellng due t the relatvely large slublty f CO 2 n ater n cmparsn th hydrcarbn cmpnents. A cmparatve study f tmes needed fr drect cntact beteen the l 28 and a range f multple- and frst-cntact mscble gasses has ndcated that the effect f aterblckng s mre detrmental t l recvery as the gas s mre mscble th the l. Ths rk ntrduces an mprtant addtnal cnsderatn fr the desgn f multcmpnent gas njectn prjects. At present, the njected gas cmpstn at reservr pressure s chsen s that t s mscble th the reservr l Ths s a necessary, but nt suffcent cndtn fr effcent dsplacement. Fr gas njectn after aterfldng (hch s usually the case), t s crtcally mprtant that the gas can drectly cntact the l at the pre scale. Water that surrund trapped l gangla can prevent ths cntact. Hever, the dsslutn f lght and ntermedate cmpnents n the njectn gas and ther dffusn thrugh ater t the l causes the l t sell and dsplace the ater. The ater barrer shrnks and eventually ruptures. Once the ater barrer ruptures, gas and l are n drect cntact and the dsplacement s effcent. Fr effcent recveres the rupture has t ccur ver a tme-scale small n cmparsn fr the tme fr gas t mve beteen njectn and prductn ells. Ths rk alls l and gas cmpstn t be assessed fr the pssble sgnfcance f aterblckng. Fr a Nrth Alaskan feld case e shed that fr mst plausble scenars ater blckng s unlkely t have a sgnfcant mpact n recvery. Hever, e llustrated by usng synthetc cases here ater blckng as lkely t be mprtant. Nmenclature A area f the l gangln [m 2 ] A area f the ater barrer [m 2 ] C.g cncentratn f cmpnent n the gas phase [ml/m 3 ] C g cncentratn f cmpnent n the gas phase, as defned by Eq. (6) [-] C. (t) cncentratn f cmpnent n the l phase [ml/m 3 ] C, cncentratn f cmpnent n the l phase, as defned by Eq. (7) [-], dffusn ceffcent f cmpnent n ater [m 2 /s] dffusn ceffcent f cmpnent n ater, as defned by Eq. (5) [-] F, mlar mass transfer rate f cmpnent n the l phase [ml/s] F, mlar mass transfer rate f cmpnent thrugh the ater barrer [ml/s] L (t) change n ater barrer/l gangln thckness ver tme due t l sellng/shrnkng L (t) length f ater barrer [m] L ( t ) dmensnless length f ater barrer [-] L, n ntal length f ater gangln [m] L (t) length f l gangln [m] ( t ) dmensnless length f l gangln [-] L L, n ntal length f l gangln [m] L rat beteen the ntal ater barrer length and the ntal l gangln length [-] M mlar mass f cmpnent [kg/ml] n c ttal number f hydrcarbn cmpnents slublty f cmpnent n ater [ml f cmpnent / ml f slutn] slublty f cmpnent n ater, as defned by Eq. (4) [-] t tme [s] t tme as defned by Eq. (8) [-] V, (t) vlume f cmpnent n the l phase [m 3 ] V (t) ttal vlume f l [m 3 ]

10 B.R.Bjeljc, A.H.Muggerdge and M. J. Blunt Greek letter densty f pure cmpnent [kg/m 3 ] exp. HTHP (ma et al.) Acknledgements The authrs sh t thank the EPRC grant GR/N 3258 fr fnancal supprt, and r. Chrs Brn frm BP fr helpful dscussns. We als sh t thank the grup frm Techncal Unversty f enmark (Prf. tendby and r. Mchelsen) fr the permssn t use ther prgram fr the mscblty predctns. (ml/ml, ppm)..... HTNPYas NTNPYas NTNP HTHPExtp. Appendx: Estmatn f slubltes and dffusvtes f cmpnents at hgh temperature - hgh pressure cndtns Under the reservr cndtns (P 26MPa, T 344K) studed hydrcarbn cmpnents are n a near-crtcal r crtcal state. Hever, ater s nt n the crtcal state (crtcal temperature f ater s 647K 24 ). Ths means that methds fr estmatn f slubltes r dffusvtes (see fr example Takahash s methd f crrespndng states at near-crtcal r crtcal regns 24 ) cannt be drectly appled. Instead e used an alternatve methd based n cmbnng the values fr slubltes and dffusvtes at standard temperature and pressure and the knn expermental values at the abve reservr cndtns. A cmplatn f experments n slubltes f a large number f alphatc hydrcarbns at standard temperature (298K) and pressure (.325MPa) can be fund n the lublty ata eres (). 5,25 Up t C 4 these data are n a gd agreement th the crrelatn prpsed by Yas, Bu, and Njahaan 26, as seen n Fg.. Fr the slubltes f alphatc hydrcarbns abve C 4 the authrs n suggest rders f magntude ler values, hch sgnfcantly devates frm the Yas, Bu, and Njahaan crrelatn, as seen n Fg.. In ur analyss e have used the Yas, Bu, and Njahaan crrelatn. The expermental values fr slubltes f ethane, prpane and n-butane under typcal reservr cndtns (P 26MPa, T 344K) exst. 4 The values fr slubltes f C 5 + alphatc hydrcarbns at these cndtns are extraplated frm standard cndtn data. We keep the rats beteen the slubltes f paraffn pars (.e. n-butane/pentane, n- butane/hexane and s n) under the nrmal P-T cndtns t be dentcal t the rats at P 26MPa and T 344K. In ur analyss the slubltes f s-hydrcarbns (smers) are taken equal t the slubltes f the crrespndng nrmal chan hydrcarbns. When a fractn cnsstng f a number f hydrcarbn cmpnents (usually referred t as a pseudcmpnent -.e. C -3 ) as cnsdered, then the slublty f the pseudcmpnent at standard P-T cndtns as calculated as the gemetrcal mean f the values fr slubltes f each cmpnent. The rats beteen the slubltes f pseudcmpnent pars (.e. C -3, C 4-9 and s n) under the nrmal P-T cndtns are kept dentcal t the rats beteen the slubltes at P 26MPa and T 344K. The rats beteen the slubltes beteen the paraffn. recmmended values (NTNP) carbn number Fg.. lubltes f alphatc hydrcarbns as a functn f hydrcarbn carbn number. NTNP at T 298K and P.MPa frm slublty data seres; NTNPYas at T 298K and P.MPa frm Yas, Bu and Njahaan 26 ; HTNPYas - at T344K and P.MPa frm Yas, Bu and Njahaan 26 ; HTHPExtp. extraplated at T 344K and P 26MPa. In ur rk fr C -4 slubltes e used the HTHP expermental values by hma, de Hemptnne and Mracchn 4 and frm these e extraplated the HTHP values fr C 5+ cmpnents n respect t HTNP values frm Yas, Bu and Njahaan 26. pars and pseudcmpnents ere als kept dentcal hen values fr slubltes at the ther reservr cndtns ere estmated (P 5.5MPa, T 383K). The same rules fr extraplatn ere appled fr estmatn f the values fr dffusvtes f all hydrcarbn cmpnents at P 26MPa and T 344K. The bnary dffusn ceffcents f the hydrcarbn cmpnents and CO 2 at the standard temperature and pressure ere btaned frm the Wlke-Chang crrelatn 27 fr nfntely dluted lquds (Fg. ). Ths s a very reasnable assumptn snce the slubltes f hydrcarbn cmpnents are extremely small. ensnless dffusvty, (-) dm carbn number Fg.. mensnless bnary hydrcarbn dffusvtes as a functn f carbn number btaned frm the Wlke-Chang crrelatn 27 fr nfntely dluted lquds.

11 77697 Effect f Cmpstn n Waterblckng fr Multcmpnent Gasflds The expermentally btaned reference value fr dffusvty at P 26MPa and T 344K as that f methane (CH 4 ) 5-9 m 2 /s (extraplated frm achs 6 ). When nndmensnalsed, ths value f methane s set t (Eq. 5). Fg. shs the dmensnless dffusvtes f alphatc hydrcarbns versus carbn number at standard temperature and pressure, as btaned by the Wlke-Chang crrelatn. The rats beteen the dffusvtes beteen the paraffn pars and pseudcmpnents ere als kept dentcal hen values fr dffusvtes at the ther reservr cndtns ere estmated (P 5.5MPa, T 383K). References., H.. and Pnczesk W. V.: ffusn-cntrlled sellng f reservr l by ndrect cntact th njectn gas, Chemcal Engneerng cence (993) 48, Mueller, T. and Lake, L. W.: A theretcal study f aterblckng n mscble fldng, Paper PE/OE 226, prceedngs f the 7 th PE/OE ympsum n Enhanced l Recvery, Aprl (99), Tulsa, OK. 3.Grgan, A. T. and Pnczesk W. V.: The rle f mlecular dffusn prcesses n tertary CO 2 fldng, Jurnal f Petrleum Technlgy (987) 39, Campbell, B. T. and Orr F. M.: Fl vsualsatn fr CO 2 / Crude-Ol dsplacements, PE Jurnal (985) 25, hearn, R. B. and Wakeman, R. J: Theretcal mass transfer mdels fr assessng tertary recvery by mscble flud dsplacement, Prc., Eurpean ympsum n Enhanced Ol Recvery, Ednburgh, (July 978) Wyle, P. and Mhanty, K. K.: Effect f ater saturatn n l recvery by near-mscble gas njectn, PE Reservr Engneerng (997) 2, Tffn,. L., ebastan, H. M. and Bergman,. F.: splacement mechansm and ater sheldng phenmena fr a rch-gas/crude-l system, PE Reservr Engneerng (99) 6, Ln, E. C. and Huang, T..: The effect f rck ettablty n ater blckng durng mscble dsplacement, PE Reservr Engneerng (99) 5, Hlm, L. W.: Mblzatn f aterfld resdual l by mscble fluds, PE/OE 326 prceedngs f the 59th Annual Techncal Cnference and Exhbtn, Hustn, Texas, (984) Grgan, A. T., Pnczesk W. V., Ruskauff, G. J. and Orr, F. M.: ffusn f CO 2 at reservr cndtns: mdels and measurements, PE Reservr Engneerng (February 988) 3, McGure, P. L. and talkup, F. I.: Perfrmance analyss and ptmsatn f the Prudhe Bay mscble gas prject, PE/OE prceedngs f the PE Internatnal Meetng n Petrleum Engneerng, Bejng, Chna, (992) hma, A., de Hemptnne, J. -C. and Jse, J.: lublty f Hydrcarbns and CO 2 mxtures n ater under hgh pressure, Industral and Engneerng Chemstry Research (999) 38, ngh, B., Rzv.. H. and Harrtt P.: Measurement f dffusvty and slublty f carbn dxde n gelatnsed starch at elevated pressures, Industral and Engneerng Chemstry Research (996) 35, hma, A., de Hemptnne, J. -C. and Mracchn G.: lublty f lght hydrcarbns and ther mxtures n pure ater under hgh pressure, Flud Phase Equlbra (998) 45, lublty ata eres: Hydrcarbns th ater and seaater. Part 2, Hydrcarbns C 8 t C 36, 38, Edted by ha,. G. and Haulat-Prsn, M. -C. (989). 6.achs, W.: The dffusnal transprt f methane n lqud ater: methd and result f expermental nvestgatn at elevated pressure, Jurnal f Petrleum cence and Engneerng (998) 2, Jaubert J. N., Neau, E., Penelux, A., Fressgne, C. and Fuchs, A.: Phase equlbrum calculatns n an Indnesan crude l usng detaled NMR analyss r a predctve methd t assess the prpertes f the heavy fractns, Industral and Engneerng Chemstry Research (995) 34, Mchelsen, M. L.: The sthermal flash prblem. Part I. tablty, Flud Phase Equlbra (982a) 9, Mchelsen, M. L: The sthermal flash prblem. Part II: Phasesplt calculatn, Flud Phase Equlbra (982b) 9, talkup, F. I. Mscble splacement. Henry L. herty eres Mngraph, cety f Petrleum Engneers f AIME: Ne Yrk. Vl. 8 (983). 2.hyeh-Yung, J. J., tadler, P.: Effect f njectant cmpstn and pressure n dsplacement f l by enrched hydrcarbn gases, PE Reservr Engneerng (995), Jhns, R. T., ah, P. and ubramanan,. K.: Effect f gas enrchment abve the MME n l recvery n enrched-gas flds, PE Jurnal (2) 5, Lee,. T., Mulds, T. P., Narayanan, R., Yungren, G., Ln, C.Y. and Wang, Y.: Optmzng mscble njectant (MI) cmpstn fr gas njectn prjects, PE paper 766, prceedngs f the PE Annual Techncal Cnference and Exhbtn, Ne Orleans, Lusana, eptember 3-Octber 3, Red, R. C., Prausntz, J. M. and Plng, B. E. The prpertes f gases and lquds. Ne Yrk: McGra-Hll (987). 25.lublty ata eres: Hydrcarbns th ater and seaater. Part, Hydrcarbns C 5 t C 7, 38, Edted by ha,. G. and Haulat-Prsn, M. -C. (988). 26.Yas, C. L., Bu, L. and Njahaan,.: Water slublty data fr 5 hydrcarbns, Chemcal Engneerng (993), Wlke, C. R. and Chang, P.: Crrelatn f dffusn ceffcents n dlute slutns, A. I. Ch. E. Jurnal (955), Fussell,.., heltn, J. L. and Grffth, J..: Effect f rch gas cmpstn n multple-cntact mscble dsplacement a cell-t-cell flash mdel study, PE Jurnal (ecember 976) 3-36.