SPE Inflow Performance Relationships for Gas Condensates Fawzi M. Guehria, SPE, Schlumberger Integrated Project Management.

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1 PE Inflw Pefmance elainhi f Ga Cndenae Fawzi M. Guehia, PE, chlumbee Ineaed Pjec Manaemen Cyih 2, ciey f Peleum Eninee Inc. Thi ae wa eaed f eenain a he 2 PE Annual Technical Cnfeence and Exhibiin held in Dalla, Texa, 1 4 Ocbe 2. Thi ae wa eleced f eenain by an PE Pam Cmmiee fllwin eiew f infmain cnained in an abac ubmied by he auh(). Cnen f he ae, a eened, hae n been eiewed by he ciey f Peleum Eninee and ae ubjec cecin by he auh(). The maeial, a eened, de n neceaily eflec any iin f he ciey f Peleum Eninee, i ffice, membe. Pae eened a PE meein ae ubjec ublicain eiew by Ediial Cmmiee f he ciey f Peleum Eninee. Elecnic educin, diibuin, ae f any a f hi ae f cmmecial ue wihu he wien cnen f he ciey f Peleum Eninee i hibied. Pemiin educe in in i eiced an abac f n me han 3 wd; illuain may n be cied. The abac mu cnain cnicuu acnwledmen f whee and by whm he ae wa eened. Wie Libaian, PE, P.O. x , ichadn, TX , U..A., fax Abac In hi w, we decibe a fa cheme bain imedeenden IP cue f a delein a-cndenae well wihu ein he ue f imulain. The mdel eflec he flwin chaaceiic inide he eei. In addiin, i i elf-checin and cnien wih he eall analyi f a-cndenae eei behai. We al ineiae he adeuacy f eei maeial balance f a-cndenae eneae he IP cue f a delein a-cndenae well. Tanien effec ae n cnideed in hi w. Inflw Pefmance elainhi (IP ) ae a ciical elemen in he dein f new well and in he mniin and imizain f exiin ducin well. In addiin Vel-ye elainhi, aiu IP mdel f diffeen well emey and diffeen flw eime hae been eened. Geneally, hee mdel ae adanae f analyical luin f inle-hae il and f inle-hae a, eneae a flw ae file wih flwin eue a a aamee. F a-cndenae well, andad dy-a delieabiliy euain baed n ichnal ein hae alway been ued a IP mdel. Unfunaely, due eee delieabiliy educin caued by cndenae blcae, hi aach i inadeuae and uually lead eneu eul. In ealiy, he eue d ha ccu in a-cndenae eei eain belw dew-in, i affeced by u hee zne, i.e. 1) inne zne whee bh hae, a and fee cndenae, ae flwin, 2) middle zne whee w hae cexi bu nly a i mbile and 3) ue zne whee nly he inle hae a i flwin. We eified he mehd wih ynheic examle and d aeemen wa achieed in all cae. Inducin Well cnucin dein and well efmance diani and imizain heaily ely n well delieabiliy mdelin, which cmbine ubula hydaulic calculain wih a eei delieabiliy mdel. The lae i eeened by a cue, which elae flw ae flwin bmhle eue f a ien fixed eei eue. Gilbe 1 induced he cnce f Inflw Pefmance elainhi (IP) f a well. Lae, Vel 2 eablihed an emiical elainhi beween ducin ae and flwin bmhle eue in luin a die eei. Hi w i baed n Welle 3 aximain, which aume ha he an-il de-auain ae i he ame a eey in in he eei a any ien ime. Vel elain aume he fllwin fm:, max wf wf whee i he il ducin ae cendin a ien flwin bmhle eue, wf. i a fixed eei eue and, max i he maximum ducin ae cendin a ze flwin bmhle eue. F well ducin belw bubble in, Feich ued he fllwin enealized euain: C i ( 2 2 ) n wf (2) whee, i i he iniial eei eue, and C and n ae cnan deemined in ichnal ein. Ohe elain baed n eady-ae and eud-eady-ae luin f inle hae hae al been ued cmue he duciiy index (PI) f well f aiu emey, i.e., eical hle, hiznal dain, muli-banched dain, ec. 2 (1)

2 2 FAWZI M. GUEHIA PE Ga Cndenae Ga-cndenae well behai i uniue in a ene ha i i chaaceized by a aid l f well duciiy. Geneally, when he flwin bmhle eue d belw he dew in, a ein f hih cndenae auain build u nea he wellbe, cauin lwe a delieabiliy mainly due a educin in a emeabiliy. Numeu auh ineiaed he henmenn, which Mua 4 efeed a a cndenaeblcae. He deined a mehd calculae he adiu f hi blcae, which w wih ime. Thi mehd euie nwlede f he a ae, eei and PVT eie. Lae, Feich 5 eeened hi cndenae blcae by aciain a ime-deenden in he andad a ae euain. The well delieabiliy l f a-cndenae well wa lae cnfimed huh numeical imulain by Kniazeff and Naille 6 and Eile e al 7,8. imilaly, Gnduin e al. 9 udied he imance f cndenae blcae by ue f adial blac-il numeical imulain. O Dell and Mille 1 induced a eudeue funcin in he a ae euain decibe he effec f cndenae blcae. Thei w clealy hw ha min cndenae blcae can inificanly educe well delieabiliy. Fuell 11 wa fi ineiae he well duciiy l ia an Euain-f-ae (EO) baed cmiinal imula. Jne, ahaan and V 12 imaily fcued n he effec f cndenae blcae n he eue anien ene beed duin dawdwn and buildu eid. Thei analyical w mae ue f eul fm an EO baed hee cmnen cmiinal adial imula. Cncenin he bunday-dminaed flw eid, hey cnfimed ha he eudeue ued by Fuell i alid a all ime. Thi eei ineal eudeue i ealuaed nly if he eue and auain file aln he eei ae eablihed a ii ia a imulain un. Well Delieabiliy Euain Euain f w-hae flw wee fi led by Mua and Mee 13 f a few ecial cae. Eine and Mua 14 udied he effec f mulihae flw n duciiy index f a luin-a die well and examined he eady-ae adial flw f il and a in a u medium. Unde cndiin f eady-ae adial flw, he il hae i ien by (3) h ln( e / w) e wf ( ) d Leine and Pa 15 exended he undeandin f luin-a die eei and well behai. They hwed ha, if i i aumed ha he decline ae f c-an il in lace i cnan eeywhee, hen he euain enin flw f il in adial cdinae can be diecly ineaed ie e ( ) d h w 2 w 2Ln A in he cae f eady-ae, a elain beween auain and eue i needed calculae he ineal n he lefhand ide f E. (4). In addiin, he eue e and he cendin auain wuld hae be nwn. y analy luin-a die eei, an euain may be deied f delein a-cndenae eei. I i exeed a whee C C wf h e 141.2ln w 3 4 d In E. (6), i he damae in. Ne ha he eue l due cndenae blcae i imlicily accuned f in he mehd by which he eudeue ineal i ealuaed. T calculae he eud-eady-ae ae euain (5),. Fean and Whin 16 ed a mehd mdel he delieabiliy f a-cndenae well. In addiin he eue/lume/emeaue (PVT) blac-il cmiinal eie and he a/il elaie emeabiliy, he ducin a-il ai (GO) i euied f each eei eue. Fean and Whin idenified he exience, a any ime f delein, f ne, w hee flw ein, deendin n he alue f he flwin bmhle eue and he eei eue. If he flwin bmhle eue i abe he iniial in-iu fluid dew in, he whle eei i inle hae and E. (5) becme a andad a ae euain wih, and ( wi), whee wi i he ieducible wae auain. If he flwin bmhle eue i belw dew in, hen he eei may cnain hee flw ein. ein 1 i defined a a zne cle he inne nea-wellbe whee bh a and il flw imulaneuly. Ouwad in he eei, ein 2 cnain a cndenae buildu whee nly a i flwin. Finally, cniuu ein 2, ein 3, which exend he limi f he eei, exi nly if he eei eue i hihe han he dew in eue. The ize f each ein chane wih ime a he eei delee. Fean and Whin ueed ha, ien he flwin e (4) (5) (6)

3 PE INFLOW PEFOMANCE ELATIONHIP FO GA CONDENATE 3 bmhle eue, ducin GO and eei eue, he ae ien by E. (5) i cmued by liin u he eudeue ineal in hee ineal. The limi f he ineal ae he eue a he bundaie f each * * ein, i.e., wf,, dew, and. i he eue a he ue bunday f ein 1. The eudeue ineal definin each ein ae ealuaed by ue f he PVT cue and he elaie emeabiliy mdified Eine-Mua aach. One f he maj findin in hi w i ha he imay caue f educed well delieabiliy wihin ein 1 i a a funcin f ( / )( ) which, i cmued ia he definiin f he ducin GO, a exeed by E. (C1). I wa al fund ha ciical il auain ha n effec n acndenae well delieabiliy. The auh dicued he hae behai chaaceiic in each ein and ned ha ein 1 behae lie a cnan cmiin exanin (CCE) cell, wheea ein 2 ac lie a cnan lume delein (CVD) cell. aed n hi, hey aued ha he duced welleam ha he ame cmiin a he inle-hae a enein ein 1 and hu he flwin GO mu be cnan huhu ein 1. The eue a * he ue bunday f ein 1,, i defined a he eue a which he ducin GO,, i he inee f he luin cndenae-a ai (CG),, which i ided in he PVT able. Unfunaely, hi mdel euie ha hee alue be eablihed a-ii by numeu imulain un and abulaed f each eei eue. New Inflw Pefmance elainhi Mdel Dicuin Pacice in field deelmen and ducin manaemen uually inle field dein aeie and cninual mniin f uface faciliy new, eei and well. Well manaemen include eula well ein and he ue f a wide aiey f diani and edicin l. IP mdelin cmbined wih ubin inae analyi ae a ey ueful elemen in a aey f well caial and eain exendiue. The cnucin f a new well huld include a cmlein deined f imum iniial fluid ae and huld al accmmdae all fuue flwin cndiin chane. Well mdelin i al a andad l f he mniin f well duciiy and f allwin he field eninee che a e emedial jb, e.., imulain, w-e, ec., in de ehabiliae he imum well efmance. On a lae cale, i i al imeaie be able imize a well efmance wihin he cnain f he uface faciliy new. F ha, a edicin n ae and ducin GO i ciical f cninuu lbal field ducin imizain. Thi i achieed ia a lanned wellhead cnl am f each well cnneced huh he manifld. We ecall ha duin ducin, a-cndenae well main flwin chaaceiic ae a fllw: A he a f ducin f a well fm a a-cndenae eei iniially abe auain eue, he duced cndenae yield (CG) i a i maximum, i.e., he alue f he luin CG a dew in eue. imilaly, he beed ducin GO i exacly he inee f he ducin CG. Thi i mainly due he fac ha he eei i eain abe he dew in and ha he cndenae blcae zne i n lae enuh educe he ecey f liuid which, emain mainly in he cndenae ich a-hae. Hwee, duin delein, a he eue d, a cndenae ein build u in he eei aea whee eue i belw dew in, cauin a educin in well delieabiliy. Thi anlae in a cninual deceae in he duced cndenae yield (duced CG) and a cninual inceae in he ducin GO. Nmally, a elaiely lae in beed in anien analyi eflec hi duciiy imaimen. Ne ha he hih in may al include he effec, e.., nea-wellbe mechanical damae, heical flw due ible aial eneain, he nn-dacy effec due ubulence. I i f aamun imance ely idenify he diffeen nea-wellbe effec ha ae cauin he duciiy index (PI) educin, befe an exenie ineenin n he well i ecmmended and execued. Geneain e ime-deenden IP cue f a acndenae well i iman in he idenificain and uanificain f well duciiy le in addiin deeminin he ih uface cnl aamee achiee imum ducin a he manifld-eaa leel. Time-deenden IP cue f a-cndenae well may be eneaed by ue f a a delieabiliy mdel ided he ducin GO i nwn f each eei eue. Deendin n he ue f he analyi, IP cue f acndenae well may be exeed in em f a flw ae. Hwee, if he eei fluid i ich, and he CG i elaiely hih, hen edicin cndenae flw ae mih be a me uiable aach. F hi cae, he anal f E. (5), i.e., he cndenae flw ae i ien by C d wf The al flw ae may be exeed a ( α) α 1 (8) α f cndenae flw ae, α whee 1 f a flw ae and α. 5 f half he al flw ae. Thi i aiculaly cnenien f enealized cmue cdin ue. We ecall ha if a well duce wih a flwin bmhle (7)

4 4 FAWZI M. GUEHIA PE eue lwe han he dew in, he ducin GO i a mnnically inceain funcin f eei eue, i.e., a ne--ne elainhi beween ducin GO and eue exi a n a a w-hae flw ein deel wihin he eei. Ealuain E. (5) E. (7) ia a well delieabiliy mdel, e.., Fean and Whin mdel, euie nwlede f ducin GO f each eei eue. Maeial alance T cnuc a able f ducin GO eu eei eue, we ineiaed he in f uin a eei maeial balance (M) echniue f a-cndenae eei, a laid u in Aendix D. We ecall he maj aumin inheen a maeial balance mdel f acndenae eei: 1. If a well i ducin fm an undeaued eei, wih a flwin bmhle eue lwe han he in-iu fluid dew in, he maeial balance echniue i n alicable, i.e., he eei eue may emain abe dew in, wheea a w-hae zne a buildin u, cauin he ducin GO inceae. 2. Maeial balance aume ha he eei eue and he hae auain ae unifm huhu he eei a all ime. Thi imlie ha nly ne ein exi, e.., a w-hae ein whee a hae flw i dicaed by a ien elaie emeabiliy e inu; e.., f il auain belw he ciical il auain, c, i i aumed ha nly leane a i flwin he wellbe, eadle f eue leel. Ineaed Mehd In hi w, we ineiae he idea f deelin a fa cheme bain ime-deenden IP cue f a delein a-cndenae well wihu ein he ue f imulain. The mdel eflec he flwin chaaceiic inide he eei. In addiin, i i elf-checin and cnien wih he eall analyi f a-cndenae eei behai. The famew f u aach i he baic w-cmnen flw euain in u medium, a ien by E. (A1) and E. (A2). Thee euain eeciely elae he ae f chane f ma f a and f il ed in a uni lume f he eei a a chen lcain, he an em a he ame lcain. We will hw ha u mdel ineae bh elemen f cniency, in he ame ii a a imula numeical cheme de ieaiely. I i beed in imulain ha afe he well abilize, in-iu flwin GO adien ae neliible wihin he ein whee bh hae ae flwin. Aendix A ie an analyical/hyical exlanain f hi behai. Fuheme, i i hwn in Aendix ha he in-iu flwin GO wihin he ein whee bh hae ae flwin, can be exeed a (9) E. (9) eeen he ai f he ae f chane f ma f a he ae f chane f ma f il. I can fuhe be exanded a 1 1 d d 1 d 1 d d d d d 1 1 d d 1 d 1 d d d d d E. (9 ) hw ha he in-iu flwin GO can be eimaed a a new eue leel ( 1), in ein 1, ided he auain file i nwn a he ame eue leel. The PVT eie,,,,, and ae eadily aailable wihin he delein eue ane a ided by he PVT cue. All deiaie may be aximaed by chd le. (9 ) Thi ue an ieaie cheme whee, ien a fixed eei eue,, and an aumed ducin GO alue, he flw ae a ien by E. (5) E. (7) can be cmued f a ecified flwin bmhle eue. Wih ein 1 bein defined ia he calculain f he eudeue ineal a ueed by Fean and Whin, he eulin auain file and he PVT eie ealuaed a a eue alue eailin wihin ein 1, ae hen ued cmue he GO alue a exeed by E. (9 ). If hi alue de n cmae wih he iinally aumed alue ued in he ealuain f he eudeue ineal, hen he ce i eeaed wih a new ducin GO alue unil bh f he alue aee wihin a ceain leance. Nmally, if he a ae a he eiu ieain i lae han he newly cmued ae, hen we deceae he ducin GO alue, ele, we inceae i. F he nex eei eue, he ducin GO alue euied a he ieain i he alue fund a he eiu eue, aumened by a ceain incemenal alue.

5 PE INFLOW PEFOMANCE ELATIONHIP FO GA CONDENATE 5 Uually, IP cue ae ued when he well dainae lume i eablihed ia an ace acin lannin. Tanien effec ae n cnideed in hi w. We will aume ha f an iniial eei eue abe he dew in, he IP cue i eneaed wih a ducin GO eual he inee f he luin CG defined a he dew in. Thi cheme ffe cniency a i ineae he an em and he accumulain em aeain eeciely in bh ide f he euain enin fluid flw wihin ein 1, ha ma balance i eeed. eul We eed he idea f eneain ime-deenden IP cue ia he mehd decibed abe and cmae he eul wih he eneaed by a ea mdel (mdified blac-il imula). Fluid eie ae aumed be funcin f eue nly, ha flw in he eei may be adeuaely decibed by a β mdel. Ou β mdel buil f ha ue i baed n he numeical luin f he flw euain (A1) and (A2) ubjec aiae iniial and bunday cndiin, wih he Lalacian ea defined in cylindical cdinae. The imula cnide ihemal flw a cylindical well which, fully aially eneae a cylindical eei. Gaiy i accuned f, wheea caillay effec ae aumed be neliible. The eei i bunded abe and belw. A he exenal eei adiu, i.e., a e, he bunday cndiin imed, culd eihe be a n-flw bunday (ealed by imemeable c) a cnan eue bunday (influx fm uide he eei). Only hydcabn fluid ae een in he eei any wae een i aumed be incmeible and immbile and n accun i aen f i eence. The emeabiliy field culd be aniic, i.e., z. eei cmacin i al accuned f a an in wih emeabiliy and iy bein funcin f eue. A i andad in eei imulain, he in zne i mdeled a a zne f aleed emeabiliy (i.e., ) cncenic wih he wellbe in accdance wih Hawin (12) fmula: 1 Ln (7) w Unde he abe aumin, flw he wellbe can be eihe heical uely adial. Fluid PVT eie and elaie emeabiliy ae inu a dicee abulaed daa; PVT eie abe he auain eue ae funcin f bh eue and auain eue. Peie a a aicula alue f eue auain ae bained by linea inelain beween abulaed daa. F he ue f alidain f numeical eul wih analyical hey, all cae eed aume ha he eei i hmeneu, iic and ha he flw i uely adial. In addiin, he eei i ealed a he ue bunday. We cnideed numeu imulain un wih diffeen fixed flwin bmhle eue. In all un, we aumed a eei emeabiliy f 5 md, iy f 8 % and a inle laye wih hicne f 15.5 f. The wellbe adiu wa e a.33 f, while he exenal eei adiu wa 1 f. eei eie ae ummaized in Table 1. The elaie emeabiliy e i ien in Table 2. Tw ye f fluid wee cnideed: a ich and a lean a-cndenae fluid wih a maximum CG f 148 b/mmcf and 55 T/MMcf, eeciely. The ey eei fluid eie ae hwn in Table 3. Fi. 1 deic he numeical imula eul hwin eei eue decline duin delein f he eei cnainin he ich a A, wheea Fi. 2 hw he CG file f he ame cndiin. Alhuh n hwn in Fi. 2, he CG mainain an aximaiely cnan alue eual he iniial luin CG, duin he ealy a f ducin. The ducin GO alue wee abulaed f each imulain un, hen ued in he delieabiliy euain, i.e., E. (7). We al ineiaed he cae whee he duced GO alue ae cmued a funcin f eue ia eei M calculain f a-cndenae eei. The eei M balance aume he exience f ne ein a m, a any ime f delein. efe he ciical il auain i eached, he whle eei cnain a inle ein, ein 2, whee bh hae cexi, bu nly a i flwin. Abe he ciical il auain, he whle eei ac a ein 1, i.e., bh hae ae flwin huhu he eei. The ducin GO file fm he fine id imula and he eei M i hwn in Fi. 3. imulain wa efmed wih a cnan flwin bmhle eue eual 2 ia and he un wa cnduced unil a lw ae limi wa eached a a eei eue lihly hihe han 2 ia. Hwee, he eei M edic eul wihin he whle PVT eie eue ane. Fi. 3 hw ha bh file cincide efecly a ealy ime f delein. I i wh nin ha he eei M eul ae indeenden f eue adien wihin he eei and hu, he ducin GO i n affeced by he eue dawdwn imed n he well, bu ahe by eei eue. Fi 4 and 5 deic he il and a ecey, eeciely, a cmued by fine id eei imulain and eei M. The il ecey file hw an inceain diceency beween bh mehd. Thi i mainly due he fac ha he fine id imula accun f all ein wihin he eei, wheea he eei M aume a inle cnibuin ein a a ime. Fi. 6 hw he IP cue eneaed f he cae f he ich a-cndenae fluid A. Gd aeemen wa achieed beween he edicin alue f u mdel and he baed n

6 6 FAWZI M. GUEHIA PE fine id imulain, a all ime. Alhuh, n hwn, he ducin GO file fm imulain un ae cnien wih he ediced in he ineaed mdel. We hen ued he ducin GO alue eneaed by he eei M, ealuae E. (7) f each eei eue and flwin bmhle eue. Ne ha a ein abe dew in, he eei M i n alicable. The mach i d a hihe eue, bu a deadin a lw eue. Fi. 7 hw a e f IP cue eneaed f lean a, by ue f eei M eul, fine id imulain and he ineaed mehd. All eul ae cnien due he fac ha cndenae blcae i n a ealen and ha all mehd educe he fine id imulain eul. Field Alicain Nmally, in a uine well manaemen ce, wellhead daa i clleced n a eula bai. Thee daa include che ize, wellhead eue, flw ae and ducin GO meaued a a ee mbile e eaa. Al, well ae hu in n a eula bai f eue meauemen duin a buildu hae. The eei eie exaced fm he eue anien analyi ae eei eue, flw caaciy, h, and in,. Hwee, in ealiy f acual c cnl meaue, field daa cllecin am may n be alway adeuae f ef well manaemen. meime, daa i ecded a diffeen ime wih diffeen flwin cndiin. In he cae, nly wellhead eue and a be, flwin adien wihin he ubula ae ecded. In he inance, me hih PI well ae aely hu in f eue buildu analyi. In hi cae, in and eei eue may n be aailable ae he well delieabiliy. The analy i hen cnfned wih idin a well diani wih limied daa. IP cue may be f ea hel educe unceainie n he miin aamee. A a-cndenae well in We Texa ducin in a 2 ace acin wa eed n a eula bai. The iniial cndenae yield wa 9 T/MMcf wih a maximum CVD liuid du f 7 %. A eei M mdel a decibed in Aendix D wa ued eimae eei eue file, nwin he ecey fac and ducin GO. IP cue and hydaulic lif cue wee eneaed and ahed n he ame l. The e in aailable wee educed by ayin he mechanical in. Fi. 8 deic he mach bained f he w e in aailalble and he in deemined i in he ane f 6. ineiaed he ue f he eei M eul in he cmuain f he well delieabiliy euain in he ii f he Fean and Whin a-cndenae well behai deciin. The fllwin ummaize u eul: F ich a-cndenae, we decibe a cnien ieaie ineaed mehd eneae IP cue. F lean a cndenae, GO alue fm he eei M mdel ae adeuae achiee d eul. The iniial luin CG can be ued a eue cle he iniial dew-in. Pducin GO deend n eei eue and n n eue dawdwn imed n he well. Field e huld al be ued calibae he well delieabiliy by unnin eniiiie n he aiu aamee cnained in E. (5) E. (7). Aendix A The flw f il and a in em f blac-il PVT, in a heeeneu u medium, nelecin aiy and caillay fce, ae ien by he fllwin euain: Oil Ga C 1. C 1. whee dene he adien, x y z [] φ (A1) [] φ (A2) and he ih-hand ide f E. (A1)-A(2) eeen he aial deiaie f he uaniie wih eec ime. The flwin a-il ai i defined a: Cncluin In hi ae, we eened a nel aach eneae IP cue f delein a-cndenae eei. We al

7 PE INFLOW PEFOMANCE ELATIONHIP FO GA CONDENATE 7 [] [] (A3) Uin E. (A3) in he a euain (A2) and exandin yield: [] [] C C φ 1 1. (A4) F he il hae, Dacy law i ien by [] ), ( x A (A5) Cmbinin E. (A5) wih E. (A4) and eaanin ie ), ( ), ( x x A C φ φ (A6) The ih-hand ide f E. (A6), eeciely accun f he ae f chane f ma f a and il ed in a uni lume f he eei a me lcain (x,y,z). The denmina ae eeciely he ma flw ae f a and il huh he lcain (x,y,z). A ln ime (cle a in, i.e., a ducin well), he ime deiaie em becme malle a me ma i bein anfeed fm fuhe u in he eei he well, wheea he denmina em emain elaiely lae. Thi imlie ha he ih-hand ide f E. (A6) e ze a lae ime ( eady-ae ), ha a ln ime (A7) E. (A7) hw ha duin abilized flw, he flwin a-il ai i he ame huhu he zne whee bh il and a ae flwin. Aendix Fuheme, if we ue E. (A1) in E. (A4), wih, we bain φ φ (1) Aumin cnan iy and uin he chain ule f deiaie, d d d dx d dx E. (1) may be ewien a (2) Aendix C E. (A3) can be ewien a ( ) 1 (C1) I i eadily hwn ha E. (C1) can be exeed in em f he il elaie lume duin a cnan cmiin exann (CCE), i.e., CCE V 1 1 ) ( (C2) Cmbinin E. (6) and (7) yield ( ) ( ) CCE V (C3) Aendix D Tan-ye mdel and idded mdel ue imila cninuiy

8 8 FAWZI M. GUEHIA PE (maeial balance) incile. F a w-hae (a/il) idded mdel miin aiy and caillay fce, he il hae and a hae aial diffeenial diffeenial euain ha cmbine Dacy-law flw and cninuiy ae E. (D1) and E. (D2). Thee euain ae in Dacy uni. Oil. (D1) Ga. (D2) φ φ The lef-hand ide f E. (D1) and E. (D2) eeen, eeciely, he an em f il (fee il il in a hae) and a (fee a a in luin) in he eei (beween blc in a idded mdel) and wuld be ze f a an-ye (ne-blc) mdel. The ih-hand ide em f he ame euain eeen, eeciely, he il and a accumulain and ducin. The cendin euain f a an-ye mdel ae bained by nin ha he lef-hand ide f E. (D1) and E. (D2) ae ze f he an-ye mdel. Delein he lef-hand ide f each euain, mulilyin by he bul lume, and chanin ilfield uni yield α V and β V whee α and β, defined by E. (D5) and E. (D6) and eeen he whle eei (D3) (D4) α (D5) β Ineain E. (D3) and E. (D4) and eaanin yield [ i( ) ] N N and i 1 (D6) G N 1 G N i The ducin GO,, exeed in cf/t, i defined a 1 / / / / (D7) (D8) E. (D6) and E. (D8) eeen w euain wih w unnwn, and, f a ien eei eue. F maeial balance calculain ue, we aume ha he elaie emeabiliy i a funcin f auain e he whle eei. Thi ue an ieaie ce, which huld yield a alue f ducin GO f each delein eei eue. Acnwledemen The auh wuld lie han chlumbee Oilfield eice f emiin ublih hi w. Nmenclaue A Aea, f 2 d Dy a lumeic fac, b/cf Oil fmain lume fac b/b i Iniial il fmain lume fac, b/b C Ga ae cnan G Oiinal a-in-lace, f 3 G Cumulaie a duced, f 3 J Pduciiy index Ablue c emeabiliy, md adial emeabiliy, md Pemeabiliy f he in zne, md Oil elaie emeabiliy Ga elaie emeabiliy N Cumulaie il ducin, b N Oiinal il in-lace, b dew Dew-in eue, ia i Iniial eei eue, ia wf Flwin bmhle eue, ia eei eue, ia e Peue a exenal bunday, ia Tal flw ae, b/day

9 PE INFLOW PEFOMANCE ELATIONHIP FO GA CONDENATE 9 w c wi Oil flw ae, b/day Ga flw ae, Mcf/Day Wellbe adiu, f in nea-wellbe adiu, f Exenal eei adiu, f Pducin GO, cf/t luin GO, cf/t luin cndenae-a ai, MMcf/T il auain, facin a auain, facin ciical il auain, facin cnnae wae auain V Pe lume, f 3 il iciy, c a iciy, c V CCE elaie il lume in cnan cmiin exeimen V CVD elaie il lume in cnan lume delein exeimen CVD Cnan lume delein CCE Cnan cmiin exanin M Maeial balance Gee ymbl Lalacian Paial deiaie φ iy iciy ubci and ueci c ciical dew dew in il a e adial elaie in luin lailiy w wellbe wf flwin bmhle I Meic Cnein Fac Ace E 1 ha API 141.5/(131.5 API) E /cm² bbl E 1 m 3 c 1. E 3 Pa. f 3.48 E 1 m F ( F-32)/1.8 E C md E 4 m 2 i E KPa efeence 1. Gilbe, W.E, : Flwin and Ga-Lif Well Pefmance, Dill. and Pd. Pac., API (1954) Vel, J. V, : Inflw Pefmance elainhi f luin-ga Die Well, JPT,. (Januay 1968) Welle, W. T, : eei Pefmance Duin Tw- Phae Flw, JPT (Feb, 1966) Mua, M. : Phyical Pincile f Oil Pducin, Mc Gaw-Hill Cmany Inc, New Y Ciy (1949). 5. Feich, M. J, : The Ichnal Tein f Oil Well, ae PE 4529 eened a he 1973 PE Annual Fall meein, La Vea, Neada, 3 eembe-3 Ocbe. 6. Kniazeff, V. J, and Naille,. A, : Tw-hae Flw f Vlaile Hydcabn, PEJ (Mach 1965) 37; Tan., AIME, Eile, C. K. umme, E. F. and P, N. L, : Ineain f Paial Diffeenial Euain f Tanien adial Flw f Ga-Cndenae Fluid in Pu ucue, PEJ (June 1965) Eile, C. K. and umme, E. F, : Ineain f Paial Diffeenial Euain f Mulicmnen, Tw-hae Tanien adial Flw, PEJ (June 1967) Gnduin, M., Iffly,., and Hun, J.: An aem edic he Time-Deendence f Well Delieabiuliy in a Cndenae Field, PEJ (June1967) 112; Tan.,AIME,24 1. O Dell, H. G, and Mille,. N, : uccefully Cyclin a Lw Pemeabiliy, Hih-Yield Ga Cndenae eei, JPT (Januay 1967) Fuell, D.D.: inle-well Pefmance Pedicin f Ga-Cndenae eei, JPT (July 1973) 258; Tan., AIME, Dyun, T. V, Jne, J., and ahaan, : Pefmance Pedicin f Ga Cndenae eei, Pae PE fi eened a he 1987 PE Annual Technical Cnfeence and Exhibiin held in Dalla, e Mua, M. and Mee, M.W.: The flw f Heeeneu Fluid Thuh Pu Media, Phyic (e. 1936) Vl. 7, Eine, H. H, and Mua, M, : calculain f Theeical Pduciiy fac, Tan, AIME (1942) 146, Leine, J.. and Pa, M.: The calculaed Pefmance f luin Ga-Die eei, PEJ (e. 1961) Tan., AIME, Vl ahaan,. and Jne, J. : Delein Pefmance f Ga-Cndenae eei,, JPT,. (Auu 1996) Fean, O and Whin, C. H, : Mdelin Ga- Cndenae Well Delieabiliy, Pae PE 3714 fi eened a he 1995 PE Annual Technical Cnfeence and Exhibiin held in Dalla, Ocbe.

10 1 FAWZI M. GUEHIA PE Table 1 eei Peie Table 3 Fluid Peie Pemeabiliy, Piy, φ Wellbe adiu, w eei exen, e Laye Thicne, h in, 5 md.8.33 f 1 f 15.5 f Iniial eei eue (ia) Dew in eue (ia) eei emeaue (F) Maximum Liuid Du duin CVD (%) ich Ga Fluid A Lean Ga Fluid Iniial CG (b/mmcf) Table 2 elaie Pemeabiliy e Geneaed uin a lynamial exein afe Kniazeff & Knaille 6 c-tan Oil API Gaiy e-1.e-1 1.e 2.5e e e-1 5.e e e e e e-2 4.e e e e e e-2 4.5e e e e e e-3 5.e e-1 2.5e e e-1.e-1 5.5e e-1.e e e-1.e-1 8.5e e-1.e e e-1.e-1 9.e e-1.e e e-1.e-1 9.5e e-1.e e e-1.e-1 1.e 1.e.e-1

11 PE INFLOW PEFOMANCE ELATIONHIP FO GA CONDENATE 11 Fi. 1 - eei Peue Pfile f ich Ga A eei Peue, ia Time, day Pduced CG, b/mmcf Fi. 2 - Pduced Cndenae-Ga ai Pfile f ich Ga A Time, day

12 12 FAWZI M. GUEHIA PE Pduced GO, cf/b Fi. 3 - Pduced Ga-Oil ai Pfile f ich Ga A eei M 4 imulain Peue, ia Fi. 4 - Oil ecey f ich Ga A Oil ecey, % imulain eei M Peue, ia Fi. 5 - Ga ecey f ich Ga A Ga ecey, % eei M imulain Peue, ia

13 PE INFLOW PEFOMANCE ELATIONHIP FO GA CONDENATE 13 Fi. 6 - IP Cue f ich Ga A 6 5 imula Ineaed Mehd eei M Peue, ia Cndenae ae, b/day Fi. 7 - IP Cue f Lean Ga A Peue, ia Cndenae ae, b/day imula Ineaed Mehd eei M

14 14 FAWZI M. GUEHIA PE Fi. 8 - We Texa Well Pefmance Mach in Peue, ia Cndenae ae, b/day