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Transcription

1 PE Pemane Pediin a Well Unde Mulihase Fl Cndiins T Mahaendajana, T Aiadji, and AK Pemadi; nsiu Tenli andun Cyih 003, iey Peleum Eninees n This ae as eaed esenain a he PE Asia Paii Oil and Gas Cneene and Exhibiin held in Jaaa, ndnesia, 5 7 Ail 003 This ae as seleed esenain by an PE Pam Cmmiee llin evie inmain nained in an absa submied by he auh(s) Cnens he ae, as esened, have n been evieed by he iey Peleum Eninees and ae subje ein by he auh(s) The maeial, as esened, des n neessaily ele any siin he iey Peleum Eninees, is ies, membes Paes esened a PE meeins ae subje ubliain evie by Ediial Cmmiees he iey Peleum Eninees Eleni eduin, disibuin, sae any a his ae mmeial uses ihu he ien nsen he iey Peleum Eninees is hibied Pemissin edue in in is esied an absa n me han 300 ds; illusains may n be ied The absa mus nain nsiuus anledmen hee and by hm he ae as esened Wie Libaian, PE, PO x , ihadsn, TX , UA, ax Absa This ae esens an analyial mehd edi duin emane a ell duin m a sluin as-dive esevi Many available analyial ehniues ublished a sluin as-dive esevi have been inended mainly daa analysis ehniues and hey ee ved be valid nly ne aiula l eime (ie, ansien l) Many have used nl Pemane elainshi (P) mehd edi he ell emane in hese esevis The shmin his mehd is ha i is based n eessin eihe ield daa numeial simulain esuls The daa ae samled n ne aiula l eime (ie, bunday-dminaed seud-seady sae l) Hene, he umes ae hihly deenden n he ndiin a hih he daa ae samled The analyial mehd in his ae addesses all l eimes (ansien, ansiin, and bunday dminaed l) The sluin als nsides ha all hases (il, as, and ae) an l This sluin is als validaed ih esuls m numeial simulain vaius luids and esevi eies nduin The bjeive his is devel a mdel eas emane a ell in a sluin-as dive esevi hee il, as and ae ae simulaneusly lin Many auhs -7 sudied he ell emane unde sluin-as dive assumin ae is immbile The main use hei sudies is analyze essue ansien and duin daa bained m his sysem They ame u ih dieen aahes, suh as essue, essue suaed, and seudessue mehds, mae use he sinle-hase sluin One hin in mmn is hey eneae hei esuls usin numeial simula hih ae hen maed ih he sinle-hase sluin usin hei mehds n his sudy, e ill als mulae he mulihase l (il, as and ae) blem in he sinle-hase l anal Heve, e aem dieen aah ha e use u mehd eneae he ell emane hih is hen maed ih he esuls m a numeial esevi simula Mahemaial Mdel The mahemaial mdel develed in his ae assumes a lamina, hiznal and adial l ih hee hases il, as and ae ih a ell a he ene he iula esevi Caillay essue is ined The esevi is nsideed hmeneus and isi The venin euain his sysem, in Day uni, is: ( ) i () a E is mleely linea and is analus he sinle-hase l blem The seudessue,, and seudime, a, ae deined as: ( ) i base d () a d (3) i 0 Whee: (4) (5) Ne ha he ue limi he seudessue ineal is he essue a he seii lain insead he aveae esevi essue The elainshi beeen sauains (il, as and ae) and essue a any ime is mued usin Es 6 and 7 Hene, elaive emeabiliy needed mue he seudessue and seudime ineals an be bained, and he sauain used his use is he aveae sauain he sysem n his sudy, e use -hase elaive emeabiliy il-as (ih nnae ae) and ilae sysems ne mehd 8-0 is used bain he hee hase exessin elaive emeabiliy il ( )

2 T MAHAENDAJANA, T AADJ, AND AK PEMAD PE s s s s s s ( s ( ) ) s (6) (7) Mdel alidain We use a numeial simula validae he analyial mdel The ell is dued a a nsan al esevi ae The luid and esevi/ell eies ae shn in Tables and and Fis and The esuls usin hese daa ae shn in Fis 3 5 n Fi 3, e mae he il, as, and ae duin m bh mdels (numeial and analyial mdels) The slid lines daa me m he numeial simula and he slid symbl daa ae m he sed analyial mdel is shn ha bh esuls ae in d aeemen This bsevain is als ue aveae sauains (Fi 4) and bm hle lin essue (Fi 5) The il ae, in eneal, deeases ih ime as he elaive emeabiliy il deeases beause he il sauain bemes smalle as he ime advanes The as duin deeases a is beause he as duin mes nly m sluin as (a his ime he as in he esevi is immbile) As he as sauain is eae han he iial as sauain, he ee-as (as eleased m il in he esevi) is saed be dued This auses he as duin ineases A lae ime, he delein aes nl he duin and he as duin deeases On he he hand, he ae duin ineases a he beinnin This may be due he deeasin ae il elaive emeabiliy is eae han he deeasin ae ae elaive emeabiliy A lae ime he ae duin deeases as he esevi essue deleed ensiiviy n Tal esevi (andae) Pduin T invesiae he ee he al esevi duin n he ell emane, e em sensiiviy analysis u dieen al esevi duins (0, 00, 00, and 500 b/day eseively) The esuls ae summaized in Fis 6 8 When e l he il ae vesus ime n he laihmi sales (Fi 6), i an be seen ha a ealy ime he il ae is aximaely nsan, and hen i deeases ih aximaely nsan sle These sles all ases ae aallel eah he This behavi indiaes ha e may be able analyze his in he daa bain he esevi eies Heve, e d n aem exle uhe his ssibiliy in his ae n eneal, e see d aeemen beeen esuls m numeial simula and hse m analyial sluin F hih duin ae (500 b/day), heve, hee is diseany n he bm hle lin essue a he ansiin l ein (in his ase a aximaely days) n his ein, he bm hle lin essue m numeial simula is le, bu i eves ba he values edied by he analyial sluin a he ully bunday dminaed l ein ensiiviy n esevi Pemeabiliy We als exeimens by usin dieen esevi emeabiliy (5, 0, and 00 md) ine he duin mde is nsan al esevi duin, he esevi emeabiliy des n seem ae he il, as, and ae duin (Fi 8) and he aveae il sauain (Fi 9) As exeed, he essue d is hihe as he emeabiliy is smalle indiaed by le bm hle lin essue smalle emeabiliy (Fi 0) Fm hese esuls e als see d aeemens beeen esuls m numeial simula and hse m analyial sluin ensiiviy n in Fa The esuls ae led in Fis 3 Fm his exeise, he ee sin nsan al esevi duin is nly bseved n he bm hle lin essue F ms ases he aeemens beeen he numeial mdel and he analyial mdel ae uie d The diseany beeen he is bseved hih sin 0 A ealy ime, he numeial sluin seems be unsable A he ansiin ein, aain, he numeial mdel is smalle ha he analyial sluin bee i eves ba he values edied by he analyial sluin a he bunday dminaed ein This behavi may be due he a ha he analyial sluin uses aveae sauain Heve, eah a nlusive saemen, uhe invesiain is aaned Cnlusins T summaize he esuls m his, e nlude ha: We have develed he analyial mdel ediin ell emane unde mulihase l ndiin in a sluin as dive esevi This mdel has been suessully validaed aains a numeial esevi simula F ms ases, he aeemens ih he numeial esevi simula ae vey d F ases hee he essue d is vey hih (suh as in a vey hih duin, a ell ih hih sin a, and in a vey l emeabiliy esevi), hee ae diseanies in he ansiin ein This shuld be subje uhe eseah 3 The seudessue and seudime ineals develed in his sudy shuld als be aliable daa analysis ell emane in a sluin as dive esevi hee ae is als lin

3 PE PEFOMANCE PEDCTON OF A WELL UNDE MULTPHAE FLOW CONDTON 3 Nmenlaue A Dainae aea, Ae il main vlume a, b/sb as main vlume a, b/s ae main vlume a, b/s il messibiliy, /si as messibiliy, /si ae messibiliy, /si al messibiliy, /si messibiliy, /si GO duin as-il ai, s/sb h esevi hiness, esevi emeabiliy, md il elaive emeabiliy as elaive emeabiliy ae elaive emeabiliy essue, sia b bubble in essue, sia i iniial essue, sia nmalized seudessue, si il ae, sb/d as ae, MCF/D ae ae, sb/d T Tal esevi (sandae) ae, b/d ime, Day a nmalized seudime, Day adius disane m ell, ell adius, s sluin as-il ai, s/sb s sluin as-ae ai, s/sb s sin a il sauain as sauain ae sauain WO duin ae-il ai, sb/sb il vissiy, as vissiy, ae vissiy, siy Nmenlaue Camah-, G and ahavan, : me Theeial esuls Useul in Analyzin Well Pemane Unde luin-gas Dive, PEFE (June 99) Camah-, G and ahavan, : Pemane Wells in luin-gas-dive esevis, ae PE 6745 esened a he 6 nd Annual Tehnial Cneene and Exhibiin he iey Peleum Eninees held in Dallas, TX, eembe 7-30, ea, K, Pees, AMM and eynlds, AC: Well Tes Analysis luin-gas-dive esevis: Pa uildu Analysis, ae PE 7048 esened a he PE Easen einal Meein held in Pisbuh, Pennsylvania, Obe - 3, Camah-, G: Cnsan-Pessue Pduin in luin- Gas-Dive esevis: Tansien Fl, PEFE (June 99) Camah-, G and ahavan, : unday-dminaed Fl in luin Gas-Dive esevis, ae PE 9009 esened a he PE Jin y Munain einal/l Pemeabiliy esevis ymsium and Exhibiin held in Denve, Clad, Mah 6-8, ea, K, Pees, AM, and eynlds, AC: ulemen PE 80, Well-Tes Analysis luin-gas-dive esevis: Pa 3 A Uniied Teamen he Pessue- uaed Mehd, ae PE Chu, W-C, Lile, TM and binsn, JC: Tansien Tes Analysis: luin-gas-dive esevi Examles, ae PE 47 esened a he 67 h Annual Tehnial Cneene and Exhibiin he iey Peleum Eninees held in Washinn, DC, Obe 4-7, 99 8 ne, HL: Pbabiliy Mdel Esimain Thee-Phase elaive Pemeabiliy, JPT (Feb 970) Aziz, K and eai, T:Peleum imulain, Alied iene Publishe, Lndn (979), Fayes, FJ and Mahes, JD: Evaluains Nmalized ne s Mehds Esimain Thee-Phase elaive Pemeabiliies, PEJ (Ail 984) 4-3 Aendix A Gvenin Euain The adial l euains il, as, and ae in he esevi ae as lls: Oil hase: (A-) Wae hase: (A-) Gas hase: s s s s (A-3) Exandin E A- il hase, e bain: (A-4) The esevi emeabiliy is assumed n hane siniianly as he essue hanes, and his is a valid assumin in ms ases We als assume ha he luid eies an be evaluaed a he aveae esevi essue Exandin E A-4 uhe, and eaanin, e have: (A-5)

4 4 T MAHAENDAJANA, T AADJ, AND AK PEMAD PE imila as E A-5, e bain ae hase: (A-6) F ee-as hase, e have ha s s s s (A-7) O e an ie s s s s (A-8) Exandin E A-3, s s s s s s s s (A-9) Exandin E A-9 uhe, e bain s s s s s s (A-0) ubsiuin Es A-4 and A-0 in E A-8, e bain s s s s s s (A-) Exandin E A- and eaanin, e bain s s s s s s s s s s s s s s (A-) Cmbinin Es A-5, A-6, and A- and simliyin, e hen bain E A-3 s s (A-3) O e an ie E A-3 as: [ ] (A-4) imliyin uhe: (A-5)

5 PE PEFOMANCE PEDCTON OF A WELL UNDE MULTPHAE FLOW CONDTON 5 Whee (A-6) The elaive emeabiliy-vissiy in he le-hand-side and he messibiliy in he ih-hand-side ae deenden un essue, hene he aial dieenial euain in E A-5 is nn-linea Ou al is lineaize E A-5 nduin seudessue i d 0 (A-7) Deinin (A-8) ubsiuin E A-8 in E A-7 ( ) i base d (A-9) Tain deivaive E A-9 ih ese essue, e bain ( ) i d d (A-0) Wiin in em seudessue E A-7 bemes (A-) ubsiuin E A-0 in E A- (A-) nduin seudime as d i a 0 (A-3) nsein seudime (E A-3) in E A-, e bain ( ) a i (A-4) We n have E A-4, hih is mleely linea and i is analus he liuid sluin Nex is deive he exessin he inne bunday ndiin nsan al esevi ae duin The al veliy is v (A-5) eiin E A-5 in em al ae and eaanin e have h π (A-6) Use seudessue in E A-6, e bain ( ) h i π (A-7) As shn in E A-7, he inne bunday ndiin u mulihase sysem is als linea vided ha seudessue (E A-9) is used Aendix auain and Pessue elainshi T mue he seudessue and seudime, nlede he elainshi beeen sauain and essue need be nn This aendix is vide a edue deeminin he aveae sauain iles as unins esevi essue The emainin as-in-lae (sluin and ee as) a any ime an be mued by E - s s G (-) Tain deivaive E - ih ese essue, e bain ( ) s s s d dg ( ) s s s ( ) ( ) ( ) s s (-) The emainin il-in-lae a any ime is N (-3) Tain deivaive E -3 ih ese essue, e bain d dn (-4) The ae-in-lae (neliible ae inlux) a any ime is W (-5) Tain deivaive E -5 ih ese essue, e bain d dw (-6) Pduin as-il ai is deined as s s GO (-7) Pduin as-il ai an als be mued by d dn d dg d dn d dg GO (-8)

6 6 T MAHAENDAJANA, T AADJ, AND AK PEMAD PE Nex is subsiue E - and E -4 in E -8 The esulin euain is hen euaed ih E -7 Ae eaanemen, e bain exessin il sauain (E - 9) s s s ( ) s s s s ) ( s (-9) Pduin ae-il ai is deined as WO (-0) Pduin ae-il ai an als be mued by d dn d dw d dn d dw WO (-) We hen euae E -0 and E -, and ae subsiuin Es -4 and -5 and eaanemen, e bain exessin ae sauain in E - (-) We, n, have euains and unnns (il and ae sauains) Theee, e an slve Es -9 and - simulaneusly bain il and ae sauains as unins essue

7 PE PEFOMANCE PEDCTON OF A WELL UNDE MULTPHAE FLOW CONDTON 7 Table Fluid Peies essue Oil FF luin GO Oil issiy Gas FF Gas issiy Wae FF luin GW Wae issiy (sia) (b/sb) (s/sb) () (b/s) () (b/s) (s/sb) () Table esevi/well Peies niial essue, i 4000 sia ubble in essue, b 4000 sia esevi hiness, h 5 Pemeabiliy, 00 md Psiy, 0 messibiliy, 3x0-6 si- Dainae aea, A 60 Ae Well adius, 033 in a, s 0 Tal sandae duin, T 00 bbl/d

8 8 T MAHAENDAJANA, T AADJ, AND AK PEMAD PE Fiue elaive emeabiliy il-ae sysem Fiue 4 Aveae sauain Fiue elaive emeabiliy as-il sysem Fiue 5 m hle lin essue Fiue 3 Pduin ae il, as and ae Fiue 6 Ee al duin ae n he il duin

9 PE PEFOMANCE PEDCTON OF A WELL UNDE MULTPHAE FLOW CONDTON 9 Fiue 7 Ee al duin ae n he aveae il sauain Fiue 9 Ee esevi emeabiliy n he aveae il sauain Fiue 8 Ee al duin ae n he bm hle lin essue Fiue 0 Ee esevi emeabiliy n he bm hle lin essue Fiue 9 Ee esevi emeabiliy n he il duin ae Fiue Ee sin n he il duin

10 0 T MAHAENDAJANA, T AADJ, AND AK PEMAD PE Fiue Ee sin n he aveae il sauain Fiue 8 Ee sin n he bm hle lin essue