Pressure Transient Analysis for Non-Newtonian Power-Law Fluid Flow in Double Porous Media and Fractal Reservoirs

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1 ssu Tas Aalyss o No-Noa o-la Flu Flo oubl oous Ma a Facal Rsvos HOU Yg M TONG g K ollg o Mahacs a opuaoal Sccha Uvsy o olu ogyg 576 houyg@upc.u.c Absac Ths pap pss a ahacal ol o as lo o h o-noa po-la lu oubl poous a a acal svo. By usg ouglas-jos pco-coco ho oba h soluo o h cosa a coo a a sgl ll a svo. Th lo bhavo s also aalyz. Fally scuss h pssu spos o h vaous paas. Th suls oba hs suy h pvous pssu as aalyss o o-noa po-la lo a acal svo pssu as hou a pacpao o a oubl poous a acal svo. ovoal ol hoogous svo s a spcal cas o hs ol. Ky os o-noa po-la lu acal svo oubl poous a ll s aalyss ouglas-jos pco-coco ho Iouco Facal goy has sho s avaag scbg copl phoo such as s appopa o scal h ouoy a osquc o poous a. I h chacs o h lu lo hough poous a s su by usg acal cocp h scbl a cogv ably o poous a a s goy sz such as acal sy a acu sz ll b as. hag a Yosos sly ouc h cocp o acal goy o pssu as olg o h aually acu svo. Hov hy popos h ol hou ay suppog oll pssu aa. B a Apla 3 hav a up o hs ccy. Th ols o lu lo hough h acal svo pla h copl svo ll s suls hch ca b ach a pla by usg covoal ols oll a coss h oll s. Thus h cocp o acal goy has poa sgcacs boh hoy a pacc o suyg lu lo svo. O h bass o hs sus haabay 4 ps a aalycal ol o aalyss o as lo o a o-noa po-la lu a acal svo. Boh cosa a a cosa pssu bouay coos su. Hs suls o oly pov a ho o h agoss o po-la lo a acal svo bu also yl a quaav aalyss o such lo syss. O h oh ha hs vsgao h olg o o po-la lu lo o acal svos. Tog g 5 a G Jal 6 popos ols o o-noa po-la lu lo acal svo h h a h oao. Aalycal soluo al spac s oba by usg Laplac aso a coposo ho. Boh cosa a a pssu a cos. I hs pap suy h o-noa po-la lu lo acu svo. Th svo s a sys cossg o a acal obc acu o b a Eucla obc a o h abov-o sus 45 h a s coucao h h acu o. Gally spag a svo l hs s as oubl poous a a acal svo. W ps a ucal pssu as ol o aal lo o o-noa po-la lu a a cylcal syy svo. A paal al quao scbg o-noa po-la lu lo oubl poous a a acal svo s v. ouglas-jos pco-coco 7 ho s us o oba h ucal soluo.th ssvy o h sys spos o h o-noa po-la h acal paas a oh paas a also a al. 8

2 8 Mahacal Mol W assu h acal pabl o b h Eucla a. Th acal o so s a Eucla a so s. Th a has coc poosy a coucas h h acal o. W a h usay-sa lo o a slghly copssbl o-noa po-la lu a cylcal sys. Alhough h pably a poosy sbuos o a acal svo hav b vaous os sus h aop h o popos by hag a Yosos Th aal supcal vlocy ca b pss as 6 u µ Fo h oulao ca o A µ H A. By usg h ollog solss vaabls yl h lo quao o o-noa lu h oubl poous a a acal svo L 3 4 Th solss vaabls a h q A π 3 G A Gb 3 L L h q A π a L L L L H A h q A G π h h al coo gv by 5 h bouay coo s gv by 6 h ou bouay coo s gv by h ollog l l 7

3 83 I apply h ollog asoao o 3-7 L L l l ca yl L 8 l L L 9 L l l W o spc ucal soluo o h pobl pos by quaos Nucal Mho W aop ouglas-jos pco-coco ho o solv h quaos 8-9. So ca oba h soluo o h ola paal al quaos 3-4. Fo ouglas-jos pco-coco ho ach quao avacs h soluo o-hal o a c. I h pco h uos occu a h lvl a h coco quaos a ucooally sabl. Boh syss o h quaos a o agoal o a s asy o solv h by usg Thoas ho. Th pco quaos o h o quaos 8-9 spcvly a / / L 3 l / L L 4 Th coco quaos o h o quaos 8-9 spcvly a L 5 l L L 6 h 3 N L g pos

4 3L lvls Ial coo I bouay coo a co b oco L L 9 Ou bouay coo 3L 4 Rsuls a scusso As ca s o h ucal soluo h gal bhavo o h sys s aalogous o h covoal Wa a Roo ol a also osas chaacscs o a acal svo. Th po-la sgs h o-no chaacscs. As s sho Fg. lo valus la o a lag pssu op. Th c o bcos cla h h gog o. Th acal so a h spcal po ac h hol pogss o h lo. As gos o h cs o h a obvous a h solss pssu cuvs vg spcvly Fg. a Fg.3. Fo a acal obc lcs h g o s coplcao. Th spcal po s h coucvy. Wh h valu o s sall h sys has b coucvy a h solss pssu op s lss. 7 8 Fg. Th ypcal cuvs h Fg. S-log plos o pssu vsus o-la a Fg.3 S-log plos o pssu vsus a Fg.4 S-log plos o pssu vsus a 84

5 W subsquly suy h ssvy o a. As pc h valus ac oly h aso po. Th agu o h pssu op s hghly ssv o a. cas h sgh o h chag a b h a a acus. Hgh valus la o a al os o h aso po Fg.4. Ssvy o s also sgca Fg.5. Lo valus la o al os o h aso po a sall pssu op. Fally s cssay o po ou ha h ha h aso po lass has ohg o o h bu s hghly p o. Th c o s o ll sgcac Fg.6. Fg.5 S-log plos o pssu vsus a Fg.6 S-log plos o pssu vsus a 5 oclusos W ps a ahacal ol o scb h sgl-ll as pssu spos o h lo o h o-noa po-la lu a oubl poous a a acal svo. Ths s a galzao o h sgl poous acal svo oly h acu o pacpag h lo. W g a la paal quao o h ola paal quao by usg a spcal asoao. Nucal soluo o h la paal quao s oba by aopg ouglas-jos pco-coco ho. Th soluos ay b us aalyzg h pssu as bhavo. solss pssu op s ssv o h po-la h acal paas a h oubl poous a paas. Th suls osa ha a ac h pocss o h lo hl a hav cs oly o h aso po. Noclaus oal copssbly pa - acal so h cv oao hcss H vscosy pably po-la pssu pa al pssu solss pssu op aal sac s acal po a/acu aco poosy soag paa solss 85

6 Subscps solss acu a llbo Rcs hag J. a Yosos Y..ssu as aalyss o acal svo. SE Fo Eval. 99Mach:3-38 B R. A. ssu Tas Fl aa Shog Facal Rsvo Sucu. IM/SE ap 9-4 s a h 99 Iaoal Tchcal Mg o h SEJu -3 algay AB 3 Apla S. Abassah. Muchaa L. asua H. Applcao o acal svo ol o c s aalyss Kaoag gohal liosa. SE haabay. S. Faouqol M. a To W. S. Tas lo bhavo o o-noa po-la lus acal svos. M/SE pap. No. IM Aual Tchcal Mg o h olu Socy o IM algay AB. May Tog g Wag Ruh. Eac Soluo a yacal haacscs o onoa o-la lu lo acal svo. Joual o Hyoyacs. 53: G Jal Tog g. Nola lu chacs o h copl lu sysm. ha Uvsy o olu ss 998 hs 7 Iou. U. a Ray H. J. J. ssu bhavo ug poly lo polu svo. Jou. E. Rsou Tch 984: