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三元复合驱数学模型及其应用

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三元 复合 数学模型 及其 应用
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là°ù:1999-08-30Á[":ÏSF²?–"v³["T€eº:7îÑ(1971-),3(qB),¹+ö¦,pV3,VY1@ïÐa”´E©ùîbÓcI|:1000-5870(2000)02-0061-03三元复合驱数学模型及其应用鲜成钢郎兆新程浩(石油大学石油工程系,北京102200)K1:yëØí¯†z”И,¾˜†ë¹Q˜Øí¯†z¥ö1z²Ø[#¯†ÄÐz²VñÏc¥ö1É.¾C`,i²†L˜W%¹í.ÉVñÏ#¥vþØÄÐC`b¾˜a¨¿®pH´Øí¯†z8",­{±ÄAM,]H¨¥ÄÐQ‹Ü™˜b¨y륔И,ɛػ²Ÿ”´EbÐS“ÄÐzÈqUTCHEM¥9زT1?C,¾˜¥9زTVL,9ØÎv–4Ú,]H=i]¨„9Ø¥×矩·SûµBçñ¥¿ÿ,V7£ü'˜¥VLŸ„L¨Ÿb1oM:Øí¯†z;”И;z²Ø;”´EÏmsË|:TE357.46ÓDSM’:A„ý¹³Øí¯†z²Ø#òÕþÄC`¥•Y,V[樔´EZEÉ›Øí¯†z¥Øùî„•YyÍs[1~4],ç©z²îÿ,ªÊL@ZÃi·CÆ‹¨b'Ó-¦ùî¥$,yëBñµV°¤æ¨‚]pH´Hq/¥q1sÐcsL©1"wLÉ›9Ø,9Væ¨Langmuir˜¸©ÑT[5]9Øb’aiH,VëŸ4¥¸Ì=|ÛpH´¥6Ú7†®[1,4],'qs=q1s1-bspH-7pHmax-7.(9)TÏ,q1s¹pH=7H¥¸Ì=;pHmax¹ÿÆai¥pH´;bs¹"”b†þ¥¸Ì=9Væ¨Langmuir˜¸©ÑT9ØbòM—Å„а5”µ1,°5”çl¹Nc=1RElLlVl.(10)°5h„VrT¹Slr-Slrc=Slrw-Slrc1+TlNc.(11)TÏ,Slr¹»lM¥—Å„;Tl¹lM°5h„wL•”;Slrc¹lM¥"¸—Å„bM1iqwL9ØT¹[5]Kcrl=Krl0(Snl)el,l=1,2;(12)Snl=Sl-Slr1-S1r-S2r.(13)TÏ,Kcrl0¹»lMM1iqÄ´;Krl¹»lMM1iqÄ´;el¹¿»lM¥·”b†þ,gMTL0p¹[5]L0p=Lw[1+(a1cp+a2c2p+a3c3p)]cSpSEP.(14)ÏcSEP=c++Bpc2+c1.(15)TÏ,a1,a2,a3¹Ȕ,®L'’ç;cSEP¹†þµrc÷;cp¹†þi;Sp¹”L0pÐcSEP1"wL¥|q,Lç¹Ȕ;c+¹BNÖ0i;c2+¹=NÖ0ib®¿gMP†þ·A¥T†®,†þ·A¥gMTVæ¨MeterZñ[5]É›9Ø,'Lp=L]+L0p-L]1+[ÛCeq/ÛC0.5]pa-1.(16)TÏ,ÛCeq¹©rgMÎq;ÛC0.5¹T†¹,gMTBöH¥gMÎq;L]¹íKgMH·AT;pa¹·”b£M1iq†®ö1^®†þ¥¸Ì=î„¥bLangmuir˜©Ñ1iq†®"”RRF¹[5]RRF=1+(RRFmax-1)Apcp,11+Bpcp,1.(17)TÏ,RRFmax¹ØXƒ1iq†®"”;cp,1¹†þ£MÏ¥i;Ap„Bp¹Ü•”bòMá|%¿òMâï„Fî,VVr¹[4]Ql=Q0lexp[Bl(pl-p0l)];(18)Q0l=1EiYil/Q0i.(19)TÏ,p0„Q0sY¹•Iââï/¥á;Bl¹âê"”b2˜p³¨Tp³âïaAT9Ø9Fsi¥ZTp³”Иb¹eŔ´ÛÛ,¨Ú¨µs„îS1â0Ebp³VñÂ/:(1)|˜SÄb(2)Tp³âïbn5Zñ(1)òFsp„,¤Â/âïZñ:div(ElQlVl)+5EiAi5t=EiBi.(20)|VlVrT„Zñ(7)}ÆT(20),"âïpw“,ðM(¨AT)Ø,V¤žBñLŸZñFbppwª,'V9Øp0„Vlb(3)ôZñ(2)¥µsT,AT9ØòFs¥9iZib(4)9ØòMiYil„„Slb9iZiaMiYil„„Sl­Wi/#62#石油大学学报(自然科学版)2000年4月1":ZiElQlSl=ElQlYilSl.(21)®¿ºIn£a²M,5V[ª¹Z2(QoSo+QwSw)=QoSo;Sw=1-So.(22)|T(21)„T(22)óëp³,VpSw„So,É7V9ØMi¹Yiw=Zi(SoQo+SwQw)SwQw.(23)(5)9ØòÕþÄ•”b(6)Rí„ç(2)[p³/BñHW„É¥´b3Ø»²ŸELè¨'˜É›Ø»²ŸE,|9زTÐS“ÄÐzÈqUTCHEM¥9زTÉ›1,I³9ØÎÐÚb9Ø^BûóXPÒ266±É›¥,=i¥Â¹96MBbNHKv¸¸«Ĕ¹50@30@5=7500b¨'˜E¹ÿôQôÄÝF¥7Vñb©ìÃs¹:14@14@5;$X=$Y=13.2m;$Zi(m)sY¹1.49,1.67,2.02,2.08„3.00b%ª¹d(ɹª,Sw¹0.5~0.6,£Ü1iqÿ¹0.020~0.350Lm2,<_1iqÿ¹0.001~0.150Lm2,ä'ÿ300m,¹ªâï9.3MPaP·bÝÊÂm1îUbÏ,4,5,9„10¹ÿÆÝb!97?HW¹1600d,†Ýÿƹ17m3/d,9g3ÁÝçݸ@â¹4.7~4.9MPab8ýTÅ^:5ÿÆ225dÈ£ç!,¤"ÿÆa/VëŸ4/†þ(0.3%VëŸ4,1%Na2CO3,0.18%†þ)¯†Ö560d,ÿÆ0.15%†þªÃÖ340d,KªÿÆ475dÐa£(0.5%Na2CO3)bòÿÆÖ¥@8îsnV1b¹ª£¥íÍFînV2bm1Ø»9ؘÝÊm'˜ÐUTCHEM˜9زT1nV3b®V3V[?C,'˜9ØÎ1UTCHEM4Úÿ2.4;9Øî¨H„hÿ10%b'˜9ØH¥Kv„KlHW„É[#X¸+”¥Kl´ûµBçñ9v,7M]«ĔH,'˜=i]¨1UTCHEM«8ÿ26.2%bƒ^®¿˜‚É›Në¥Mÿ9Ø,iOÄÐQ‹Ü™"dÉ›†Ø¥eÄ,yN,9ØÎvv4Úb]H,®¿‚In±ÄAM#î#¥vþÄ•”,P=i]¨9vvhbV1ÿÆÖ¥@8îsÖv(W)/%v(S)/%w(P)/%c(Cl)/(mol#L-1)c(Ca)/(mol#L-1)c(Na)/(mol#L-1)c(H)/(mol#L-1)c(CO3)/(mol#L-1)11.0000.132590.003350.1348111.0250.005220.9970.0030.180.000140.003350.26645111.0025060.269431.000.150.119790.003350.1220111.00250.005241.0000.0590.00270.1043111.0430.0942V2¹ª£¥íÍFîíÍëíÍcc/(mmol#L-1)íÍëíÍcc/(mmol#L-1)_111019.8Ã0.0071206)94.29741Öô71.73722Á0.3189084o59.00000m2„m3óUTCHEM„'˜É›»BªØ»²ŸE¥9زTb®¿'˜¨¥¸ëfï^UTCHEM¥†s9زT,yN9زT9{µµY,Œsƒ?p^BÁ¥,Vü'˜„„Ÿ4i¥9Ø^’¥bV3Õ˜¥9زT19ؘ9ØHWt/min9Ø„”HW„É/dKv´Kl´X¸+”Kv´Kl´=i]¨/MB'Ó˜17550800.68570.0103900.10.00211923.2UTCHEM59355400.46370.0088180.10.00207831.4(下转第69页)#63#第24卷第2期鲜成钢等:三元复合驱数学模型及其应用5²‚(1)˜?퍮pH´¥Øí¯†zÄÐQ‹›¹bQ‹þÕi¥9Ø]UTCHEM1µM’¥Ú,7O£Ú¥-4/,9ØÎ÷Úb(2)˜ÏuY¯†zÏö1Q‹„Q1Q‹,Vô²BL=fƒ%ç^ŽIn¹ª£ÏÃÖ0¥•Yb(3)M]iHÁÖ0¥a{v¿ÃÖ0¥a{b’ÃÖ0i1ÁÖ0i®BñBñ[”)H,V[‚InÃÖ0¥M1Q‹,ƒ";?4ÚØλ?£9ØÚb(5)µCa2+H,%8MgCO3ö1i¿†{,†{[“MgCO3‚^æ†b(6)ÃÖ0clq+¬í•Y,a{‚ö•YaA¥µr.lb•IÓD:[1]BhuyanD,etal.Mathematicalmodelingofhigh-pHchemicalflooding[J].SPE17398,1988.[2]BhuyanD.DevelopmentofCompositionalReservoirSim-ulator[D].Dissertation,UTatAustin,1989.228~231.[3]ChengKH.Chemicalconsumptionduringalkalineflood-ing:Acomparativeevaluation[J].SPE/DOE14944,1986.[4]WBGuenther÷.ÄÐÜ™[M].zü,©r.öêê:F²vÐñ,1989.181~184.[5]ïVl,ô¿.a¯†z”И[J].F²Ð,1994,15(2):76~88.[6]YunShiyi,YangPuhua,etal.NumericalsimulationofAlkaline/surfactant/polymerflooding[J].SPE29904,1995.[7]BhuyanD,etal.Simulationofhigh-pHcorefloodexper-imentsusingacompositionalchemicalfloodsimulator[J].SPE21029,1991.(责任编辑陈淑娴)(上接第63页)m27765dHc£„sƒm37765dHVëŸ48s”(@103)sƒ4²‚(1)yëØí¯†z”И,æ¨N˜?É›L=¥ç©”´E9Øb(2)ÐÄÐzÈqUTCHEMM1,'˜¥9ØŸ?z,µ<¥‹¨w<N´b•IÓD:[1]BhuyanD.DevelopmentofCompositionalReservoirSim-ulator[D].UTatAustin,1989.[2]ïVl,©.ÿÄÐ4z²”´E(؂†s)[J].F²Ð,1988,9(1):51~60.[3]ïVl,ô¿.a¯†z”И[J].F²Ð,1994,15(2):76~88.[4]YuanShiyi,YangPuhua,DaoZhongqiuandShenKuiy-ou.Numericalsimulationofalkali/surfactant/polymerflooding[J].SPE29904,1995.[5]NajiSaad.FieldScaleSimulationofChemicalFlooding[D].UTatAustin,1989.(责任编辑陈淑娴)#69#第24卷第2期程浩等:三元复合驱化学反应平衡模型及其应用voir,theinterlayerdifferencewouldleadtononuniformityofinjectionprofileandinfluencewaterdisplacementefficiency.Fortheinjectionwellwhichneedsfracturing,asimulationmodelofinjectionpredictionoffracturedwellisconstructedinthispaper.Therelationsamonginjectionandformationproperties,fractureparameters,injectionpressureareanalyzed.Theresultsshowthattheinterlayercontradictioncanbereducedandtheinjec-tionprofilecanbeimprovedbyreasonaldesignofdifferentfractureparametersforfracturedinjectionwell.Injec-tionprofilesofsixwellsaretested,andfourwellshavecompletelyreachedthelevelofinjectingscheme.Itisshownthatthemethodispracticallyusefilltoinjectionprofilemodificationofinjectionwellinmultizonehetero-geneousreservoir.Keywords:waterinjectivityprofilemodification;injectionwell;hydraulicfracturing;numericalsimulation;mathematicalmodelAboutthefirstauthor:ZhangShi-cheng,male,associateprofessor,obtainedMSdegreefromtheUniversityofPetroleum,China.NowheisengagedinteachingandresearchonreservoirsimulationattheDepartmentofPetroleumEngineeringintheUniversityofPetroleum,China(Beijing:102200).GaiYing-jie,FanHai-junandChenYue-ming/ACHANCE-CONSTRAINEDMODELWITHRANDOMPARAMETERSFDRPROGRAMMINGMEASURESOFOILFIELD/2000,24(2):58~60Themeasuresforprogrammingoilfieldisveryimportantinoilfielddevelopment.Somescholarshaveestablishedthedeterminationmodelsforprogrammingproduction-stabilizingmeasuresofoilfield,inwhichparametersareallpre-determined.Inpracticalproduction,manyoilfieldproduction-factorscannotbedeterminedinadvance.Thispaperpresentsachance-constrainedrandomplanningmodelforprogrammingthemeasuresofoilfieldwithuncertainfactors.Thegeneticalgorithmsolutionisgiven.ThemethodhasbeenappliedtoJin45oilfield.Theresultshowsthattherandomprogrammethodisaveryefficientforplanningoutoilfielddevelopment.Keywords:stableproduction;measure;program;mathematicalmodel;randomparameters;objectivefunction;constraints;geneticalgorithmAboutthefirstauthor:GaiYing-jie,male,seniorengineer,obtainedMSdegreefromXiangtanUniversityin1989.NowheisinpursuitofhisPh.DdegreeattheDepartmentofPetroleumEngineeringintheUni-versityofPetroleum,China(Dongying:257062).XianCheng-gang,LangZhao-xinandChengHao/DEVELOPMENTANDAPPLICATIONOFMATHE-MATICALMODEISFORALKALINE-SURFACIANT-POLYMERFLOODING/2000,24(2):61~63Thealkaline-surfactant-polymer(ASP)mathematicalmodelscandescribefluidflowingmechanismofASPfloodingindetail.Inthemodels,thetransportofchemicalcomponentsinporousmediumintheprocessofASPfloodingisformulated.Inthedevelopingprocessofthemodels,physiochemicalpropertiesofoilfloodingwereconsideredcomprehensively,andmicroemulsionphasewasneglected.Anewchemicalreactionequilibriummod-elfeasiblefortheASPsystemwithlowpHvaluewasadopted.Aprogramwasmadetosimulatethe3Dreservoirandtheexperimentalcoreflooding.TherunningspeedofthenewmodelisfastertwotimesthanthatofthechemicalfloodingsoftwareUTCHEM,whilethecalculatingaccuracyremainsalmostthesame.Lessmemoryas-sumptionandlongertimestepareattainedbythemodels.Thecomputationexamplesshowthatthemodelsarereliableandpractical.Keywords:ASPflood;oildisplacement;numericalsimulation;mathematicalmodelAboutthefirstauthor:XianCheng-gang,male,graduatedfromtheUniversityofPetroleumin1994.NowheisinpursuitofhisPh.DdegreeattheDepartmentofPetroleumEngineeringintheUniversityofPetroleum,China(Beijing:102200).ChengHao,XianCheng-gangandLangZhao-xin/ANEWCHEMICALREACTIONEQUILIBRIUMMODELINALKALINE-SURFACTANT-POLYMERFLOODANDITSAPPLICATION/2000,24(2):64~69Inordertoobtainareliablechemicalreactionequilibriummodelinalkaline-surfactant-polymerflood,newphys-i#Ö#JournaloftheUniversityofPetroleum,China(EditionofNaturalScience)Vol.24No.2Apr.2000
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