• / 6
  • 下载费用:5 下载币  

SPE-18442-PA

关 键 词:
SPE 18442 PA
资源描述:
ReservoirSimulationofGenerallyAnisotropicSystemsGautamS.Shlralkar,SPE,AmocoProductionCo.Summary.Thispaperpresentsnumericaltechniquesforthesimulationofreservoirsystemscharacterizedbyanondiagonaltensorrepresentationofarealpermeability.Anine-pointmethodofdiscretizationforcalculatingreservoirflowandawell-inflowmodelbasedontheconceptofequivalentwellblockradiusarepresented.IntroductionPetroleumreservoirsaregenerallyrecognizedtoexhibitheterogeneity(spatialvariationsinrockproperties)andanisotropy(unequalvaluesofdirectionalpropertiesatagivenlocation).Anisotropicreservoirpropertiesareinheritedfromthedepositionalenvironment,leadingtovariationsinpermeabilitydirectionality.1Thedegreeandnatureofanisotropyarealsoaffectedbysmall-scaleheterogeneityandthusdependonthemeasurementscale.2Itisimportanttobeabletosimulateanisotropicsystemsnumericallywherethedirectionoftheprincipalaxescanvaryspatially.Inmostreservoirsimulators,theprincipalaxesinthearealplanearealignedwiththegridaxes.Wecallthis"particularanisotropy"todistinguishitfrom"generalanisotropy,"wheretheprincipalaxesofarealpermeabilitymaychangeindirectionfromlocationtolocation,causingthemtobeinclinedatsomeangletothegridaxes.Tothebestofmyknowledge,onlyoneprevioustreatment3ofsuchsystemsforcalculatingtransmissibilitiesexists.Nodiscussionappearsintheliteratureonthequestionofawell-inflowmodel.Herein,Idescribebothamethodforgeneratingtransmissibilitiesandawell-inflowmodel.CalculationofTransmissibilitiesFig.1showsagenerallyanisotropicsystem.Theprincipalaxesofpermeabilitykmaxandkminareinclinedatanangle8tothexandyaxesofthenumericalgrid.Darcy'slawisthenexpressedasUx=-(kxxaplax+kxyaplfJy)/p........................(1)anduy=-(kyyaplay+kyxaplax)/p.,.....................(2)wherekxx=kmin+(kmax-kmin)Cos28,...................(3)kyy=kmin+(kmax-kmin)sinZ8,.......................(4)andkxy=kyx=(kmax-kmin)sin8cos8...................(5)Notethat,whilekxxandkyyarealwayspositive,kxybecomesnegativefor7r/2kyoax,anday)intoanequivalentanisotropicsystem(characterizedbyk,ax'.anday'),wherek=(kxky)'12,.....................................(22)ax'=(k/kx)'Aax,...............................(23)anday'=(kxlky)'i4ay...............................(24)Thismethodisalsoeffectiveinreducingthegrid-orientationeffectassociatedwithadverse-mobility-ratiodisplacements.4Toretainthesedesirablefeatures,thenine-pointmethodproposedherefor409,!"""-......'I;yt..xyFig.1-Schematlcofagenerallyanisotropicsystem.11--------III:'TIIII\Y:\~x-------2~y~xFig.2-Four-nodeelementusedtoderivenine-pointtransmissibilities.o22.54567.5908(degrees)Fig.3-RangeofpositivetransmissibilitiesforproposedninepointMethod1,squaregrid,homogeneoussystem.410TABLE1-PARAMETERSFORTERTIARY-CONTACTMISCIBLESOLVENTINJECTIONQuarterFive-Spoton40·AcrePatternAreaReservoirthickness,ftPermeabilityPorosityInitialpressure,psiaInitialwatersaturationWaterviscosity,P-w'cpOil·componentviscosity,/Lo'cpSolventviscosity,II-s'cpOil-componentdensity,Ibm/ft3Solventdensity,Ibm/ft3Waterdensity,Ibm/ft3Viscosityofoilphase,P-oil20(seeFig.4)0.081000.70.71.00.160.660.662.4/Loil=xo/Lo+(1-xo)P-s'whereXo=oleicmassfractionProducerBHPlimit,psia100Injectionrate,ft3/D83.4Water/OilRelativePermeabilitySor=0.3,S/w=0.2kro=[(1-So,-Sw)/(1-So,-Siw)]3krw=O.S[(Sw-S/w)/(1-So,-S;w))3,forSw~(1-So,)p10md4~y/Fig.4-0lagonalandparallelgridsusedtomodelquarterofananisotropicfive-spot.SPEReservoirEngineering,August1990100...------------------,800.20.40.6DiagonalgridParalielgrid0.8OriginalHydrocarbonPoreVol.Injected1.2Fig.5-Predictedrecoveryinaquarterofananisotropicfivespot:diagonalandpara"elgrids.TABLE2-PARAMETERSFORWATERFLOODPROBLEMSQuarterFive-Spoton40-AcrePatternAreaReservoirthickness,ft200Permeability(8=20°),mdkmaxkminPorosityInitialpressure,psiaInitialwatersaturationInitialgassaturationWaterviscosity,Jlw'cpWaterdensity,Ibm/ft3Separatoroildensity,Ibm/ft3Separatorgasdensity,Ibmlft3Rockcompressibility,psi-1Injectorandproducerwellboreradius,ftInjectorBHPlimit,psiaProducerBHPlimit,psia30150.107500.200.100.762.4530.06593x10-63.52,000100Water/OilRelativePermeabilitySameasinTable1Gas/OilRelativePermeabilitykro=(1-2Sg)3,forSg;;a0.5krg=1.5625Sg2,forSg;;a0.8Black-OilFluidPropertiesPressureBoJloBgJlgRs(psi)(RB/STB)(cp)(RB/Mscf)~(Mscf/STB)50.01.03903.60055.040700.008300.05000100.01.05553.02027.171800.008500.07500200.01.07252.46013.237300.009000.10750300.01.08452.1708.592500.009550.13875400.01.09551.9656.270800.010050.16750500.01.10701.8104.877950.010600.19500600.01.11851.6903.949450.011150.22125700.01.13001.6053.270000.011730.24875800.01.14151.5432.784950.012300.27500900.01.15301.4952.320000.012880.302501,000.01.16451.4652.097150.013500.328751,090.01.17501.4451.876500.014100.356001,100.01.17491.4461.865520.014170.356002,000.01.16601.5700.877600.020450.356004,000.01.14621.8450.567000.035700.35600generallyanisotropicsystems(Method1)isformulatedasanaturalextensionofthepreviousmethodandisdefinedbyT14=(qx-qxy)(qy-qxy)/3(qx+qy-2qxy),............(25)T23=T14+qxy,..................................(26)Tl3=[(kxxhlJ+(kxxhh](Tx)edge/4(kxxh),.............(27)T24=[(kxxhh+(kxxh)4](Tx)edge/4(kxxh),..............(28)TJ2=[(kyyhlJ+(kyyhh](Ty)edge/4(kyyh),.............(29)SPEReservoirEngineering,August199040(5E(51040080012001ime.daysMe1hodI-MethodII•••16002000Fig.6-Predictedoilrecovery,waterfloodInagenerallyanisotropicsystem.andT34=[(kyyhh+(kyyh)4](Ty)edge/4(kyyh),............(30)where(Tx)edge=qx-T14-T23.......................(31)and(Ty)edge=qy-T14-T23..........................(32)Theaboveformulationisforqxyf;O.Ifqxy
展开阅读全文
  石油文库所有资源均是用户自行上传分享,仅供网友学习交流,未经上传用户书面授权,请勿作他用。
0条评论

还可以输入200字符

暂无评论,赶快抢占沙发吧。

关于本文
本文标题:SPE-18442-PA
链接地址:http://www.oilwenku.com/p-70341.html

当前资源信息

吾王的呆毛

编号: 20180607204940407432

类型: 共享资源

格式: PDF

大小: 422.17KB

上传时间: 2018-06-08

相关搜索

广告招租-6
关于我们 - 网站声明 - 网站地图 - 资源地图 - 友情链接 - 网站客服客服 - 联系我们
copyright@ 2016-2020 石油文库网站版权所有
经营许可证编号:川B2-20120048,ICP备案号:蜀ICP备11026253号-10号
收起
展开