• / 12
  • 下载费用:5 下载币  

1-s2.0-S0013795215300296-main

关 键 词:
s2 S0013795215300296 main
资源描述:
awleyfaTheperwhicnbepatfracisotpywingapowerrelationwiththechangeoftheintersectionanglebetweentwofrac-lityoffntionsydrogngandintrinsickmasmedia,andrenderthehandlingofwaterflowpathandthefracturenetworksystemplaysasignificantroleindeter-methodtoevaluatetheequivalentpermeabilitytensorforthefracturedresseffectontheper-thatthein-siturockEngineeringGeology196(2015)171–182ContentslistsavailableatScienceDirectEngineeringlength,orientation,spacingandinterconnectivityofthefractures,anditisrelatedtothehydraulicperformanceofeachfracturewhichisgovernedbyitsroughnessandaperture(Liu,2005).stressesandtheembeddeddepthcanaffectitspermeabilitybecauseoftheireffectsonapertures.LeungandZimmerman(2012)proposedamethodforestimatingtwo-dimensionalmacroscopiceffectivehy-rockmasses.Specifically,thepermeabilityanisotropyoffracturedrockmassesisgreatlyaffectedbythegeometricfeatures,suchasdensity,etal.(2008)andRongetal.(2013)studiedthestmeabilityoffracturedrockmassesandshowedminingthepermeabilityinrockmasses.Theexistenceofdiscontinuitiesmakesahighdegreeofpermeabilityanisotropyinfracturedrockmasses(Zhang,2013).Theparametersofthedistributedfracturesdirectlygovernthehydraulicbehaviourofrockmassesinvolvingnumerousarbitrarilyorientedjointsandfaults.Highlyfracturedrockmassesaretreatedashomogeneousanisotropicporousmediawhentheconceptofrepresentativeelementaryvolume(REV)isapplicable.Leeetal.(1995),TalbotandSirat(2001),ZhouThedeterminationofthepermeabilityoffbeenstudiedbymanyresearchers.Parsons(1⁎Correspondingauthor.E-mailaddress:guowei.ma@uwa.edu.au(G.Ma).http://dx.doi.org/10.1016/j.enggeo.2015.07.0210013-7952/©2015ElsevierB.V.Allrightsreserved.inthefracturedrockrocksarethemainfloweffectandthespatialvariationofthefractureswerenotconsideredintheanalyticalmethod.Oda(1985)andOdaetal.(1987)developedamassesintractable.Discontinuitiesinhard1.IntroductionEffectiveevaluationofthepermeabiincreasinglyattractedresearchers'attethefieldsofgeotechnicalapplication,hvoirexploitation,civilengineering,minipositories,etc.(Berkowitz,2002).Thefaults,fracturesetsandcracks,makerofracturepatterns,thehydro-geometricanisotropyfactorgivesanaccuratecorrelationwiththepermeabilityan-isotropy.Ananisotropicconductivityindexisfurtherdefinedtoevaluatethedirectionalhydraulicconnectivityofthefracturesystem.Basedonthisapproach,thepermeabilityanisotropyofafracturenetworksystemcanbequicklyassessedthroughthecorrelationwiththehydro-geometricanisotropyfactorandtheanisotropicconduc-tivityindex.©2015ElsevierB.V.Allrightsreserved.racturedrockmasseshasduetoitsimportanceineology,petroleumreser-environmentalwastere-cdiscontinuities,suchasseshighlyheterogeneousapparentpermeabilityoffracture-rocksystems,includingbothregularfracture-matrixmodelsandheterogeneousfracturesystems.Thehet-erogeneousfracturesystemswerebuiltbyplacingfracturesinagivenpattern,suchasasquarepatternoratriplehexagonalpattern.Snow(1969)proposedananalyticalmethodtocalculatethepermeabilitytensoroffracturedrockmassesbasedonstatisticalinformationoffrac-tures.Therelationshipbetweenthefracturegeometryandtheperme-abilityanisotropyhasalsobeenassessed.However,thefinitesizeAnisotropicconductivityindexturesets.Varyingthenumberandlengthratioofthefracturesetsalsoaltersthepermeabilityanisotropy.InallPipenetworkmethodabilityanisotropyvariesfolloInvestigationofthepermeabilityanisotropyFengRen,GuoweiMa⁎,GuoyangFu,KeZhangSchoolofCivil,EnvironmentalandMiningEngineering,TheUniversityofWesternAustralia,CrabstractarticleinfoArticlehistory:Received18June2014Receivedinrevisedform28June2015Accepted22July2015Availableonline23July2015Keywords:Hydro-geometricanisotropyPermeabilityanisotropyFracturedrockmassesAhydro-geometricanisotropscalefracturedrockmasses.andhydraulicapertureprousingapipenetworkmethodlawtovalidatethecorrelatiooffracturenetworks.Fracturstudytheeffectsofdifferentthusonthepermeabilityanonthepermeabilityanisotrojournalhomepage:www.elsevier.com/locate/enggeoracturedrockmasseshas966)studiedtheoverallof2Dfracturedrockmassesy,WA6009,PerthAustraliactorisderivedforbettercorrelationwiththepermeabilityanisotropyoffield-hydro-geometricanisotropyfactorconsiderstheorientation,length,spacingtiesofadiscretefracturenetwork.NumericalsimulationsarecarriedoutbyhsimulatesthefracturesasconnectedanddirectedpipesobeyingDarcy'setweenthehydro-geometricanisotropyfactorandthepermeabilityanisotropyternsfromsimpletocomplexwithascaleof10mby10maregeneratedtoturedistributionsonthehydro-geometricanisotropyoffracturenetworksandropy.Itisfoundthattheaperturesizeanddistributionhaveasignificanteffectthataffectsthemainpermeabledirectionofthefracturenetworks.Theperme-Geologydraulicconductivitybyusingparametersoffracturenetwork,suchasfracturedensityandaperturedistribution.Theirworkisvalidforisotro-picnetworks.PermeabilitytensorswereusedtorepresentthehydraulicfeaturesoftheREVandthusforthesimulationofanequivalentcontin-uummodel.ThepermeabilitytensorcanprovideacomprehensiveInordertoconsiderthehighlyheterogeneousanddirectionallyde-pendentnatureofthefracturedrockmassesinnumericalsimulations,a2Dpipenetworkmodel(withaunitthicknessinthethirddirection)hasbeenpresentedtodeterminetheequivalentpermeabilityofthefracturedrockmasses(Lietal.,2014;Priest,1993).Inthispaper,ahydro-geometricanisotropyfactor(HAF)isproposedtoestimatethepermeabilityanisotropyinagivendirectionofafracturenetwork.DifferentfracturenetworkpatternswithdifferentHAFsaregenerated,andtheirpermeabilityanisotropyratios(PAR)areevaluatedbyapplyingthepipenetworkmethod.Themacroscopicpermeabilityanisotropyofthefracturedrockmassescausedbythegeometricanisot-ropy,includingthevariationofindividualfracturepermeability,isstud-ied.A2Danisotropicconductivityindexisalsointroducedtoquantifythedirectionalhydraulicconnectivityforaspecificfracturenetwork.2.Ahydro-geometricanisotropyfactor(HAF)forfracturenetworksThegeometricanisotropyandhydraulicanisotropyoffracturenet-172F.Renetal./EngineeringGeology196(2015)171–182insightintothepermeabilityanisotropyoffracturenetworksifitisreadilyavailable.However,insomecases,theinformationofafrac-turenetworkislimited,anddifficulttocollect.Forexample,deter-miningoftheprobabilitydensityfunctionsofrandomvariablesinthegeometriesoffracturenetworksisstillapracticalchallenge(Rongetal.,2013).Apartfromthederivationoftheequivalentpermeability,manyre-searcheshavealsofocusedonthephenomenaofpermeabilityanisotro-pyofafracturenetworksystemanditsorigin.BalbergandBinenbaum(1983)usedtheconductingstickmodeltostudytherelationshipbe-tweenthemicroscopicanisotropyandthepercolationthresholdofafracturesystem.Theirstudydidnotemphasisetherelationshipbe-tweenthefracturepatternsandtheanisotropyofthesystem.ZhangandSanderson(1995)definedapracticalgeometricanisotropyfactorAftodescribetheeffectsoforientationandspacingoffracturesonthepermeabilityanisotropy.Theirresultsshowedthatthefractureorienta-tionwasamainfactorcontrollingthegeometricanisotropyandtheper-meabilityanisotropy.However,theirmodeldidnotconsiderthehydraulicbehaviourofeachfractureandinterconnectivityeffectsonthepermeabilityanisotropy.Thetotalpermeabilityoffracturedrockmassesisgovernedbythepermeabilityofthefracturesystemandthepermeabilityoftherockmatrix.Whensimulatingthepermeabilityofafracturedhardrock,itisreasonabletoignorethepermeabilityofthematrixrock,andonlytoconsiderthepermeabilityoffracturenetworks.Therefore,theindividualpermeabilityofeachfractureinthenetworkcanaffectthemacroscopicpermeabilityofthefracturedrockmasses.Researcheshavealsoshownthatnotallthefractureswithinrockmassescontributetotheflow.Infact,onlyasmallportionofthefrac-turesisconductiveandcontributestofluidflow(LongandBillaux,1987;TalbotandSirat,2001).Densefracturenetworksarenotnecessar-ilyhydraulicallyconnected(Berkowitz,2002).Therefore,theconnectiv-ityhasimportanteffectsonthepermeabilityanisotropy.Percolationtheoryisaneffectivetooltocharacterizetheconnectivityoffracturenetworks.Generally,theissueofconnectivityofadiscretefracturenet-workmainlyconcernsthepercolationofthewholeregion(Berkowitz,1995;Robinson,1983;Sahimi,1993).Itfocusesonfracturenetworksrequiredtoconnectthespecificregion(percolatingstate).Differentin-dicatorshavebeenproposedtoinvestigatethepermeabilityofafrac-turedsystemwhenusingthepercolationtheory.HestirandLong(1990)andSahimi(1993)suggestedusingXf,theaveragenumberofin-tersectionsperfracture;whileDershowitzandHerda(1992)preferredusingaconductiveintensity,P32(P21in2D),whichisafracturearealintensityparameter(averagelengthperunitareaintwo-dimensionalcases).Thesetwoconnectivityindicatorscannotreflectthedirectionalpermeabilityofa3Dfracturenetwork.Morerecently,Xuetal.(2006)proposedaconnectivityindex,CI,toquantifytheconnectivityprobabil-itybetweentwopointsinspace.However,itcannotdescribethedirec-tionalityforaspecific3Dfracturenetworkmodel.Factorsthataffectthepermeabilityfeatures,suchasstress(BaghbananandJing,2008;TalbotandSirat,2001;Yangetal.,2010;Zhangetal.,2007;Zhouetal.,2008),andtemperature(Mooreetal.,1994;Summersetal.,1978)canalsobestudiedbythemethodsoffieldsurveys,laboratoryexperimentsandnumericalsimulations.How-ever,theyarebeyondthescopeofthisstudy.Anumberofnumericalsimulationmethodshavebeendevelopedforevaluatingthepermeabilityofafracturedrockmass.Thesecangen-erallybeclassifiedintothreecategories,namely,continuummodels,discretefracturenetworkmodelsandhybridmodels(Neuman,2005).Eachmethodhasitsowndistinctadvantagesanddisadvantagesandsuitsdifferentsituationsandproblems.Afracturedporousmediumoradualporositymediumisalwaysanalysedbycouplingfracturenetworkswithapermeablematrix.Thesehybridmodelsexplicitlydelineatethefracturesystemandcon-siderthepermeabilityofthematrix.Whenthematrixislesspermeable,thefluidflowinthediscretefracturenetworkbecomesdominantinthefracturedrockmass.worksaretwomajorcausesofthepermeabilityanisotropyofafrac-turedrockmass.Thegeometricanisotropyoffracturenetworksiscausedbythenon-uniformdistributionofgeometricproperties,suchastheorientation,length,andspacingetc.,whilethehydraulicanisotro-pyarisesfromhydraulicheterogeneity,whichisthenon-uniformdistri-butionofthehydraulicpropertiesoffractures,suchasapertureandroughness.Inordertoinvestigatethegeometricanisotropyandhydraulican-isotropyofafracturenetwork,acombinedhydro-geometricanisotropyfactor(HAF)isproposed.Ininvestigatingtwoarbitraryorthogonaldi-rectionsXandYwithasamplingareaLxandLyasshowninFig.1,theequivalentpermeabilityinagivendirectioncanbeevaluatedas,keq¼QAμ∇p;ð1Þwherekeqistheequivalentpermeabilityofthefracturedrockmassinastudydirection(directionX,forexample).QistheoutflowratefromtheareaAataspecificlengthofLx,and∇pisthepressuregradientinthedi-rection.μisthedynamicviscosityofthefluid.IfthesameboundaryconditionwithaconstantpressuregradientisassumedinboththeXandtheYdirectionsandconsideringaunitthick-nessofthemodel,theratiooftheequivalentpermeabilityofthetwoor-thogonaldirectionscanbeexpressedas,keq;xkeq;y¼QxQyLxLy;ð2ÞFig.1.Hydro-geometricanisotropyoffracturesystem.173F.Renetal./EngineeringGeology196(2015)171–182wherethesubscriptsxandydenotesthetwodirections.Intheabovederivation,linearvariationofhydraulicheadisassumed,whichissup-portedbyLongetal.(1982)andOda(1985)ifasufficientnumberoffracturesarecontainedandwellconnected.Thepressuregradientinthestudydirectionisuniformoverthewholeflowregion.Duetotherandomnessofthefractures,QxisdifferentatdifferentsectionsperpendiculartotheXdirection.Inordertoobtaintheaver-agedflowrateQxfromthediscretefracturesoverthevolume,atypicaleffectivefractureithathasthedipangleofθi(0≤θi≤90°)withrespecttotheXdirectioninthesamplingareaisconsidered,asshowninFig.1.AnarbitrarycrosssectionalareaAxthatisperpendiculartotheXdirectionisselectedtocalculatetheflowrate.Thus,theflowratethroughtheareaAxisQx=∑qi,whereqiistheflowrateofthefracturethatintersectswithAx.IftheareaAxscansalongtherangeLx,theoverallvolumetricav-eragedflowrateQxcanbeobtainedasfollows,Qx¼Xnxi¼1λiqiLxLy;ð3Þwherenxisthenumberoftheeffectivefracturesinthearea;λiisthelengthweightfactorwithorientationeffectconsideredofthefractureithatisscannedbytheareaAx.Itcanbeobtainedas:λi¼licosθiLx:ð4ÞHere,liistheeffectivefracturelength(excludingthedeadtipsateachend),andqiistheflowrateforasinglefracture,whichcontainstheinformationofthecharacteristichydraulicbehaviourofeachfrac-tureinthesystem.Theroughnessandfracturewidtharetwokeypa-rametersgoverningthefluidflowinthefracture.Usually,theeffectsofroughnessandmechanicalapertureonthefracturepermeabilitycanbedescribedbytheirhydraulicapertures(Renshaw,1995).There-fore,qiisfoundtobeqi¼∇pcosθia3i12μ;ð5Þwhereaiistheequivalenthydraulicaperture,whichreflectshydraulicpropertyofeachfracturethatwasinfluencedbythemechanicalaper-tureandtheroughnessofthefracturewall.Eq.(5)alsoimpliesthattheflowinthefractureisalaminarflow;therefore,thecubiclawisap-plicable.TheonsetofReynoldsnumberfromtransitiontoaturbulentflowvariesfrom1800to4000foraparallelsmoothplatemodel,whichcanbeloweredbythesurfaceroughnessofthefracture(Parsons,1966).Itisworthmentioningthatthefracturesinvolvedintheanalysisshouldbeeffective.Aneffectivefracturemeansthatthefractureshouldcontributetothefluidflowfromoneboundarytotheoppositebound-aryinthesurveydirection.Inthisway,thefractureconnectivitycanbetakenintoconsideration.Anyisolatedfractureswillbeidentifiedau-tomaticallyandexcludedfromthecalculation.Theorientationandlengthofthefracturesareconsideredbythelengthweightfactorλandtheflowrateqofeacheffectivefracture.Theflowrateinthederiva-tionalsoreflectsthehydrauliccharacteristicsofeachfracture.Finally,thesummationofqiandtheaveragingcrosssectionflowrateQoverthewholedomain,reducetherandomnesseffectofafracturedistribu-tion.Inthisway,italsoreflectsthelengtheffectofeachfracture,thespacingoffracturesetsandtheintensityofthefracturesystem,andmakestheresultsstatisticallymoreaccurate.FortheYdirection,theoverallvolumetricallyaveragedflowrateQycanbeobtainedusingthesameapproach.Then,theHAFdenotedbyGfisdefinedbytheratioofthevolumetricallyaveragedequivalentpermeabilityinthetwoorthogonaldirectionsas,Gf¼limLx→∞Ly→∞keq;xkeq;y¼limLx→∞Ly→∞QxQyLxLy:ð6ÞBysubstitutingEqs.(4)and(5)intoEq.(3),andthensubstitutingEq.(3)intoEq.(6),thefactorGfisreformulatedasGf¼limLx→∞Ly→∞Xnxi¼1licos2θia3iXnyj¼1ljsin2θja3j:ð7ÞWhenthesamplingareatendstobeinfinity,thescaleandrandom-nesseffectsofthefracturedistributioncanbeeliminated.Therefore,theHAFcanbeusedtoestimatethepermeabilityanisotropytogetherwiththehydro-geometricinformationofthefracturedrockmasses.Inpractice,itisoftendifficulttocollectallinformationconcerningthefractures.Inmostcases,undergroundinformationoffracturegeom-etryisderivedfromboreholeloggings.Thenumberofopenfracturesthatintersectaboreholeandtheirorientationscanbedetermined,whereasthefracturedensityandthefracturelengthsaredifficulttoes-timatefromaloggingmethod(LongandWitherspoon,1985).Inaprac-ticalcalculation,thecrosssectionalflowratecanbeaddedupbycountingthefracturesthatintersectwiththescanlinesorboreholesandbeaveragedoverthescanlinesorboreholelinesaccordingly.Infact,thelengthweightfactorλreflectsthecharacteristicsoflengthandorientationdistributionsoffractures.Togetherwiththepositiondistributionoffractures,thelengthweightfactorλcanreflecttheprob-abilityofafracturethatisintersectedb
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:1-s2.0-S0013795215300296-main
链接地址:http://www.oilwenku.com/p-70390.html

当前资源信息

吾王的呆毛

编号: 20180607204341689282

类型: 共享资源

格式: PDF

大小: 2.69MB

上传时间: 2018-06-08

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