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ID:34520245
大小:2.06 MB
页数:39页
时间:2019-03-07
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1、ht.1.EngngSri.Vol.20.No.6.pp.691-135.1982OOZO-7225/82/060697-39sO3.WtlPrintedinGreatBritain.PergamonPressLtd.COMPRESSIBLEPOROUSMEDIAMODELSBYUSEOFTHETHEORYOFMIXTURESRAYM.BOWENRiceUniversity,Houston,TX77001,U.S.A.Abstract-Thisarticleutilizestheusualformalismofthetheoryofmixturestoformu
2、latecompressibleporousmediamodels.Theformulationallowsfortheeffectsofimmiscibilityandvariablevolumefractions.Inaddition,itallowsfortheeffectsofporerelaxationbytreatingthevolumefractionsasinternalstatevariables.Anattemptismadetorelatethegeneralresultstoclassicalporousmediamodels.Inpar
3、ticular,circumstancesarepresentedwhichallowonetoproperlydefineaporepressureforeachfluidconstituent.Thisarticlealsocontainsthelinearporoelasticitymodelwhichresultsfromaformallinearizationofthefieldandconstitutiveequations.Onebriefsectionisdevotedtothespecializationofthislinearmodeltot
4、heonefirstproposedbyBiot.1.INTRODUCTIONTHISARTICLEconcernstheformulationofaporousmediamodelcapableofdescribingtheeffectsofimmiscibilityandvariablevolumefractions.Manymodelsbaseduponthetheoryofmixturesassumethatalloftheconstituentsinthemixturearecompletelymiscible.Suchanassumptionisno
5、talwaysapplicablewhenonewishestoapplythemodeltothestudyoffluidsflowinginaporoussolid.Inaddition,certainclassicalporousmediamodelsassumethateitherthefluidvolumefraction(porosity)isaconstantoritisdeterminedateachinstantoftimebythestrainofthesolidandoneotherstatevariablesuchasafluidpore
6、pressure.Theobjectiveofthisworkistoutilizethetheoryofmixturestoformulateamodelofamixtureconsistingofacompressibleelasticsolidandanarbitrarynumberofcompressibleimmisciblefluids.Thevolumefractionofeachfluidappearsasanindependentvariableintheconstitutiveequationsandisassumedtoobeyacerta
7、inratetypeconstitutiveequation.Simplystated,thevolumefractionsaretreatedformallylikeinternalstatevariables.Suchrelationshipshavebeenfoundusefulformodelswhichattempttodescribethecollapseofporesresultingfromexternalloading[l].Thegeneralityoftheassumedratelawsissuchthatonecanspecializet
8、hemodeltoone
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