Compressible porous media models by use of the theory of mixtures.pdf

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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