Comparison of Network Generation Techniques for Unconsolidated Porous Media

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ComparisonofNetworkGenerationTechniquesforUnconsolidatedPorousMediaRiyadhAl-Raoush,KarstenThompson,andClintonS.Willson*ABSTRACTFirst,wediscussnetworkmodelsandtechniquesfordeterminingthepore-scalepropertiesandcharacteris-Whilenetworkmodelsofporousmaterialshavetraditionallybeentics;second,wedescribetheregularandrandomporousconstructedusingregularordisorderedlattices,recentdevelopmentsallowthedirectmodelingofmorerealisticstructuressuchasspheremediasystemsusedtovalidateandevaluatethetech-packings,microtomographicimages,orcomputer-simulatedmateri-niquesweareproposing;third,wepresenttheimprove-als.Oneoftheobstaclesinthesenewerapproachesisthegenerationmentsmadetotwonetworkgenerationtechniquesofnetworkstructuresthatarephysicallyrepresentativeoftherealbasedontheirknownlimitations;fourth,wevalidatesystems.Inthispaper,wepresentandcomparetwodifferentalgo-thesealgorithmsusingregularpackings;andfinally,werithmstoextractporenetworkparametersfromthree-dimensionalevaluateandcomparethenetworkrepresentationsofimagesofunconsolidatedporousmediasystems.Thefirstapproach,randompackingsgeneratedbythesetechniques.whichutilizesapixelizedimageoftheporespace,isanextensiontounconsolidatedsystemsofamedial-axisbasedapproach(MA).ThesecondapproachusesamodifiedDelaunaytessellation(MDT)oftheBACKGROUNDgrainlocations.ThetwoalgorithmsarevalidatedusingtheoreticalEarlymodelsdevelopedtoaccountforpore-scalepackingswithknownpropertiesandthenthenetworksgeneratedpropertiesidealizedtheporespaceascollectionsoffromrandompackingarecompared.Fortheregularpackings,bothcapillarytubesandprovidedsimpleanalyticalsolutionsmethodsareabletoprovidethecorrectporenetworkstructure,includ-ingthenumber,size,andlocationofinscribedporebodies,thenum-topredictcontinuum-scalepropertiessuchasperme-ber,size,andlocationofinscribedporethroats,andtheconnectivity.ability.However,thesemodelsfailedtoincorporatetheDespitethegoodagreementfortheregularpackings,therewereinterconnectivityoftheporespace.Thustheideaofdifferencesinboththespatialmappingandstatisticaldistributionsinrepresentingtheporespaceasatwo-orthree-dimen-networkpropertiesfortherandompackings.Thediscrepanciesaresionalnetworkemergedfromthepioneeringworkbyattributedtothepixelizationatlowresolution,non-uniquenessoftheFatt(1956a,b,c).Duetothecomplexityofthepore-inscribedpore-bodylocations,anddifferencesinmergingprocessesspacemorphology,theporebodiesandthroatsareusu-usedinthealgorithms,andservetohighlightthedifficultyincreatingallyrepresentedbysimplifiedshapes.Porebodieshaveauniquenetworkfromacomplex,continuumporespace.beenrepresentedbyspheresorcubes,whileporethroatshavebeenrepresentedbycylindersorotherductswithnon-circularcross-sections.Althoughnet-Waterandsolutetransportandthedistributionworkmodelscanbetwo-orthree-dimensional,two-ofphasesinsubsurfacesystemsaredirectlyre-dimensionalnetworkshavesignificantlimitationsinlatedtothegeometryandthetopologyoftheporespacehowtheyrepresenttheinterconnectivityofrealthree-andcanhaveastronginfluenceoncontinuumscaledimensionalmedia(ChatzisandDullien,1977).Com-properties.Whilemanyprocessesrelatedtositeassess-monthree-dimensionalnetworksarerandom(e.g.,mentandremediationareusuallystudiedusingacontin-LowryandMiller,1995)orcubiclatticeswithcoordina-uumapproach,pore-scalemodelingisconsideredapow-tionnumberofsix(orsmallerifbondsareremoved).erfultooltobetterunderstandthephysicalprocessesInactualporousmediasystems,however,theconnectiv-involvedandtodeterminemacroscaleconstitutiverela-ityisdistributed,andcanhavevalueslargerthansixtionshipsthatcanbedifficulttoobtainexperimentally.(Kwiecienetal.,1990).OnesolutiontothisproblemisThemostcriticalpartofconstructinganetworkmodeltousephysicallyrepresentativenetworks,whichdonotistheidentificationoftheporestructure.Thiscanbeemployanunderlyinglatticebutinstead,mapthetruedoneusingeitherusingcomputer-generatedporousme-porestructureofamediumontoanetwork(Bryantetdiasystemsorthroughtheuseofnon-destructiveim-al.,1993a).Consequently,theyretainmorecompletelyagingtechniques(e.g.,synchrotronmicrotomography).thetrueporemorphologyandanyinherentspatialcor-Thesignificantchallengeliesinthegenerationofnet-relations.workstructuresthatarephysicallyrepresentativeoftheNetworkmodelshavebeenusedtostudyawiderangerealmaterialsofinterest.ofsingleandmultiphaseflowprocessesincludingrela-Inthispaperwepresentthedevelopmentofandtivepermeability(BluntandKing,1990,Rajarametcomparetwoimprovedtechniquesforgeneratingphysi-al.,1997,FischerandCelia,1999);theeffectofporecallyrealisticnetworkmodelsofgranularporousmedia.structureonrelativepermeabilityandcapillarypressurehysteresisintwophasesystems(JerauldandSalter,R.Al-RaoushandC.S.Willson,Dep.ofCivilandEnvironmental1990);predictionofpermeability(Bryantetal.,1993a);Engineering,LouisianaStateUniv.,BatonRouge,LA70808;K.Thompson,Dep.ofChemicalEngineering,LouisianaStateUniv.,investigationofthefunctionalrelationshipbetweencap-BatonRouge,LA70808.Received6June2002.*Correspondingau-illarypressure,saturation,andinterfacialareas(Reevesthor(cwillson@lsu.edu).andCelia,1996);predictionofpermeabilitiesandresi-PublishedinSoilSci.Soc.Am.J.67:1687–1700(2003).SoilScienceSocietyofAmericaAbbreviations:MA,medial-axisbasedapproach;MDT,modifiedDe-launaytessellation.677S.SegoeRd.,Madison,WI53711USA1687