A dual-porosity model for simulating the preferent

WATERRESOURCESRESEARCH,VOL.29,NO.2,PAGES305-319,FEBRUARY1993ADual-PorosityModelforSimulatingthePreferentialMovementofWateJrandSolutesinStructuredPorousMediaH.H.GERKElANDM.T.VANGENUCHTENU.S.SalinityLaboratoη，USDA,ARS,Riverside,CaliforniaAone-dimensionaldual-porositymodelhasbeendevelopedforthepurposeofstudyingvariablysaturatedwaterfiowandsolutetransportinstructuredsoilsorfracturedrocks.Themodelinvolvestwooverlayingcontinuaalthemacroscopiclevel:amacroporeorfractureporesystemandalesspermeablematrixporesystem.Waterinbothporesystemsisassumedtobemobile.VariablysaturatedwaterfiowinthematrixaswellasinthefractureporesystemisdescribedwiththeRichards'equation,andsolutetransportisdescribedwiththeconvection-dispersionequation.Transferofwaterandsolut~~sbetweenthetwoporeregionsissimulatedbymeansoffirst-orderrateequations.Themasstransfertermforsolutetransportincludesbothconvectiveanddiffusivecomponents.Theformulationleadstotwocoupledsystemsofnon1inearpartialdifferentialequationswhichweresolvednumericallyusingtheGalerkinfiniteelementmethod.Simulationresultsdemonstratethecomplicatednatureofsolut巳l巳achinginstructured,unsaturatedporousmediaduringtransientwaterfiow.Sensitivitystudiesshowtheimportanceofhavingaccurateestimatesofthehydraulicconductivitynearthesurfaceofsoilaggregatesorrockmatrixblocks.Theproposedmodeliscapableofsimulatingpreferentialfiowsituationsllsingparameten,whichcanberelatedtophysicalandchemicalpropertiesofthemedium.INTRODUCTIONPorousm巳diaoftenexhibitavarietyofhet巳rogenelÏties，suchasfractures,fissures,cracks,andmacroporesorinter­aggregatepores,andsometimesalsoshowdynamicíinstabil­itiesofth巳wettingfrontduringinfiltration.Thesemicro­scopicstructuresorprocessesaffectwaterandsolutemovementatthemacroscopicallevelbycreatingnonuni啕formflowfieldswithwidelydifferentvelocities.Suchphe­nomenaareoftenrefemedtoaspreferentialflow[Beven,1991].Th巳yhavebeenextensivelystudiedforexploitationoffissuredgroundwaterandpetroleumreservoirs[Barenblattetal.,1960;WarrenandRoot,1963].Similarprobl巳msarereportedalsoforflowandtransportinunsaturat巳dfracturedrocks[EvansandNicholson,1987;PruessandWang,1987;Wa晖，1991],formacroporousorstructuredfielldsoils[BevenandGermann,1982;Nielsenetal.,1986;SteenhuisandParlange,1.99月，anclevenforseeminglyhomogeneouscoarse-texturedsoils[HiUandParlangι1972;Glassetal.,1989;Kung,1990a,b;BakerandHillel,1991].Preferentialflowleadstoanappan~ntnonequilibniumsituationwithrespecttothepressureheadorthesoluteconcentration,orboth[BrusseαuandRao,1990;Wang,1991],andsevere1ylimitsourabilitytopredlÌctflowandtranspo口proæssesinundisturbedmedia.Flowandtransportinstructuredporousmediaarefre­quentlydescribedusingdouble-porosity(ordual)mode1s.Suchanapproachassumesthatthemediumconsistsoftworegions,oneassociatedwiththemacropor巳orfracturenetworkandtheotherwithalesspermeableporesystemofsoilaggregatesorrockmatrixblocks.Double-porositymod­elsmaybeobtainedusingvolumeaveragingtechniques[Longetal.,1982;Moench,1984]or,alternatively,withth巳methodofhomogenization[Arbogastetal.,1990;Hornung1NowatDestedt,Germany.ThispaperisnotsubjecttoU.S.copyright.Publishedin1993byth巳Am巳ricanGeophysicalUnion.Papernumber92飞NR02339.αndShowalter,1990]whichassumesthatthemediumisperiodicatasmall巳rscale.Bothmethodsyieldequivakntresultsatthemacroscopicscale[WheatcraftandCushman,1991]forsingle-phaseflowanddiffusion-typemodels.Dual­porositymodelsassum巳thatbothwaterflowandsol.utetransportcanbedescribedbytwoequationswhich:arecoupledusingatermcharacterizingtheexchangeoffluidorsolùtesbetweenthetwoporeregions.Specialcasesinclude(1)compartmentorfìrst-orderratemodelsinwhÌChflowortransportbetweenthematrixblocksisassumedtobenegligible,(2)fìssuredmediummodelswhich,inaddition,assumethestoragetermforthefissurestobenegligible，自，nd(3)microstructuremod巳lswhichconsiderthedynamicsofflowandtransportatthelocalscaleofindividualmatrixblocks[HornungandShowalter,1990].Alargenumberofmodelsusingthetwo-domainormu1ti­domainconcepthavebeenus巳dtodescribewaterfiowand/orsolutetransportinmacroporoussoils[e.g.,Edwardsetal.,1979;HoogmoedandBouma,1980;BevenandGermann,1981;Davidson,1985;BruggemanandMo­staghimi,199日，unsaturatedfracturedrocks[Berkowitzetal.,1988;Dudleyetal.,1988],andfissuredgroundwatersystems[Barenblattetal.,1960;DuguidandLee,1977;Bibby,1981].Compartmentmodelshav巳beensuggestedforflowinfracturedreservoirsandsolutetransportinstruc­turedsoils[WarrenandRoot,1963;CoatsandSmith,1964;vanGenuchtenandWierenga,1976].Severalauthorsalsoassumedaspecifìcgeometryofthemacroporesorfracturesforwaterflow[WangandNarasimhan,1985;Pruessetal.,1990α]orsolutetransport[NeretnieksandRasmuson,1984;vanGenuchtenandDalton,1986].Mostofthesemodelsarelimitedtoconditionsofwat巳rsaturationorsteadystatefiow,towaterftowonly,ortoconditionsforwhichfloworstora,geinoneporesystemcanb巳neglected.Othershaveconsider­ablysimplifi巳dtherepresentationofthefractureandmatrixblockgeom巳try.Unfortunately,well-definedgeometry­basedmodelsaredifficulttoapplytoactualfieldsituatíonssincetheyrequireanexcessiveamountofinformationaboutthegeometryofthestruct