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DispersiveTransport&Advection-dispersionEquation(ADE)Derivation(推导)oftheAdvection-DispersionEquation(ADE)3.NodensityeffectsFick’slawdescribesdiffusionofionsonamolecularscaleasionsdiffusefromareasofhighertolowerconcentrations.(Zheng&BennettFig.3.8.)Weneedtointroducea“law”todescribedispersiontoaccountfor(解释)thedeviation(偏差)ofvelocitiesfromtheaveragelinearvelocitycalculatedbyDarcy’slaw.WewillassumethatdispersionfollowsFick’slaworinotherwordsthatdispersionis“Fickian(费克方程)”.Thisisanimportantassumption;itturnsoutthattheFickianassumptionisnotstrictlyvalid(有效的)nearthesourceofthecontaminant.AdvectivefluxD*istheeffectivemoleculardiffusioncoefficient[L2T-1]fA=qxcFigurefromFreeze&Cherry(1979)FigurefromWangandAnderson(1982)Derivation(推导)oftheADEfor1Duniformflowand3Ddispersion(e.g.apointsourceinauniformflowfield)DefinitionoftheDispersionCoefficientina1DuniformflowfieldADEfor1Duniformflowand3DdispersionSimplerformoftheADEEffectsofdispersionontheconcentrationprofileEffectsofdispersiononthebreakthroughcurveFigurefromWangandAnderson(1982)BreakthroughCurve(浓度比值和时间的曲线)FigurefromFreeze&Cherry(1979)MacroscopicDispersion(causedbythepresenceofheterogeneities(异质性))Dispersivity()isameasureoftheheterogeneitypresentintheaquifer.Dispersionina3DflowfieldDispersionCoefficient(D)Ina3Dflowfielditisnotpossibletosimplifythedispersiontensortothreeprincipalcomponents.Ina3Dflowfieldwemustconsiderall9componentsofthedispersiontensor.GeneralformoftheADE:EffectoflongitudinalandtransversedispersivitiesontheplumeconfigurationFigure3.24.fromZheng&Bennett