pegase project developments in marthe code

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1、PEGASEProjectDevelopmentsinMARTHEcodeDominiqueTHIERYJun200112 LangmuirandFreundlichsorption1.1ImplementationintheMARTHEcodeSorptionwithLangmuirandFreundlichisothermshasbeenimplementedinMARTHE(Thiéry1990,1993,1994,1995).a)LangmuirisothermTheclassicalLangmuirsorptioni

2、sothermnotationfortherelationbetweensolidphaseconcentrationSMandliquidphaseconcentrationCis:With:SM=Solidphasemassconcentration[kg/kg]C=Liquidphasevolumetricconcentration[kg/m3]Q=Totalsitesforsolidphaseconcentration[kg/kg]KL=Langmuirconstant[m3/kg]Asamatteroffactitism

3、orephysicalandmorepracticaltowritethisrelationintermofsolidphasevolumetricconcentrationSV(massofproductperterrainvolume).SV=rb.SM.IthasthenthesamedimensionthantheliquidphaseconcentrationC(andisexpressedinthesameunit).rb=Drysoildensity[kg/m3](about1600 kg/m3forasolclas

4、sicalsoil).Withthesevariables,Langmuirisothermwrites:orsimpler,indimensionalform,asusedinMARTHE:With:·CREF=1/KL=Referenceconcentration[kg/m3].Itistheliquidphaseconcentrationabovewhichtheeffectofthesolidphaseishalved.·SVMAX=rb.Q=Maximalsolidphasevolumetricconcentration

5、[kg/m3].Itisthesolidphasevolumetricconcentration,whichcorrespondstoaninfiniteliquidphaseconcentration.b)FreundlichisothermTheclassicalFreundlichsorptionisothermnotationfortherelationbetweensolidphaseconcentrationSMandliquidphaseconcentrationCis:SM=KF.CB12 With:B=Exp

6、onent(generally<1)KF=Freundlichconstantinunit[m3/kg]BItshouldbenotedthatKFunitisgenerallycomplexbecauseitdependsonexponentB.UsingsolidphasevolumetricconcentrationSV,Freundlichisothermwrites:SV=KFV.CBWith:KFV=rb.KF=VolumetricFreundlichconstantin[kg/m3](1-B)InMARTHE,Fre

7、undlichisothermisdescribedby2parameters:·KFV=rb.KF=VolumetricFreundlichconstantin[concentrationunit](1-B).·A2=B(Dimensionlessexponent)Remarks:·whenB=1thisisothermbecomeslinearwithKFVidenticaltoavolumetricRho_kd(dimensionless)·SettingItappearsthatSV = C(whichcorrespond

8、stoRho_kd=1)whenC = CREF·ExceptwhenB=1,whenC=0theratioSV/C->infinite,whichcorrespondstoaretardationfactorequaltoinfinity.1.1