ORIGINALARTICLEHowtoestimateisotopefractionationsofaRayleigh-likebutdiffusion-limiteddisequilibriumprocess?ZiXuanGuan1,2•YunLiu2,3,4Received:21September2022/Revised:25November2022/Accepted:28November2022/Publishedonline:12December2022©TheAuthor(s),underexclusivelicencetoSciencePressandInstituteofGeochemistry,CASandSpringer-VerlagGmbHGermany,partofSpringerNature2022AbstractTheRayleighdistillationisotopefractionation(RDIF)modelisoneofthemostpopularmethodsusedinisotopegeochemistry.Numerousisotopesignalsobservedingeologicprocesseshavebeeninterpretedwiththismodel.TheRDIFmodelprovidesasimplemathematicsolutionforthereservoir-limitedequilibriumisotopefractionationeffect.Duetothereservoireffect,tremendouslylargeisotopefractiona-tionswillalwaysbeproducedifthereservoirisclosetobeingdepleted.However,inrealsituations,manyprerequisitesassumedintheRDIFmodelareoftendifficulttomeet.Forinstance,itrequirestherelocatedmaterials,whichareremovedstepbystepfromonereservoirtoanotherwithdifferentiso-topecompositions(i.e.,withisotopefractionation),tobeiso-topicallyequilibratedwithmaterialsinthefirstreservoirsimultaneously.This‘‘quickequilibriumrequirement’’isindeedhardtomeetifthefirstreservoirissufficientlylargeortheremovalstepisfast.Thewholefirstreservoirwilloftenfailtore-attainequilibriumintimebeforethenextremovalstarts.ThisproblemledtheRDIFmodeltofailtointerpretisotopesignalsofmanyrealsituations.Hereadiffusion-coupledandRayleigh-like(i.e.,reservoir-effectincluded)separationprocessischosentoinvestigatethisproblem.Wefindthatthefinalisotopefractionationsarecontrolledbyboththediffusionprocessandthereservoireffectsviathedisequilibriumsepa-rationprocess.Duetoitscomplexity,wechoosetouseanumericalsimulationmethodtosolvethisproblembydevel-opingspecificcomputingcodesfortheworkingmodel.Accordingtooursimulationresults,theclassicalRDIFmodelonlygovernsisotopefractionationscorrectlyatthefinalstagesofseparationwhenthereservoirscale(orthicknessofthesystem)isreducedtotheorderofmagnitudeofthequotien...
