How to estima...rium process__Zi Xuan Guan.pdf

ORIGINAL ARTICLEHow to estimate isotope fractionations of a Rayleigh-likebut diffusion-limited disequilibrium process?Zi Xuan Guan1,2Yun Liu2,3,4Received:21 September 2022/Revised:25 November 2022/Accepted:28 November 2022/Published online:12 December 2022 The Author(s),under exclusive licence to Science Press and Institute of Geochemistry,CAS and Springer-Verlag GmbH Germany,part ofSpringer Nature 2022Abstract The Rayleigh distillation isotope fractionation(RDIF)model is one of the most popular methods used inisotope geochemistry.Numerous isotope signals observed ingeologicprocesseshavebeeninterpretedwiththismodel.TheRDIF model provides a simple mathematic solution for thereservoir-limitedequilibriumisotopefractionationeffect.Dueto the reservoir effect,tremendously large isotope fractiona-tions will always be produced if thereservoir is close to beingdepleted.However,in real situations,many prerequisitesassumed in the RDIF model are often difficult to meet.Forinstance,itrequirestherelocatedmaterials,whichareremovedstep by step from one reservoir to another with different iso-tope compositions(i.e.,with isotope fractionation),to be iso-topically equilibrated with materials in the first reservoirsimultaneously.This quick equilibrium requirement isindeed hardto meet if the firstreservoirissufficiently largeortheremovalstepisfast.Thewholefirstreservoirwilloftenfailto re-attain equilibrium in time before the next removalstarts.This problem led the RDIF model to fail to interpret isotopesignals of many real situations.Here a diffusion-coupled andRayleigh-like(i.e.,reservoir-effect included)separationprocess is chosen to investigate this problem.We find that thefinalisotopefractionationsarecontrolledbyboththediffusionprocess and the reservoir effects via the disequilibrium sepa-ration process.Due to its complexity,we choose to use anumerical simulation method to solve this problem by devel-oping specific computing codes for the working model.Accordingto oursimulationresults,theclassical RDIF modelonlygovernsisotopefractionationscorrectlyatthefinalstagesof separation when the reservoir scale(or thickness of thesystem)isreducedtotheorderofmagnitudeofthequotientofthediffusivityandtheseparationrate.TheRDIFmodelfailsinother situations and the isotope fractionations will be diffu-sion-limited when the reservoir is relatively large,or the sep-aration rate is fast.We find that the effect of internal isotopedistribution inhomogeneity caused by diffusion on the Ray-leigh-like separation process is significant and cannot beignored.This method can be applied to study numerous geo-logic and planetary processes involving diffusion-limiteddisequilibrium separation processes including partial melting,evaporation,mineral precipitation,core segregation,etc.Importantly,wefindthatfarmoreinformationcanbeextractedthrough analyzing isotopic signals of such disequilibriumprocesses than those of fully equilibrated ones,e.g.,reservoirsize and the separation rate.Such information may provide akey to correctly interpreting many isotope signals observedfrom geochemical and cosmochemical processes.Keywords Isotope fractionation Reservoir isotopeeffect Rayleigh-like distillation process Diffusionalisotope effect Numerical modeling Disequilibriumprocess Yun L1School of Earth and Space Science,Peking University,Beijing 100871,China2State Key Laboratory of Ore Deposit Geochemistry,Instituteof Geochemistry,Chinese Academy of Sciences,Guiyang 550081,China3International Center for Planetary Science,College of EarthScience,Chengdu University of Technology,Chengdu 610059,China4CAS Center for Excellence in Comparative Planetology,Hefei 230026,China Acta Geochim(2023)42(1):2437https:/doi.org/10.1007/s11631-022-00587-21 IntroductionThe isotope fractionations occurred during separationprocesses often involve the reservoir effect.Importantly,ifthe size of a reservoir is limited,tremendously significantisotope effects will appear at the end of the separationprocess.Numerous important geologic and planetary pro-cesses are related to such reservoir isotope effects,e.g.,partial melting,evaporation,mineral precipitation,andcore segregation.To deal with such isotope effects,theRayleigh distillation isotope fractionation(RDIF)modelhas been widely applied to those processes.For instance,the RDIF was used as the theoretical basis for quantitativeinterpreting isotope fractionations during crystallizationandmeltingprocessesinigneousrocksystems(Morse 2006),determining the natural gas genesis,sourcerock type,maturity,and calculating the potential gas rate ofthe source rock(Clayton 1991;Kinnaman et al.2007),studying the evaporation isotope effects in water forobtaining information of the humidity and temperaturefactors on the surface of the water(Stewart 1975;Bar-Matthews 1996;Worden et al.2007),determining theextent of volatiles loss from samples such as tektites,chondrites,and rock samples from the terrestrial planets(Ritcher et al.2002;Wimpenny et al.2019),etc.Tradit