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The MoMaS Reactive Transport Benchmark Presentation of the Models

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18 pages
The MoMaS Reactive Transport BenchmarkPresentation of the Models1 2Jérôme Carrayrou Michel Kern1Université Louis Pasteur, IMFS, Strasbourg, France2INRIA Rocquencourt, FranceModelling Reactive Transport in Porous MediaStrasbourg, January 21-24, 2008Carrayrou & Kern (IMFS,& INRIA) Reactive transport benchmark 23rd Jan 2008 1 / 13Plan1 Introduction2 Mathematical model3 Geometry and chemical data4 ConclusionsCarrayrou & Kern (IMFS,& INRIA) Reactive transport benchmark 23rd Jan 2008 2 / 13ConsequencesSynthetic chemical systemSmall number of species / reactionsUnrealistic stoichiometry, equilibrium constantsSeveral levels of difficultyMotivationDesign decisionsCompare numerical methods and codes for reactive transportBias towards nuclear waste disposalFixed physical / chemical modelSimple chemical system, with high numerical complexityNo thermodynamic databaseCarrayrou & Kern (IMFS,& INRIA) Reactive transport benchmark 23rd Jan 2008 3 / 13MotivationDesign decisionsCompare numerical methods and codes for reactive transportBias towards nuclear waste disposalFixed physical / chemical modelSimple chemical system, with high numerical complexityNo thermodynamic databaseConsequencesSynthetic chemical systemSmall number of species / reactionsUnrealistic stoichiometry, equilibrium constantsSeveral levels of difficultyCarrayrou & Kern (IMFS,& INRIA) Reactive transport benchmark 23rd Jan 2008 3 / 13Time discretizationExplicit /implicitLower /higher ...
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CMI(nreK&uoryarratiacReA)RIIN,&FSkramdr322naJ1800trvespantborchen/13
The MoMaS Reactive Transport Benchmark Presentation of the Models
1 Université Louis Pasteur, IMFS, Strasbourg, France
2 INRIA Rocquencourt, France
Modelling Reactive Transport in Porous Media
Strasbourg, January 21-24, 2008
Jérôme Carrayrou 1 Michel Kern 2
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2
Introduction
Mathematical model
4
3
1
Conclusions
3
Geometry and chemical data
Plan
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Design decisions
Motivation
Compare numerical methods and codes for reactive transport Bias towards nuclear waste disposal Fixed physical / chemical model Simple chemical system, with high numerical complexity No thermodynamic database
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btropsnartevitcaReA)RIIN,&FSIMn(
Design decisions Compare numerical methods and codes for reactive transport Bias towards nuclear waste disposal Fixed physical / chemical model Simple chemical system, with high numerical complexity No thermodynamic database
Motivation
Consequences Synthetic chemical system Small number of species / reactions Unrealistic stoichiometry, equilibrium constants Several levels of difficulty
1/30038Jan223rdmarkenchryuoK&reCraar
mp/iciliplExiticehgidrorwoLth/reTiitazitnoemidcserO,etrreSocroortnlolGlDba,DSA,NAEropsilttniTgioetrateornottoiterasablaudilpuoC)dehoetgminaterOpdspaitredAemtseviteuriep(h,ressticaJ2n0048amkr32drortbenchvetranspeR)Aitca&,SFIRNIer&KIMn(raarouyrroCym,meitemC)UP,...ebraralgineal,noitulosmetsysarnelin-non(toew
Methods
Finite element / volumes, Ellam, particles, ...
Stability, numerical diffusion, efficiency
Main questions
31/
Space discretization
Features
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Space discretization Features Stability, numerical diffusion, efficiency Methods Finite element / volumes, Ellam, particles, ...
Time discretization Explicit /implicit Lower /higher order Adaptive time step (heuristic, residual based)
13
Main questions
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CPU time, memory
Coupling methods Operator splitting To iterate or not to iterate, OS error control Global DSA, DAE, Newton (non-linear system solution, linear algebra, ...)
Space discretization Features Stability, numerical diffusion, efficiency Methods Finite element / volumes, Ellam, particles, ...
Time discretization Explicit /implicit Lower /higher order Adaptive time step (heuristic, residual based)
(IMFKernNRIAS,&IaCor&urryahmncbertdJ3rk2arvitcaeR)opsnarte
Flow and Transport
13
ωT M j t + T F j + r . ω uT M j − r . D r T M j = ω X k ac k , j f k ( C i , Cc k )
Dispersion tensor D = α T ω | u | I + ( α L α T ) ω u |u | u T M j (resp. T F j ) total mobile (resp. immobile) for concentration component j , kinetic source term, rate f k ( C i , Cc k )
Saturated flow : Darcy’s law ( ω u = K r h r . ( ω u ) = 0
Transport model
20an5/08
ω porosity, u Darcy velocity
atrvnoioasfmj=sTisaXaSjjCsisesnojjCSi=KsiNxMYj=1Cs=iiKxNYM=jX1iasaasMawnlioctuimiuqerbilmehClacirdJan200chmark23
NxM X as ij X j + as i , s S CS i j = 1
681/3
Reactions
NxM X a ij X i C i j = 1
A)RIacReFSIMIN,&ropsnebtevitnartisCS=1ascSXi=S+Nre(nuoK&arryCirai+jCai=1XicM+NXjSTiSCjisa1=iXScN
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NxM C i = K i Y X ja ij j = 1
NxM CS i = Ks i Y X jas ij S as is j = 1
NxM X a ij X i C i j = 1
Reactions
NxM X as ij X j + as i , s S CS i j = 1 Mass action laws
3/1enchortbanspvetr0068aJ2n32dramkr
uqlibiirehimacelCumrrCaroayKeu&(IrneactIA)R&INRMFS,ebcnoptrarsnvite0820andJ3rk2arhm
Reactions
NxM X a ij X i C i j = 1
NxM X as ij X j + as i , s S CS i j = 1 Mass action laws
NxM CS i = Ks i Y X jas ij S as is j = 1
NxM C i = K i Y X ja ij j = 1
Conservation of mass
NcS TS = S + X as is CS i i = 1
NcM NcS T j = X j + X a ij C i + X as ij CS i i = 1 i = 1
31/6
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