The MoMaS Reactive Transport Benchmark Presentation of the Models
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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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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
2
Introduction
Mathematical model
4
3
1
Conclusions
3
Geometry and chemical data
Plan
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
1/30038n2Jard23rkmachenbtropsnartevitca
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
Methods
Finite element / volumes, Ellam, particles, ...
Stability, numerical diffusion, efficiency
Main questions
31/
Space discretization
Features
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
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)
Flow and Transport
13
ω∂ T 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
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
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
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
