1 The reactive transport benchmark J. Carrayrou Institut de Mécanique des Fluides et des Solides, Laboratoire d’Hydrologie et de Géochimie de Strasbourg, Université de Strasbourg - CNRS, UMR 7517

2 Participants Amir L, Kern M. INRIA Rockencourt Hoffmann J., Knabner P., Kräutle S. University of Erlangen-Nuremberg, Department of Mathematics, Erlangen, Germany de Dieuleveult C., Erhel J. INRIA Rennes; ANDRA Van der Lee J., Lagneau V. Ecole des Mines de Paris Mayer K.U. University of British Columbia, Dept. of Earth and Ocean Sciences, Vancouver, BC, Canada MacQuarrie K.T.B University of New Brunswick, Dept. of Civil Engineering, Fredericton, NB, Canada

3 Outline Introduction: objectives of the benchmark The 1D easy level Some results

4 Some questions… (about the resolution)

5 Operator Splitting / Global Approach Operator Splitting: Iterative – Non iterative OS scheme OS errors Global Approach: Scheme : DSA / DAE Resolution of non linear system CPU time / Memory

6 Space discretisation Objectives –Stability –Numerical diffusion –Efficiency Finite Elements / Volumes Particle Tracking ELLAM methods…

7 Time discretisation Explicit / Implicit Higher order Adaptive time step –Heuristic –Predictor-corrector

8 About convergence… Iterative method for chemistry Iterative method for transport (SIA) Iterative method for global approach What about very small concentration –From transport C = … –Numerical problem if C = 0

9 The 1D easy-level benchmark Medium-level Hard-level 2D

10 Reactive transport modelling Advection – Diffusion – Reaction equation U pore velocity D dispersion tensor (non diagonal) ω porosity T M total mobile concentration T F total fixed concentration

11 Equilibrium chemistry Reactions Mobile SpeciesNon mobile Species Mass action laws Conservation laws

12 The 1D reactive domain High permeability Low porosity Low reactivity Low permeability High porosity High reactivity

13 Chemical reactions injected

14 Some results

15 Main features of the compared codes

16 CPU time for advective case

17 Very close results

18 Localized differences

19

20 CPU time dispersive case

21 Dispersive case is more disciminative

22 Conclusion

23 New methods Reduction scheme (Hoffmann et al.) –Reduces the set of coupled variables –Reduces the computing time –Available for all the approaches Method of lines (de Dieuleveult and Erhel) –High precision using coarse meshes –CPU time long Newton-Krylov (Amir and Kern) –Some problems –Some very promising results

24 Difficulties More preparation on the intercomparison criteria –Definition of the key – point of the solution –Giving a reference solution Maybe a more realistic problem ?

25 For a next benchmark Development using many codes –Some points are clearly visible using SNIA or SIA approach but not for global one Cooperation between many teams –Having many codes –Is it realistic ? Keeping a well defined problem

26 Carrayrou J., M. Kern, P. Knabner (2009). Reactive transport benchmark of MoMaS, Comp. Geosci., on line first. Carrayrou, J. (2009). Looking for some reference solutions for the Reactive Transport Benchmark of MoMaS with SPECY, Comp. Geosci., on line first. de Dieuleveult, C., Erhel, J. (2009) A global approach for reactive transport: application to the benchmark easy test case of MoMaS, Comp. Geosci., on line first. Hoffmann J., Kräutle S., Knabner P. (2009) A Parallel Global-Implicit 2-D Solver for Reactive Transport Problems in Porous Media based on a Reduction Scheme and its Application to the MoMaS Benchmark Problem. Comp. Geosci., under revision. Lagneau, V. van der Lee, J. (2009) HYTEC results of the MoMas reactive transport benchmark, Comput. Geosci., on line first. Mayer, K.U., and K.T.B. MacQuarrie (2009). Formulation of the multicomponent reactive transport code MIN3P and implementation of MoMaS benchmark problems, Comp. Geosci, on line first. Carrayrou J., Hoffmann J., Knabner P., Kräutle S., de Dieuleveult C., Erhel J., Van der Lee J., Lagneau V., Mayer K.U., MacQuarrie K.T.B (2009). A synthesis of the MoMaS reactive transport results, Comp. Geosci, under revision. Articles

27 Conférences Eurotherm, 2008 Albi International Workshop on reactive transport, 2008 Strasbourg SIAM, 2009 Leipzig