Research topic: Reactive transport in porous media

Scientific context

Model description

The transport equations are mass conservation with advection and dispersion. The velocity field comes from previous steady-state flow computations. Chemistry equations can be at equilibrium or kinetic. They include aqueous reactions, sorption, ion exchanges, precipitation or dissolution. Unknowns are the total concentrations of mobile and immobile main species. Equations are a set of coupled nonlinear Partial Differential Algebraic Equations (PDAE).

The transport equations are spatially discretized by a finite element method with an unstructured mesh ; advection is discretized by an upwind scheme and dispersion is discretized by a centered scheme. In the framework of methods of lines, it allows to use any ODE solver after spatial discretization.

Two types of numerical couplings are compared :

a so-called Sequential Iterative Approach; time discretization is done with the implicit Euler scheme. The nonlinear problem is solved at each timestep by a block nonlinear relaxation, solving first the transport equations for mobile species with immobile species as a reaction term, then the chemistry equations with an updated total of mobile and immobile species.
a so-called global approach; it follows the method of lines with a set of discrete DAE to solve. We use the solver Sundials, with varying timesteps and varying orders.

Currently, simulations are done in 1D or 2D domains and the number of fixed species is known in advance.

Publications and results

C. de Dieuleveult, J. Erhel and M. Kern
A global strategy for solving reactive transport equations
Journal of Computational Physics, 2009, Volume 228, 6395-6410
C. de Dieuleveult and J. Erhel
A global approach to reactive transport: application to the MoMas benchmark
Computational Geosciences, 2009
de Dieuleveult, C. & Erhel, J.
A numerical model for coupling chemistry and transport
International Conference on SCIentific Computation And Differential Equations, SciCADE 2007 (contributed talk), 2007
Erhel, J. & de Dieuleveult, C.
Nonlinear methods for reactive transport simulations
Int. conf. on Approximation and Iterative Methods (invited talk), 2006

Objectives and projects

The global approach has been successfully applied to the Momas benchmark on reactive transport (easy test case, 1D and 2D). It has also been applied to Alliances test cases (1D and 2D). However, the CPU time is quite high. The main objective is now to reduce this CPU time. A first approach is to reduce the size of the linear system by a subsitution technique. A second approach is to deal with the tolerance and convergence parameters of the DAE solver. Another objective is to allow for precipitation and dissolution with a variable number of minerals, by using a complementary problem formulation and a semi-smooth Newton method. We have developed a software implementing the global approach and plan to continue this development.

Another objective is to design a reactive particle tracker.

Participants

This topic started in the Sage team (participant J. Erhel) with the Hydrogrid project (2002-2005), in collaboration with J. Carrayrou, from IMFS at Strasbourg and M. Kern, from the team Estime at INRIA-Rocquencourt.
The research continued in the Sage team (participant J. Erhel), with the Ph-D of C. de Dieuleveult, started in 2005 and finished in 2008.

Now the research is still in progress, in collaboration with J. Carrayrou and M. Kern.

Grants

This work was supported by the ACI Grid with the project Hydrogrid in 2002-2005.

It was supported by a grant from ANDRA in 2005-2008 and by projects of the GdR Momas in 2004-2009.

C. de Dieuleveult was hired by ANDRA during her Ph-D. She has now a research position at Ecole des Mines de Paris.