A global method for coupling transport with chemistry in heterogeneous porous media

Modeling reactive transport in porous media, using a local chemical equilibrium assumption, leads to a system of advection-diffusion PDE's coupled with algebraic equations. When solving this coupled system, the algebraic equations have to be solved at each grid point for each chemical species and at each time step. This leads to a coupled non-linear system. In this paper a global solution approach that enables to keep the software codes for transport and chemistry distinct is proposed. The method applies the Newton-Krylov framework to the formulation for reactive transport used in operator splitting. The method is formulated in terms of total mobile and total fixed concentrations and uses the chemical solver as a black box, as it only requires that on be able to solve chemical equilibrium problems (and compute derivatives), without having to know the solution method. An additional advantage of the Newton-Krylov method is that the Jacobian is only needed as an operator in a Jacobian matrix times vector product. The proposed method is tested on the MoMaS reactive transport benchmark.Comment: Computational Geosciences (2009) http://www.springerlink.com/content/933p55085742m203/?p=db14bb8c399b49979ba8389a3cae1b0f&pi=1

Looking for some reference solutions for the reactive transport benchmark of MoMaS with SPECY

International audienceNumerical benchmark can be an efficient way to validate reactive transport codes. The reactive transport benchmark of GNR MoMaS is here presented and solved on its easy 1D version. The reactive transport code SPECY is presented with a brief description of its main numerical methods: discontinuous finite elements for solving advection, mixed hybrid finite elements for solving dispersion and Newton–Raphson method to linearise the equilibrium chemistry and respect of the chemically allowed interval and positive continuous fractions methods to increase the robustness of the chemistry resolution. By successive mesh and time step refinement, we use the reactive transport code SPECY to look for a reference solution to this problem

On the efficiency of the direct substitution approach for reactive transport problems in porous media

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