This paper is concerned with numerical methods for the modeling of flow and transport of contaminant in porous media. The numerical methods feature the mixed finite element method over triangles as a solver to the Darcy flow equation and a conservative finite volume scheme for the concentration equation. The convective term is approximated with a Godunov scheme over the dual finite volume mesh, whereas the diffusion–dispersion term is discretized by piecewise linear conforming triangular finite elements. It is shown that the scheme satisfies a discrete maximum principle. Numerical examples demonstrate the effectiveness of the methodology for a coupled system that includes an elliptic equation and a diffusion–convection–reaction equation arising when modeling flow and transport in heterogeneous porous media. The proposed scheme is robust, conservative, efficient, and stable, as confirmed by numerical simulations.

Contaminant transport in a fractured porous medium can be modeled, under appropriate conditions, with a double porosity model. Such a model consists of a parabolic equation with a coupling term describing contaminant exchange between the fractures, which have high permeability, and the matrix block, which has low permeability. A locally conservative method based on mixed finite elements is used to solve the parabolic problem, and the calculation of the coupling term, which involves the solution of diffusion equations in the matrix blocks, is based on an analytic expression. Numerical experiments show that this semi-analytic method for the coupling term is accurate and faster than several other methods but at a small expense of computer memory.

Performance assessment of a deep geological disposal requires the definition of a series of assumptions of very different natures. The particular features of the site studied, the amount and the characteristics of the waste to be disposed of, or the definition of the various assumptions and parameters used to build the transfer model must be specifically defined. The multiple sources of differences related to the assumptions made by the teams involved in this international exercise make the interpretation difficult when a broad comparison of results obtained is considered. The work performed and the results obtained within the recent SPA project (Spent fuel Performance Assessment) however enabled to draw some general conclusions on the main radionuclides and parameters that potentially govern the radiological impact of a spent fuel geological repository. The particular importance of 129 I was notably highlighted as well as the possible role of transuranic elements. For 129 I, matrix degradation rate and dilution were found to have a predominant influence on the calculated dose. For transuranic elements, disposal system was found to delay the arrival of activity into biosphere over a very long period of time. A relatively wide range of breakthrough times were however observed depending on sorption modelling in geosphere in particular. As for transuranic relative dose contribution, a determining influence was played by solubility limit values.

A variety of models are considered: one-phase flow in a porous medium, two-phase flow in a porous medium with two rock types, and one-phase flow in a porous medium with fractures. For each of these models the domain of calculation is divided into subdomains corresponding to the physics of the problem. Then it is shown how to rewrite the problems as interface problems to use nonoverlapping domain decomposition.