Reactive transport in porous media

Understanding mass transfer phenomena in the subsurface is becoming increasingly important for environmental issues: predicting pollution and remediation strategies, assessing the feasibility of a nuclear underground storage site or a carbon dioxide sequestration site. These studies usually involve interaction between several phenomena, such as transport and chemistry. Under the hypothesis of local equilibrium, the model couples transport PDEs with local algebraic chemical equations. In this talk, we present numerical methods for the simulation of a coupled model folr reactive transort. We briefly
recall the methods for the individual models: flow simulations are based on Darcy s law, and require accurate methods (based on mixed
finite elements) for computing the velocity in heterogeneous situations. The velocity is the main input for the transport model, an advection-dispersion type equation, possibly with sharp fronts. This is solved using a combination of finite volume (for advection) and mixed finite element (for the dispersion--diffusion part). Chemical equations are solved by a variant of Newton s method. We give a formulation for the coupled model based on aqueous and fixed total
concentrations, and show how the usual fixed point method for the nonlinear coupled problem can be replaced by a Newton-Krylov method.
This leads to a global formulation for the coupled problem that enables keeping the transport and chemistry codes (usually written by
different groups) separate. A key point for the efficiency of the method is the design of a suitable preconditioner for the linearized (matrix free) problem. We study formulations that respect the block structure of the problem, and analyze several block preconditioners on a
simplified model, using the field of values of the Jacobian.

This is joint work with Laila Amir and Abdelaziz Taakili.