Section: New Results

Coupled models in hydrogeology

Characterizations of Solutions in Geochemistry

Participants : Jocelyne Erhel, Tangi Migot.

We study the properties of a geochemical model involving aqueous and precipitation-dissolution reactions at a local equilibrium in a diluted solution. This model can be derived from the minimization of the free Gibbs energy subject to linear constraints. By using logarithmic variables, we define another minimization problem subject to different linear constraints with reduced size. The new objective function is strictly convex, so that uniqueness is straightforward. Moreover, existence conditions are directly related to the totals, which are the parameters in the mass balance equation. These results allow us to define a partition of the totals into mineral states, where a given subset of minerals are present. This precipitation diagram is inspired from thermodynamic diagrams where a phase depends on physical parameters. Using the polynomial structure of the problem, we provide characterizations and an algorithm to compute the precipitation diagram. Numerical computations on some examples illustrate this approach. This work, supported by ANDRA, was presented at a workshop [29] and will be published in the journal Computational Geosciences [23].

Reactive transport in multiphase flow

Participants : Jocelyne Erhel, Bastien Hamlat.

Reactive transport modeling is a critical issue for energy industry, with application to carbon capture and storage (CCS) and geothermy. In this work, we focus on mathematical modeling and numerical solution of reactive transport in porous media. We study reaction kinetics leading to the appearance or disappearance of pure phases and present a mathematical model of PDEs with discontinuous right-hand sides. We propose a regularization process to obtain a PDE system with continuous right-hand sides which can be numerically solved. Using a simple academic case, we illustrate the benefits of our approach.

This work, supported by IFPEN, was presented at a workshop [30] and an international conference [35].