Section: New Results

Models and simulations for transport in porous media

Transport in highly heterogeneous porous medium

Participants : Jocelyne Erhel, Géraldine Pichot, Nadir Soualem.

This work is done in collaboration with A. Beaudoin, from University of Poitiers (Pprime) and J.-R. de Dreuzy, from Geosciences Rennes. It is done in the context of the Micas project ( 8.1.2 ).

It has been presented at a conference and a paper is in preparation [28] .

We study the transport of an inert species in a 2D heterogeneous porous medium via a Random Walk Particle Tracking (RWPT) method. The main objective is to derive the macroscopic properties of the transport by the means of Monte-Carlo simulations in large domains. Conditions to reach asymptotic macro-dispersion coefficients are given. We also present our on-going research about the RWPT method in presence of discontinuities within the domain.

Transport in discontinuous porous medium

Participants : Jocelyne Erhel, Géraldine Pichot.

This work is done in collaboration with A. Lejay, from Inria Nancy. It is done in the context of the Micas project ( 8.1.2 ).

It is published in the proceedings of a conference and submitted in a journal [30] , [44] .

We study a diffusion process in a 1D discontinuous medium using a random walk approach. Our main contribution is to encompass two existing numerical methods in the unified framework of the Skew Brownian Motion. This theoretical approach allows to detail and justify the derived algorithms. Numerical simulations are performed on two test cases to show that the algorithms can deal with the discontinuity in the diffusion coefficient.

Reactive transport

Participants : Édouard Canot, Jocelyne Erhel, Souhila Sabit, Nadir Soualem.

This work is done in the context of the MOMAS GNR ( 8.1.1 ) and the contract with Andra ( 7.1 ).

It has been presented at a workshop and a paper is in preparation [33] . The software GRT3D (see section 5.6 ) is described in a report [48] .

We have developed a method coupling transport and chemistry, based on a method of lines such that spatial discretization leads to a semi-discrete system of algebraic differential equations (DAE system). The main advantage is to use a complex DAE solver, which controls simultaneously the timestep and the convergence of Newton nonlinear iterations [53] . Analysis done with several numerical experiments showed that most of CPU time is spent in solving the linear systems of Newton iterations. We have reduced this computational time by reducing the size of the system; numerical experiments with large 2D domains show the efficiency.