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Section: New Results

Coupled models in hydrogeology

Coupling of subsurface and seepage flows

Participants : Jocelyne Erhel, Jean-Raynald de Dreuzy.

Hillslope response to precipitations is characterized by sharp transitions from purely subsurface flow dynamics to simultaneous surface and subsurface flows. Locally, the transition between these two regimes is triggered by soil saturation. Here we develop an integrative approach to simultaneously solve the sub- surface flow, locate the potential fully saturated areas and deduce the generated saturation excess over- land flow. This approach combines the different dynamics and transitions in a single partition formulation using discontinuous functions. We propose to regularize the system of partial differential equations and to use classic spatial and temporal discretization schemes. We illustrate our methodology on the 1D hillslope storage Boussinesq equations. We first validate the numerical scheme on previous numerical experiments without saturation excess overland flow. Then we apply our model to a test case with dynamic transitions from purely subsurface flow dynamics to simultaneous surface and subsurface flows. Our results show that discretization respects mass balance both locally and globally, converges when the mesh or time step are refined. Moreover the regularization parameter can be taken small enough to ensure accuracy without suffering of numerical artefacts. Applied to some hundreds of realistic hillslope cases taken from Western side of France (Brittany), the developed method appears to be robust and efficient. This study performed within the H2MNO4 ANR project has been published in the journal Advances in Water Ressources [21].

Characterizations of Solutions in Geochemistry

Participant : Jocelyne Erhel.

We study the properties of a geochemical model involving aqueous and precipitation-dissolution reactions at a local equilibrium. By reformulating the model as an equivalent optimization problem, we prove existence and uniqueness of a solution. It is classical in thermodynamic to compute diagrams representing the phases of the system. We introduce here the new precipitation diagram that describes the mineral speciation in function of the parameters of the system. 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, is part of the H2MNO4 initiative. It has been recently submitted to a journal for publication [46].

Reactive transport in fractured-porous media

Participants : Yvan Crenner, Jean-Raynald de Dreuzy, Jocelyne Erhel.

Fractures must be carefully considered for the geological disposal of radioactive wastes. They critically enhance diffusivity, speed up solute transport, extend mixing fronts, and in turn, modify the physico-chemical conditions of reactivity in the Excavation Damaged Zone (EDZ) of the galleries. On the other hand, the pyrite oxidation could be considered like the main reaction due to the diffusion of oxygen through the gallery. Moreover, we assume that this reaction is complete in these geological conditions. First, we propose a numerical explicit reactive transport model in a fractured medium for an overall reaction. Afterwards, we present simulations outputs of the pyrite-oxygen reaction in EDZ zone. This study supported by ANDRA has been published in a conference [27].

Reactive transfers for multi-phasic flows

Participants : Jocelyne Erhel, Bastien Hamlat.

This study focuses on the mathematical modeling of reactive transfers for multi-phasic flows in porous medium. This study supported by IFPEN has been presented in a conference paper [37].