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Pré-publication, Document de travail

Gradient discretization of two-phase flows coupled with mechanical deformation in fractured porous media

Francesco Bonaldi 1, 2 Konstantin Brenner 1, 2 Jérôme Droniou 3 Roland Masson 1, 2
1 COFFEE - COmplex Flows For Energy and Environment
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR7351
Abstract : We consider a two-phase Darcy flow in a fractured porous medium consisting in a matrix flow coupled with a tangential flow in the fractures, described as a network of planar surfaces. This flow model is also coupled with the mechanical deformation of the matrix assuming that the fractures are open and filled by the fluids, as well as small deformations and a linear elastic constitutive law. The model is discretized using the gradient discretization method [20], which covers a large class of conforming and non conforming schemes. This framework allows for a generic convergence analysis of the coupled model using a combination of discrete functional tools. Here, we describe the model together with its numerical discretization, and we prove a convergence result. This is, to our knowledge, the first convergence result for this type of models taking into account two-phase flows and the non-linear poromechanical coupling. Previous related works consider a linear approximation obtained for a single phase flow by freezing the fracture conductivity [29, 30]. Numerical tests employing the Two-Point Flux Approximation (TPFA) finite volume scheme for the flows and P2 finite elements for the mechanical deformation are also provided to illustrate the behavior of the solution to the model.
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Pré-publication, Document de travail
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https://hal.archives-ouvertes.fr/hal-02549111
Contributeur : Francesco Bonaldi <>
Soumis le : lundi 30 novembre 2020 - 13:35:54
Dernière modification le : mardi 1 décembre 2020 - 03:45:25

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  • HAL Id : hal-02549111, version 2

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Francesco Bonaldi, Konstantin Brenner, Jérôme Droniou, Roland Masson. Gradient discretization of two-phase flows coupled with mechanical deformation in fractured porous media. 2020. ⟨hal-02549111v2⟩

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