1887

Abstract

Summary

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 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. In this work, the model is derived and discretized using the gradient discretization method which covers a large class of conforming and non conforming discretizations. This framework allows a generic convergence analysis of the coupled model using a combination of discrete functional tools. The convergence of the discrete solution to a weak solution of the model is proved using a priori and compactness estimates. This is, to our knowledge, the first convergence result for this type of models taking into account two-phase flows and the nonlinear poro-mechanical coupling including the cubic nonlinear dependence of the fracture conductivity on the fracture aperture. Previous related works consider a linear approximation obtained for a single-phase flow by freezing the fracture conductivity. Numerical experiments are presented to illustrate this result using a Two-Point Flux Approximation cell centered finite volume scheme for the flow and a P2 finite element method for the mechanics. Iterative coupling algorithms are investigated to solve the coupled discrete nonlinear systems at each time step of the simulation.

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2020-09-14
2021-09-27
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