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We consider a two-phase Darcy flow in a fractured porous medium consisting ina matrix flow coupled with a tangential flow in the fractures, described as anetwork of planar surfaces. This flow model is also coupled with the mechanicaldeformation of the matrix assuming that the fractures are open and filled bythe fluids, as well as small deformations and a linear elastic constitutivelaw. The model is discretized using the gradient discretization method [26],which covers a large class of conforming and non conforming schemes. Thisframework allows for a generic convergence analysis of the coupled model usinga combination of discrete functional tools. Here, we describe the modeltogether with its numerical discretization, and we prove a convergence resultassuming the non-degeneracy of the phase mobilities and that the discretesolutions remain physical in the sense that, roughly speaking, the porositydoes not vanish and the fractures remain open. This is, to our knowledge, thefirst convergence result for this type of models taking into account two-phaseflows in fractured porous media and the non-linear poromechanical coupling.Previous related works consider a linear approximation obtained for a singlephase flow by freezing the fracture conductivity [36, 37]. Numerical testsemploying the Two-Point Flux Approximation (TPFA) finite volume scheme for theflows and $\mathbb P_2$ finite elements for the mechanical deformation are alsoprovided to illustrate the behavior of the solution to the model.

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