Highlights• Energy-stable model and scheme for coupled two-phase flow and contact mechanics in discrete fracture networks • Mechanics conforming discretization coupled with P 0 Lagrange multipliers to circumvent singularities, local contact equations • Flow discretization in the abstract gradient discretization framework accounting for a large family of schemes • Investigation of nonlinear algorithms both for the contact mechanics and for the fully coupled problem • Validation on benchmark 2D examples and application to a realistic axisymmetric case study

We consider a two-phase Darcy flow in a fractured and deformable porous medium for which the fractures are described as a network of planar surfaces leading to so-called hybrid-dimensional models. The fractures are assumed open and filled by the fluids and small deformations with a linear elastic constitutive law are considered in the matrix. As opposed to \cite{bonaldi:hal-02549111}, the phase pressures are not assumed continuous at matrix fracture interfaces, which raises new challenges in the convergence analysis related to the additional interfacial equations and unknowns for the flow. As shown in \cite{BHMS2018,gem.aghili}, unlike single phase flow, discontinuous pressure models for two-phase flows provide a better accuracy than continuous pressure models even for highly permeable fractures. This is due to the fact that fractures fully filled by one phase can act as barriers for the other phase, resulting in a pressure discontinuity at the matrix fracture interface.    The model is discretized using the gradient discretization method \cite{gdm}, 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. In this work, the gradient discretization of \cite{bonaldi:hal-02549111} is extended to the discontinuous pressure model and the convergence to a weak solution is proved.  Numerical solutions provided by the continuous and discontinuous pressure models are compared on gas injection and suction test cases using a Two-Point Flux Approximation (TPFA) finite volume scheme for the flows and $\P_2$ finite elements for the mechanics.

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In the Andra repository concept, a large amount of hydrogen gas will be generated through radiolysis of water and corrosion of metal parts from the infrastructure and the packages containing radioactive waste. The fate of the gas could have a significant impact on the rate of resaturation of the porous media, and needs to be accounted for in order to make accurate predictions of the long-term evolution of the repository. The central zone of the repository consists of a 4.5-kmlong network of galleries which connect the storage zones with the surface through three shafts. These shafts, which will be backfilled and sealed after closure, will have a key role in gas and water exchange between the repository and the overlying aquifer. The aim of this work was to describe the evolution in time of both the water and gas flows in the central zone up to the end of the hydraulic-gas transient. The issue was addressed by means of numerical simulations. The simulations produced local predictions of flow rates and pressures, water saturation and amounts of dissolved gas. The results were analysed to determine how water and gas flows combine in the central zone, when the saturation of the seal will be complete, when the free gas will reach the overlying aquifer, and when the saturation of the central zone will be complete.