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A model coupling a three dimensional gas liquid compositional Darcy flow and a one dimensional compositional free gas flow is presented. The coupling conditions at the interface between the gallery and the porous medium account for the molar normal fluxes continuity for each component, the gas liquid thermodynamical equilibrium, the gas pressure continuity and the gas and liquid molar fractions continuity. This model is applied to the simulation of the mass exchanges at the interface between the repository and the ventilation excavated gallery in a nuclear waste geological repository. The spatial discretization is essentially nodal and based on the vertex approximate gradient (VAG) scheme. Compared with classical nodal approaches such as the Control Volume Finite Element method, the VAG scheme has the advantage to avoid the mixture of different material properties and models in the control volumes located at the interfaces. The discrete model is validated using a quasi analytical solution for the stationary state, and the convergence of the VAG discretization is analysed for a simplified model coupling the Richards approximation in the porous medium and the gas pressure equation in the gallery. [ABSTRACT FROM AUTHOR]

This paper presents a finite volume discretization of two-phase Darcy flows in discrete fracture networks taking into account the mass exchange between the matrix and the fracture. We consider the asymptotic model for which the fractures are represented as interfaces of codimension one immersed in the matrix domain, leading to the so called hybrid dimensional Darcy flow model. The pressures at the interfaces between the matrix and the fracture network are continuous corresponding to a ratio between the normal permeability of the fracture and the width of the fracture assumed to be large compared with the ratio between the permeability of the matrix and the size of the domain. The discretization is an extension of the Vertex Approximate Gradient (VAG) scheme to the case of hybrid dimensional Darcy flow models. Compared with Control Volume Finite Element (CVFE) approaches, the VAG scheme has the advantage to avoid the mixing of the fracture and matrix rocktypes at the interfaces between the matrix and the fractures, while keeping the low cost of a nodal discretization on unstructured meshes. The convergence of the scheme is proved under the assumption that the relative permeabilities are bounded from below by a strictly positive constant. This assumption is needed in the convergence proof in order to take into account discontinuous capillary pressures in particular at the matrix fracture interfaces. The efficiency of our approach compared with CVFE discretizations is shown on two numerical examples of fracture networks in 2D and 3D. [ABSTRACT FROM AUTHOR]

The numerical simulation of two-phase flow in a porous medium may lead, when using coupled finite volume schemes on structured grids, to the appearance of the so-called Grid Orientation Effect (GOE). We propose in this paper a procedure to eliminate this phenomenon, based on the use of new fluxes with a new stencil in the discrete version of the convection equation, without changing the discrete scheme for computing the pressure field. Numerical results show that the GOE does not significantly decrease with the size of the discretization using the initial scheme on the coupled problem, but that it is efficiently suppressed by the new procedure, even on coarse meshes. A mathematical study, based on a weak BV inequality using the new fluxes, confirms the convergence of the modified scheme in a particular case. [ABSTRACT FROM PUBLISHER]