Hybrid Dimensional Modelling and Discretization of Two Phase Darcy Flow through DFN in Porous Media

We provide a model for two phase Darcy flow through discrete fracture networks (DFN) in porous media, in which the d−1 dimensional flow in the fractures is coupled with the d dimensional flow in the matrix, leading to the so called hybrid dimensional Darcy flow model. It accounts for fractures acting either as drains or as barriers, since it allows pressure jumps at the matrix-fracture interfaces. The model also permits to treat discontinuous capillary pressure at the material interfaces as well as gravity dominated flow. In particular, it incorporates upwind normal fluxes that are needed to reproduce gravitational segregation inside the DFN. We adapt the Vertex Approximate Gradient (VAG) scheme to this problem, in order to account for anisotropy and heterogeneity aspects as well as for applicability on general meshes. For diphasic flow, we present several test cases, and use VAG to compare our hybrid dimensional model to a hybrid dimensional model that assumes continuous pressure at the matrix fracture interfaces and to the generic equidimensional model, in which fractures have the same dimension as the matrix. This does not only provide quantitative evidence about computational gain, but also leads to deep insight about the quality of the reduced models.