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

In our work, we extend the monophasic model proposed in [17], [10] to diphasic flow. We thus provide a model for two phase Darcy flow through fracture networks 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 gravity dominated flow as well as discontinuous capillary pressure at the material interfaces.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. Several test cases are presented to compare our hybrid dimensional model to the hybrid dimensional, continuous pressure model (proposed in [7]) 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 proposed reduced model.