Hybrid Dimensional Modelling and Discretization of Darcy Flow through Fractured Porous Media (Julian Hennicker, Unige)

17.10.2017 14:00

Todays engineers and scientists dealing with subsurface flow widely agree that the presence of fractures in the rock matrix has a major influence on the global flow behaviour, in general. Because of the large contrasts in fracture apertures and matrix length scales, in addition to strongly heterogeneous fracture and matrix rock types, numerical simulation rapidly reaches its limits for equi-dimensional models, in which fractures have to be meshed accordingly to their apertures. Therefore, the derivation of so-called hybrid-dimensional models, in which the fractures are represented as entities of codimension one w.r.t. the matrix, and the development of adapted numerical schemes, has drawn a lot of attention. In this presentation, we will start with monophasic flow and then extend the monophasic model to diphasic flow. We thus provide a hybrid dimensional model for two phase Darcy flow. It accounts for fractures acting either as drains or as barriers, since it allows for 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. The numerical analysis is carried out in an extended gradient schemes framework. In so doing, we prove convergence for this large class of numerical schemes, which has not been achieved before for flow in complex DFN. For diphasic flow, we present several test cases, and use VAG to compare the hybrid dimensional model to the equi-dimensional model. This does not only provide quantitative evidence about computational gain, but also leads to deep insight about the quality of the proposed reduced model.

Lieu

salle 623, Séminaire d'analyse numérique

entrée libre