Hybrid dimensional modeling of multi-phase Darcy flows in fractured porous media

Julian Hennicker 1, 2
2 COFFEE - COmplex Flows For Energy and Environment
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR7351
Abstract : This thesis investigates the modelling of Darcy flow through fractured porous media and its discretization on general polyhedral meshes. We follow the approach of hybrid dimensional models, invoking a complex network of planar fractures. The models account for matrix-fracture interactions and fractures acting either as drains or as barriers, i.e. we have to deal with pressure discontinuities at matrix-fracture interfaces. In the case of two phase flow, we present two models, which permit to treat gravity dominated flow as well as discontinuous capillary pressure at the material interfaces. The numerical analysis is performed in the general framework of the Gradient Discretisation Method, which is extended to the models under consideration. Two families of schemes namely the Vertex Approximate Gradient scheme (VAG) and the Hybrid Finite Volume scheme (HFV) are detailed and shown to fit in the gradient scheme framework, which yields, in particular, convergence. For single phase flow, we obtain convergence of order 1 via density results. For two phase flow, the existence of a solution is obtained as a byproduct of the convergence analysis. Several test cases are presented. For single phase flow, we study the convergence on different types of meshes for a family of solutions. For two phase flow, we compare the hybrid-dimensional models to the reference 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 models.
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Julian Hennicker. Hybrid dimensional modeling of multi-phase Darcy flows in fractured porous media. Other. Université Côte d'Azur, 2017. English. ⟨NNT : 2017AZUR4057⟩. ⟨tel-01614307⟩

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