Two-phase Discrete Fracture Matrix models with linear and nonlinear transmission conditions

Springer Science and Business Media LLC - Tập 10 - Trang 1-35 - 2019
Joubine Aghili1,2, Konstantin Brenner1,2, Julian Hennicker3, Roland Masson1,2, Laurent Trenty4
1Team COFFEE, Inria Sophia Antipolis - Méditerranée, Valbonne, France
2Laboratoire J.A. Dieudonné, UMR 7351 CNRS, Université Côte d’Azur, Nice, France
3Université de Genève, Geneva, Switzerland
4Andra, Chatenay-Malabry, France

Tóm tắt

This work deals with two-phase Discrete Fracture Matrix models coupling the two-phase Darcy flow in the matrix domain to the two-phase Darcy flow in the network of fractures represented as co-dimension one surfaces. Two classes of such hybrid-dimensional models are investigated either based on nonlinear or linear transmission conditions at the matrix–fracture interfaces. The linear transmission conditions include the cell-centred upwind approximation of the phase mobilities classically used in the porous media flow community as well as a basic extension of the continuous phase pressure model accounting for fractures acting as drains. The nonlinear transmission conditions at the matrix–fracture interfaces are based on the normal flux continuity equation for each phase using additional interface phase pressure unknowns. They are compared both in terms of accuracy and numerical efficiency to a reference equi-dimensional model for which the fractures are represented as full-dimensional subdomains. The discretization focuses on Finite Volume cell-centred Two-Point Flux Approximation which is combined with a local nonlinear solver allowing to eliminate efficiently the additional matrix–fracture interfacial unknowns together with the nonlinear transmission conditions. 2D numerical experiments illustrate the better accuracy provided by the nonlinear transmission conditions compared to their linear approximations with a moderate computational overhead obtained thanks to the local nonlinear elimination at the matrix–fracture interfaces. The numerical section is complemented by a comparison of the reduced models on a 3D test case using the Vertex Approximate Gradient scheme.

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