Equivalent permeability tensor in fractured media : an algebraic approach.

Rachid Ababou (1) , Philippe Renard (2)

1 IMFT - Institut de mécanique des fluides de Toulouse
2 UNINE - Université de Neuchâtel = University of Neuchatel

This work is part of an extensive investigation on the equivalent permeability of heterogeneous and fractured media. We focus here on the problem of Darcian/Poiseuille flow in an irregular network of fracture segments (in 2D) or conduits (in 2D or 3D). An exact algebraic relation between the mean flux vector(Q) and the mean hydraulic gradient (J) is developed through a mathematical analyzis of the network flow problem, based on concepts from graph theory, leading to a discrete definition of DIV and GRAD operators. The resulting equivalent permeability is a 2nd rank tensor Kij, not necessarily symmetric and not necessarily positive-definite. Its properties are analyzed for given types of boundary conditions and averaging procedures.

Mots clés: Upscaling; Equivalent conductivity; Heterogeneous porous media; Fractured media; Fracture networks; Darcy-Poiseuille flows; Linear algebra; Graphs

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

Rachid Ababou, Philippe Renard. Equivalent permeability tensor in fractured media : an algebraic approach.. MAMERN11: 4th International Conference on Approximation Methods and Numerical Modelling in Environment and Natural Resources May 23-26, 2011, May 2011, Saidia, Morocco. ⟨hal-00967860⟩