Equivalent permeability tensor in fractured media : an algebraic approach.

摘要

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.