Rigorous derivation of discrete fracture models for Darcy flow in the limit of vanishing aperture

We consider single-phase flow in a fractured porous medium governed by Darcy's law with spatially varying hydraulic conductivity matrices in both bulk and fractures. The width-to-length ratio of a fracture is of the order of a small parameter E and the ratio Kf */Kb* of the characteristic hydraulic conductivities in the fracture and bulk domains is assumed to scale with Ea for a parameter a is an element of R. The fracture geometry is parameterized by aperture functions on a submanifold of codimension one. Given a fracture, we derive the limit models as E - 0. Depending on the value of a, we obtain five different limit models as E - 0, for which we present rigorous convergence results.