Modeling flow in porous media with fractures; discrete fracture models with matrix-fracture exchange

This article is concerned with a numerical model for flow in a porous medium containing fractures. The fractures are modeled as $(d-1)$-dimensional surfaces inside the $d$-dimensional matrix domain, and a mixed finite element method containing both $d$ and $(d-1)$ dimensional elements is used. The method allows for fluid exchange between the fractures and the matrix. The method is defined for single-phase Darcy flow throughout the domain and for Forchheimer flow in the fractures. We also consider the case of two-phase flow in a domain in which the fractures and the matrix are of different rock type.