Modeling Flow in Porous Media with Fractures; Discrete Fracture Models with Matrix-Fracture Exchange

摘要

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 now 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.