Discrete fracture‐matrix model of poroelasticity

Abstract

The paper presents the derivation and analysis of a poroelasticity model in a domain with fracture represented by a codimension‐one manifold. The system of saturated flow and linear elasticity both in the rock matrix and in the fracture coupled through an appropriate interface condition is obtained from a continuum description by integration and semi‐discretization in the normal direction of the fracture. The existence and uniqueness of a weak solution are proved with the help of an iterative splitting, whose convergence rate is analyzed. The analysis is complemented by a numerical example.