Modeling Fractures in a Poro-Elastic Medium

Abstract

We present a fracture model in a poro-elastic medium. The model describes the fracture as a curve or surface according to the dimension, the width of the crack being included into the equation of flow in the fracture. The discretization uses mixed finite elements for the fluid and continuous finite elements for the porous medium’s displacement. The numerical scheme is solved by an algorithm that decouples, on one hand, the computation of the mechanics from that of the fluid, and on the other hand, the computation of the flow in the reservoir from that in the fracture. The model is illustrated by a numerical experiment.