Fully Coupled XFEM Model for Flow and Deformation in Fractured Porous Media with Explicit Fracture Flow

Abstract

A hydromechanical model with explicit fracture flow is presented for the fully coupled analysis of flow and deformation in fractured porous media. Extended finite-element method (XFEM) was utilized to model the fracture discontinuity in the two-dimensional plane-strain mechanical model. Two flow models, a one-dimensional laminar flow within the fracture and a two-dimensional Darcy flow through porous media, were considered. The flow domains were coupled through a mass exchange term (leak-off) accounting for discontinuous Darcy flow velocity across the fracture. Particular attention was given to the coupling of the flow domains with the mechanical model. Spatial and temporal discretization was achieved using the standard Galerkin method and the finite-difference technique, respectively. Unlike the successive coupled models in which the results of the mechanical model are used to update the fracture flow model and vice versa, the fully coupled hydromechanical formulation is solved simultaneously. The model was verified against several closed-form solutions from the literature. The impact of coupled fracture flow and formation flow on the fracture response to external mechanical loading as well as internal hydraulic loading from fluid injection was investigated, and the results are discussed.