XFVM Modelling of Fracture Aperture induced by Shear and Tensile Opening

Abstract

In reservoir simulation, it is important to understand the mechanical behaviour of fractured rock and the effect of shear and tensile displacements of fractures on their aperture. Tensile opening directly enhances the fracture aperture, whereas shear of a preexisting rough-walled fracture creates aperture changes dependent on the local stress state. Since fracture dilatation increases reservoir permeability, both processes must be included in a realistic and consistent manner into the mechanical reservoir simulation model. Here, we use the extended finite volume method (XFVM) to conduct flow and geomechanics simulations. In XFVM, fractures are embedded in a poroelastic matrix and are modelled with discontinuous basis functions. On each fracture segment the tractions and compressive forces are calculated, and one extra degree of freedom is added for the shear and tensile displacement, respectively. To embed multiple intersecting fractures into non-conforming Cartesian grids of a given resolution, a merging technique is utilized which locally adapts fracture geometry and topology. Merging critical segments by retaining only the weakest links allows us to embed any kind of intersecting and branching fractures into the grid. In this particular XFVM implementation, we assume that linear elasticity and steady state fluid pressure adequately constrain the effective stress. This allows us to integrate the stress equation to obtain force balances and then solve for the grid deformation, and the fracture shear and tensile displacements. In this paper, shear dilatation is not calculated a posteriori, but it enters the equations such that aperture changes directly affect the stress state. This is accomplished by adding shear dilatation to the displacement gradients and, therefore ascertains a consistent representation in the stress-strain relations and force balances. We illustrate and discuss the influence of this newly added term in simple test cases and in a realistic layer-restricted two-dimensional fracture network subjected to plausible in situ stress and pore pressure conditions.