A DG-based interface element method for modeling hydraulic fracturing in porous media

Abstract

Fracture propagation coupled with fluid flow in porous media has very important applications in fracking in oil and gas reservoirs, corrosion in ceramics, and degradation of human bones. Modeling fracture failure in porous media governed by the coupled solid and fluid field equations is challenging and time-consuming. This paper extends discontinuous Galerkin (DG) finite element methods to model crack openings in porous media through exploiting an easy construction of interfaces for potential crack paths by locally breaking continuous elements. Consequently, a finite element mesh for fracture apertures is completely and gracefully constructed using DG interface objects as well as the definitions of jumps of displacements across the DG interfaces defined for bulk matrices. Furthermore, rigid cohesive laws often adopted for crack openings can be naturally implemented in DG formulations without introducing artificial stiffness, which may eventually improve the performance for implicit formulations in handling crack openings in porous media. In this work, we perform a consistent, fully implicit, and fully coupled hybrid DG/continuous finite element formulation for three field equations including the solid, bulk fluid, and fluid in fracture apertures resulting from crack openings. We verify our DG formulation and implementation using the Khristianovich-Geertsma-DeKlerk analytical solutions. Finally, we further demonstrate a good performance of the proposed DG method by modeling fracking in an oil reservoir containing two nature fractures.