Discontinuous and continuous Galerkin methods for compressible single-phase and two-phase flow in fractured porous media

Abstract

Accurate simulation of flow behaviors in fractured porous media is challenging. We present a discontinuous Galerkin (DG) approximation and continuous Galerkin (CG) approximation for compressible single- and two-phase flow in porous media with conducting (high permeable) and blocking (low permeable) fractures using a mixed-dimensional approach in which the fracture is described as a reduced-dimensional interface coupled with linear transmission conditions. The proposed DG/CG method was first verified with single-phase fractured flow benchmark cases and then applied to time-dependent single-phase flow cases. The simulated results demonstrate that the DG/CG method is capable of capturing the continuity as well as the jump in pressure between the two sides of the matrix-fracture interface. For the two-phase flow cases, we verify the DG/CG method with a reference case involving a complex fracture configuration. Subsequently, we analyze several cases to study two-phase flow through a single fracture and a discrete fracture network in two dimensions. Overall, the simulation results show that the developed DG/CG approach can reliably predict the flow behaviors for single- and two-phase flow in fractured porous media.