Discontinuous and continuous Galerkin methods for compressible single-phase and two-phase flow in fractured porous media. (October 2021)

• Record Type: Journal Article
• Authors: Ma, Tianran; Zhang, Keni; Shen, Weijun; Guo, Chaobin; Xu, Hao
• Is Part Of: Advances in water resources. Volume 156(2021)
• Publication Date: 2021-10
• Subjects: Fractured porous media -- Discontinuous Galerkin -- Compressible flow -- Discrete fractured model; Hydrology -- Periodicals; Hydrodynamics -- Periodicals; Hydraulic engineering -- Periodicals; 551.48
• DOI: 10.1016/j.advwatres.2021.104039
• Languages: English
• ISSNs: 0309-1708

Abstract

Highlights: Discontinuous and continuous Galerkin approximations for compressible single-phase and two-phase flow in fractured porous media were developed. Conducting and blocking fractures were modelled as reduced-dimensional interfaces for flow in porous media. The continuity and jumps in pressure and saturation between the two sides of the matrix-fracture interface were captured. 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.