Enriched Galerkin discretization for modeling poroelasticity and permeability alteration in heterogeneous porous media

Abstract

In this paper, we utilize the enriched Galerkin (EG) finite element method for the flow equation in Biot's system, which provides a robust locally conservative flux in heterogeneous porous media. The computational algorithm to solve the coupled system with the permeability alteration is presented with the linearization and Picard's iterative scheme. The block structure is utilized for the linear system in numerical discretization, and the computer code is shared in the open-source platform. In the numerical experiments, we compare the proposed EG method with the classical continuous Galerkin (CG) and discontinuous Galerkin (DG) finite element methods in different scenarios, including the North sea reservoirs setup. While DG and EG methods provide similar approximations for the pressure solutions, the CG method produces spurious oscillations in fluid pressure and volumetric strain solutions near the material interfaces, especially for the soft materials. The difference of flux approximation between EG and DG methods is insignificant; still, the EG method demands approximately two and three times fewer degrees of freedom than the DG method for two- and three-dimensional geometries.