A stabilized mixed discontinuous Galerkin formulation for double porosity/permeability model

TL;DR

This paper introduces a stable mixed discontinuous Galerkin formulation for the double porosity/permeability model, enabling accurate and efficient simulation of fluid flow in porous media with multiple pore-networks, applicable to geological and hydrocarbon recovery contexts.

Contribution

The paper presents a novel, stable mixed DG formulation for the DPP model that allows equal-order interpolation, is residual-based, mesh-independent, and supports non-conforming meshes, improving simulation robustness.

Findings

The formulation is proven to be consistent, stable, and convergent.

It supports non-conforming discretizations and distorted meshes.

It improves local mass balance and captures physical instabilities.

Abstract

Modeling flow through porous media with multiple pore-networks has now become an active area of research due to recent technological endeavors like geological carbon sequestration and recovery of hydrocarbons from tight rock formations. Herein, we consider the double porosity/permeability (DPP) model, which describes the flow of a single-phase incompressible fluid through a porous medium exhibiting two dominant pore-networks with a possibility of mass transfer across them. We present a stable mixed discontinuous Galerkin (DG) formulation for the DPP model. The formulation enjoys several attractive features. These include: (i) Equal-order interpolation for all the field variables (which is computationally the most convenient) is stable under the proposed formulation. (ii) The stabilization terms are residual-based, and the stabilization parameters do not contain any mesh-dependent parameters. (iii) The formulation is theoretically shown to be consistent, stable, and hence convergent. (iv) The formulation supports non-conforming discretizations and distorted meshes. (v) The DG formulation has improved element-wise (local) mass balance compared to the corresponding continuous formulation. (vi) The proposed formulation can capture physical instabilities in coupled flow and transport problems under the DPP model.