A Locally Conservative Mixed Finite Element Framework for Coupled Hydro-Mechanical-Chemical Processes in Heterogeneous Porous Media

TL;DR

This paper introduces a mixed finite element framework combining locally conservative schemes for simulating coupled hydro-mechanical-chemical processes in heterogeneous porous media, ensuring local mass conservation with computational efficiency.

Contribution

It develops a novel combined discretization approach that guarantees local mass conservation for complex reactive flow and deformation in heterogeneous media, including nonlinear reactions.

Findings

Framework is robust across various heterogeneity levels.

Ensures local mass conservation in coupled processes.

Efficient for complex reactive flow simulations.

Abstract

This paper presents a mixed finite element framework for coupled hydro-mechanical-chemical processes in heterogeneous porous media. The framework combines two types of locally conservative discretization schemes: (1) an enriched Galerkin method for reactive flow, and (2) a three-field mixed finite element method for coupled fluid flow and solid deformation. This combination ensures local mass conservation, which is critical to flow and transport in heterogeneous porous media, with a relatively affordable computational cost. A particular class of the framework is constructed for calcite precipitation/dissolution reactions, incorporating their nonlinear effects on the fluid viscosity and solid deformation. Linearization schemes and algorithms for solving the nonlinear algebraic system are also presented. Through numerical examples of various complexity, we demonstrate that the proposed framework is a robust and efficient computational method for simulation of reactive flow and transport in deformable porous media, even when the material properties are strongly heterogeneous and anisotropic.