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

arXiv: https://arxiv.org/abs/2010.04994 · HTML: https://mlsanity.com/paper/2010.04994/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Oct 2020.

## Built on by (most cited first, 5 of 5)

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- [Non-intrusive reduced order modeling of natural convection in porous media using convolutional autoencoders: comparison with linear subspace techniques](https://mlsanity.com/paper/2107.11460/) (2021)
- [Reduced order modeling for flow and transport problems with Barlow Twins self-supervised learning](https://mlsanity.com/paper/2202.05460/) (2022)
- [Non-intrusive reduced order modeling of poroelasticity of heterogeneous media based on a discontinuous Galerkin approximation](https://mlsanity.com/paper/2101.11810/) (2021)
- [Progressive reduced order modeling: empowering data-driven modeling with selective knowledge transfer](https://mlsanity.com/paper/2310.03770/) (2023)

## Abstract (arXiv)

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.