Limiting analysis of a crystal dissolution and precipitation model coupled with the unsteady stokes equations in the context of porous media flow

TL;DR

This paper analyzes a complex coupled PDE-ODE system modeling crystal dissolution and precipitation in porous media, establishing existence, uniqueness, and upscaling of solutions through iterative limit analysis and modified extension operators.

Contribution

It introduces a novel iterative limit analysis for a nonlinear coupled system with multiscale features and proves the existence and uniqueness of solutions, including an upscaled model.

Findings

Proved existence of a unique global weak solution.

Established the upscaled model's well-posedness.

Developed a modified extension operator for upscaling.

Abstract

We study the diffusion-reaction-advection model for mobile chemical species together with the dissolution and precipitation of immobile species in a porous medium at the micro-scale. This leads to a system of semilinear parabolic partial differential equations in the pore space coupled with a nonlinear ordinary differential equation at the grain boundary of the solid matrices. The fluid flow within the pore space is given by unsteady Stokes equation. The novelty of this work is to do the iterative limit analysis of the system by tackling the nonlinear terms, monotone multi-valued dissolution rate term, space-dependent non-identical diffusion coefficients and nonlinear precipitation (reaction) term. We also establish the existence of a unique positive global weak solution for the coupled system. In addition to that, for upscaling we introduce a modified version of the extension operator. Finally, we conclude the paper by showing that the upscaled model admits a unique solution.