A multiscale quasilinear system for colloids deposition in porous media: Weak solvability and numerical simulation of a near-clogging scenario

TL;DR

This paper develops a multiscale quasilinear model for colloid deposition in porous media, analyzing its weak solvability and providing numerical simulations that illustrate near-clogging scenarios.

Contribution

It introduces a novel coupled reaction-diffusion and elliptic system with a feedback mechanism, and proves its weak solvability using Schauder's fixed point theorem, along with a convergent numerical method.

Findings

Numerical simulations demonstrate colloid concentration behavior near clogging.

The model captures multiscale interactions in porous media.

A convergent iterative scheme for approximating solutions is established.

Abstract

We study the weak solvability of a quasilinear reaction-diffusion system nonlinearly coupled with an linear elliptic system posed in a domain with distributed microscopic balls in $2D$. The size of these balls are governed by an ODE with direct feedback on the overall problem. The system describes the diffusion, aggregation, fragmentation, and deposition of populations of colloidal particles of various sizes inside a porous media made of prescribed arrangement of balls. The mathematical analysis of the problem relies on a suitable application of Schauder's fixed point theorem which also provides a convergent algorithm for an iteration method to compute finite difference approximations of smooth solutions to our multiscale model. Numerical simulations illustrate the behavior of the local concentration of the colloidal populations close to clogging situations.