On the homogenization of multicomponent transport

TL;DR

This paper develops a homogenization method for multicomponent transport systems in porous media with periodic structures, using spectral analysis and two-scale convergence to derive effective models in strong convection regimes.

Contribution

It introduces a novel combination of factorization and two-scale convergence techniques for homogenizing coupled parabolic systems with periodic coefficients.

Findings

Derived effective equations for multicomponent flow in porous media.

Validated the homogenization approach through an adsorption model example.

Provided a framework for analyzing strongly convective multicomponent systems.

Abstract

This paper is devoted to the homogenization of weakly coupled cooperative parabolic systems in strong convection regime with purely periodic coefficients. Our approach is to factor out oscillations from the solution via principal eigenfunctions of an associated spectral problem and to cancel any exponential decay in time of the solution using the principal eigenvalue of the same spectral problem. We employ the notion of two-scale convergence with drift in the asymptotic analysis of the factorized model as the lengthscale of the oscillations tends to zero. This combination of the factorization method and the method of two-scale convergence is applied to upscale an adsorption model for multicomponent flow in an heterogeneous porous medium.