Effective Macrodiffusion in Solute Transport Through Heterogeneous Porous Media

TL;DR

This paper uses homogenization to derive an effective macroscopic model for solute transport in highly heterogeneous porous media, validated through numerical simulations showing good agreement with detailed heterogeneous models.

Contribution

It introduces a homogenization-based approach to model macrodiffusion in heterogeneous porous media, including numerical methods for effective property computation.

Findings

Effective hydraulic conductivity and macrodiffusivity tensor computed numerically.

Simulations show good agreement between heterogeneous and effective medium models.

Spatial moments, L2 errors, and concentration contours confirm model accuracy.

Abstract

Homogenization method is used to analyse the equivalent behavior of transient flow of a passive solute through highly heterogeneous porous media. The flow is governed by a coupled system which includes an elliptic equation and a linear convection-diffusion concentration equation with a diffusion term small with respect to the convection, i.e. a high Peclet number is considered. Asymptotic expansions lead to the definition of a macroscale transport model. Numerical computations to obtain the effective hydraulic conductivity and the macrodiffusivity tensor have been carried out via finite volume methods. Numerical experiments related to the simulations of solute transport have been performed comparing the heterogeneous medium to the corresponding effective medium. The results of the simulations are compared in terms of spatial moments, L2 errors and concentration contours. Results obtained from the simulations using the model obtained by the homogenization method show good agreement with the heterogeneous simulations.