A continuous time random walk model of transport in variably saturated heterogeneous porous media

TL;DR

This paper introduces a unified continuous time random walk model for fluid and solute transport in variably saturated heterogeneous porous media, deriving nonlinear PDEs and validating with Monte Carlo simulations.

Contribution

It develops a general framework using fractal MIM CTRW to model heterogeneity effects in porous media transport, deriving new nonlinear PDEs.

Findings

Derived nonlinear PDEs for heterogeneous media transport.

Validated model solutions against Monte Carlo simulations.

Applicable to various initial and boundary conditions.

Abstract

We propose a unified physical framework for transport in variably saturated porous media. This approach allows fluid flow and solute migration to be treated as ensemble averages of fluid and solute particles, respectively. We consider the cases of homogeneous and heterogeneous porous materials. Within a fractal mobile-immobile (MIM) continuous time random walk framework, the heterogeneity will be characterized by algebraically decaying particle retention-times. We derive the corresponding (nonlinear) continuum limit partial differential equations and we compare their solutions to Monte Carlo simulation results. The proposed methodology is fairly general and can be used to track fluid and solutes particles trajectories, for a variety of initial and boundary conditions.