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

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.

12 pages, 9 figures

References in corpus (7)

• Fractional Calculus: Some Basic Problems in Continuum and Statistical Mechanics
• Depinning of three-dimensional drops from wettability defects
• Generalized Diffusion
• Continuous-time random-walk approach to normal and anomalous reaction-diffusion processes
• A model of dispersive transport across sharp interfaces between porous materials
• Mass transport subject to time-dependent flow with non-uniform sorption in porous media
• A nonlinear random walk approach to concentration-dependent contaminant transport in porous media

Cited by in corpus (5)

• Universal cover-time distribution of heterogeneous random walks
• Variational integrator for fractional Euler-Lagrange equations
• Variational integrators of fractional Lagrangian systems in the framework of discrete embeddings
• A class of fractional optimal control problems and fractional Pontryagin's systems. Existence of a fractional Noether's theorem
• Variational integrator for fractional Pontryagin's systems. Existence of a discrete fractional Noether's theorem