Method of model reduction and multifidelity models for solute transport in random layered porous media

TL;DR

This paper develops a hierarchical stochastic model for solute transport in layered porous media, extending classical dispersion theory to account for random permeability and velocity fluctuations, revealing non-monotonic dispersion behavior.

Contribution

It introduces a novel hierarchical model that generalizes Taylor-Aris dispersion to stochastic layered media with explicit equations for concentration and dispersion.

Findings

Velocity fluctuations can non-monotonically enhance dispersion.

Maximum dispersion enhancement occurs at a specific correlation length.

The model provides explicit expressions for effective velocity and dispersion.

Abstract

This work presents a hierarchical model for solute transport in bounded layered porous media with random permeability. The model generalizes the Taylor-Aris dispersion theory to stochastic transport in random layered porous media with a known velocity covariance function. In the hierarchical model, we represent (random) concentration in terms of its cross-sectional average and a variation function. We derive a one-dimensional stochastic advection-dispersion-type equation for the average concentration and a stochastic Poisson equation for the variation function, as well as expressions for the effective velocity and dispersion coefficient. We observe that velocity fluctuations enhance dispersion in a non-monotonic fashion: the dispersion initially increases with correlation length {\lambda}, reaches a maximum, and decreases to zero at infinity. Maximum enhancement can be obtained at the correlation length about 0.25 the size of the porous media perpendicular to flow.