Upscaling transport in heterogeneous media featuring local-scale dispersion: flow channeling, macro-retardation and parameter prediction

TL;DR

This study investigates how local-scale dispersion affects flow channeling, macro-retardation, and parameter prediction in heterogeneous media, revealing the importance of flow channeling and effective retardation in transport modeling.

Contribution

It introduces a Monte Carlo approach to analyze the interplay of local dispersion with heterogeneity, and develops empirical equations for CTRW parameter prediction based on heterogeneity statistics.

Findings

Flow channeling occurs at all heterogeneity levels.

Significant effective retardation is associated with increased flow channeling.

Limited Taylor-type macrodispersion is observed and explained.

Abstract

Many theoretical treatments of transport in heterogeneous Darcy flows consider advection only. When local-scale dispersion is neglected, flux-weighting persists over time; mean Lagrangian and Eulerian flow velocity distributions relate simply to each other and to the variance of the underlying hydraulic conductivity field. Local-scale dispersion complicates this relationship, potentially causing initially flux-weighted solute to experience lower-velocity regions as well as Taylor-type macrodispersion due to transverse solute movement between adjacent streamlines. To investigate the interplay of local-scale dispersion with conductivity log-variance, correlation length, and anisotropy, we perform a Monte Carlo study of flow and advective-dispersive transport in spatially-periodic 2D Darcy flows in large-scale, high-resolution multivariate Gaussian random conductivity fields. We observe flow channeling at all heterogeneity levels and quantify its extent. We find evidence for substantial effective retardation in the upscaled system, associated with increased flow channeling, and observe limited Taylor-type macrodispersion, which we physically explain. A quasi-constant Lagrangian velocity is achieved within a short distance of release, allowing usage of a simplified continuous-time random walk (CTRW) model we previously proposed in which the transition time distribution is understood as a temporal mapping of unit time in an equivalent system with no flow heterogeneity. The numerical data set is modeled with such a CTRW; we show how dimensionless parameters defining the CTRW transition time distribution are predicted by dimensionless heterogeneity statistics and provide empirical equations for this purpose.