Non-Fickian Mechanism of Contaminant Transport in Unsaturated Heterogeneous Soils.

Contaminant transport through natural, heterogeneous soil formations has been well documented as scale-dependent. A dispersion coefficient used in the classical second-order advection-dispersion equation must grow with mean travel distance in order to match the moment (usually the second-order) of the solute plume. Scale-dependent dispersion can result in non-Fickian behaviors which have been attributed to intrinsic heterogeneity of natural media. Important progresses have been made in nonlocal transport theories, including the fractional advection-dispersion equations that have been applied extensively to describe the non-Fickian transport for nonreactive tracers in saturated zone. In this study, we investigate the non-local mechanism under gravity-dominated conditions in unsaturated soils. The ultimate goal is to understand and characterize efficiently the scale effect on contaminant transport in the unsaturated heterogeneous soils. We first simulate fine scale flow and contaminant transport in the unsaturated zone under gravity-dominated conditions based on distributed heterogeneous hydraulic parameters. The probability density function characterizing particle jump statistics is then defined based on the simulated velocity distributions in unsaturated soils. The jump size density is introduced into the framework of continuous time random walks, to define the corresponding stochastic process (continuously in space and time) and then derive the underlying governing transport equation. By comparing these two results from the fine grid scale modeling based on traditional advection and dispersion equations and those from the unsaturated zone extension of the nonlocal approach, we establish relationships between critical fractional parameters and soil hydraulic properties.