Quantifying Transport of Arsenic in Both Natural Soils and Relatively Homogeneous Porous Media using Stochastic Models

Abstract

Core Ideas A tempered time fractional‐derivative equation to model Arsenic transport in soil is proposed. Arsenic kinetics of leaching and flushing was affected by multi‐rate sorption–desorption. Model parameters changed with soil properties, such as clay content and pH condition. The widespread distribution of arsenic in soils is a pollution source that jeopardizes human health, and the transport of arsenic (As) under various conditions is not fully understood and quantified. This study proposes a tempered time fractional advection‐dispersion equation (fADE), to model the rate‐limited diffusion and sorption–desorption of As in soil. Applications show that the time fADE can effectively capture skewed breakthrough curves (BTCs) of As leaching from natural soils, which contain multiple stages of desorption that cannot be fully described by the single‐rate mass transfer (SRMT) model. The time fADE model parameters change with soil properties, such as clay content and pH condition. For comparison purposes, a series of As injection column experiments packed with glass beads were conducted to generate BTCs under various hydrologic conditions. Applications show that the time fADE and the multi‐rate mass transfer (MRMT) model perform better than the SRMT model in characterizing non‐Fickian dynamics, especially for prolonged retention, in most runs of leaching and flushing experiments. Parameters in the MRMT model and the time fADE can be linked to simplify the fitting procedure. Such simplification and representation of experimental conditions demonstrate the promise and applicability of the time fADE model for capturing As transport in soil.