Stochastic analysis of one-dimensional transport of kinetically adsorbing solutes in chemically heterogeneous aquifers

A small perturbation approach is used to analyze the impact of chemical heterogeneity on the one-dimensional transport of a pollutant that undergoes linear kinetic adsorption. We make an important simplifying assumption that the aquifer is physically homogeneous but chemically heterogeneous. The aquifer is assumed to be comprised of two distinct zones: reactive and nonreactive; a Bernoulli random process is used to characterize the spatial distribution of reactive zones along the aquifer. We develop analytical solutions to study the distribution of the ensemble mean, standard deviation, and coefficient of variation of the dissolved concentration after an instantaneous injection of contaminant. In addition, numerical solutions based on a Monte Carlo approach are used to determine the validity of the analytical solutions. Finally, an analysis involving temporal and spatial moments is used to derive expressions for the large-scale effective parameters (velocity and dispersion) that capture the impact of chemical heterogeneity. Temporal moment analysis provides closed-form analytical expressions for the asymptotic effective velocity and dispersion, while spatial moment analysis explains the effect of chemical heterogeneity on the preasymptotic value of these effective parameters. A key result from our analysis shows that chemical heterogeneity creates ''pseudokinetic'' or ''macrokinetic'' conditions characterized by a time-dependent effective retardation coefficient even when the local equilibrium assumption is invoked.