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 chemica l heterogeneity on the one-dimensional transport of a pollutant that u ndergoes linear kinetic adsorption. We make an important simplifying a ssumption that the aquifer is physically homogeneous but chemically he terogeneous. The aquifer is assumed to be comprised of two distinct zo nes: reactive and nonreactive; a Bernoulli random process is used to c haracterize the spatial distribution of reactive zones along the aquif er. We develop analytical solutions to study the distribution of the e nsemble mean, standard deviation, and coefficient of variation of the dissolved concentration after an instantaneous injection of contaminan t. In addition, numerical solutions based on a Monte Carlo approach ar e 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 dis persion) that capture the impact of chemical heterogeneity. Temporal m oment analysis provides closed-form analytical expressions for the asy mptotic effective velocity and dispersion, while spatial moment analys is explains the effect of chemical heterogeneity on the preasymptotic value of these effective parameters. A key result from our analysis sh ows that chemical heterogeneity creates ''pseudokinetic'' or ''macroki netic'' conditions characterized by a time-dependent effective retarda tion coefficient even when the local equilibrium assumption is invoked .