Temporal Moments Analysis of Transport in Chemically Heterogeneous Porous Media

Abstract

Temporal moments analysis is used to study the impact of chemical heterogeneity on the one-dimensional transport of a pollutant that undergoes linear kinetic adsorption. We make an important simplifying assumption by considering that the aquifer is physically homogeneous, but chemically heterogeneous. The aquifer is assumed to be comprised of distinct reactive and nonreactive zones; in the reactive zones the pollutant undergoes linear kinetic adsorption. The distribution of reactive sites along the porous medium is characterized using two different approaches, stochastic and deterministic. A Bernoulli random process is used in the first approach, whereas a Fourier series is used in the second. In the stochastic approach the adsorption rate constant is also allowed to vary randomly. An approximate analytical solution for the temporal moments of the stochastic problem and an exact solution for the periodic problem are obtained. Temporal moments derived from this analysis are used to compute effective parameters (velocity and dispersion) as a function of the distance from the initial contaminant injection. Our results show that the overall effective dispersion coefficient is a sum of three terms accounting for the processes of equilibrium adsorption, kinetic adsorption, and chemical heterogeneity, respectively. We examine the impact of the adsorption rate parameter upon overall spreading and show that the magnitude of this rate parameter governs the relative contribution of chemical heterogeneity. A comparison between the effective parameters for the stochastic and periodic problem and the sensitivity of the results to physical and chemical parameters are also addressed.