Spatial Moment Equations for a Groundwater Plume with Degradation and Rate-Limited Sorption

Abstract

In this paper, the authors analytically derive the solution for the spatial moments of groundwater solute concentration distributions simulated by a one-dimensional model that assumes advective-dispersive transport with first-order degradation and rate-limited sorption. Sorption kinetics are assumed to be governed by a first-order rate model, and degradation is assumed to occur in the aqueous (i.e., mobile) phase only. As an extension of a previously published moment analysis of a model with similar assumptions, an explicit analytical solution is presented for the zeroth, first, and second spatial moments, as well as equations that describe the behavior of the first and second moments at long times. Moment simulations show that when the degradation rate is relatively large compared to the sorption rate, there are time periods in which the first and second spatial moments of the solute concentration distribution (the mean and variance, respectively) decrease over time. At long times, it is seen that the first and second moments increase linearly with time, indicating that velocity and dispersion are constant.