Alternative Solution for Advective-Dispersive Flow of Reagent Solutes in Clay Liners

Abstract

An analytical solution for the advection-dispersion equation, including sorption effects, was first proposed by Akio Ogata and Robert Banks in 1961. This solution allows the computation of the percentage of dissipation of the contamination plume at a given point in space and time. However, environmental engineers generally wish to determine the time period necessary for this dissipation to take place to reach a minimum acceptable level established in environmental laws. This paper presents a simplified solution that closely matches the exact solution but has the advantage of allowing a numerical-analytical computation of the flow time and/or thickness of the clay liner, using a scheme also developed in this paper. The proposed solution is compared with the simplified solution known as first-order approximation. The comparison shows that, contrary to the method proposed here, the first-order approximation does not satisfy the limit case of purely diffusive flow and gives unsafe estimates of the solute concentration, by as much as 50% lower than the exact values.