Analytic solutions to the advective contaminant transport equation with non-linear sorption

Abstract

SUMMARYThis paper considers advective transport of a soluble contaminant through saturated soil with non-linear sorption of the contaminant onto a stationary porous media. The non-linear sorption isotherms considered in the transport analysis are the Langmuir and Freundlich sorption isotherms. A special case of the Freundlich sorption isotherm is the linear sorption isotherm, and it is shown that in this case transport through a homogeneous soil results in the initial concentration pro"le simply being translated in the direction of the groundwater #ow. However, when the sorption isotherm is non-linear the initial concentration pro"le distorts as it is translated with the groundwater #ow, leading to the development of concentration shock fronts and rarefactions. Analytic solutions to the non-linear "rst-order hyperbolic equations are developed for a number of contaminant transport problems of practical signi"cance. It is shown that in the case of the Langmuir sorption isotherms, shock fronts develop at the leading edge of the concentration pro"le while for the Freundlich sorption isotherm shock fronts may develop at either the leading or trailing edge of the concentration pro"le.

A comprehensive study on numerical analysis of contaminant migration process in compacted clay liner and underlying aquifer for MSW landfill

“…The following Langmuir's isotherm sorption is commonly used to describe the non-linear sorption relationship of soil and contaminants (Sheng & Smith, 1999) …”

“…For the non-linear sorption, the production of contaminants is related to the advection velocity and concentration, and the transmission velocity tends to increase from the zone of high concentration towards the zone of low concentration. While, for the linear sorption, the advection velocity depends on the hysteresis facto rather than the concentration (Sheng & Smith, 1999). Although the non-linear sorption enhances breakthrough ability, the amount of contaminants passing through the CCL obviously decreases.…”

Semi-analytical solutions of a contaminant transport equation with nonlinear sorption in 1D

“…Analytical solutions for the purely convective case of contaminant transport with nonlinear sorption using simple initial and boundary data have been described by Sheng and Smith [26]. Independently, a general case of piecewise constant initial and boundary data was solved by different analytical methods in [16] for the same equation, where long-time behaviours such as collapses of shocks were likewise considered.…”

“…Particularly, the rarefaction waves w * (y, t) and u * (y, t) are given by the same formulas (26) and (27).…”

Assessment of the contamination of drinking water supply wells by pesticides from surface water resources using a finite element reactive transport model and global sensitivity analysis techniques

“…Degradation kinetics are assumed to follow a first-order rate with half lives for aerobic and for anaerobic conditions. Despite the fact that for many pollutants sorption is often better described by non-linear isotherms, linear sorption isotherms were considered when calculating the retardation factor, because low concentrations are expected and computations are simplified by avoiding sorption related concentration shock fronts and rarefactions (Sheng and Smith, 1999). Such a simplification is a common assumption in reactive transport modeling (Schäfer et al, 1998;Henderson et al, 2009).…”