Analytical Solution of the One-Dimensional Transport of Ionic Contaminants in Porous Media with Time-Varying Velocity

Abstract

The one-dimensional convection–dispersion equation has been widely used to describe the migration process of contaminant leachate through barriers. However, most of the existing solutions are limited to simple conditions. In this study, a one-dimensional convection–dispersion model with time-dependent velocity was established while considering the change in the permeability coefficient. The analytical solution of the model was obtained by using the integral transformation method. Based on the analytical model, three special conditions were assumed for comparison. The results showed that the concentration levels of pollutants inside the barrier would significantly increase with the increase in the flow velocity, and the pollutant concentrations inside the barrier would be increased by four times compared with the normal flow velocity when the flow rate increased by two times. The transports of heavy metal ions with variable velocities through soil–bentonite and soil–attapulgite barriers were predicted under field conditions. The predicted results showed that the breakthrough time would be reduced by as much as two times. In engineering practice, a barrier’s service performance can be improved by controlling the temperature of the seepage field and improving the chemical compatibility of the barrier materials.