Mathematical modeling of pollutant transport in river Fena in Ghana

Abstract

In this study, we derived two analytical solutions to a one-dimensional Advection-Diffusion Equation (ADE). The ADE is solved using a constant and exponentially decaying inlet boundary condition, together with Dirichlet and Neumann outlet conditions. The analytic solutions are shown to be simple if a combination of the initial concentration and the transformed boundary condition results in a non-zero singularity pole of inverse Laplace transform. The differences between the two analytic solutions are elucidated. Moreover, the analytical solutions are compared to some observational data from the Fena River in the Ashanti region of Ghana where illegal mining activities (locally referred to as “galamsey”) have been reported. The analytical results well capture the concentration of iron at two sampling locations for both the Dirichlet and Neumann models but poorly predict the concentration at a third location. Some possible reasons for this discrepancy have been hypothesized for future investigations.