An Analytical Approach to Contaminant Transport with Spatially and Temporally Dependent Dispersion in a Heterogeneous Porous Medium

This study presents an analytical solution to the one-dimensional advection-dispersion equation (ADE) for a semi-infinite heterogeneous aquifer system with space and time-dependent groundwater velocity and dispersion coefficient. The dispersion coefficient is assumed to be proportional to the groundwater flow velocity. In addition, retardation factor, first-order decay and zero-order production terms are also considered. Contaminants and porous media are assumed to be chemically inert. Initially, it is assumed that some uniformly distributed solutes are already present in the aquifer domain. The input point source is considered uniformly continuous and increasing nature in a semi-infinite porous medium. The solutions are obtained analytically using the Laplace Integral Transform Technique (LITT). The nature of the concentration profile of the resulting solution for different parameters in different time domains is illustrated graphically.