Parametric Effects on River Pollution in Heterogeneous Porous Media: An Analytical Approach

This study presents an approximate analytical solution to the one-dimensional advection-dispersion equation for conservative solute transport in a heterogeneous porous medium. The model incorporates a uniform pulse-type point source and assumes an initial pollution profile that is exponentially decreasing. To accurately reflect environmental heterogeneity, both the dispersion coefficient and flow velocity are treated as time- and position-dependent functions. Using the Reduced Differential Transform Method (RDTM), general solutions are derived for two distinct cases: decreasing and increasing unstable variations in velocity and dispersion. Comprehensive numerical and graphical analyses are conducted to compare these scenarios. The findings illustrate the profound impact of unstable parameters and heterogeneity on the pollutant concentration profile. Furthermore, the results specifically highlight how the initial dispersion coefficient dictates river pollution dynamics, providing valuable insights for water quality modeling.