Mathematical modeling of groundwater contamination with varying velocity field

In this study, analytical models for predicting groundwater contamination in isotropic and homogeneous porous formations are derived. The impact of dispersion and diffusion coefficients is included in the solution of the advection-dispersion equation (ADE), subjected to transient (time-dependent) boundary conditions at the origin. A retardation factor and zero-order production terms are included in the ADE. Analytical solutions are obtained using the Laplace Integral Transform Technique (LITT) and the concept of linear isotherm. For illustration, analytical solutions for linearly space- and time-dependent hydrodynamic dispersion coefficients along with molecular diffusion coefficients are presented. Analytical solutions are explored for the Peclet number. Numerical solutions are obtained by explicit finite difference methods and are compared with analytical solutions. Numerical results are analysed for different types of geological porous formations i.e., aquifer and aquitard. The accuracy of results is evaluated by the root mean square error (RMSE).