Solute transport with decay type input source in one-dimensional heterogeneous groundwater: analytical solution

The process of aquifer remediation extends with the growing dependence on groundwater.Mathematical model of solute transport in porous media is important tool used to characterise the extent of approximating the shape, size and position of a contaminant.In the present study, an unsteady solute transport model advection-diffusion equation (ADE) is taken and analytical solutions were obtained by using Laplace integral transformation technique (LITT).The concentration is predicted in presence and absence of source, i.e., firstly initially medium (aquifer/air) is not supposed to be solute free, i.e., initially domain is already polluted/contaminated and secondly the medium is clean, taking decay type exponential input at origin.The dependence of velocity on space variable is of linear non-homogeneous nature due to heterogeneity of the semi-infinite horizontal dispersion medium.The dispersivity is considered square of the velocity which represents the seasonal variation of the year in tropical regions.