One-dimensional spatially dependent solute transport in semi-infinite porous media: an analytical solution

Abstract

The present study is an attempt to describe analytical solution of spatially dependent solute transport in one-dimensional semiinfinite homogeneous porous domain. In this mathematical model the dispersion coefficient is considered spatially dependent while seepage velocity is considered exponentially decreasing function of space. Dispersion parameter and velocity are directly proportional to each other. Space dependent retardation factor is also taken. The nature of porous media and solute pollutant are considered chemically non-reactive. Initially porous domain is considered solute free and the input source condition is considered uniformly continuous. A new transformation is introduced to solve the advection dispersion equation. The analytical solution is obtained by using Laplace Transformation Techniques (LTT). The effects of spatial dependence on the solute concentration dispersion of various physical parameters are explained with help of different graphs.

Keywords: Diffusion, Seepage velocity, Retardation, Aquifer, Laplace transformation, Pollutant