Analytical Solutions for Scale and Time Dependent Solute Transport in Heterogeneous Porous Medium

Abstract

Contaminated groundwater has been a serious problem across the world for many years as it has a bad impact on the quality of groundwater as well as on the environment. This study considers the solute transport problem in a heterogeneous porous medium with scale and time-dependent dispersion. The heterogeneity of porous media at the microscopic level facilitates dispersion, which affects groundwater flow patterns and solute distribution. For this work, the porous formation is assumed to be of semi-infinite length and of adsorbing nature. The key parameters such as dispersion coefficient and groundwater velocity are considered to be spatially and temporally dependent functions in degenerated forms. In addition, the first-order decay and zero-order production terms are also considered as time-dependent functions. Initially, it is assumed that the aquifer is uniformly polluted. Two different types of input sources namely uniform and varying nature are considered along the flow at one end in two separate cases, while concentration gradient, at non-source end boundary, is supposed to be zero. An analytical solution of the current boundary value problem is obtained using the Laplace Integral Transform Technique (LITT). The results obtained from the proposed problem are demonstrated graphically for a particular time functions in dispersion and groundwater velocity.