Solute Transport in a Semi-Infinite Geological Formation with Variable Porosity

Abstract

Using the Laplace integral transform technique (LITT), an analytical solution to the advection–dispersion–reaction (ADR) equation for a semi-infinite homogeneous geological formation is derived, considering the effect of a retardation factor, zero-order production, and a first-order decay constant. The initial pollutant concentration is considered space dependent in the direction of longitudinal flow in the formation (i.e., aquifer and aquitard). At one end of the aquifer, i.e., the origin, pollutant through time-dependent source concentration is taken into account; but at the other end of the aquifer, the concentration gradient is assumed to be zero due to the uniform flow of the contaminant with respect to the spatial variable. The analytical solution may help evaluate the pattern of concentration for exponentially decreasing or sinusoidally varying unsteady flow in different types of geological formations with average porosity values. The analytical solution is compared with a numerical solution, and they are found to be in very good agreement. The accuracy of the solution is verified with root-mean-square-error (RMSE or RMS-error) analysis.