Analytical Solution for One-Dimensional Solute Dispersion with Time-Dependent Source Concentration along Uniform Groundwater Flow in a Homogeneous Porous Formation

Abstract

An analytical solution for the space-time variation of contaminant concentration in one-dimensional uniform groundwater flow in a homogenous semi-infinite porous formation (e.g., aquifer) subjected to time-dependent source contamination is derived. The temporally dependent dispersion in the aquifer is investigated under two conditions. First, the temporally dependent dispersion distribution in the aquifer is considered as a sinusoidally varying function and, second, the temporally dependent dispersion distribution is treated as an exponentially increasing function of time. It is assumed that initially the aquifer is not solute free; i.e., the aquifer is not clean and the initial concentration is an exponentially decreasing function of the space variable and is tending to zero toward infinity. The concept that dispersion is directly proportional to the seepage velocity is employed. The analytical solution is illustrated using an example and may help benchmark a numerical code and solution.