Analytical solutions for solute transport in a vertical aquifer section

Analytical solutions are developed for modeling solute transport in a vertical section of a homogeneous aquifer with steady uniform groundwater flow. The source is assumed to be located at the top (or the bottom) of the aquifer, and the initial concentration is assumed to be zero everywhere in the aquifer. Both constant-flux and constant-concentration sources are treated. For cases of a constant-flux source, we present exact analytical solutions considering the following transport mechanisms: advection in the horizontal direction, dispersions in both horizontal and vertical directions, adsorption, and biodegradation. For cases of a constant-concentration source, we present simplified analytical solutions by neglecting dispersion in the horizontal direction. For both kinds of sources, the solutions for aquifers with a relatively large or small thickness are presented and compared. The solutions for the two different source conditions are also compared for similar cases. The comparisons indicate that simpler solutions, used in appropriate cases, can give the same results as those given by more complex solutions. Example calculations are given to show the movement of the contamination front, the steady-state concentration profiles, and the applications to determine dispersivities. The analytical solutions developed in this study can be useful in site characterization, groundwater monitoring, and remediation.