Impact of thin aquitards on two-dimensional solute transport in an aquifer

The influence of aquitards on solute transport in an aquifer is an important and often overlooked process for subsurface contaminant transport. In particular, slow advection (leakage) into an aquitard is often neglected in previous analytical treatment of solute transport, making such analytical solutions unsuitable for benchmarking numerical simulations of transport when aquitard leakage exists. In this study, a semi-analytical solution to the two-dimensional conservative solute transport in an aquifer bounded by thin aquitards is derived in the Laplace domain. The governing equation in the aquifer (not aquitard) incorporates terms accounting for advection, longitudinal dispersion, and transverse vertical dispersion. Both one-dimensional vertical advection and molecular diffusion are considered for aquitard transport. The solutions are derived under conditions of steady-state flow and the first- and third-type transport boundary conditions in the aquifer along with assuming the continuity of concentration and vertical mass flux at aquifer and aquitard interfaces. The solutions in the real time domain are obtained by numerically inverting the solutions in the Laplace domain using the Stehfest (1970) algorithm. The semi-analytical solutions are compared with those from Zhan et al. (2009b), which considered aquitard leakage in infinitively thick aquitards. The concentration profiles, breakthrough curves and distribution profiles in the aquifer are different from those of Zhan et al. (2009b) at small ratios of the aquitard/aquifer thickness; whereas, the results of both are consistent for thick bounding aquitards. This study reveals that the residence time distribution (RTD) in the main aquifer is related to the aquitard/aquifer thickness ratios, Peclet numbers and porosities of adjacent aquitards. The results also suggest that MT3DMS (a commonly applied transport code) cannot successfully simulate solute transport at the aquifer-aquitard interfaces. The presented solutions improve available solutions for transport processes in an aquifer bounded by thin aquitards with leakage. The developed solutions can be directly extended to cases when the vertical hydrodynamic dispersion of the aquitards is considered by simply replacing the effective molecular diffusion coefficients of the aquitard by the vertical hydrodynamic dispersion coefficients of the aquitards.