Influence of recharge rates on steady-state plume lengths

A large number of potentially contaminated sites reported worldwide require cost- and time-effective assessment of the extent of contamination and the threats posed to the water resources. A significant risk assessment metric for these sites can be the determination of the maximum (i.e., steady-state) contaminant plume length (L_max). Analytical approaches in the literature provide an option for such an assessment, but they include a certain degree of uncertainty. Often, the causes of such uncertainties are the simplifications in the analytical models, e.g., not considering the influence of hydrogeological stresses such as recharge, which impact the plume development significantly. This may lead to an over- or underestimation of L_max. This work includes the influence of the recharge for the effective estimation of L_max. For that, several two-dimensional (2D) numerical simulations have been performed by considering different aquifer thicknesses (1 m- 4 m) and recharge rates (ranging from 0 to 3.6 mm/day). From the numerical results of this work, it has been deduced that 1) the application of the recharge shortens L_max, and the recharge entering the aquifer top causes the plume to tilt, 2) the reduction percentage in L_max depends on the recharge rate applied and the aquifer thickness, and 3) the reduction percentage varies in a non-linear manner with respect to the recharge rate for a fixed aquifer thickness. Based on these results, a hybrid analytical-empirical solution has been developed for the estimation of L_max with the inclusion of the recharge rate. The proposed hybrid analytical-empirical solution superimposes an empirically obtained correction factor onto an analytical solution. Although extensive confirmation steps of the developed model are required for including the effect of the recharge on aquifer hydraulics, the proposed expression improves the estimation of the L_max significantly. The hybrid analytical-empirical solution has also been confirmed with a selection of limited field contamination sites data. The hybrid model result (L_hyb) provides a significant improvement in the estimation, i.e., an order of magnitude lower mean relative error compared to the analytical model.