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.

在世界范围内报告的大量潜在污染场地需要对污染的程度和对水资源的威胁进行具有成本效益和时间效益的评估。这些站点的重要风险评估指标可以是最大（即，稳态）污染物羽流长度（L _max）的确定。文献中的分析方法为这种评估提供了一种选择，但它们包含一定程度的不确定性。通常，这种不确定性的原因是分析模型的简化，例如，不考虑水文地质应力（例如补给）的影响，而这会严重影响羽流的发育。这可能会导致L _max的高估或低估。这项工作包括充电对L _max有效估计的影响。为此，通过考虑不同的含水层厚度（1 m至4 m）和补给速率（范围为0至3.6 mm /天），进行了几个二维（2D）数值模拟。从这项工作的数值结果，可以得出以下结论：1）应用补给会缩短L _max，并且进入含水层顶部的补给会导致羽流倾斜； 2）L _max的减少百分比取决于补给率3）减少百分比相对于固定含水层厚度的补给率呈非线性变化。

基于这些结果，混合分析经验的解决方案已被开发用于估计大号_最大一起列入补给速率。提出的混合分析-经验解决方案将根据经验获得的校正因子叠加到分析解决方案上。尽管需要开发模型的大量确认步骤来包括补给对含水层水力的影响，但建议的表达式显着改善了L _max的估计。通过选择有限的现场污染站点数据，也已经证实了混合分析-经验解决方案。混合模型结果（L _hyb）在估计上提供了显着改进，即与分析模型相比，平均相对误差降低了一个数量级。