Residence Times in aquifers result from their internal structure, from the hydrodynamic transport processes and from the recharge conditions to which they are exposed. Beyond the already known residence time distributions (RTD) for either constant aquifer thickness and/or uniform recharge, we investigate the effect of both distributed aquifer thickness and distributed recharge. We develop a semi-analytical approximation of the RTD for generic trapezoidal aquifers exposed to linearly-variable recharges. The solution is derived for a homogeneous 2D cross-sectional aquifer in steady-state conditions following the Dupuit-Forchheimer assumption according to which the vertical head gradients are much smaller than the horizontal head gradients. Close agreement with 2D numerical simulations demonstrates the relevance of the Dupuit-Forchheimer assumption to estimate RTDs as long as the aquifer thickness remains an order of magnitude smaller than the aquifer length. At equivalent aquifer volume, geometrical structure and recharge conditions result in non-trivial and complex RTD shapes that may be uniform, Gamma-like, power-law-like shapes as well as any intermediary shapes. The variety of RTD shapes encountered show the need to systematically include the aquifer structure and recharge conditions in the assessment of RTDs and for their subsequent use for problematics related to water quality. The semi-analytical approximation can be further used in a variety of aquifer systems in complement with other existing solutions as a Lumped Parameter Model for RTDs.

中文翻译：

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非均匀含水层补给和厚度条件下的停留时间分布 - 基于 Dupuit-Forchheimer 假设的分析方法

含水层中的停留时间由其内部结构、水动力传输过程和它们所暴露的补给条件决定。除了已知的恒定含水层厚度和/或均匀补给的停留时间分布 (RTD) 之外，我们还研究了分布式含水层厚度和分布式补给的影响。我们为暴露于线性可变补给的通用梯形含水层开发了 RTD 的半解析近似值。根据 Dupuit-Forchheimer 假设，垂直水头梯度远小于水平水头梯度，为稳态条件下的均质 2D 横截面含水层推导出该解。只要含水层厚度保持比含水层长度小一个数量级，与 2D 数值模拟的密切一致表明 Dupuit-Forchheimer 假设与估计 RTD 的相关性。在等效的含水层体积、几何结构和补给条件下，RTD 形状可能是均匀的、类似伽马的、类似幂律的形状以及任何中间形状。遇到的各种 RTD 形状表明需要在 RTD 评估中系统地包括含水层结构和补给条件，并随后将其用于与水质相关的问题。半解析近似可以进一步用于各种含水层系统，作为 RTD 的集总参数模型与其他现有解决方案相辅相成。