A non-plugged abandoned well may cause unwanted flows and solute transport between aquifers. This research provides a novel analytical model to calculate the leakage rate in an abandoned well between a confined aquifer and an unconfined aquifer under steady-state flow conditions. The abandoned well is treated as a passive preferential flow channel connecting a confined aquifer receiving injection from a separate well and an overlying unconfined aquifer; an impermeable aquiclude separates the two aquifers. A closed-form analytical solution for the steady-state leakage rate through an abandoned well is derived. The concerned abandoned well in this study fully penetrates the receiving unconfined aquifer but only penetrates the ceiling of the injecting confined aquifer with a very small screen length (with respect to the confined aquifer thickness). The injection well is sealed from the receiving unconfined aquifer and fully penetrating in the injecting confined aquifer. The solution developed in this study is compared with a previous solution by Avci (1994) (Avci, 1994. Evaluation of flow leakage through abandoned wells and boreholes. (9), 2565–2578). Compared to Avci (1994), this research has two different assumptions: (1) The Avci solution assumed that the leakage effect occurs between two confined aquifers, and leakage concerned in this research occurs between an injecting confined aquifer and a receiving unconfined aquifer. (2) The abandoned well in the Avci (1994) solution fully penetrates both the receiving and injecting confined aquifers, while the abandoned well in this research fully penetrates the receiving unconfined aquifer but only penetrates the ceiling of the injecting confined aquifer with a minor screen length. In both this study and the Avci (1994), the injecting well is isolated from the receiving aquifer and fully penetrating in the injecting aquifer. The results show that the two solutions have similarities in thin confined aquifers but are much different in relatively thick confined aquifers (with thickness greater than 10 m). Using the Sobol method for global sensitivity analysis, we tested controls of the hydraulic conductivity ratio between confined and unconfined aquifers, the transmissivity of the confined aquifer over the injection rate per unit screen length, and the aquifer thickness on model performance. The results show that the model is most sensitive to the transmissivity of the confined aquifer over the injection rate per unit screen length. This research can be applied in multiple applications, such as modeling the leakage effect among two aquifers involving stormwater recharge and using a monitoring well to detect the existence of abandoned wells when the abandoned wells are not visible on the surface or not documented, among others.

中文翻译：

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废弃井流体泄漏的新型分析模型

未堵塞的废弃井可能会导致含水层之间出现不必要的流动和溶质迁移。这项研究提供了一种新颖的分析模型，用于计算稳态流动条件下承压含水层和非承压含水层之间的废弃井的泄漏率。废弃井被视为被动优先水流通道，连接承压含水层（接受来自单独井的注入）和上覆非承压含水层；不透水的隔水层将两个含水层分开。推导了废弃井稳态泄漏率的封闭式解析解。本研究中涉及的废弃井完全穿透接收非承压含水层，但仅穿透注入承压含水层的顶部，且筛网长度非常小（相对于承压含水层厚度）。注入井与接收无承压含水层密封，并完全穿透注入承压含水层。本研究中开发的解决方案与 Avci (1994) 先前的解决方案进行了比较（Avci, 1994。通过废弃井和钻孔的流量泄漏评估。(9), 2565–2578）。与Avci（1994）相比，本研究有两个不同的假设：（1）Avci解假设渗漏效应发生在两个承压含水层之间，而本研究涉及的渗漏发生在注入承压含水层和接收非承压含水层之间。(2) Avci(1994)解决方案中的废弃井完全穿透了接收承压含水层和注入承压含水层，而本研究中的废弃井完全穿透了接收非承压含水层，但仅穿透了带有小筛管的注入承压含水层的顶板长度。在本研究和 Avci (1994) 中，注入井均与接收含水层隔离，并完全穿透注入含水层。结果表明，在薄层承压含水层中，两种解有相似之处，但在较厚承压含水层（厚度大于10 m）中，两种解有很大不同。使用 Sobol 方法进行全局敏感性分析，我们测试了承压含水层和非承压含水层之间的水力传导率比、承压含水层对单位筛网长度注入速率的透射率以及含水层厚度对模型性能的控制。结果表明，该模型对单位屏幕长度注入速率下承压含水层的透射率最为敏感。这项研究可应用于多种应用，例如对涉及雨水补给的两个含水层之间的渗漏效应进行建模，以及当废弃井在地表上不可见或没有记录时使用监测井来检测废弃井的存在等。