Abstract This study presents a new analytical model to predict the pressure changes in a monitoring well and the leakage rate due to the leakage through an incomplete-sealed well in a closed system. Different from previous analytical models, herein we develop a new model to simulate the leakage of a leaky well which is incomplete-sealed and connects with the storage aquifer in a certain segment. Based on the problem description and assumptions, the governing equations with corresponding definite conditions are presented and solved by means of Laplace transform, Fourier cosine transform and Duhamel's principle. Verification of the developed model is achieved by comparing with existing analytical model. Then, the leakage rates and pressure changes are calculated for different key factors and sensitivity analyses are conducted. Obviously, a higher permeability accelerates the fluid exchange between the storage aquifer and the monitoring aquifer. Thus, with the increase of the leakage permeability, the leakage from the storage aquifer is more intensive but the ultimate leakage rate is invariable. With the decrease of the dimensionless distance, the seepage resistance along the leakage path is decreasing, resulting in the greater leakage between the two aquifers. Similarly, the dynamic equilibrium is unaffected by the position of the leakage segment. The incomplete seal of the leaky well only affects the spherical flow stage and this effect is relatively small. Therefore, the dimensionless leakage height has no obvious effect on the leakage. The increase of the storativity ratio enlarges the pressure difference between the two aquifers and increases the ultimate leakage rate to achieve the dynamic equilibrium. The leakage in the case with greater storativity ratio increases more significantly. This paper presents a simple and efficient analytical solutions for the leakage through an incomplete-sealed well and extends the applicability of the previous models.

中文翻译：

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不完全密封井渗漏分析模型

摘要 本研究提出了一种新的分析模型来预测监测井中的压力变化和由于封闭系统中不完全密封井泄漏引起的泄漏率。与以往的分析模型不同，本文开发了一种新的模型来模拟某段不完全密封的与蓄水层相连的漏水井的渗漏情况。在问题描述和假设的基础上，利用拉普拉斯变换、傅里叶余弦变换和杜哈梅尔原理，提出并求解了具有相应确定条件的控制方程。开发模型的验证是通过与现有的分析模型进行比较来实现的。然后，计算不同关键因素的泄漏率和压力变化，并进行敏感性分析。明显地，较高的渗透率加速了储存含水层和监测含水层之间的流体交换。因此，随着渗漏渗透率的增加，蓄水层的渗漏更加强烈，但最终渗漏率不变。随着无量纲距离的减小，沿渗漏路径的渗流阻力减小，导致两个含水层之间的渗漏增大。类似地，动态平衡不受泄漏段位置的影响。泄漏井的不完全密封只影响球形流动阶段，这种影响相对较小。因此，无量纲泄漏高度对泄漏没有明显影响。蓄水比的增加使两个含水层之间的压差增大，增加了极限渗漏率，以达到动态平衡。存储比越大的情况下，泄漏量增加越显着。本文针对不完全密封井的泄漏提出了一种简单有效的分析解决方案，并扩展了先前模型的适用性。