In the past, many mathematical models based on the dual-porosity (DP) concept were developed to describe the groundwater flow in fractured aquifer systems. Most of them seemingly have problems in predicting accurate drawdown at the early and/or intermediate times as compared with field measured data. Thus, this study proposes a new analytical model with a generalized transfer term (GTT) to describe the flow induced by pumping in such systems. The new model is nonlinear because the GTT representing the matrix-to-fracture flux gives different weights to the fracture and matrix drawdowns. The GTT reduces to the existing first-order transfer term if the weight equals zero and second-order term if the weight is one. The present model also includes a leakage term accounting for flow from the overlain or underlain aquitard. The drawdown solution of the model is developed based on the Laplace transform method and integration by parts formula and then verified through the comparison with the finite-element solution. The effect of different weight values in the GTT on the DP flow is investigated. Additionally, the sensitivity analysis is performed to assess the impact of the change in each of the aquifer parameters on the flow. Furthermore, the present solution is used to analyze two sets of pumping drawdown data from test sites in Canada and India. We found that the drawdown predictions from the present solution fit field measured data very well, suggesting that the present model can adequately describe the real-world DP flow system.

中文翻译：

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裂隙含水层中恒速泵送引起的双孔隙介质流动的广义非线性输水项分析模型

过去，开发了许多基于双孔隙度 (DP) 概念的数学模型来描述裂缝含水层系统中的地下水流。与现场测量数据相比，它们中的大多数似乎在预测早期和/或中间时间的准确压降方面存在问题。因此，本研究提出了一种具有广义传递项 (GTT) 的新分析模型来描述此类系统中由泵送引起的流动。新模型是非线性的，因为代表基质到裂缝流量的 GTT 赋予裂缝和基质压降不同的权重。如果权重为零，则 GTT 减少到现有的一阶转移项，如果权重为 1，则 GTT 减少到现有的二阶转移项。本模型还包括考虑来自上层或下层透水层的流量的泄漏项。基于拉普拉斯变换方法和分部公式积分得到模型的压降解，并通过与有限元解的比较进行验证。研究了 GTT 中不同权重值对 DP 流的影响。此外，执行敏感性分析以评估每个含水层参数的变化对流量的影响。此外，本解决方案用于分析来自加拿大和印度测试站点的两组抽水压降数据。我们发现，本解决方案的压降预测非常适合现场测量数据，表明本模型可以充分描述真实世界的 DP 流动系统。