Abstract In this article, a new model is presented for imparting unsteady flow to a partially penetrating pumping well with wellbore storage placed in double-permeability confined aquifers to investigate the wellbore drawdown transient behavior. In this model, both the fracture and matrix systems are connected directly with the wellbore as flow pathways, while comprehensively considering the crossflow between the matrix and the fractures. The top and bottom boundaries are assumed to be impermeable, and the outer side boundaries could be infinite. Subsequently, Laplace transformation and finite Fourier cosine transformation are employed to obtain analytical solutions of the dual-permeability flow model in the Laplace domain. The derived analytical solution is general and can be reduced to several other previous results. The numerical inversion algorithm of Stehfest is used to solve the wellbore drawdown in the real time domain. Subsequently, the model is validated by comparing it with previous results. Groundwater flow characteristics are analyzed in detail and divided into five flow stages: wellbore storage flow, early-radial flow, quasi-spherical flow, crossflow between the matrix and the fractures, and quasi-radial flow. The different flow stages show some special values on the drawdown and its derivative log-log plots. There is a hump/dip feature in the semi-logarithmic curve of the drawdown derivative, which are inherent characteristic for dual-permeability flow behavior. The effects of some important parameters of the aquifer or pumping wells on drawdown and its derivative, such as wellbore storage coefficient, penetration ratio, crossflow coefficient, storativity ratio, transmissivity ratio, dimensionless aquifer thickness of anisotropy and skin factor, are analyzed and discussed in detail.

中文翻译：

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双渗透性承压含水层中带有井筒储存的部分渗透抽水井的不稳定流动

摘要 在本文中，提出了一种新模型，用于将非定常流动传递给部分渗透泵井，该泵井将井筒储存在双渗透性受限含水层中，以研究井筒压降瞬态行为。在该模型中，裂缝和基质系统均作为流动通道直接与井筒相连，同时综合考虑了基质和裂缝之间的错流。假设顶部和底部边界是不可渗透的，外侧边界可以是无限的。随后，采用拉普拉斯变换和有限傅里叶余弦变换，得到拉普拉斯域双渗透率流动模型的解析解。导出的解析解是通用的，可以简化为其他几个先前的结果。Stehfest数值反演算法用于实时域求解井眼压降。随后，通过将模型与之前的结果进行比较来验证模型。对地下水流动特征进行了详细分析，分为井筒蓄存流、早期径向流、准球形流、基质与裂缝间错流、准径向流五个流动阶段。不同的流动阶段在回撤及其衍生对数图上显示了一些特殊值。压降导数的半对数曲线中存在驼峰/倾角特征，这是双渗透流动行为的固有特征。含水层或抽水井的一些重要参数对压降及其导数的影响，如井筒蓄水系数、渗透比、错流系数、