The Forchheimer and Izbash equations have been long employed to investigate the behavior of non‐Darcian flow toward a well in various aquifer systems, but both two equations inevitably introduce problems such as more or less empirical nature, and dimensional unbalance. Therefore, this work makes the attempt to introduce the fractional Darcian model for characterizing the non‐Darcian behavior flow toward a fully penetrating well in a confined aquifer instead of the Forchheimer and Izbash equations. In this study, a fractional Darcian model‐based analytical solution in the time domain is obtained by means of Laplace transform and linearization approximation. The proposed analytical solution of this study can be readily reduced to the classical Theis solution for Darcian flow. Meanwhile, the late‐times and steady‐state analytical solutions for non‐Darcian flow described using the fractional Darcian model are also developed. Moreover, a comparison with previous analytical solutions shows that the newly derived analytical solution in this study is sufficiently accurate at later times. The influences of different parameters on transient drawdown are investigated. The results indicate that the fractional derivative order and hydraulic conductivity have a large influence on drawdown compared with other parameters. The introduction of fractional Darcian model in this study could also provide potential application for further investigations of non‐Darian flow behavior toward fully or partially penetrating wells in different aquifer systems, which can be very beneficial for hydrology and other related fields.

中文翻译：

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基于分数达西模型的有限含水层中流向完全穿透井的非达西流解析解

Forchheimer 和 Izbash 方程长期以来一直被用来研究各种含水层系统中非达西流向井的行为，但这两个方程都不可避免地引入了诸如或多或少的经验性质和维度不平衡等问题。因此，这项工作尝试引入分数达西模型来表征承压含水层中完全穿透井的非达西行为流，而不是 Forchheimer 和 Izbash 方程。在本研究中，通过拉普拉斯变换和线性化近似获得了基于分数达西模型的时域解析解。本研究提出的解析解可以很容易地简化为达西流的经典泰斯解。同时，还开发了使用分数达西模型描述的非达西流的后期和稳态解析解。此外，与之前的解析解的比较表明，本研究中新导出的解析解在以后的时间里是足够准确的。研究了不同参数对瞬态回撤的影响。结果表明，与其他参数相比，分数阶导数和导水率对水位下降的影响较大。本研究中引入分数达西模型还可以为进一步研究不同含水层系统中完全或部分穿透井的非达西水流行为提供潜在的应用，这对于水文学和其他相关领域非常有益。