Abstract Fractional Darcian model and fractional Swartzendruber model are proposed for non-Darcian flows with high and low velocity in the paper, respectively. The analytical solutions of the fractional derivative models are given and all parameters are determined based on test data. The dependence of fractional derivative models on parameters such as fractional derivative order and threshold hydraulic gradient are analyzed by sensitivity studies. The fractional derivative models provide better description of non-Darcian flow in porous media under the conditions of high and low velocity. Furthermore, the memory effectiveness of fractional calculus is discussed, showing that the fractional derivative order is an indicator of non-Darcian flow in porous media.

中文翻译：

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多孔介质中非达西流动的分数导数法

摘要 本文分别针对高速和低速非达西流动提出了分数达西模型和分数Swartzendruber模型。给出了分数阶导数模型的解析解，所有参数均根据试验数据确定。通过敏感性研究分析了分数阶导数模型对分数阶导数阶和阈值水力梯度等参数的依赖性。分数阶导数模型可以更好地描述多孔介质中高速和低速条件下的非达西流动。此外，还讨论了分数阶微积分的记忆有效性，表明分数阶导数阶是多孔介质中非达西流动的指标。