Darcy’s law (which states that a fluid flow rate is directly proportional to the pressure gradient) is shown to be accurate in a rather narrow range of flow velocities. Numerous studies show that at low pressure gradients gas slippage effect occurs, which gives overestimated flow rates compared to Darcy’s law. At higher flow rates, Darcy’s law is usually replaced by the Forchheimer equation which accounts for inertial forces including a quadratic term in the flow rate. Darcy’s and Forchheimer’s laws and the problem of detecting transitions between their ranges of applicability are discussed in this study. Analysis of experimental data shows that deviation from Darcy’s law is governed by the Forchheimer number, which is defined by the authors as a product of tortuosity and Reynolds number. The use of the Forchheimer number and semi-analytical approaches enables us to describe non-Darcy flow as a simple universal equation valid for any flow geometry. Comparison of the experimental data with predictions based on a semi-analytical model shows excellent agreement for a wide range of reservoir properties.

达西定律（表明流体流速与压力梯度成正比）被证明在相当窄的流速范围内是准确的。大量研究表明，在低压梯度下会发生瓦斯滑移效应，与达西定律相比，这会高估流量。在较高的流速下，达西定律通常由Forchheimer方程代替，该方程考虑了惯性力，其中包括流速的二次项。这项研究讨论了达西定律和福希海默定律以及检测其适用范围之间的过渡问题。对实验数据的分析表明，与达西定律的偏差由Forchheimer数控制，该数由作者定义为曲折度和雷诺数的乘积。借助Forchheimer数和半解析方法，我们可以将非达西流描述为对任何流几何都有效的简单通用方程。将实验数据与基于半分析模型的预测结果进行比较表明，对于广泛的储层性质，它具有极好的一致性。