Non-Darcy flow through porous media is of great significance in hydraulics, oil and gas engineering, biomedical science, chemical and civil engineering etc. However, it is difficult to fully grasp the nature of fluid flow through porous media from macroscopic scale alone. Based on the statistically fractal scaling laws of pore structures, a new fractal pore-throat chain model (FPTCM) for non-Darcy flow through the isotropic porous media is developed. The analytical expressions for the Darcy and non-Darcy permeability as well as non-Darcy coefficient are derived accordingly. In order to explore the local flow field of high-speed non-Darcy flow through porous media, the finite element method is also carried out on an equivalent pore-throat unit. The predicted permeability by FPTCM shows better agreement with present numerical results and available experimental data, compared with commonly used semi-empirical formulas including Kozeny-Carman and Ergun equations. It has been found that both Darcy and non-Darcy permeability as well as non-Darcy coefficient strongly relate to the pore structures of porous media. The non-Darcy permeability is positively correlated to porosity, pore fractal dimension and Darcy permeability, while it is negatively related to tortuosity fractal dimension and pore size range. The non-Darcy coefficient shows opposite correlation with these parameters. The present work can provide theoretical basis for oil and gas development, nuclear waste treatment, carbon dioxide geological sequestration etc.

中文翻译：

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一种新的分形孔喉链模型，用于多孔介质中的非达西流


通过多孔介质的非达西流在水力学、石油和天然气工程、生物医学、化学和土木工程等领域具有重要意义。然而，仅从宏观尺度上很难完全掌握流体流经多孔介质的性质。基于孔隙结构的统计分形缩放定律，开发了一种新的非达西流经各向同性多孔介质的分形孔喉链模型 （FPTCM）。相应地推导出达西和非达西磁导率以及非达西系数的解析表达式。为了探究高速非达西流通过多孔介质的局部流场，还对等效孔喉单元进行了有限元方法。与常用的半经验公式（包括 Kozeny-Carman 和 Ergun 方程）相比，FPTCM 预测的磁导率与目前的数值结果和可用的实验数据具有更好的一致性。已经发现，达西和非达西渗透率以及非达西系数都与多孔介质的孔隙结构密切相关。非达西渗透率与孔隙率、孔隙分形维数和达西渗透率呈正相关，而与曲折分形维数和孔径范围呈负相关。非达西系数与这些参数呈相反的相关性。本研究可为油气开发、核废料处理、二氧化碳地质封存等提供理论依据。