A new fractal pore-throat chain model for non-Darcy flow through porous media

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.