Pressure drop and fractal non-Darcy coefficient model for fluid flow through porous media

Abstract

Pressure drop loss of fluid flow through porous media is a key issue in many science fields. It has been shown that the non-Darcy coefficient plays a major role in the determination of pressure drop loss. However, the existing prediction models of the non-Darcy coefficient are very divergent, thus requiring to be improved. In this work, a fractal non-Darcy coefficient model for incompressible fluid flow through microporous media materials is established based on the fractal characteristics and fractal capillary bundle model of porous media. The fractal non-Darcy coefficient is expressed as a function of the area ratio between pore and representative elementary volume, pore area fractal dimension, tortuous dimension, porosity, permeability, average tortuosity, maximum pore diameter and mean particle diameter. In this expression, each parameter has a specific physical meaning. The prediction results of our model are compared with the existing experimental data to verify the reliability of the proposed model, and the relationship between the non-Darcy coefficient and each physical parameter has been analyzed thoroughly. The results are helpful to better understand how microstructures of porous media affect the non-Darcy coefficient of fluid flow.