A New Fractal Permeability Model for Porous Media Based on Rough Capillary Channels

Abstract

Porous media are assumed as a bunch of curved capillaries of rough pore-solid surface, with capillary size distributions and surface roughness following the fractal scaling laws, for which a permeability model is derived to capture both tortuosity and roughness of the pore space in this work. First, the fractal geometry theory and the regarding methods are used to simulate tortuosity and roughness, and then, the permeability of porous media is linked to pore area fractal dimension, tortuosity fractal dimension, relative mean roughness, and other structural parameters (e.g., characteristic length and maximum and minimum pore size). Each parameter in the proposed model has specific physical meaning, which is able to reveal certain mechanisms that affect permeability comprehensively. For several porous media samples, the predicted permeability data based on the current fractal model are compared with the experimental measurement data and the permeability model predictions for other porous media with smooth capillary channels. A good agreement was found between the predicted values of the new permeability fractal model and the experimental data.