A multifractal model for predicting the permeability of dual-porosity media with rough-walled fractures and variable cross-sectional pore channels

The seepage of rock strata is greatly influenced by the pore network and fracture network; however, the prediction of permeability becomes challenging due to the changes in the cross section of pore channels and the morphology of fractures. In this study, a novel pore-fracture permeability model based on a fractal theory is proposed, and the analytical solutions of the model are given. In contrast to the traditional smooth parallel plate and uniform cross section straight capillary, this model not only considers the roughness of the fracture surface, but also the cross section variation and tortuosity of the pore channel. The comparisons between the calculated results and the experimental data verify the reliability of this model. The quantitative analyses of microscopic parameters indicate a positive correlation between the permeability and the fractal dimension, size, and proportion of pores and fractures. Conversely, there is a negative correlation with roughness, tortuosity, and cross-sectional changes. The range in which the seepage contribution of pores cannot be ignored is determined. Two logarithmic relationship expressions for permeability are presented. This study contributes to explore the effects of the geometry and morphology of the pore-fracture media on seepage and supplements the studies on the permeability models.