Pore permeability model based on fractal geometry theory and effective stress

A reasonable coal seam permeability model should be established to accurately estimate the extraction effectiveness of coalbed methane (CBM). Existing permeability models typically ignore the influence of pore structure parameters on the permeability, leading to an overestimation of the measured permeability, and consequently, the CBM production cannot be effectively predicted. This paper presents a novel permeability model based on discrete pore structures at the micro–nano scale. The model considers the interaction between the pore fractal geometry parameters, coal deformation and CBM transport inside these pores. The contributions of key pore geometry parameters, including the maximum pore diameter max, minimum pore diameter min, porosity f0, and fractal dimensions Df and DTm, to the initial permeability were investigated. A numerical analysis showed that the influence of fractal dimension on the permeability can be demonstrated by three structural parameters max, min, and f0. The initial permeability increases exponentially as min in proportion to max and f0. In addition, min, f0, and max are positively correlated with the macroscopic permeability of the coal, with min having the most significant influence on the permeability evolution process. This research provides a theoretical foundation for revealing the gas flow mechanism within coal seams and enhancing the extraction effectiveness of CBM.