Pore Permeability Model Based on Fractal Geometry Theory and Effective Stress

Abstract 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, minimum pore diameter, porosity, and fractal dimensions, to the initial permeability were investigated. A numerical analysis showed that the influence of fractal dimension on the permeability is finally reflected in the influence of pore structure parameters. The initial permeability is exponential to the minimum pore diameter and proportional to the maximum pore diameter and porosity. In addition, the macroscopic permeability of the coal is positively correlated with the maximum pore diameter, minimum pore diameter, and porosity, with the minimum pore diameter 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.