Analysis of coal permeability model set and prediction effect based on cubic law and meso-scale deformation law

To accurately predict the evolution of coal permeability under varying gas pressures, a permeability evolution model set was developed based on the cubic law and meso-scale deformation principles, and its accuracy was validated. The effects of parameter variations on model evolution were analyzed, the influence of parameter changes on the maximum permeability ratio was investigated, sensitivity indices were identified, and the relationship between the internal swelling coefficient and the fracture adsorption strain coefficient was discussed. The permeability model set includes the true strain model, the equal matrix width model, and the equal volume model. The results indicate that these three types of models characterize three distinct deformation features of representative elements at the meso-scale. Among them, only the true strain model can describe the internal swelling effect, where the internal swelling coefficient represents the ratio of the volume strain of the representative element to the matrix volume strain when only adsorption effects are considered. For coal in the Qinshui Basin, smaller internal swelling coefficients and larger fracture adsorption strain coefficients have the most significant impact on the permeability ratio, with changes in the internal swelling coefficient and fracture adsorption strain coefficient causing the maximum permeability ratio to increase by 34.29 and 24.60～38.07 times, respectively. Compared with the true strain model under identical conditions, the equal volume and equal matrix width models tend to significantly overestimate the maximum permeability ratio. The deviation of the equal volume model reaches a maximum of 28.81 and a minimum of 8.31 under the influence of the Langmuir maximum adsorption strain and initial fracture porosity, respectively. Additionally, the parameter sensitivity indices of the equal volume and equal matrix width models are notably high, which means that deviations in parameter values can easily lead to reduced predictive accuracy, particularly for the Langmuir maximum adsorption strain and Langmuir pressure constant. The internal swelling coefficient and fracture adsorption strain coefficient exhibit a nonlinear relationship only when the fracture volume strain is equal across the three models. The proposed three types of permeability models, which reflect meso-scale deformation principles and are applicable to various operating conditions, systematically reveal the influence mechanisms of key model parameters. This provides theoretical guidance for fundamental sciences such as the elasticity mechanics of porous media and seepage mechanics, as well as practical engineering applications, including coalbed methane development, mine gas control, and carbon sequestration.