Comparative analysis of coal permeability models accounting for the stress-strain state of the rock mass

Coal seam permeability is a key parameter controlling degassing efficiency, the intensity of methane emission, and the safety of mining operations. As permeability decreases with depth and is critically dependent on the stress-strain state, its reliable prediction requires models capable of adequately describing the interaction between sorption-induced deformation, poroelastic effects, and fracture aperture closure mechanisms. Owing to the absence of a unified approach for permeability assessment under complex stress-strain conditions, the objective of this study was to systematize and compare the principal empirical and analytical models describing this dependence. To this end, an analytical review of models accounting for sorption-elastic deformation, porosity evolution, effective stress effects, thermoelastic behavior, and cleat system parameters was conducted. Model comparison was performed through numerical simulations of permeability variation over an effective stress range of 0–50 MPa and at depths of up to 1500 m. The models incorporated parameters such as the Biot coefficient, deformation modulus, sorption compressibility, initial permeability, and geometric characteristics of fractures. The results of the parametric calculations demonstrate that, despite conceptual differences, all models exhibit a common trend of nonlinear permeability reduction with increasing effective stress. This behavior reflects the physical processes of pore space compression and fracture aperture reduction. It was established that the most intensive permeability decline occurs within the effective stress range of 5–15 MPa, corresponding to active cleat closure, whereas at depths exceeding 1000 m permeability changes tend to stabilize due to exhaustion of the deformation potential of the fracture structure. Overall, the analysis revealed differing model sensitivities to geomechanical parameters, with the influence of sorption-induced deformation being comparable to that of poroelastic effects. Model selection is shown to be condition-dependent: the Seidle (1992) model is most suitable for accounting for sorption-induced deformation, the Palmer & Mansoori (1998) model for deep coal seams with variable porosity, and the Karkashadze & Hautiev (2015) model for describing elastic deformation effects. The derived relationships can be applied to assess the natural permeability of coal seams in undisturbed rock masses.