An Improved Coal Permeability Model with Variable Cleat Width and Klinkenberg Coefficient

The evolution of permeability in coal seams plays an important role in the exploitation of coalbed methane, and the Klinkenberg effect is an important factor affecting the permeability. In most studies, the Klinkenberg coefficient is considered a constant although it is closely related to the cleat width which changes dynamically due to the competing processes of change in effective stress and adsorption induced deformation. In this work, based on the double strain spring model and the effective stress principle, a new stress–strain relationship is proposed for cleat space. In addition, the influence of the adsorption induced swelling effect on coal deformation is considered. By considering both stress-induced strain and adsorption-induced strain, the cleat width model and Klinkenberg coefficient model are established. Finally, we develop an improved permeability model with variable cleat width and Klinkenberg coefficient based on cubic law. This improved permeability model is compared with experimental data and several classical models under conditions of constant effective stress and constant confining stress. Furthermore, the relationship between Klinkenberg coefficient and pore pressure under different conditions is analyzed. Our results indicate that the improved apparent permeability model matches the experimental data well and has a wider range of applications.