Influence of coal deformation on the Knudsen number of gas flow in coal seams

Highlights: • A new model of Knudsen number with coal deformation is established. • Influences of coal deformation on Knudsen number for gas flowing are discussed. • Variation Klinkenberg coefficient model is rewritten with Knudsen number. The effective stress and pore pressure can change the fracture aperture, which in turn can change the methane Knudsen number and transitions between gas flow regimes. A novel Knudsen number (Kn) model for gas flow under coal deformation was established; a revised permeability model was formulated and used to obtain an equation for the Klinkenberg coefficient b. The predictions of the revised permeability model were in good agreement with experimental data, and the parameters used to determine the gas Kn were obtained. An increase in the pore pressure under coal deformation causes the fracture aperture to increase and the gas molecular mean free path to decrease, thereby decreasing the Kn. Thus, the critical pore pressure for the transition between gas flow regimes is reduced. The gas Kn for a deformed fracture is higher than that for a constant fracture aperture. The critical fracture aperture for the transition between gas flow regimes increases under coal deformation. The Klinkenberg coefficient b for methane is a variation value that increases as Kn decreases. The Kn variation is very important for determining the coal permeability and which can be used to resolve problems in CBM recovery.