A Coal Permeability Model with Variable Fracture Compressibility Considering Triaxial Strain Condition

Fracture compressibility and strain boundary conditions are key factors in the evolution of coal permeability. Previous research has shown that fracture compressibility of coal is variable. Generally, the uniaxial strain condition is adopted for field coalbed methane (CBM) recovery. In this study, we assumed that the coal samples were under triaxial strain conditions combined with McKee’s stress-dependent fracture compressibility function and the improved Shi-Durucan permeability model. A new permeability model, with variable fracture compressibility, was derived. Considering variable fracture compressibility, the calculated results of the model were closer to the experimental values than the model with constant fracture compressibility. Based on previous experimental data, the responses of fracture compressibility to effective stress, gas pressure, gas type, and coal rank were analyzed. Coal fracture compressibility generally decreased with increase in effective stress. With increasing pore pressure, coal fracture compressibility first decreased and then increased when the experimental gas was CO2, CH4, or N2; it first increased and then decreased when the experimental gas was He. The stronger the adsorption capacity of the gas, the greater the coal fracture compressibility under uniform pore pressure. Numerical results of CBM production can be more accurate when the uniaxial and triaxial strain conditions are assumed for a coal seam far away from and near a wellhead, respectively.