An effective stress-dependent dual-fractal permeability model for coal considering multiple flow mechanisms

Coal permeability is significantly affected by the multi-scale pore-fracture size distribution. More importantly, the pore-fracture size is changed by the effective stress, swelling/shrinkage under the influence of gas sorption, and different flow mechanisms. In conventional dual-porosity models, these effects are normally studied separately and the impacts of heterogeneous structure on permeability are neglected. In this study, a dual-fractal permeability model was proposed to quantitatively investigate the impacts of coal internal structure on the permeability. In the improved permeability model, the fractal dimension and the pore-fracture size of the coal are linked with porosity, which are dependent on the evolution of effective stress and matrix shrinkage. Besides, multiple flow mechanisms were also incorporated into the model. The proposed model was verified with field data and achieved a good agreement. The sensitivity studies and model results indicate that: (1) pore/fracture size distributions affect the contribution ratios of versatile flow regimes and to total gas flux and the total permeability; (2) fractal dimensions of matrix and fracture systems increase with the decline of pore pressure; (3) increment of matrix permeability is jointly decided by the transition of flow regime and effective stress, while the fracture permeability is dominated by effective stress.