Understanding competing effect between sorption swelling and mechanical compression on coal matrix deformation and its permeability

Coal deformation during gas depletion primarily involves the effective stress controlled bulk compression and gas sorption/desorption-induced coal matrix swelling/shrinkage. The two concurrent deformation behaviors can significantly impact coal permeability. Majority coal permeability models are defined as a cubic function of coal porosity, in which the porosity is a linear superposition of bulk strain and sorption strain. Nevertheless, laboratory measurements have observed that besides the sorption-induced swelling the injected gas pressure can also hydrostatically compress coal matrix. The observations reflect the complexity of fracture-matrix interaction on the coal porosity, which brings significant challenges to the reliable prediction of the evolution of coal permeability. In this study, we developed an experimental approach to separating the sorption-induced swelling strain of coal matrices and hydrostatic compression. We also modified a coal-gas interaction model by introducing an internal swelling coefficient and implemented into a coupled numerical model. Our experimental results based on nitrogen injection show that gas pressure rise can increase both the swelling strain and hydrostatic compressive strain of the coal specimen. If the measured coal strain is uncorrected, the corresponding isothermal sorption-strain parameters will be underestimated, resulting in the overestimation of the coal permeability. Numerical modeling results show that when the confining stress remains unchanged, the matrix swelling contribution to narrow the fracture width can attenuate with the increasing pore pressure. When the effective stress remains unchanged, the matrix swelling contribution can increase. Comparison of the published permeability data and these modeling results suggests that the actual contribution of the matrix deformation to fracture is significantly related to geomechanical state of coal reservoir, indicating that the internal swelling coefficient should be considered as a key variable when selecting a coal permeability model.