When adsorbing gas is injected into coal, the gas fills in the fractures quickly and a pressure difference between matrix and fractures is created. Because of this difference, there is a pressure gradient within the matrix. The gradient evolves with time from the initial equilibrium (zero gradient) to the final equilibrium (zero gradient), so does the adsorption–swelling induced matrix deformation. Previous studies have not taken this effect into consideration. In this study, we hypothesize that the pressure gradient affects the expansion of the gas-invaded area/volume with the matrix and the propagation of the expansion front creates a non-uniform deformation within the matrix. Under this hypothesis, a relation between coal permeability and the expansion of the gas-invaded area with the matrix can be established. When the gas-invaded area is localized in the vicinity of the fracture wall, the expansion of the matrix within this area narrows the fracture opening. We define this as local swelling/shrinking. This local swelling/shrinking is controlled primarily by the coal internal structure. When the gas-invaded area is further spread over the matrix, the expansion of the whole matrix may narrow or widen the fracture opening depending on the external boundary conditions. This global swelling/shrinking is controlled primarily by the external boundary conditions. These conceptual understandings are defined through strain rate-based coal permeability models for both the matrix and the fractures. This strain rate based time-dependent permeability model was verified against experimental observations, that couples coal deformation, the gas flow in the matrix system and gas flow in the fracture system.