Previous studies have concluded that classical poroelasticity-based permeability models cannot explain why coal permeability changes under the condition of both variable and constant effective stresses. There are two effective stress systems, one for the fracture system and the other for the matrix system. When coal permeability is measured, the effective stress in fractures is thought as constant while that in coal matrices remains changing with time. When gas is injected and reaches a steady state in fractures, the gas diffuses from the fracture wall into the matrix. During this diffusion process, the gas adsorbs onto coal grains. This adsorption results in coal matrix swelling. In this study, we introduce a novel concept of the volumetric ratio, the ratio of the gas-invaded area to the whole matrix area, to quantify the impact of matrix swelling area expansion on the evolution of coal permeability. The gradual matrix pressure increase near fracture walls enhances local swelling. Meanwhile, because the matrix near fracture walls contributes most to local effects, expanding of the gas invaded zone continuously weakens the matrix-fracture unequilibrium and local effects. Finally, the matrix is completely invaded by the injected gas with a new equilibrium state and local effects end. The effective stress in our model can be either constant or time-dependent. A fracture pressure loading function is applied to depict gas injection with time-dependent effective stresses. The modeling results are verified against various experimental data. We find that the evolution of coal permeability from the initial state to the final equilibrium state is a result of the propagation of gas invaded areas from the fracture wall into the matrix. Our model can be utilized to generate a series of coal permeability maps that explain a variety of lab and field observations.