Coal permeability measurements are normally conducted under the assumption that gas pressure in the matrix is equalized with that in fracture and that gas sorption-induced swelling/shrinking strain is uniformly distributed within the coal.However,the validity of this assumption has long been questioned and differential strain between the fracture strain and the bulk strain has long been considered as the primary reason for the inconsistency between experimental data and poroelasticity solutions.Although efforts have been made to incorporate the impact into coal permeability models,the fundamental nature of those efforts to split the matrix strain between fracture and coal bulk remains questionable.In this study,a new concept of differential swelling index(DSI)was derived to theoretically define the relation among sorption-induced strains of the coal bulk,fracture,and coal matrix at the equilibrium state.DSI was a function of the equilibrium pressure and its magnitudes were regulated by the Langmuir constants of both the matrix and the coal bulk.Furthermore,a spectrum of DSI-based coal permeability models was developed to explicitly consider the effect of differential strains.These models were verified with the experimental data under the conditions of uniaxial strain,constant confining pressure,and constant effective stress.