Fractional permeability model for deep coal considering creep effect

In order to consider the effect of creep of deep coal on the permeability, the three-dimensional constitutive equation for nonlinear creep of deep coal considering volumetric creep, the Kozeny-Carman equation and the equation for permeability of fractured coal are combined to establish a fractional permeability model based on the creep effect. The creep-seepage experimental data of gas-containing coal is used to fit the permeability model and determine the physical parameters, and the permeability evolution is simulated under different experimental conditions. The results show that the permeability model decreases gradually in the elastic and viscoelastic creep stages, which is consistent with the physical process that the initial pores are gradually reduced during the creep process of deep coal in the low stress stage. In the viscoplastic creep stage, the permeability model can characterize the evolution of the accelerated creep stage, that is, the rapid increase stage of permeability. In addition, the sensitivity analysis of the key parameters in the fractional permeability model is carried out. It is found that with the increase of the parameter α₀ of deep coal, the rapid increase stage of the permeability is more likely to occur. The higher the fractional derivative order, the faster the rate of permeability decline in the elastic and viscoelastic creep stages, and the slower the tendency of permeability increase in the viscoplastic creep stage.