Abstract: Coal, as a typical sedimentary rock, has a naturally anisotropic feature. For simplicity, coal is considered as an isotropic material in the study of coal permeability, and the corresponding isotropic permeability models have been proposed. However, the actual situation of gas-solid coupling in the field and laboratory tests cannot be well reflected by these models. In this paper, coal is treated as transversely isotropic, and an anisotropic permeability model is developed by using different directional modulus reduction ratios as the key parameters. The developed model is further implemented in COMSOL multiphysics software to comprehensively investigate the effect of coal anisotropy on gas diffusion and penetration. Theoretical and numerical results show that different directional modulus reduction ratios ( ) reflect the degree of anisotropy of the coal structure. When is different, the coal permeability is also not the same. Coal permeability is mainly governed by mechanical effects and desorption effects, and meanwhile, these two effects on each direction of the permeability of coal are controlled by boundary conditions. is a reflection of these two effects. Under the uniaxial strain or displacement control boundary condition, the horizontal modulus reduction ratio ( ) has more significant effect on the amount of permeability change in the vertical direction ( ) than on that in the horizontal direction ( ). However, the vertical modulus reduction ratio ( ) has less effect on than on .

Key words: coal containing methane, elastic modulus reduction ratio, desorption effects, permeability model, anisotropic, gas-solid coupling