Anisotropic permeability evolution of coal with effective stress variation and gas sorption: Model development and analysis

• The internal swelling has been discussed in detail.
• An anisotropic permeability model is developed and validated.
• The internal swelling ratio varies with respect to the confining stress.
• Permeability anisotropy under uniaxial strain conditions is evaluated.
• Permeability has strong anisotropy in both magnitudes and variations.

Anisotropy is an important intrinsic attribute of the coal permeability, a crucial property for coal–gas activities such as coalbed methane recovery and enhanced coalbed methane production using carbon dioxide injection. In this paper, we propose an analytical model in order to represent the anisotropic permeability evolution of coal due to effective stress change and gas sorption, and this model captures the anisotropic characteristics in both mechanical properties and gas sorption-induced directional strains. We select a representative elementary volume of improved matchstick geometry where the coal matrix blocks are connected by the matrix bridges rather than completely separated by the cleats. According to this geometry, only part of the matrix swelling contributes to the cleat aperture alteration, and an internal swelling ratio is introduced in order to represent the effects of the matrix swelling on the cleat porosity and the permeability. This model is independent of any specific boundary conditions and can be extended to different representations of the prescribed boundary conditions, i.e., uniaxial strain, constant confining stress, constant effective stress and constant pore pressure conditions. The model is validated by matching it against three sets of laboratory permeability data measured with adsorbing gases under constant confining stress, constant effective stress and constant pore pressure conditions. Under constant confining stress conditions, by assuming the internal swelling ratio to be invariant, the model agrees well with the measured permeability data. As for the constant effective stress conditions, where both the pore pressure and the confining stress varies, the constant internal swelling ratio makes the model deviate from the experimental observations. This indicates that the internal swelling ratio varies under the varying confining stress conditions. Under constant pore pressure conditions, the model values are lower than the laboratory ones due to the increasing confining stress-induced matrix shrinkage. In order to identify the anisotropic features of the directional permeabilities under in situ conditions, a simplified and idealized modeling under uniaxial strain conditions is conducted by introducing an anisotropic permeability ratio to represent the ratio of one directional permeability to another. The modeling results clearly demonstrate the strong anisotropy in both magnitudes and variation trends of the directional permeabilities.