Permeability Model Sets Based on REV Strains and the Mesoscale Deformation Law of Coal and Sensitivity Analysis of Key Parameters

Accurate prediction of permeability can be of great help in the exploitation of coal-bed methane resources. Based on the representative element volume (REV) and cubic law, a series of novel permeability models have been derived in this study, which can be categorized into the model sets of cubic law equivalent (CLE), constant matrix width (CMW), and constant REV volume (CRV), enabling a more realistic representation of the mesoscale deformation behavior of coal under stress environments. The CLE model set containing the real strain relations matches the experimental data better than the CMW model set containing the simplified strain relations. However, the two-parameter fitting (PF-2) errors for both the CMW and CLE model sets are very large. For CMW model sets, the errors of the bulk modulus obtained by PF-2 range from 18.046% to 47.526%, and the maximum fitting errors of the adsorption strain coefficients are 220.648%, 85.461%, and 21.635% for N₂, CH₄, and CO₂; for CLE model sets, the errors of the fracture bulk modulus are close to those of the CMW model set, with the smallest error of 13.953% for the CO₂ experiment and larger errors of 47.705% and 47.700% for the N₂ and CH₄ experiments, respectively. The bias in model predictions is dependent on the fitting error and parameter sensitivity. For the CMW model set, the sensitivities of the bulk modulus and the fracture bulk modulus are consistent and similar to the adsorption strain coefficient, with highly significant sensitivities for all three parameters; in the CLE model set, the sensitivities of the fracture bulk modulus and the internal swelling coefficient are highly significant. The internal swelling coefficient reflects the driving effect of the adsorption-induced VSRM on VSR, which is just the opposite of the adsorption strain coefficient’s influence on the model.