Influence of the effective stress coefficient and sorption-induced strain on the evolution of coal permeability: Model development and analysis

Abstract A series of coal permeability experiments was conducted for coal samples infiltrated both with non-adsorbing and adsorbing gases – all under conditions of constant pressure difference between the confining stress and the pore pressure. The experimental results show that even under controlled stress conditions, coal permeability decreases with respect to pore pressure during the injection of adsorbing gases. This conclusion is apparently not congruent with our conceptual understanding: when coal samples are free to swell/shrink then no effect of swelling/shrinkage strain should be apparent on the permeability under controlled stress conditions. In this study, we developed a phenomenological permeability model to explain this enigmatic behavior of coal permeability evolution under the influence of gas sorption by combining the effect of swelling strain with that of the mechanical effective stress. For the mechanical effective stress effect, we use the concept of natural strain to define its impact on the change in fracture aperture; for the swelling strain effect, we introduce a partition ratio to define the contribution of swelling strain to the fracture aperture reduction. The resulting coal permeability model is defined as a function of both the effective stress and the swelling strain. Compared to other commonly used models under specific boundary conditions, such as Palmer–Mansoori (P–M), Shi–Durucan (S–D) and Cui–Bustin (C–B) models, our model results match the experimental measurements quite well. We match the experimental data with the model results for the correct reason, i.e. the model conditions are consistent with the experimental conditions (both are stress-controlled), while other models only match the data for a different reason (the model condition is uniaxial strain but the experimental condition is stress-controlled). We have also implemented our permeability model into a fully coupled coal deformation and gas transport finite element model to recover the important non-linear responses due to the effective stress effects where mechanical influences are rigorously coupled with the gas transport system.