In current dual porosity/permeability models, there exists a fundamental assumption that the adsorption-induced swelling is distributed uniformly within the representative elementary volume (REV), irrespective of its internal structures and transient processes. However, both internal structures and transient processes can lead to the non-uniform swelling. In this study, we hypothesize that the non-uniform swelling is responsible for why coal permeability in experimental measurements is not only controlled by the effective stress but also is affected by the adsorption-induced swelling. We propose a concept of the swelling triangle composed of swelling paths to characterize the evolution of the non-uniform swelling and serve as a core link in coupled multiphysics. A swelling path is determined by a dimensionless volumetric ratio and a dimensionless swelling ratio. Different swelling paths have the same start and end point, and each swelling path represents a unique swelling case. The swelling path as the diagonal of the triangle represents the case of the uniform swelling while that as the two perpendicular boundaries represents the case of the localized swelling. The paths of all intermediate cases populate inside the triangle. The corresponding relations between the swelling path and the response of coal multiphysics are established by a non-uniform swelling coefficient. We define this method as the triangle approach and corresponding models as swelling path-based ones. The proposed concept and models are verified against a long-term experimental measurement of permeability and strains under constant effective stress. Our results demonstrate that during gas injection, coal multiphysics responses have a close dependence on the swelling path, and that in both future experiments and field predictions, this dependence must be considered.

Download PDF:

Keywords: Transient process, Heterogeneity, Swelling triangle, Swelling path, Non-uniform swelling coefficient