An analytical transient coal permeability model: Sorption non-equilibrium index-based swelling switch

Long-term permeability experiments have indicated that sorption-induced swelling can switch from internal to bulk depending on the evolutive sorption status. However, this sorption swelling switch mechanism has not been considered in current analytical permeability models. This study introduces a normalized sorption non-equilibrium index (SNEI) to characterize the sorption status, quantify the dynamical variations of matrix swelling accumulation and internal swelling partition, and formulate the sorption swelling switch model. The incorporation of this index into the extended total effective stress concept leads to an analytical transient coal permeability model. Model results show that the sorption swelling switch itself results in the permeability switch under stress-constrained conditions, while the confined bulk swelling suppresses the permeability recovery to the continuous reduction under displacement-constrained conditions. Model verifications show that current experimental observations correspond to the early stages of the transient process, and they could be extended to the whole process with these models. This study demonstrates the importance of the sorption swelling switch in determining permeability evolution using simple boundary conditions. It provides new insights into experimentally revealing the sorption swelling switch in the future, and underscores the requirement of a rigorous model for complex coupled processes in large-scale coal seams.