Impact of equilibration time lag between matrix and fractures on the evolution of coal permeability

In conventional dual porosity models, the interactions between matrix and fractures are normally characterized through two equilibrium systems within the same REV (representative elementary volume). This pseudo-steady approach cannot capture the true impact of the non-equilibrium period within each system since it ignores the true transient nature of the fracture-matrix interaction. In this study, a conventional dual porosity model is extended to include the impact of equilibration time lag between matrix and fractures caused by their contrasting properties. To incorporate this important mechanism, the matrix REV is divided into two sub-REVs by using the MINC concept (Multiple Interacting Continua). The time lag effect is defined as a function of the difference between the strain in the matrix REV and that in the sub-matrix REV, and incorporated into a coal permeability model. Consequently, the coal permeability evolves also from initial to final equilibrium. Conventional dual porosity/permeability models represent two end points (initial and final equilibrium) while this new permeability model represents the evolution of coal permeability between these two end points. The model is verified against experimental observations of the evolution of coal permeability under a constant effective stress that extend for more than 80 days. If effective stress remains unchanged, conventional permeability models predict no permeability changes while our new model predicts that coal permeability evolves as a function of time from initial to ultimate equilibrium. Our results suggest that the impact of matrix strain variations on the evolution of coal permeability is significant and should not be ignored.