Fractal Apparent Permeability Model for Coal under the Coupling Actions of Stress and Water

The environment of coal reservoirs is complex and variable, with various factors, not independent, but interlocking and coupled. However, their coupling effects have rarely been considered in previous theoretical studies. In addition, when a fractal theory was applied to analyze the permeability of coal, the linkage between fractal dimensions and the pore radius under external factors has usually been ignored. In this study, two parameters, pore compressibility and dynamic water saturation, were introduced to quantitatively represent the internal interactions between stress and water. Based on the results, dynamic fractal dimensions under the coupling actions of stress and water were obtained by considering variation in the pore radius and the assignment status of gas and water, following which an apparent permeability model of coal, with dynamic fractal dimensions, was established. The newly developed model was verified by reference to published experimental data. The results showed that stress dominated changes in the fractal dimension for pore-size distribution under the coupling actions of stress and water; however, changes in the fractal dimension for tortuosity was dominated, in turn, by stress and water. Subsequently, it was found that the fractal apparent permeability model could match the experimental data well. It revealed that the newly developed model could predict the evolution of coal permeability under dynamic changes in stress and water. Further, under the coupling actions of stress and water, the apparent permeability of coal possessed a positive correlation with the fractal dimension for pore-size distribution or water-dominated fractal dimension for tortuosity, while it was negatively correlated with the critical capillary radius or stress-dominated fractal dimension for tortuosity. In addition, the evolution of the apparent permeability was consistent with specific fractal dimensions and dynamic fractal dimensions, but the evolution of the slippage factor revealed an opposite result. Consequently, this initiates a new analytical perspective into investigating change mechanisms relating to coal permeability.