A fractal approach to fully-couple coal deformation and gas flow

Although the impact of matrix microstructures on the evolution of coal permeability is significant, this impact has not been included in the analysis of coupled multiple processes during the extraction of coal seam gas. Previous studies normally investigate the relation between microstructures and coal porosity or permeability through imaging characterization techniques. In this study, we developed a fractal permeability model that defines coal permeability as a function of effective stress. In this model, coal microstructure is characterized by three fractal parameters: (1) fractal dimension of pore size; (2) fractal dimension of throat tortuosity; and (3) maximum pore size. These fractal dimensions may evolve with the effective stress through porosity. We applied this fractal permeability model to fully couple coal deformation and gas flow. Model results illustrate the significant differences between the fractal approach and the classical cubic model between permeability and porosity. When the porosity remains unchanged, the permeability calculated by the classical cubic model remains as a constant. However, the fractal permeability changes due to different microstructural parameters. These results show that the macroscopic permeability of coal is directly proportional to the fractal dimension and the maximum pore size, and is inversely proportional to the fractal dimension of the throat tortuosity. These characteristics cannot be captured by the classical cubic porosity-permeability model.