Fractal theory-based permeability model of fracture networks in coals

Fractures in coal reservoirs, which act as the major seepage pathways for coalbed methane (CBM), determine the permeability and CBM productivity of coal reservoirs. Research on the relationships between fracture structures and reservoir permeability is of great theoretical and practical significance for the accurate prediction of CBM productivity. Based on the classical cubic law-based permeability model, as well as the fractal theory, fracture network structures, and effective stress, this study built a permeability model containing complex bending fractures, which was then combined with the S & D (Shi-Durucan) model to build the permeability model of fractured coals under the action of true triaxial stresses. Then, gas seepage experiments under true triaxial stresses were conducted, followed by the comparison of the results of the final permeability model with the experimental results and the fitting data of the S & D model. As shown by the comparison results, the results of the permeability model agreed well with the experimental results and thus can reflect the trend of the influence of stress on permeability under the loading of triaxial stresses. The comparison results also indicate that the permeability model built in this study can reflect the anisotropy of coal permeability more effectively than the S & D model. Using this permeability model, this study quantitatively analyzed the effects of fracture structures of coals on coal permeability. The results indicate that the coal permeability exhibited positive power-law relationships with porosity \phi (0.05-0.41), fractal dimension D_f (2.37-2.81), maximum fracture length l_max (3.5-8.0 cm), and proportionality coefficient β (0.010-0.065) and negative power-law relationships with tortuosity fractal dimension D_Tf (2.005-2.275) and fracture dip angle θ (10°-80°). The results of this study will play an important role in accurately predicting the permeability of coal reservoirs and revealing the flow mechanisms of CBM in coal reservoirs.