Numerical investigation of migration mechanism for coal-bed methane flow through cleats with rough surfaces in coal reservoir

To estimate the productivity of coal-bed methane (CBM), the premise is the effective description of CBM migration mechanism. The authors have developed a new fracture-permeability relative model by coupling the general Kozeny-Carman equation and the classical cubic law of fracture flow, which takes into account the effects of external and internal friction. In the model developed, the hydraulic tortuosity is responsible for the internal friction, and the surface tortuosity for external friction effect, which is defined as the area ratio between cleat rough surface and the projected one on the macro-flow plane. Consequently, the authors modelled the cleats composed of rough surfaces characterized by the theory of fractal geometry, and simulated the CBM flow through them by lattice Boltzmann method. In addition, the authors investigated the effects, such as surface fractal dimension, absolute surface roughness, as well as the relative surface roughness, on the CBM flow. Based on the results obtained, the validity of the newly derived fracture-permeability relationship is verified by comparative analyses. The results reveal that the newly developed model accounting for the effects of external and internal friction, can effectively describe the migration law of CBM through rough cleats.