Permeability of large-scale fractures with ununiform proppant distributions in coalbed methane development

The coalbed methane (CBM) productivity is directly determined by the fracture permeability during hydraulic fracturing, which is regulated by the distribution of proppants. The proppant may be unevenly distributed in the fracture because of variables like the architecture of the fracture and the characteristics of the sand-carrying fluid. This study used two types of random functions to produce different ununiform distributions of proppant clusters in large-scale fractures, with the aim of investigating the effect of these distributions on the overall permeability of the fracture. A model of fluid-structure coupling is proposed. The closure of large-scale fractures under in-situ stress is analyzed using solid mechanics and the penalty function; the CBM flowing in proppant clusters and the high-speed channel between them is simulated using Darcy's law and the Navier–Stokes equation, respectively; and the overall permeability of fractures is computed using the fluid pressure drop throughout the fracture and the fluid flowing velocity in the fracture's outlet. Since most CBM flows along high-speed channels between the proppant clusters, the simulated findings show that the overall permeability of fractures with an uneven distribution of proppant clusters is significantly higher than that of the proppant cluster itself. As CBM becomes more discretely distributed, the proportion of CBM flowing within the proppant cluster continuously drops. As the permeability of the proppant cluster increases, the volume ratio of proppant clusters decreases, and the distribution of proppant clusters becomes more discrete, the overall permeability of the fracture continuously increases.