Mathematical model for stimulation of CBM reservoirs during graded proppant injection

A modelling-based prediction of well productivity enhancement for recently developed technology for stimulation of natural fracture systems in CBM reservoirs is presented. The proposed technology can also be used for productivity enhancement of gas wells in other unconventional reservoirs, i.e., shales and tight gas reservoirs. Injection of proppant particles with increasing size and decreasing concentration results in deep percolation of proppant into the natural fracture system, expansion of the stimulated zone and increase of well productivity index. A modified mathematical model for well indices during graded particle injection, accounting for stress changes in coal beds, is developed. The model is based on analytical solution for quasi ID problem with coupling of axisymmetric fluid flow and geomechanics. The results of previous computational fluid dynamic studies have been used to determine hydraulic resistance due to proppant placement in the fractured system. Explicit analytical equations were derived for stress, pressure and permeability distributions, as well as for the well index during injection and production. Results of previous computational fluid dynamics studies were used to determine the hydraulic resistance resulting from proppant plugging in the fractured system. By applying the effect of proppant concentration and fracture deformation, a critical stimulation radius is introduced beyond which proppant placement decreases coal permeability and well productivity index. This model has been applied for a real field case, and the effect of injection pressure on well productivity index and stimulation radius is presented. The results show significant increase in productivity index due to graded proppant injection in CBM reservoirs.A. Keshavarz, A. Khanna, T. Hughes, M. Boniciolli, A. Cooper and P. Bedrikovetsk