Productivity model of gas flow in CBM fractured reservoirs considering desorption and diffusion

Fractured vertical wells are the most frequently adopted means in development of coalbed methane. For hydraulic fracturing wells, gas flow field could be divided into two regions with different flow mechanisms: Darcy flow in elliptical region around artificial fractures, and nonlinear high-velocity flow in artificial fractures. Considering methane desorption and diffusion equilibrium, a mathematical model for steady gas flow in hydraulic fracturing wells was established based on conservation laws of mass and motion. According to the analytical solution derived here, productivity equation was presented considering the effect of fracture parameters. Numerical results illuminated the effect of desorption rate and fracture parameters on productivity. Production of coalbed methane grew with the increase of desorption rate. With increasing half-length and width of hydraulic fracture, production of single fractured well increased with decreasing increment and approached a plateau. The quantitative analysis in the paper could provide a theoretical foundation for reasonable development design.