Numerical investigation of gas flow rate in shale gas reservoirs with nanoporous media

Theoretical analysis of transport mechanism of gas flow in shale gas reservoirs with nanoporous media was carried out on the basis of molecular kinetic theory. The motion equation and mathematical model of shale gas transport in multi-scale medium are established in this article. The pressure distribution equation of radial flow was derived, and the computing method of the control area of gas well was presented. Additionally, the volume flow rate equations of vertical and horizontal fractured wells were obtained. Through Newton iterative method, volume flow rate was analyzed, considering various factors such as production pressure drawdown, fracture half-length, fracture conductivity, fracture spacing and diffusion coefficient. According to the numerical results, the volume flow rate of the gas well increases when the diffusion coefficient grows. Consequently diffusion in shale gas reservoirs with nanoporous media plays an important role. With increase of fracture half-length, the volume flow rate increases first and then tends towards stability. Moreover, for certain length of the horizontal wellbore, when fracture spacing increases and the number of the fractures lessens, the control area and the volume flow rate of the gas well decreases. Therefore, there is an optimum allocation among these factors to achieve maximum volume flow.