A new seepage model for shale gas reservoir and productivity analysis of fractured well

The shale gas reservoirs are rich in nano-micro scale pores. The flow regime and gas flow state are not clearly understood and applied to the hydraulic fractured wells, which is crucial for economic production of shale gas. Beskok and Karniadakis equation can describe the relationship between flow velocities and pressure gradient, which considers the molecular collisions with the pore walls. But the equation is too complex to be applied. In this paper, the Beskok and Karniadakis equation is simplified. Based on this, we establish the multi-scale seepage model considering of diffusion, slippage and desorption effect. Considering on the influence of sorption and the poromechanical response to the permeability, by use of elliptical flow model considering on the coupling of the matrix and the fractures, the productivity equation of vertical and horizontal fractured well in consideration of diffusion, slip and desorption absorption is obtained. Furthermore, we numerically study the influencing factors such as fracture conductivity, fracture penetration ratio and the status of the gas and obtain critical parameters that control this process. Compared with the field production data, this model is verified effectively and practically. It is concluded that the desorbed gas contributes 10-15% to the total gas production. The paper provides a better model for shale gas production prediction.