Mathematical model of fractured horizontal well in shale gas reservoir with rectangular stimulated reservoir volume

Production performance analysis of shale gas development has posed a great challenge for scientific researchers owing to the complex percolation mechanisms and massive hydraulic fracturing. The unique accumulation and transporting mechanisms in multiscaled shale pores, such as adsorption, desorption, diffusion, and slippage, lead to gas seepage behaviors deviating from Darcy flow. Compared to previous studies, this paper presents a comprehensive mathematical model incorporating all the above percolation mechanisms for multistage fractured horizontal wells, in which rectangular stimulated reservoir volume (SRV) is taken into account. A numerical solution for such a complex model is obtained by extending the boundary element method to application. The verification of our method is confirmed by comparison to semi-analytical results of a simplified model. From the well testing type curves, nine flow regimes were identified, most of which are not observed in conventional linear flow models. The effects of sensitive parameters, such as fracture number, size and permeability of the SRV, and formation permeability, on pressure type curves were investigated. The comprehensive model in this paper provides another method to guide the development of shale gas reservoirs, including interpretation of formation properties, guiding fracturing design, and conducting post-fracture evaluation.