Productivity model for gas reservoirs with open-hole multi-fracturing horizontal wells and optimization of hydraulic fracture parameters

Multi-fractured horizontal wells are commonly employed to improve the productivity of low and ultra-low permeability gas reservoirs. However, conventional productivity models for open-hole multi-fractured horizontal wells do not consider the interferences between hydraulic fractures and the open-hole segments, resulting in significant errors in calculation results. In this article, a novel productivity prediction model for gas reservoirs with open-hole multi-fractured horizontal wells was proposed based on complex potential theories, potential superimposition, and numerical analysis. Herein, an open-hole segment between two adjacent fractures was regarded as an equivalent fracture, which was discretized as in cases of artificial fractures. The proposed model was then applied to investigate the effects of various parameters, such as the angle between the fracture and horizontal shaft, fracture quantity, fracture length, diversion capacity of fractures, horizontal well length, and inter-fracture distance, on the productivity of low permeability gas reservoirs with multi-fractured horizontal wells. Simulation results revealed that the quantity, length, and distribution of fractures had significant effects on the productivity of low permeability gas reservoirs while the effects of the diversion capacity of fractures and the angle between the fracture and horizontal shaft were negligible. Additionally, a U-shaped distribution of fracture lengths was preferential as the quantity of fractures at shaft ends was twice that in the middle area.