Abstract: Multistage fractured horizontal wells (MFHWs) can greatly improve single well productivity in low permeability reservoirs and improve their development benefits. The accurate calculation of gas well productivity and analysis of related influencing factors are the basis for fracturing optimization and scientific development of gas reservoirs. Herein, a rigorous mathematical model was established for the calculation of MFHW productivity in low permeability reservoirs. Laplace transforms, the superposition principle, boundary discretization method of integral equations, matrix theory, and other mathematical methods were used to successfully solve the proposed model and to perform quantitative calculations and analysis of the production capacity with various influencing factors. The effects on gas well productivity due to the effective thickness of the gas layer, gas reservoir permeability, number of fractures, fracture half-length, and flow conductivity of the fractures were analyzed. The difference in the inflow rate from the stratum to each fracture was also determined. When the effective thickness of the gas layer or the permeability of the gas reservoir increases, the gas well production capacity increases almost linearly. When the number of fractures, fracture half-length, and flow conductivity of the fracture increase, the output increases with an initially higher rate of increase which slows during the later stage. The inflow rate from the stratum to each fracture remains largely unchanged during the early stages, but the difference in the later stage is clear, where the flow rate is greater at the ends compared to that observed in the middle.

Key words: low permeability reservoir, multistage fractured horizontal well, productivity model, influencing factors, flow conductivity