低渗气藏多级压裂水平井产能模型及影响因素

多级压裂水平井（MFHW）能大幅度提高低渗气藏的单井产能，提高低渗气藏的开发效益，而准确计算气井产能并分析其影响因素是压裂优化设计、气藏科学开发的基础。为低渗气藏MFHW产能计算建立了一个严格的数学模型，综合运用Laplace变换、叠加原理、积分方程的边界离散求解法、矩阵理论等数学方法成功地对模型进行了求解，并对不同因素影响下的产能进行了定量计算和分析，分析了气层有效厚度、气藏渗透率、压裂缝条数、压裂缝半长、压裂缝导流能力对气井产能的影响，同时也分析了地层流入各条压裂缝流量的差异。研究结果表明，气层有效厚度或气藏渗透率增大时，气井产量几乎呈线性增大；压裂缝条数、压裂缝半长、压裂缝导流能力增大，产量增大，但前期增速快，后期增速慢；地层流入各条压裂缝的流量在早期差别不大，晚期差别明显——端部流量大于中部流量。

Productivity Model and its Influencing Factors for Multistage Fractured Horizontal Wells in Low Permeability Reservoirs

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.