目前压裂水平井作为页岩气藏的主要开发模式，由于页岩气藏渗流模式在发育良好的天然裂缝以及纳米级孔隙基础上衍生的极为复杂，准确建立渗流数学模型以及对其求解和应用于现场开发生产有着重要的意义。基于三线性渗流理论，考虑解吸—吸附项重新建立页岩气藏压裂水平井产能模型，借助拟压力与无因次量及拉普拉斯变换等数学方法推导出井底压力公式，并通过无因次产量和无因次井底拟压力的关系运用数值反演推导得到页岩气水平井产量计算公式，最后运用公式对气井生产的影响因素进行分析并验证单井产能递减规律。结果表明，推导出的公式能够准确计算和预测页岩气藏产量变化及产能递减规律，同时也能提供压裂设计工艺参数对应的优化分析条件。
Fracturing horizontal wells are the main development mode of shale gas reservoirs.The shale gas reservoir seepage pattern is extremely complicated based on well-developed natural fractures and nano-scale pores.Therefore，it is of great significance to accurately establish the mathematical model of seepage and solve and apply it to the on-site development and production.Based on the trilinear seepage theory，the desorption-adsorption term is used to re-establish the horizontal well productivity model of shale gas reservoirs，and the bottom hole pressure formula is derived by mathematical methods such as pseudo-pressure and dimensionless and Laplace transform.Through the relationship between dimensionless production and dimensionless bottomhole pseudo-pressure，the calculation formula of shale gas horizontal well production is derived by numerical inversion.Finally，the influencing factors of gas well production are analyzed by formula and the law of single well productivity decline is verified.The results show that the derived formula can accurately calculate and predict the yield variation and capacity decline law of shale gas reservoirs，and also provide the optimal analysis conditions corresponding to the process parameters of fracturing design.
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