The existing single phase flowback mathematical model at the early time is applicable to tight oil and gas reservoirs, not suitable for shale gas reservoirs since there is no single phase flow, but gas and water two-phase flow at the early time of flowback.The plots of gas and water flow rate versus time and GWR versus cumulative gas production are depicted using fractured horizontal wells of North America certain shale gas reservoir.Gas and water exist at the same time in the former plot, indicating free gas depletion in the fracture;also, in the latter plot, the flowback is separated into two distinct regions according the slope, and the reason of 'V shape' of plot is analyzed.Based on the gas early time flowback region, the physical model of fracture system is developed, and then the material balance equation and diffusivity equation is deployed to deduce to obtain the two phase flowback mathematical model at the early time successfully, which shows the linear relationship of normalized pseudo pressure and pseudo time.Field case is applied to make an analysis of the new mathematical model, as a result, the model can match the field data well and get a fitted straight line, whose slope can estimate the initial fracture volume, and intercept can display the value relationship between fracture half-length and fracture permeability.In this paper, the research on the flowback data is carried out innovatively.On this basis, the mathematical model of the flowback applied to evaluate fracture parameters is deduced, which provides a new method for understanding the fracture characteristics.%目前存在的早期单相流返排的数学模型适用于致密油气储层,不适用于页岩气储层,这是因为页岩气井早期返排阶段不存在单相流,而是气水两相流.利用北美某页岩气储层压裂水平井的返排数据分别绘制气水产量随时间的变化曲线和气水比随累积产气量的变化曲线,气水产量曲线在早期返排阶段气水同产,表明裂缝中存在自由气的消耗;而气水比曲线根据斜率的正负将返排分为两个阶段,并针对曲线的"V型"进行原因分析.针对气体早期返排阶段,建立裂缝系统物理模型,运用物质平衡方程和扩散方程,推导得到页岩气井早期两相流返排数学模型,数学方程表明:等效压力与拟时间呈线性关系.应用现场实例对数学模型进行分析,结果表明,该模型能够较好地拟合现场数据,拟合得到的直线斜率可用于估算原始裂缝体积,截距可以给出裂缝半长和裂缝渗透率之间的关系.本文创新性地对返排数据进行调研分析,在此基础上得出适用于现场估算裂缝参数的返排数学方程,从而为认识裂缝特征提供了新的方法.
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