Abstract For most shale gas wells, frequent shut-ins and nozzle size changing often occur, leading to significant discontinuities in production data. This study proposes a new production data analysis (PDA) method to address the abrupt change issue based on the virtual equivalent time. With the virtual equivalent time, the qualities of type curve matching and production data analysis can be improved when there are abrupt changes in production data. The mathematical model with a variable flow rate provides new definitions of normalized pseudopressure and pseudotime with consideration of the pressure dependent permeability for multi-fractured horizontal wells in shale gas reservoirs. Subsequently, the virtual equivalent time is calculated based on the average formation pressure to consider the abrupt changes of the production data, which also can reduce the time of superposition principle calculations. Duhamel's principle, Laplace transform and inversion, and Newman's method are employed to solve the PDA model, which is validated by analytical and numerical solutions. Then sensitivity analysis are performed on the dimensionless constrained axial modulus, which shows that the larger the dimensionless constrained axial modulus, the lower and later the curves. Finally, a field case study is carried out using the proposed method. The results show that by using the virtual equivalent time, the matching qualities are good, and the issue caused by abrupt changes is satisfactorily addressed. Therefore, it has great potential for estimating the formation parameters and predicting the well production performance more effectively and practically.

中文翻译：

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页岩气藏生产数据分析新方法

摘要 对于大多数页岩气井来说，经常会发生频繁关井和喷嘴尺寸变化，导致生产数据的显着不连续性。本研究提出了一种新的生产数据分析（PDA）方法来解决基于虚拟等效时间的突变问题。利用虚拟等效时间，可以在生产数据发生突变时提高类型曲线匹配和生产数据分析的质量。具有可变流量的数学模型提供了归一化伪压力和伪时间的新定义，同时考虑了页岩气藏中多裂缝水平井的压力相关渗透率。随后，考虑生产数据的突变，根据平均地层压力计算虚拟等效时间，这也可以减少叠加原理计算的时间。采用杜哈梅尔原理、拉普拉斯变换和反演以及纽曼方法求解PDA模型，并通过解析解和数值解进行验证。然后对无量纲约束轴向模量进行敏感性分析，表明无量纲约束轴向模量越大，曲线越低越靠后。最后，使用所提出的方法进行现场案例研究。结果表明，采用虚拟等效时间，匹配质量良好，较好地解决了突变引起的问题。因此，它在更有效、更实用地估计地层参数和预测井生产动态方面具有很大的潜力。