Arps双曲线递减模型的多解性和不确定性

Multi-solution and uncertainty of Arps’hyperbolic exponential decline model

ARPS于1945年基于对油气井产量递减曲线数据的统计、分析,提出了具有重要理论意义的递减率概念及其微分表达式,并首创建立了指数递减模型、双曲线递减模型和调和递减模型,其中双曲线递减模型是Arps递减模型的核心。指数递减模型因具有简单易行的特点,在国际上得到了广泛应用。通过应用研究发现,属于经验性的双曲线递减模型,因其存在明显的不确定性,在实际中应用得很少。由双曲线递减模型简化得到的调和递减模型也几乎没有应用。同时,通过对Arps双曲线递减模型,与陈元千泛指数递减模型的对比性应用结果表明,n=0.5的双曲线递减模型是Arps双曲线递减模型的最佳选择,可有效地用于页岩气井产量和井控可采储量的评价。

In 1945,ARPS proposed the theoretically significant decline rate and its differential form based on the statistics and analysis of the production decline curve.The exponential decline model,hyperbolic decline model,and harmonic de⁃cline model were first built,of which the hyperbolic decline model was the core of the Arps decline model.The exponential decline model has been widely used due to its simplicity and ease of operation.The application research shows that the em⁃pirical hyperbolic decline model is rarely used in practice because of its obvious uncertainty.The harmonic decline model simplified from the hyperbolic decline model has hardly been applied.At the same time,the Arps hyperbolic decline model with n=0.5 is the best choice through the comparison with the generic exponential decline model by Chen Yuanqian,which can be effectively used to predict the production rate and recoverable reserves of shale gas wells.