基于对勾函数的新型天然气压缩因子计算关联式

A new correlation for calculating natural gas compressibility factor based on hook function

关键词:  天然气  经验公式  压缩因子  Standing-Katz图版  非线性曲面拟合

Key words:  natural gas  empirical formula  compressibility factor  Standing-Katz chart  nonlinear surface fitting

摘要:

为了解决目前工程上使用的天然气压缩因子计算方法的计算精度不足、计算效率较低、适用范围较小的问题,分析了天然气压缩因子图版特征,利用非线性曲面拟合方法对中低压图版和高压图版的6 988组数据进行拟合,得到了一种对勾函数形式的、适用于0.2≤p_pr≤30.0压力范围的新型天然气压缩因子经验公式,拟合值与图版值的平均绝对误差、平均相对误差和均方根误差分别为0.012 51、0.013 59和0.017 57,拟合效果良好。利用237组中低压天然气压缩因子实测数据和219组高压天然气压缩因子实测数据对该方法进行验证,并与其他5种常用的显式或隐式的计算方法进行对比。验证结果表明,利用该方法得出的计算结果与实测值之间的平均绝对误差、平均相对误差和均方根误差分别为0.018 95、0.015 08和0.024 19,计算精度较高且优于其他5种方法,能够在矿场实践中快速准确地预测出不同条件下的天然气压缩因子。 

Abstract:

In order to solve the problems of insufficient calculation accuracy, low calculation efficiency and small application range of the calculation method for natural gas compressibility factor currently used in engineering, the characteristics of the natural gas compressibility factor charts are analyzed. The nonlinear surface fitting method is used to fit the 6 988 data of Standing-Katz chart,and a new empirical formula of natural gas compressibility factor in the form of hook function is obtained, which is suitable for the pressure range of 0.2≤p_pr≤30.0. The mean absolute error, mean relative error and root mean square error between the fitting values and the chart values are 0.012 51, 0.013 59 and 0.017 57 respectively, so the fitting effect is good. The proposed method is verified by 237 measured data of natural gas compressibility factor under low and medium pressure conditions and 219 measured data under high pressure conditions, and compared with the other five common explicit or implicit methods. The verification result shows that the mean absolute error, mean relative error and root mean square error between the calculated values and the measured values are 0.018 95,0.015 08 and 0.024 19 respectively, and the method is superior to the other five methods because of its higher calculation accuracy. The new method can be used to predict the natural gas compressibility factor quickly and accurately in practice.