📐 核心公式
🔹 压缩因子 Z 表达式\[ Z = 1 + \left(A_1 + \frac{A_2}{T_{pr}} + \frac{A_3}{T_{pr}^3} + \frac{A_4}{T_{pr}^4} + \frac{A_5}{T_{pr}^5}\right)\rho_{pr} + \left(A_6 + \frac{A_7}{T_{pr}} + \frac{A_8}{T_{pr}^2}\right)\rho_{pr}^2 - A_9\left(\frac{A_7}{T_{pr}} + \frac{A_8}{T_{pr}^2}\right)\rho_{pr}^5 + A_{10}\left(1 + A_{11}\rho_{pr}^2\right)\frac{\rho_{pr}^2}{T_{pr}^3}e^{-A_{11}\rho_{pr}^2} \]
🔹 残差与导数\[ F(\rho_{pr}) = \rho_{pr} - 0.27\frac{p_{pr}}{T_{pr}} + \big(A_1+...\big)\rho_{pr}^2 + \big(A_6+...\big)\rho_{pr}^3 - A_9\big(...\big)\rho_{pr}^6 + \frac{A_{10}}{T_{pr}^3}\rho_{pr}^3(1+A_{11}\rho_{pr}^2)e^{-A_{11}\rho_{pr}^2} \]\[ F'(\rho_{pr}) = 1 + 2\rho_{pr}\big(A_1+...\big) + 3\rho_{pr}^2\big(A_6+...\big) - 6\rho_{pr}^5 A_9\big(...\big) + \frac{A_{10}}{T_{pr}^3}e^{-A_{11}\rho_{pr}^2}\left[3\rho_{pr}^2 + A_{11}(3\rho_{pr}^4 - 2A_{11}\rho_{pr}^6)\right] \]
🔹 压缩系数精确公式
拟对比密度 \(\rho_R = \dfrac{0.27 p_{pr}}{Z T_{pr}}\)
由复合函数求导: \(\displaystyle \frac{\partial Z}{\partial p_{pr}} = \frac{\partial Z}{\partial \rho_R} \frac{\partial \rho_R}{\partial p_{pr}}\)，经过代换得到最终表达式：
\[
C_{pr} = \frac{1}{p_{pr}} - \frac{0.27}{Z^3 T_{pr}} \left[ \frac{ \frac{\partial Z}{\partial \rho_R} }{ 1 + (\rho_R / Z) \frac{\partial Z}{\partial \rho_R} } \right]
\]
真实压缩系数: \(C_g = \dfrac{C_{pr}}{p_{pc}}\) (单位 1/MPa)