(1)	$\begin{array}{l}\displaystyle Z = A + (1-A) \cdot \exp(-B) + C\cdot p^D\end{array}$

(2)	$\begin{array}{l}\displaystyle A=1.39 \cdot (T_{\rm pr}-0.92)^{0.5} - 0.36 T_{\rm pr} - 0.1\end{array}$

(3)	$\begin{array}{l}\displaystyle D=10^F\end{array}$

(4)	$\begin{array}{l}\displaystyle B=(0.62-0.23 T_{\rm pr}) \cdot p_{\rm pr} + \left( \frac{0.066}{T_{\rm pr}-0.86} -0.037 \right) \cdot p_{\rm pr}^2 + 0.32 \cdot 10^{-E} \cdot p_{\rm pr}^2\end{array}$

(5)	$\begin{array}{l}\displaystyle E=9 \cdot (T_{\rm pr}-1)\end{array}$

(6)	$\begin{array}{l}\displaystyle C=0.132-0.32 \, \ln(T_{\rm pr})\end{array}$

(7)	$\begin{array}{l}\displaystyle F=0.3106-0.49 T_{\rm pr}+0.1824 T_{\rm pr}^2\end{array}$

where

$\begin{array}{l}Z\end{array}$	Compressibility Z-factor	$\begin{array}{l}T_{\rm pc}\end{array}$	pseudo-critical temperature	$\begin{array}{l}T_{\rm pr} = T/T_{\rm pc}\end{array}$	pseudo-reduced temperature
$\begin{array}{l}p\end{array}$	fluid pressure	$\begin{array}{l}p_{\rm pc}\end{array}$	pseudo-critical pressure	$\begin{array}{l}p_{\rm pc} = p/p_{\rm pc}\end{array}$	pseudo-reduced pressure

References

Beggs DHU, Brill JPU (1973) A study of two-phase flow in inclined pipes. J Pet Technol 25:607–617

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