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

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

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

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

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

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

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

where

$\begin{array}{l}Z\end{array}$	Z-factor
$\begin{array}{l}T\end{array}$	fluid temperature	$\begin{array}{l}T_{pr} = T/T_{pc}\end{array}$	pseudo-reduced temperature (or reduced temperature $\begin{array}{l}T_{r}\end{array}$ in case of pure substances)	$\begin{array}{l}T_{pc}\end{array}$	pseudo-critical temperature (or critical temperature $\begin{array}{l}T_{c}\end{array}$ in case of pure substances)
$\begin{array}{l}P\end{array}$	fluid pressure	$\begin{array}{l}P_{pr} = P/P_{pc}\end{array}$	pseudo-reduced pressure (or reduced pressure $\begin{array}{l}P_{r}\end{array}$ in case of pure substances)	$\begin{array}{l}P_{pc}\end{array}$	pseudo-critical pressure (or critical pressure $\begin{array}{l}P_{c}\end{array}$ in case of pure substances)

Reference

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

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