Explicit Z-factor correlation @model for the natural gas in the wide range of pseudo-reduced temperature $\begin{array}{l}1.0 < T_{pr} \leq 3.0\end{array}$ and pseudo-reduced pressure $\begin{array}{l}0.2 \leq P_{pr} \leq 30\end{array}$ :

(1)	$\begin{array}{l}\displaystyle Z = a_1 + a_2 \cdot P_{pr} \cdot T_{pr}^{-1} + a_3 \cdot P_{pr}^{a_5} \cdot 10^{- a_6 \cdot T_{pr}} - a_4\cdot P_{pr} \cdot 10^{-a_7 \, T_{pr}}\end{array}$

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)

and

$\begin{array}{l}a_1 = 1.008505\end{array}$	$\begin{array}{l}a_2 = 0.04623\end{array}$	$\begin{array}{l}a_3 = 0.862707\end{array}$	$\begin{array}{l}a_4 = 2.324825\end{array}$
$\begin{array}{l}a_5 = 1.368627\end{array}$	$\begin{array}{l}a_6 = 0.636778\end{array}$	$\begin{array}{l}a_7 = 0.649787\end{array}$

Reference

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