Implicit 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 $\begin{array}{l}0.2 \leq P_{pr} \leq 30\end{array}$

and also a specific range of $\begin{array}{l}0.7 < T_{pr} \leq 1.0\end{array}$ and $\begin{array}{l}P_{pr} < 1.0\end{array}$ :

(1)	$\begin{array}{l}\displaystyle Z = \frac{0.27 \, P_{pr}}{y \, T_{pr}}\end{array}$

(2)	$\begin{array}{l}\displaystyle 1 + T_1 \, y +T_2 \, y^2 + T_3 \, y^5 + T_4 \, y^2 \, (1+ A_8 \, y^2) \cdot \exp \left( - A_8 \, y^2 \right) - \frac{T_5}{y} = 0\end{array}$

(3)	$\begin{array}{l}\displaystyle T_1 = A_1 + \frac{A_2 }{ T_{pr} } + \frac{A_3 }{ T_{pr}^3 }\end{array}$

(4)	$\begin{array}{l}\displaystyle T_2 = A_4 + \frac{A_5 }{ T_{pr} }\end{array}$

(5)	$\begin{array}{l}\displaystyle T_3 = \frac{A_5 \, A_6 }{T_{pr}}\end{array}$

(6)	$\begin{array}{l}\displaystyle T_4 = \frac{A_7 }{T_{pr}^3}\end{array}$

(7)	$\begin{array}{l}\displaystyle T_5 = \frac{0.27 \, P_{pr} }{T_{pr}}\end{array}$

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

$\begin{array}{l}A_1 = 0.31506237\end{array}$	$\begin{array}{l}A_2 = -1.0467099\end{array}$	$\begin{array}{l}A_3 = -0.57832729\end{array}$	$\begin{array}{l}A_4 = 0.53530771\end{array}$
$\begin{array}{l}A_5 = -0.61232032\end{array}$	$\begin{array}{l}A_6 = -0.10488813\end{array}$	$\begin{array}{l}A_7 = 0.68157001\end{array}$	$\begin{array}{l}A_8 = 0.68446549\end{array}$

Reference

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