Implicit Z-factor Correlations @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)	$\begin{array}{l}\displaystyle 1 + T_1 \, y + T_2 \, y^2 + T_3 \, y^5 + T_4 \, y^2 \, (1+ A_{11} \, y^2) \, \exp (- A_{11} \, y^2) - T_5/y = 0\end{array}$

(3)	$\begin{array}{l}\displaystyle T_1 = A_1 + \frac{A_2}{T_{pr}} + \frac{A_3}{T_{pr}^3} + \frac{A_4}{T_{pr}^4} + \frac{A_5}{T_{pr}^5}\end{array}$

(4)	$\begin{array}{l}\displaystyle T_2 = A_6 + \frac{A_7}{T_{pr}} + \frac{A_8}{T_{pr}^2}\end{array}$

(5)	$\begin{array}{l}\displaystyle T_3 = A_9 \cdot \left[ \frac{A_7}{T_{pr}} + \frac{A_8}{T_{pr}^2} \right]\end{array}$

(6)	$\begin{array}{l}\displaystyle T_4 =\frac{A_{10}}{T_{pr}^3}\end{array}$

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

or

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

(9)	$\begin{array}{l}\displaystyle R_5 \, y^2 \, (1+ A_{11} \, y^2) \cdot \exp \left( - A_{11} \, y^2 \right) + R_1 \, y - \frac{R_2}{y} +R_3 \, y^2 - R_4 \, y^5 +1 = 0\end{array}$

(10)	$\begin{array}{l}\displaystyle R_1 = A_1 + A_2 \, t + A_3 \, t^3 + A_4 \, t^4 + A_5 \, t^5\end{array}$

(11)	$\begin{array}{l}\displaystyle R_2 = \frac{0.27 \, P_{pr}}{T_{pr}}\end{array}$

(12)	$\begin{array}{l}\displaystyle R_3 = A_6 + A_7 \, t + A_8 \, t^2\end{array}$

(13)	$\begin{array}{l}\displaystyle R_4 = A_9 \cdot ( A_7 \, t + A_8 \, t^2)\end{array}$

(14)	$\begin{array}{l}\displaystyle R_5 = A_{10} \, t^3\end{array}$

(15)	$\begin{array}{l}\displaystyle t= \frac{1}{T_{pr}}\end{array}$

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

$\begin{array}{l}A_1 = 0.3265\end{array}$	$\begin{array}{l}A_2 = -1.070\end{array}$	$\begin{array}{l}A_3 = - 0.5339\end{array}$	$\begin{array}{l}A_4 = 0.01569\end{array}$	$\begin{array}{l}A_5 = - 0.05165\end{array}$	$\begin{array}{l}A_6 = 0.5475\end{array}$
$\begin{array}{l}A_7 = -0.7361\end{array}$	$\begin{array}{l}A_8 = 0.1844\end{array}$	$\begin{array}{l}A_9 = 0.1056\end{array}$	$\begin{array}{l}A_{10} = 0.6134\end{array}$	$\begin{array}{l}A_{11} = 0.7210\end{array}$

Reference

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