Implicit Z-factor correlation @model for the natural gas in the wide range of pseudo-reduced temperature $\begin{array}{l}1.05 \leq T_{pr} \leq 3\end{array}$ and pseudo-reduced pressure $\begin{array}{l}0.2 \leq P_{pr} \leq 15\end{array}$ :

(1)	$\begin{array}{l}\displaystyle Z = \frac{A_1 \, P_{pr}}{y}\end{array}$

(2)	$\begin{array}{l}\displaystyle -A_1 \, P_{pr} + \frac{y+y^2+y^3-y^4}{(1-y)^3} - A_2 \, y^2 + A_3 \, y^{\, A_4} = 0\end{array}$

(3)	$\begin{array}{l}\displaystyle A_1 = 0.06125 \cdot t \cdot \exp \left[ -1.2 (1-t)^2 \right]\end{array}$

(4)	$\begin{array}{l}\displaystyle A_2 = 14.76 \, t - 9.76 \, t^2 +4.58 \, t^3\end{array}$

(5)	$\begin{array}{l}\displaystyle A_3 = 90.7 \, t -242.2 \, t^2 + 42.4 \, t^3\end{array}$

(6)	$\begin{array}{l}\displaystyle A_4 = 2.18 + 2.82 \, t\end{array}$

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

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)

Reference

Hall, K.R., Yarborough, L., 1973. A new equation-of-state for Z-factor calculations. Oil Gas J. 71, 82–92.

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