Peng–Robinson EOS @model

@wikipedia

One of the cubic equations of real gas state defining the Compressibility factor $\begin{array}{l}Z(p, T)\end{array}$ as a function of Gas pressure $\begin{array}{l}p\end{array}$ and Gas temperature $\begin{array}{l}T\end{array}$ :

(1)	$\begin{array}{l}\displaystyle Z^3 - (1-B) \, Z^2 +(A-2B-3B^2) \, Z -(AB-B^2-B^3) = 0\end{array}$

(2)	$\begin{array}{l}\displaystyle A=\frac{a \, \alpha \, p}{ R^2 \, T^2}\end{array}$

(3)	$\begin{array}{l}\displaystyle B=\frac{b \, p}{ R \, T}\end{array}$

(4)	$\begin{array}{l}\displaystyle a = 0.45724 \cdot \frac{R^2 \, T_c^2}{p_c}\end{array}$

(5)	$\begin{array}{l}\displaystyle b = 0.07780 \cdot \frac{R \, T_c}{p_c}\end{array}$

(6)	$\begin{array}{l}\displaystyle \alpha = \left( 1 + \kappa \, (1-T_r^{0.5}) \right)^2\end{array}$

(7)	$\begin{array}{l}\displaystyle \kappa = 0.37464 + 1.54226 \, \omega -0.26992 \, \omega^2\end{array}$

where

$\begin{array}{l}Z\end{array}$	Compressibility factor	$\begin{array}{l}p_c\end{array}$	critical pressure
$\begin{array}{l}p\end{array}$	Gas pressure	$\begin{array}{l}T_c\end{array}$	critical temperature
$\begin{array}{l}T\end{array}$	Gas temperature	$\begin{array}{l}T_r = T/T_c\end{array}$	reduced temperature
$\begin{array}{l}R\end{array}$	Gas constant	$\begin{array}{l}\omega\end{array}$	accentric factor

Once compressibility Z-factor $\begin{array}{l}Z(p, T)\end{array}$ is known the gas density $\begin{array}{l}\rho\end{array}$ can be calculated as:

(8)	$\begin{array}{l}\displaystyle \rho(p, T) = \frac{1}{Z(p,T)} \cdot \frac{M}{R} \cdot \frac{p}{T}\end{array}$

where

$\begin{array}{l}M\end{array}$

Gas molar mass

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Peng–Robinson EOS @model