∇

The Peng-Robinson [57] equation of state for gases.

Density, \(\rho\) [kg/m\(^3\)]

\[\rho = \frac{p}{Z R T}\]

Here, \(Z\) is computed from the cubic equation:

\[Z^3 - (1 - B)Z^2 + (A - 2B - 3B^2)Z - (AB - B^2 - B^3) = 0\]

Where:

\[A = \frac{\alpha a p}{R^2 T^2}; B = \frac{bp}{RT}.\]

with:

  • \[a = 0.45724 \frac{R^2 T_c^2}{p_c}\]
  • \[b = 0.07780 \frac{R T_c}{p_c}\]
  • \[\alpha = \left(1 + \kappa (1 - T_r^{0.5}) \right)^2\]
  • \[\kappa = 0.37464 + 1.564226 \omega - 0.26992 \omega^2\]
  • \[T_r = \frac{T}{T_c}\]

Entropy, \(S\) [J/kg/K ]

\[S = ...\]

Compressibility, \(\psi\) [s\(^2\)/m\(^2\)]

\[\psi = \frac{1}{Z R T}\]

Usage

The PengRobinsonGas equation of state is specified as:

equationOfState
{
    Tc          <scalar>;
    Vc          <scalar>;
    Pc          <scalar>;
    omega       <scalar>;
}

Where

  • Tc : Critical temperature [K]
  • Vc : Critical volume [m\(^3\)/kmol]
  • Pc : Critical pressure [Pa]
  • omega : Accentric factor [-]

Further information

Source code