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Virial equations of state

Hayden-O'Connell

Hayden and O'Connell have provided a method of predicting the second virial coefficient for multi-compound vapour mixtures. The method is quite complicated (see Prausnitz et al., 1980) but is well suited to ideal and non-ideal systems at low pressures. You must input the association parameters. A library of association parameters is provided with TEA in the file HAYDENO.IPD.

Hayden-O'Connell with Chemical theory

This is an extension on the Hayden O'Connell virial model, which takes the association of molecules into account (see Prausnitz et al., 1980). Since the mole fractions are a function of the association, an iterative method (here Newton's method) must be used to obtain them in order to compute the virial coefficients.

Derivatives of compressibilities are determined by perturbation, and therefore all quantities derived from that (volume, density, fugacity, enthalpy, ...)

Tsonopoulous

The two-term virial equation:
\begin{displaymath} P = {R T \over V} + {B R T \over V} \end{displaymath}

The method of Tsonopoulous for estimating virial coefficients is recommended for hydrocarbon mixtures at low pressures. It is based on an earlier correlation due to Pitzer.

$\displaystyle B$ $\textstyle =$ $\displaystyle \sum^c_{i=1} \sum^c_{j=1} y_i y_j B_{ij}$
$\displaystyle B_{ij}$ $\textstyle =$ $\displaystyle {R T_{c,ij} \ P_{c,ij}}\left( B^{(0)}_{ij} + \omega_{ij} B^{(0)}_{ij} \right)$
$\displaystyle B^{(0)}_{ij}$ $\textstyle =$ $\displaystyle 0.1445 - {0.33 \over T_r} - {0.1385 \over T_r^2} - {0.0121 \over T_r^3} - {0.000607 \over T_r^8}$
$\displaystyle B^{(1)}_{ij}$ $\textstyle =$ $\displaystyle 0.0637 + {0.331 \over T_r^2} - {0.423 \over T_r^3} {-0.0008 \over T_r^8}$
$\displaystyle \omega_{ij}$ $\textstyle =$ $\displaystyle {\omega_i + \omega_j \over 2}$
$\displaystyle Z_{c,ij}$ $\textstyle =$ $\displaystyle {Z_{ci} + Z_{cj} \over 2}$
$\displaystyle V^{1/3}_{c,ij}$ $\textstyle =$ $\displaystyle {V^{1/3}_{ci} V^{1/3}_{cj} \over 2}$
$\displaystyle T_{c,ij}$ $\textstyle =$ $\displaystyle (1 - k_{ij}) \sqrt{ T_{ci} T_{cj} }$
$\displaystyle P_{c,ij}$ $\textstyle =$ $\displaystyle {Z_{c,ij} R T_{c,ij} \over V_{c,ij}}$

Binary interaction parameters kij must be supplied by the user. For paraffins, kij can be calculated with:
\begin{displaymath} k_{ij} = 1 - {8 \sqrt{V_{ci} V_{cj}} \over (V^{1/3}_{ci}+Vc^{1/3}_{cj})^3} \end{displaymath}

Temperature Correlation

Temperature correlated values for the virial coefficient are available from TEA (PCD) data files.