Table 4 Parameters of EOSs and mixing rules.

ZJ

Parameter α and b are calculated as functions of temperature and pressure. For complex mixtures,\(b_{i} = b_{i}^{ZJ} \left[ {1 + b_{0} \left( {\frac{T}{{T_{C} }} - 1} \right)} \right]\)

¹⁰²

RK

\(\begin{gathered} a = {0}{\text{.42748}}\frac{{R^{2} T_{C}^{2.5} }}{{P_{C} }} \hfill \\ b = {0}{\text{.08664}}\frac{{RT_{C} }}{{P_{C} }} \hfill \\ \end{gathered}\)

¹⁰³

SRK

\(\begin{gathered} a = {0}{\text{.42747}}\frac{{\left( {RT_{C} } \right)^{2} }}{{P_{C} }} \hfill \\ b = {0}{\text{.08664}}\frac{{RT_{C} }}{{P_{C} }} \hfill \\ m = 0.48508 + 1.5517\omega - 0.1561\omega^{2} \hfill \\ \alpha = \left[ {1 + m\left( {1 - \sqrt {T_{r} } } \right)} \right]^{2} \hfill \\ c = \frac{{0.40768RT_{C} (0.29441 - Z_{RA} )}}{{P_{C} }} \hfill \\ Z_{RA} = 0.29506 - 0.08775\omega \hfill \\ \end{gathered}\)

^103,104

PR

\(\begin{gathered} \alpha = \left[ {1 + m\left( {1 - \sqrt {T_{r} } } \right)} \right]^{2} \hfill \\ a = 0.45724\frac{{(RT_{C} )^{2} }}{{P_{C} }} \hfill \\ m = 0.3796 + 1.485\omega - 0.1644\omega^{2} + 0.01667\omega^{3} \hfill \\ b = {0}{\text{.07780}}\frac{{RT_{C} }}{{P_{C} }} \hfill \\ c = \frac{{0.40768RT_{C} (0.29441 - Z_{RA} )}}{{P_{C} }} \hfill \\ {\text{For non - hydrocarbons and hydrocarbons lighter than C}}_{{7}} : \hfill \\ c = \frac{{0.50033RT_{C} }}{{P_{C} }}(0.25969 - Z_{RA} ) \hfill \\ Z_{RA} = 0.29506 - 0.08775\omega \hfill \\ \end{gathered}\)

^103,104

PC-SAFT

\(\begin{gathered} {\tilde{\text{a}}}^{{{\text{hc}}}} = \overline{m}{\tilde{\text{a}}}^{{{\text{hs}}}} + {\tilde{\text{a}}}^{{{\text{chain}}}} = \overline{m}{\tilde{\text{a}}}^{{{\text{hs}}}} - \sum\limits_{i} {x_{i} } (m_{i} - 1)\ln g_{ij}^{hs} \hfill \\ \overline{m} = \sum\limits_{i} {x_{i} } m_{i} \hfill \\ {\tilde{\text{a}}}^{{{\text{hs}}}} = \frac{1}{{\zeta_{0} }}\left[ {\frac{{3\zeta_{1} \zeta_{2} }}{{1 - \zeta_{3} }} + \frac{{3\zeta_{2}^{3} }}{{\zeta_{3} (1 - \zeta_{3} )^{2} }} + \left( {\frac{{\zeta_{2}^{3} }}{{\zeta_{3}^{2} }} - \zeta_{0} } \right)\ln (1 - \zeta_{3} )} \right] \hfill \\ \zeta_{n} = \frac{\pi }{6}\rho \sum\limits_{i} {x_{i} } m_{i} d_{i}^{n} \, n \in \left\{ {0,1,2,3} \right\}, \, \eta = \zeta_{3} \hfill \\ d_{i} = \sigma_{i} \left[ {1 - 0.12\exp \left( { - 3\frac{{\varepsilon_{i} }}{kT}} \right)} \right] \hfill \\ g_{ij}^{hs} = \frac{1}{{1 - \zeta_{3} }} + \left( {\frac{{d_{i} d_{j} }}{{d_{i} + d_{j} }}} \right)\frac{{2\zeta_{2} }}{{(1 - \zeta_{3} )^{2} }} + \left( {\frac{{d_{i} d_{j} }}{{d_{i} + d_{j} }}} \right)^{2} \frac{{2\zeta_{2}^{2} }}{{(1 - \zeta_{3} )^{2} }} \hfill \\ {\tilde{\text{a}}}^{{{\text{dis}}}} = - 2\pi \rho I_{1} \left( {\eta ,\overline{m}} \right)\overline{{m^{2} \varepsilon \sigma^{3} }} - \pi \rho \overline{m}C_{1} \left( {\eta ,\overline{m}} \right)I_{2} \left( {\eta ,\overline{m}} \right)\overline{{m^{2} \varepsilon^{2} \sigma^{3} }} \hfill \\ I_{1} \left( {\eta ,\overline{m}} \right) = \sum\limits_{i = 0}^{6} {a_{i} } (\overline{m})\eta^{i} { , }I_{2} \left( {\eta ,\overline{m}} \right) = \sum\limits_{i = 0}^{6} {b_{i} } (\overline{m})\eta^{i} \hfill \\ \end{gathered}\)

where a_i and b_i depend on the chain length as given in Gross and Sadowski¹⁰⁵

\(\begin{gathered} C_{1} = \left[ {1 + \overline{m}\frac{{8\eta - 2\eta^{2} }}{{\left( {1 - \eta } \right)^{4} }} + (1 - \overline{m})\frac{{20\eta - 27\eta^{2} + 12\eta^{3} - 2\eta^{4} }}{{\left[ {\left( {1 - \eta } \right)\left( {2 - \eta } \right)} \right]^{2} }}} \right] \hfill \\ \overline{{m^{2} \varepsilon \sigma^{3} }} = \sum\limits_{i} {\sum\limits_{j} {x_{i} x_{j} } } m_{i} m_{j} \left( {\frac{{\varepsilon_{ij} }}{kT}} \right)\sigma_{ij}^{3} \hfill \\ \overline{{m^{2} \varepsilon^{2} \sigma^{3} }} = \sum\limits_{i} {\sum\limits_{j} {x_{i} x_{j} } } m_{i} m_{j} \left( {\frac{{\varepsilon_{ij} }}{kT}} \right)^{2} \sigma_{ij}^{3} \hfill \\ \varepsilon_{ij} = \sqrt {\varepsilon_{i} \varepsilon_{j} } \left( {1 - k_{ij} } \right) \hfill \\ \sigma_{ij} = \frac{{\left( {\sigma_{i} + \sigma_{j} } \right)}}{2} \hfill \\ \end{gathered}\)

The expressions for the contributions from the dispersion and ideal gas are identical to those of Gross and Sadowski¹⁰⁵

^105,106

Van der Waals one-fluid mixing rules

\(\begin{gathered} a = \sum\limits_{i = 1}^{N} {\sum\limits_{j = 1}^{N} {z_{i} z_{j} \sqrt {a_{i} a_{j} } } } \left[ {1 - k_{ij} (T)} \right] \hfill \\ b = \sum\limits_{i = 1}^{N} {z_{i} b_{i} } \hfill \\ \end{gathered}\)

^103,107