PengRobinson Equation of State
The PengRobinson (PR) equation of state (EOS) is a cubic EOS which was initially developed by Peng and Robinson in 1976^{1} and was modified in 1978 to enhance the phase behavior predictions of the model^{2}. The PR EOS is a common EOS used in many areas of petroleum and chemical engineering.
PR EOS Structure
The PR EOS model is defined by
where \(a\) and \(b\) are the EOS model parameters. The pure component parameters (\(a\) and \(b\)) can be calculated by
In equations \eqref{eq:a_pr}, \eqref{eq:b_pr} and \eqref{eq:alpha} the coefficients \(\Omega_a\) and \(\Omega_b\) , and the value of \(\alpha(T)\) can be calculated by
Component Properties
The component properties are composed of the critical pressure (\(p_c\)), critical temperature (\(T_c\)), accentric factor (\(\omega\)) and molecular weight (\(MW\)). Another important component property for cubic EOS models are the volume shift factors descried by Peneloux in 1982^{3}. The volume shifts were introduced as a correction term to the phase behaviour predictions of the molar volume predictions.
Mixing Rules
Note
The main article for cubic EOS models describes the mixing rules with some more detail.
The original mixing rule developed by van der Waals is a quadratic mixing rule. The set of equations describing the mixing are given by
where \(a_{ij}=\sqrt{a_ia_j}\), \(u_i\) can be the liquid composition (\(x_i\)), vapor composition (\(y_i\)) or the total composition (\(z_i\)) and \(a_i\) and \(b_i\) are the component EOS parameters for component \(i\).
Modifications to the \(a\) and \(b\) mixing rules were developed to enhance the performance of the EOS models. The most common modified mixing rules are given by
where \(k_{ij}\) is often referred to as the binary interaction parameter (BIP) or sometimes referred to as the binary interaction coefficient (BIC).

D. Y. Peng and D. B. Robinson. A new twoconstant equation of state. Industrial & Engineering Chemistry Fundamentals, 15:59–64, 1976. ↩

D. B. Robinson and D. Y. Peng. The characterization of the heptanes and heavier fractions for the GPA PengRobinson programs. Gas processors association, 1978. ↩

A. Péneloux, E. Rauzy, and R. Fréze. A consistent correction for redlichkwongsoave volumes. Fluid phase equilibria, 8:7–23, 1982. doi:https://doi.org/10.1016/03783812800022. ↩