Cubic equations of state are widely used for phase equilibrium calculations. They are simple and reliable, especially for hydrocarbon mixtures. Unfortunately, common choices such as the Peng-Robinson and Soave-Redlich-Kwong equations of state, systematically predict both qualitatively and quantitatively incorrect phase behaviors for long chain n-alkane + aromatic and naphthenic mixtures unless negative binary interaction parameter (k
ij) values are used [1, 2]. Binary interaction parameters are typically obtained by fitting vapour-liquid equilibrium (VLE) data for binary mixtures. In the absence of data, interaction parameter values are obtained from generalized correlations typically leading to positive values [3,4] or are set to zero. Experimental VLE data for these mixtures are scarce and therefore reliable methods for estimating k
ij values in the absence of experimental data are needed to support industrial process design and optimization calculations. In this study, methods for estimating k
ij values for cubic EOS for binary mixtures of aromatics with long chain n-alkanes are evaluated. Options explored include obtaining k
ij values by regressing liquid phase activity coefficients from an
a priori predictive model, the COnductor like Screening MOdel for Real Solvents (COSMOS-RS) [5] and the PC-SAFT EOS [6] (based on statistical associating fluid theory), and a predictive group-contribution k
ij estimation approach â PPR78 (predictive 1978, PengâRobinson EOS) [7]. Calculated temperature-dependent interaction parameter values for 15 representative long chain n-alkane + aromatic binary mixtures are benchmarked against Peng-Robinson EOS k
ij values fitted to high precision VLE data [8]. The resulting skew and dispersion of predicted vs experimental k
ij values is discussed and best practices for estimating cubic EOS k
ij values for such mixtures are described.
References:
 [1] Ahitan, S., Satyro, M. A., Shaw, J. M. Systematic misprediction of n-alkane + aromatic and naphthenic hydrocarbon phase behavior using common equations of state. J. Chem. Eng. Data 2015, 60, 3300-3318.
[2] Ahitan, S., Shaw, J. M. Quantitative comparison between predicted and experimental binary n-alkane+ benzene phase behaviors using cubic and PC-SAFT EOS. Fluid Phase Equilib. 2016, 428, 4-17.
[3] Gao, G.; Daridon, J.; Saint-Guirons, H.; Xans, P.; Montel, F. A simple correlation to evaluate binary interaction parameters of the Peng-Robinson equation of state: binary light hydrocarbon systems. Fluid Phase Equilibria 1992, 85-93.
[4] Chueh, P. L.; Prausnitz, J. M. Vapor-liquid equilibria at high pressures: Calculation of partial molar volumes in nonpolar liquid mixtures. AIChE J. 1967, 6, 1099-1107.
[5] Klamt, A.; Eckert, F. COSMO-RS: a novel and efficient method for the a priori prediction of thermophysical data of liquids. Fluid Phase Equilibria 2000, 1, 43-72.
[6] Gross, J.; Sadowski, G. Perturbed-Chain SAFT: An Equation of State Based on a Perturbation Theory for Chain Molecules. Ind. Eng. Chem. Res. 2001, 4, 1244-1260.
[7] Jaubert, J.; Vitu, S.; Mutelet, F.; Corriou, J. Extension of the PPR78 model (predictive 1978, PengâRobinson EOS with temperature dependent kij calculated through a group contribution method) to systems containing aromatic compounds. Fluid Phase Equilib. 2005, 1â2, 193-211.
[8] Liu, Q. MSc. Thesis, University of Alberta (in progress 2017).
