A simple and generalized model to represent the vapor-liquid equilibria and the liquid-molar-volume of alcohol-alkane binary mixtures

A simple thermodynamic model to describe the vapor-liquid equilibria and liquid densities of alcohol-alkane type mixtures is developed. The proposed model is based on a two-parameter cubic equation of state translated in volume and the Huron-Vidal-NRTL mixing rules. Generalized expressions in terms of the critical temperature and the critical pressure of alcohols and alkanes are developed for the binary energy interaction parameters (A₁₂, A₂₁) and the non-random mixing constant (α₁₂) that appears in the NRTL activity model. To obtain the generalized expressions, the homologous series concept is used as follows: in first place, four series composed by an alcohol between ethanol and 1-pentanol with some n-alkanes between butane and n-undecane are selected. For each series, it is supposed that each binary parameter (A₁₂, A₂₁ and α₁₂) can be described as a linear function in terms of the ratio RT_c/P_c of n-alkanes. The slope and the intercept of generalized expressions for each series are determined by minimizing the total absolute relative deviation in bubble pressure. Finally, it is found that all the slopes and the intercepts for parameters A₁₂ and A₂₁ can been correlated as quadratic functions in terms of the RT_c/P_c ratio of alcohols. Also, it is found that for all the series, the same generalized expression can be used to get parameter α₁₂. In total, 22 mixtures are used to develop the model. The average absolute relative deviation in bubble pressure (AADP) estimated is 1.65%. Also, the average absolute deviation in the vapor phase molar fraction (DY) is 0.007. To validate the proposed model, calculations are performed for 31 binary mixtures that include branched alcohols and branched alkanes that were not used during the development of the model. In general, predictions are adequate and results obtained are similar to those reported in literature for associating models like the Cubic-Plus-Association (CPA), the Statistical Association Fluid Theory (SAFT) and the Group Contribution Association (GCA) equations of state. The AADP for the new model is 2.80%, while the DY value is 0.009. Finally, liquid densities predictions are performed for 22 alcohol-alkane mixtures and it is found that calculated values are in good agreement with experimental data. The average absolute relative deviation calculated in liquid density is 1.16%. In total 645 densities and 1030 bubble pressures are predicted satisfactorily with the proposed model.