Example 4-11: VLE and LLE calculation of the methanol + n-hexane mixture

Chapitre d'équation 3 Section 1

Methanol is a polar and associating molecule. It forms strongly non-ideal mixtures with hydrocarbons: both liquid-liquid phase splits and azeotropic behaviour are encountered. For the binary methanol + n-hexane at atmospheric pressure, a heteroazeotrope is observed at low pressure. In figure 1, the ability of several models to represent this complex system is shown. We draw the reader's attention to several points:

Properties used in the fit: the NRTL parameters have been fitted separately on VLE and LLE data, resulting in two different models. When NRTL is fitted on VLE, it represents these data correctly, but results in a total mismatch for LLE (except possibly at low temperature, but this may be due to pure luck). When NRTL is fitted on LLE, its representation of the VLE curve is seriously impaired, although the azeotropic behaviour is still visible.

The parameters fitted on vapour-liquid equilibrium may not be suitable for liquid-liquid equilibrium calculations, and vice-versa.

Extrapolation of properties: for some applications, it may be important to have good predictions of Henry constants, in addition to the azeotropic behaviour. In the figure below, the quality of this property prediction can be evaluated by looking at the slopes of the bubble temperatures with respect to composition. It is clear that none of the models fitted on the azeotropic VLE is capable of calculating this property correctly. The model most suited for this type of extrapolation is that using a Wertheim association term (SAFT).

Figure 1: Vapour-liquid and liquid-liquid equilibria of the methanol + n-hexane mixture at atmospheric pressure (data from Raal et al. 1972 [1]).

Very often, no experimental data are available for fitting parameters. In that case, a fully predictive model should be used. UNIFAC is very often considered as the most appropriate method. Recently, the group contribution polar PC-SAFT (GC-PPC-SAFT) EoS has been developed whose aim is to provide a predictive approach for phase equilibrium calculations of polar and associating molecules[2, 3]. Figure 2 compares both UNIFAC and GC-PPC-SAFT on the same mixture as above. It shows that UNIFAC better predicts the bubble temperature of the mixture, but is unable to calculate the liquid-liquid phase split correctly.

Figure 2: Vapour-liquid and liquid-liquid equilibria of the methanol + n-hexane mixture at atmospheric pressure (data from Raal et al. 1972 [1]). The GC-PPC-SAFT parameters are from Mourah [4].

References

[1] RAAL J.D., CODE R.K., BEST D.A., Examination of ethanol-n-heptane, methanol-n-hexane systems using new vapor-liquid equilibrium still, Journal of Chemical & Engineering Data, 1972, 17, n°2, p. 211-216. http://dx.doi.org/10.1021/je60053a019

[2] NGUYEN-HUYNH D., PASSARELLO J.P., TOBALY P., DE HEMPTINNE J.C., Modeling Phase Equilibria of Asymmetric Mixtures Using a Group-Contribution SAFT (GC-SAFT) with a k(ij) Correlation Method Based on London's Theory. 1. Application to CO2 + n-Alkane, Methane plus n-Alkane, and Ethane plus n-Alkane Systems, Industrial & Engineering Chemistry Research, 2008, 47, n°22, p. 8847-8858. http://dx.doi.org/10.1021/ie071643r

[3] NGUYEN-HUYNH D., PASSARELLO J.P., TOBALY P., DE HEMPTINNE J.C., Application of GC-SAFT EOS to polar systems using a segment approach, Fluid Phase Equilibria, 2008, 264, n°1, p. 62-75. http://dx.doi.org/10.1016/j.fluid.2007.10.019

[4] MOURAH M., NGUYENHUYNH D., PASSARELLO J.P., DE HEMPTINNE J.C., TOBALY P., Modelling LLE and VLE of methanol+n-alkane series using GC-PC-SAFT with a group contribution kij, Fluid Phase Equilibria, 2010, 298, n°1, p. 154-168. http://dx.doi.org/10.1016/j.fluid.2007.10.019