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2816
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Ind. Eng. Chem. Res. 1996, 35, 2816
Comments on “Multiple Steady States in Homogeneous Azeotropic Distillation” Thomas E. Gu 1 ttinger and Manfred Morari* Automatic Control Laboratory, Swiss Federal Institute of Technology, ETH-Z, CH-8092 Zurich, Switzerland
Using van Laar for Ternary Mixtures Sir: In Bekiaris et al. (1993), the van Laar model was used to calculate the vapor-liquid equilibrium of the two example mixtures acetone-benzene-heptane and acetone-chloroform-methanol. We are very grateful to Prof. Michael L. Michelsen from the Department of Chemical Engineering of the Technical University of Denmark for his remarks concerning this issue. He pointed out that the multicomponent version of the van Laar equation is thermodynamically inconsistent for the parameters used in the two cases mentioned above. Such inconsistencies were studied in detail by Heidemann and Mandhane (1975). Briefly, the six A-parameters cannot be chosen independently as was done by Bekiaris et al. (1993). There is an implicit tie that the product of three of the parameters must be equal to the product of the remaining three, which was not the case for the published choice of parameters. This implies that the parameters of three binary mixtures cannot, except by chance, be applied to describe a ternary mixture. In this paper, we want to show the implications of this unfortunate choice for the acetone-benzene-heptane results from Bekiaris et al. (1993). Similar results were obtained for the acetone-chloroform-methanol examples. Implications for the ∞/∞ Methods First, we want to point out that the ∞/∞ analysis itself does not depend at all on the choice of the thermodynamic model. Second, we only need information about the location of the azeotropes to apply this method, i.e., to predict the occurrence of multiple steady states for ∞/∞ columns (columns with infinite length or an infinite number of trays operated at infinite reflux). We can get the necessary information without referring to a particular thermodynamic model, e.g., from experimental data. Comparison of Simulations Using Wilson instead of van Laar For finite columns, we redid our calculations using the Wilson model with the parameters in Table 1. Not surprisingly, no qualitative changes occurred and multiple steady states still exist in a reasonable range of the operating parameter (the distillate flowrate). To show the quantitative differences, we restrict ourselves to discuss the results of Figure 16 of Bekiaris et al. (1993) for the case of a reflux-to-feed ratio of R/F ) 50. The corresponding column setup can be seen in Figure 15 of the original paper, and the results of the comparison are shown in Figure 1. The main difference is that the concentration of the binary acetone-heptane azeotrope, which is equal to the distillate composition on the lower steady-state branch for small distillate flowrates, changed from 93.2% (van Laar) to 93.6% (Wilson). Furthermore, the limit point of the lower steady-state branch has moved from D ) 94.4 (van Laar) to D ) 95.3 (Wilson), enlarging the range of the operating parameter where multiple steady states exist. This is because the distillate composition “stays longer” at the binary azeo* Author to whom correspondence should be addressed. Phone: +41 1 632-7626. Fax: +41 1 632-1211. E-mail:
[email protected].
Table 1. Binary Parameters for the Wilson Equation of Aspen Plus (1995) Obtained from the Aspen Plus Library for the Binary L-I and from Thermopack for L-H and I-Ha component j component i
acetone
benzene
heptane
acetone (L) benzene (I) heptane (H)
1.0000 0.5528 0.2740
1.0985 1.0000 0.5290
0.5100 1.1750 1.0000
a Thermopack are thermodynamic routines provided by Prof. M. F. Doherty and J. Knapp (University of Massachusetts, Amherst).
Figure 1. Original and recalculated bifurcation diagram for a column with N ) 44 trays, entrainer-to-feed ratio E/F ) 1, and reflux-to-feed ratio R/F ) 50. The distillate flow rate is the bifurcation parameter. Figure 16 from Bekiaris et al. (1993).
trope when the VLE is modeled with the Wilson equation. The second limit point (on the upper branch) is essentially unchanged (van Laar, D ) 90.3; Wilson, D ) 90.5). Conclusions (1) The van Laar model cannot be extended easily to ternary mixtures without consistency problems as shown by Heidemann and Mandhane (1975). (2) Although the choice of the van Laar model for the simulations of Bekiaris et al. (1993) was unfortunate, neither the ∞/∞ analysis itself nor the application of this method suffers from that choice. (3) The simulations for finite columns with the Wilson model are qualitatively the same as those obtained with the van Laar model, but there are small quantitative differences. Literature Cited Aspen Technology Inc. Aspen Plus Release 9 Reference Manual: Physical Property Methods and Models, 1995. Bekiaris, N.; Meski, G. A.; Radu, C. M.; Morari, M. Multiple Steady States in Homogeneous Azeotropic Distillation. Ind. Eng. Chem. Res. 1993, 32, 2023-2038. Heidemann, R. A.; Mandhane, J. M. Ternary Liquid-Liquid Equilibria: the van Laar Equation. Chem. Eng. Sci. 1975, 30, 425-434.
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