Source of axparimantal data: M. IB
Source of axparimantal data: M. IB
mer, Wilson, Heil, and nonrandom two-liquid (NRTL), among others. They all have their particular strengths, which are beyond our scope [6, 8, 13, 16].
These models for two-component systems are readily generalized to systems of three, four or more components. No additional assumptions are needed.
For this example, let us use the Wilson equation because it is simple, having only two parameters per binary pair, and can predict azeotropes. If we want VLE data for 1 atm system pressure, we can assume that the vapor-phase fugacity is ideal (i.e., <t>, = 1). and so can determine liquid-phase activity directly from K via Eq. 1.
From the literature data, we can do a regression and get the Wilson parameters for the methanol-water and acetone-methanol pairs. For water-acetone, we do the same for K data from UNIFAC. Once all the Wilson parameters are in hand, the Wilson equation can be used to simulate the three-component system. No correction for vapor-phase nonideality is needed at 1 atm pressure.
Table II shows the result for six different liquid compositions (i.e., six simulations), and compares the calculated boiling points and vapor compositions with experimental ones . For this system, the results are very good, though at first it seemed that the problem was out of reach due to lack of data for one of the binary pairs.
This approach of combining UNIFAC and experimental data also offers a way of using UNIFAC to get VLE data for systems that include small amounts of noncondensables—e.g., methane, hydrogen or air. UNIFAC alone cannot handle noncondensables, but if experimental VLE data are available for them, or if they can be considered ideal, then the approach above will work.
The same approach also provides a means of handling immiscible liquid phases, but the Wilson equation does not apply to immiscibles. Instead, the Heil  or NRTL  equations may be used to represent the thermodynamic properties of the two liquid phases.
The method is analogous to that used for partially missing data: Find liquid-liquid equilibria for the components in the literature, or use UNIFAC if no data are available; do a regression to get the Heil or NRTL parameters; then simulate the multicomponent system. Note that errors in activity coefficients can have a larger effect on liquid-liquid equilibria than on vapor-liquid equilibria, so extra care should be exercised to obtain good data .
If a system includes a polymer, UNIFAC is not able to simulate it. But the Heil equation, developed specifically for polymers dissolved in nonideal solvent, can represent such a multicomponent system. Once again, the method is to get available experimental VLE data for each binary pair, except those including the polymer, and to use UNIFAC to fill in missing binary data. Then the Heil parameters may be calculated by regression analysis. The needed parameters for the binaries including the polymer may be obtained from experimental data or from known Heil parameters.
Then, as in the case of the missing data, we can use the Heil equation to simulate the multicomponent system. In this way we can represent nonideal polymer/solvent systems quite accurately.
UNIFAC is a very handy tool when used within its boundaries, and even handier when the boundaries can be extended. But it should be used as a last resort, not as a first; experimental data from literature or laboratory are always preferable.
Still, even published experimental data should be regarded with some skepticism rather than uncritically assumed to be correct. It is better to have a few reliable data points than a lot of doubtful ones.
When using UNIFAC or any of the Gibbs-Duhem equation models, it is good to remember that even a slight extrapolation beyond its capability—especially around the critical point—can give erroneous results. To check any such calculated results, use the integral or differential tests for VLE consistency as discussed in .
In the end, always ask: Do the VLE data look reasonable? Do other similar systems behave this way? Vapor-liquid equilibrium is a complicated subject, and good engineering design demands that VLE data be as accurate as possible.
1. Andiappan. A.. McLean. A. Y., Adv. Chem. Sejl. 115. 93 (1972).
2. Balzhiser. R. E_. Samuels. M. R.. and Ehassen. J. D.: "Chemical Engineering Thermodynamics: The Study of Energy. Entropy and Equilibrium." Prentice-Hall, Engiewood Cliffs. N.J.. 1972.
S. Fredenslund. A. Gmehling. J., and Rasmussen. P.: "Vapor-Liquid Equilibria Using UNIFAC." Elsevier, New York. 1977.
4. Fredenslund. A.. Gmehling, J., and Rasmussen. P.. Ind Eng. Chat. Proctts Da. Dev., 21, 118(1981).
5. Green. S. J., and Vener. R. E.. ImL Eng. Chem.. 47. 103 (1955).
6. Heil. J. F.. and Prausnhz, J. M.. AIChE J.. 12. 678 (1966).
7. Heil J. ?.. Doctoral dissertation. Univ. California. Berkeley (1965).
8. Holmes, J. H.. and Van Winkle, M., Ind. Eng. Chem.. 62. 21 (1970).
9. Othmer. D. F.. Manu, M. C.. and Levy, S. L. Ind. Eng. Own.. 44. 1872 (1952).
10. Prausnhz. J. M.. Ecken. C A.. Orye, R. V.. and O'Gonnell, J. P.: "Computer Calculations for Mulbcomponent Vapor-Liquid Equilibria," Prentice-Hall. En-gtewood Cliffs. N.J., 1967.
11. Prausnhz, J. M.: Personal Communication, December 1982.
12. Rod. R. C, Prausnhz, J. M., and Sherwood, T. K.: "The Properties of Gases and Liquids." 3rd ed.. McGraw-Hill, New York. 1977.
13. Reran. H.. and Piausnio. J. M.. AIChE J. 14. 135 (1968).
14. Skjdld-Joergensen. S., Kobe, B.. Gmehling, J., and Rasmussen. P.. Ind. Eng Chem. Proas Dei. Den., 18. 714 (1979).
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Robot F. Wilcox is a process engineer wish Jacobs Engineering Group, Inc., P.O. Box 53495. Houston. TX 77052; teL (713) 626-2020. He has over five years of experience in piocess design, much of it in ^..hring nonideal distillations- He also does detailed design engineering, and feasibility and cost studies. Mr. Wilcox has a B.S. in chemical engineering from Purdue University, and is registered in Texas.
1.3 EXPERIMENTAL AND LITERATURE SOURCES
Laboratory equipment used for VLE determination often appears simple ! in principle, cut its design and operation to obtain good data is I riddled with pitfalls. The objective of this section is to give the ¡engineer a feel for the difficulties involved. A more detailed idiscussion is given by Hala et al (53) and Null (2).
¡RECIRCULATING STILLS (Figure 1.18a) This apparatus appears simple ¡and straight forward, but has the following traps:
(i) The liquid must be thoroughly agitated to give a uniform liquid composition. This can be achieved either by the boiling action or mechanically.
(ii) There must be no condensation in the line from the still to the condenser. Such condensation causes "reflux" and a change in vapor composition.
(iii) Partial evaporation of samples must be avoided. Similarly, presence of vapor bubbles in liquid samples must be avoided.
(iv) Entrainment of liquid droplets to the condenser must be avoided.
(v) The line from the condensate receiver to the still must be small enough to prevent back-mixing of reboiler liquid, and large enough to ensure that the entering liquid does not create regions of non-unifom composition in the still.
(vi) Pressure drop between the still and pressure measurement point must be minimal. This is especially important in measurements carried out under deep vacuum.
(vii) The temperature measurement should measure the liquid temperature - not the superheated vapor temperature or the entering liquid temperature.
(viii) Degradation of material may be a problem if it is heat sensitive.
(ix) Leaks must be prevented and the instruments must be functioning properly. Leak prevention is especially important when the still operates under vacuum, where inerts accumulation may have a large influence on the equilibrium.
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