Page 372 - Chemical engineering design

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DESIGN INFORMATION AND DATA
Activity coefficients at infinite dilution
The constants in any of the activity coefficient equations can be readily calculated from
experimental values of the activity coefficients at infinite dilution. For the Wilson equation:
ln 1 D ln A 12 A 21 C 1 8.39a
1
ln 1 D ln A 21 A 12 C 1 8.39b
2
1
where , 1 D the activity coefficients at infinite dilution for components 1 and 2,
1 2
respectively,
A 12 D the Wilson A-value for component 1 in component 2,
A 21 D the Wilson A-value for component 2 in component 1.

Relatively simple experimental techniques, using ebulliometry and chromatography, are
available for the determination of the activity coefficients at infinite dilution. The methods
used are described by Null (1970) and Conder and Young (1979).
Pieratti et al. (1955) have developed correlations for the prediction of the activity coeffi-
cients at infinite dilution for systems containing water, hydrocarbons and some other
organic compounds. Their method, and the data needed for predictions, is described by
Treybal (1963) and Reid et al. (1987).

Calculation of activity coefficients from mutual solubility data
For systems that are only partially miscible in the liquid state, the activity coefficient in the
homogeneous region can be calculated from experimental values of the mutual solubility
limits. The methods used are described by Reid et al. (1987), Treybal (1963), Brian (1965)
and Null (1970). Treybal (1963) has shown that the Van-Laar equation should be used
for predicting activity coefficients from mutual solubility limits.

Group contribution methods
Group contribution methods have been developed for the prediction of liquid-phase
activity coefficients. The objective has been to enable the prediction of phase equilibrium
data for the tens of thousands of possible mixtures of interest to the process designer to
be made from the contributions of the relatively few functional groups which made up the
compounds. The UNIFAC method, Fredenslund et al. (1977a), is probably the most useful
for process design. Its use is described in detail in a book by Fredenslund et al. (1977b),
which includes computer programs and data for the use of the UNIFAC method in the
design of distillation columns.
A method was also developed to predict the parameters required for the NRTL equation:
the ASOG method, Kojima and Tochigi (1979).
More extensive work has been done to develop the UNIFAC method, to include a wider
range of functional groups; see Gmeling et al. (1982) and Magnussen et al. (1981).
The UNIFAC equation is the preferred equation for use in design, and it is included as
a sub-routine in most simulation and design programs.