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Group-contribution VLE methods

The group-contribution methods consider a liquid mixture to be a mixture of functional groups, rather than a mixture of molecules. Table I lists the groups currently included in the UNIFAC model. The properties of a mixture, then, are determined by the properties of the groups rather than of the molecules. This is like scaleup to molecules from smaller elements. For example, the mixture of dimethyl ether (CHsOCHs) and benzene (QHe) can be considered a mixture of CHS, CHsO and aromatic CH groups.

The value of this approach is that VLE data for thousands of liquid mixtures of interest in chemical process technology can be gotten from data on a much smaller number (perhaps 50 to 100) of functional groups. More groups can be considered, but in the limit, when each molecule constitutes a "group," the efficiency of the approach will be lost. This is already the case for a few molecular species in the UNIFAC model, as Table I shows.

The idea of estimating mixture properties from group contributions is not new. Langmuir proposed such a concept over 50 years ago. In the 1960s, a team at Shell developed the Analytical Solution of Groups (ASOG) method. This was followed by an extension (Prausnitz and coworkers [J ]) of Guggenheim's quasi-chemical the ory of liquid mixtures. In this extension, known as the universal quasi-chemical (UNIQUAC) theory, the important independent variables are the concentrations of the functional groups, rather than the molecules, in the liquid mixture. The combination of the functional-group concept with the analytical results of this theory is known as the UNIFAC (UNIQUAC functional-group activity coefficients) method.

In the UNIFAC method, the liquid-phase activity coefficient (y,) for a given component in a mixture is assumed to consist of two distinct contributions: a combinatorial (entropy) part, essentially due to differences in the size and shape of the molecules in the mixture; and a residual (enthalpy) part, essentially due to energy interactions among molecules.

The combinatorial contribution is computed from functional-group parameters: normalized Van der Waals group volumes, and interaction surface areas. These are determined independendy, from molecular-structure data on the components. In the conventional UNIFAC method, the temperature dependence of the liquid-phase activity coefficient is incorporated in the other, residual, contribution. But a recent paper [2] did suggest including temperature here.

In calculating the residual contribution, the UNIFAC method becomes empirical, in that the residual activity coefficients depend not only on the concentrations of groups but also on the interactions between groups. The group-interaction parameters (¿wa«, # a^,, a^ = 0) are regressed from experimental VLE data for a number of mixtures. This task has been performed with the aid of the Dortmund Data Bank (University of Dortmund, West Germany), which presendy contains over 10,000 sets of VLE data.

The actual UNIFAC equations are rather complex, and will not be presented here. The equations appear in a number of sources, e.g., [3,4]; other sources [5,6] present complete FORTRAN programs to implement them. Procedures for using these calculations in the computerized design of distillation columns have been published [5,7], and UNIFAC calculation packages are accessible through timesharing systems.

The selection of groups from which to construct molecules is somewhat arbitrary. Table I shows the current UNIFAC groups, and makes a distinction between main groups and subgroups. Subgroups within a main group usually have various degrees of substitution at the carbon atom. For example: The "CH2" main group, from which alkanes would be constructed, is divided into four subgroups: CHS, CH2, CH and C. Note that some single compounds are main groups in themselves: methanol, water, carbon tetrachloride, carbon disulfide, furfural, 1,2-ethanediol, dimethyl sulfoxide and acrylonitrile.

Within the 40 main groups currendy included in the UNIFAC method, there are a total of 76 subgroups. Each has its own pair of functional-group parameters: group volume and interaction surface area. Since these are obtained from pure-component data, values for all subgroups are readily available [5].

The binary group-interaction parameters are not all available, however. In UNIFAC, these parameters (a^) are defined only for the main groups. That is, subgroup parameters are the same within a main group. This means that a complete table of the parameters for all 40 main groups would be a 40x40 square matrix, with a total of 1,560 nonzero entries—since all the diagonal entries (a^) are zeroes. At the present time, values have been estimated (from VLE data) for about 45% of these off-diagonal a», values. These are published in [5]. The missing values are a problem, but UNIFAC can be used today for thousands of important chemical mixtures.

And researchers are continually adding to the UNIFAC pool. For instance, a team in Israel [9] recendy suggested two new silicon main groups, "SiH2" and "SiO," and several subgroups for each. Binary group-interaction parameters were also published [9] for these two groups with each other and with these groups from Table I: CH2," "ACH," "ACCH2," "OH," "COOH" and "CCL," As is the case with much good VLE data, there undoubtedly exist other group definitions and interaction parameters developed by workers who cannot publish them.

This article will not compare UNIFAC VLE data with experimental data because numerous such comparisons have been published [3-5]. These comparisons generally attest to the accuracy and reliability of the UNIFAC

Group representation of example compounds Fig. 1

method. For example, computed vapor-phase mole fractions (yd are typically within 0.01 of the experimental values. But the method does have limitations.

One obvious limitation has already been alluded to: Components must be constructed from the defined groups, and group-interaction parameters must be available. As work progresses, new groups will be added and some of the unknown parameters will be obtained.

In its present state, UNIFAC cannot accommodate electrolytes—i.e., components that ionize. Neither can it handle very large molecules, such as most polymers: The largest components in the Dortmund Data Bank, from which the interaction parameters were regressed, correspond to C12 molecules. Extrapolating to significantly larger molecules is not recommended.

At the other extreme of molecular weight, all components should be condensable (not merely soluble) within the temperature and pressure ranges of interest. This eliminates many gases. The current temperature and pressure limitations again derive from the range in the Data Bank: 300K to 425K, and total system pressure up to 6 atm. Extrapolating significantly beyond these ranges is not recommended.

What about nonideal liquid-liquid equilibria (LLE)? In theory, the parameters and equations used for VLE estimation can also be used for LLE. But the results are less accurate, so parameters especially for LLE have been published [70]. Predicting the solubility of gases in liquids via UNIFAC has also been discussed [2/].

Two examples of using the UNIFAC method are presented below. Both are binary systems of practical interest for which no VLE data are openly published. The first binary system is as-2-butene (C2B) and

UNIFAC VLE for c/s-2-butene/MTBE system at 60 psia

Table II

Mol« friction C2B

Liquid-phaw activity coefficient

Mol« friction C2B

Liquid-phaw activity coefficient

Temperature °C |
*1 |
V\ |
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