Gus K. Georgeton and Jude T. Sommerfeld, Georgia Institute of Technology
Q Chemical engineers use vapor-liquid equilibrium (VLE) data in designing many types of separation processes and equipment. Experimental VLE data are of course the best, but when such data are not available the engineer has to make a choice: run an experiment, or try an estimation method.
This article oiitlines the UNIFAC group-contribution method of computing multicomponent VLE data, and explains its capabilities and limitations. To illustrate the method's value, UNIFAC-calculated VLE data are presented for two binary systems of practical interest for which no published data exist: cu-2-butene/methyl tert-butyl ether (C2B/MTBE); and diethanolamine/triethanol amine (DEA/TEA).
The general condition for vapor-liquid equilibrium in any multicomponent system is that, for all components, the fugacity of a component in the liquid phase must be equal to its fugacity in the vapor phase. For a given component I, this is expressed:
For a component below its critical point, the standard-state liquid fugacity (/?) of such a component is often replaced with the pure component's vapor pressure (P"). This vapor pressure is generally assumed to be independent of the total pressure (P)\ its dependence on temperature (T) is often represented by expressions such as the Antoine equation:
Whereas many distillation operations in the petroleum industry are characterized by high pressures, distillations in the chemical industry occur primarily at low to medium pressures—i.e., from subatmospheric (vacuum operation) to 5 or 6 atmospheres. At such pressures, the vapor-phase mixture may be assumed to be ideal (unless association or dissociation occurs in the vapor phase), which means that the vapor-phase fugacity coefficient for each component (<t>,) may be set equal to 1.
Typical petroleum and chemical distillations also differ in liquid-phase behavior. In the petroleum industry, many distillations involve hydrocarbons of similar structure—e.g., members of homologous series, such as al-kanes, or isomers. Such liquid mixtures are generally assumed to be ideal, in which case the liquid-phase activity coefficient for each component (%) is set equal to 1. Liq-uid-phase ideality is rarely assumed, however, in chemi-cal-industry distillations, which are usually characterized by mixtures of components having widely different functional groups (e.g./CHO, CHsO, NH2 groups). Liquid mixtures of water and almost anything else are significantly nonideal because of the polarity of water.
The problem of characterizing vapor-liquid equilibrium for chemical mixtures thus generally reduces to that of adequately representing the behavior of liquid-phase activity coefficients. At low to medium pressures typical of chemical operations, these are usually assumed to be independent of total pressure. Their dependence on temperature is often ignored, too, in VLE estimation models.
The traditional VLE models for liquid mixtures employ some empiricism, in that analysis and correlation of experimental data are required. Examples include the Van Laar, Margules, Wilson and nonrandom two-liquid (NRTL, Renon) models. Some of these were developed for binary mixtures only, but in most cases extensions for handling multicomponent mixtures have been added.
But what about liquid mixtures for which there are no experimental VLE data? Until recently, the engineer who needed such data to design a separation process had few options. The data could be determined experimentally, which is costly and time-consuming; or they could be estimated, with great uncertainty. There is also a regular-solution theory, proposed many years ago to model liquid mixtures, but this is strictly valid only for nonpolar mixtures whose molecules, though chemically dissimilar, are of similar size.
Thus, there is a need for reliable methods of estimating liquid-phase activity coefficients in multicomponent mixtures in the absence of experimental data. Group-contribution methods, such as the UNIFAC method described below, seek to address this need.
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