Vapor-Liquid Equilibria Applications

Assuming the vapor phase does not deviate too strongly from ideal gas behavior, 

Selected Activity Coefficient Binary Interaction Constants 

Note From Gmehling, J. and U. Onken, Vapor-Liquid Equil. Data Collection, Dechema Chemistry Data Series, Port Washington, NY, Scholium International, Inc., 1977. With permission. 

The phase behavior of two binaries, pentane-hexane and methanol-water, is checked against ideal solution behavior. The partial pressure and total pressure isotherms calculated according to Raoult s law at35°C are compared to expected actual isotherms. The component vapor pressures at 35°C are as follows  

FIGURE 1.3 (a) Pressure-composition isotherms for pentane-hexane (Example 1.7), (b) 

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Binary and ternary forms of the NRTL equation were evaluated and compared to other equations for vapor-liquid equilibrium applications by Renon and Prausnitz, Larson and Tassios, Mertl, Marina and Tassios, and Tsu-boka and Katayama. In general, the accuracy of the NRTL equation is comparable to that of the Wilson equation. Although is an adjustable constant, there is little loss in accuracy over setting its value according to the rules described above. Methods for determining best values of NRTL binary parameters are considered in detail in the above references. Mertl tabulated NRTL parameters obtained from 144 sets of data covering 102 different binary systems. Other listings of NRTL parameters are also available. 

Application of the algorithm for analysis of vapor-liquid equilibrium data can be illustrated with the isobaric data of 0th-mer (1928) for the system acetone(1)-methanol(2). For simplicity, the van Laar equations are used here to express the activity coefficients. 

The maximum-likelihood method is not limited to phase equilibrium data. It is applicable to any type of data for which a model can be postulated and for which there are known random measurement errors in the variables. P-V-T data, enthalpy data, solid-liquid adsorption data, etc., can all be reduced by this method. The advantages indicated here for vapor-liquid equilibrium data apply also to other data. 

Vapor/liquid equilibrium (XT E) relationships (as well as other interphase equihbrium relationships) are needed in the solution of many engineering problems. The required data can be found by experiment, but such measurements are seldom easy, even for binaiy systems, and they become rapidly more difficult as the number of constituent species increases. This is the incentive for application of thermodynamics to the calculation of phase-equilibrium relationships. 

Figure 9-96. Vapor-liquid equilibrium showing X and application cases referred to in the text. Used by permission, Koshy, T. D., and Rukovena, F. Jr., Hydrocarbon Processing V. 85, No. 5 (1986) p. 64 all rights reserved.

Thermodynamic energy terms (and equilibrium constants) may differ for compounds containing different isotopic species of an element. This effect is described in theoretical detail by Urey (1947), and applications to geochemistry are discussed by Broecker and Oversby (1971) and Faure (1977). A good example is the case of the vapor/liquid equilibrium for water. The vapor pressure of a lighter isotopic species, H2 0, is higher relative to that of heavier species, (or HD O), and others. 

A model is needed to calculate liquid-liquid equilibrium for the activity coefficient from Equation 4.67. Both the NRTL and UNIQUAC equations can be used to predict liquid-liquid equilibrium. Note that the Wilson equation is not applicable to liquid-liquid equilibrium and, therefore, also not applicable to vapor-liquid-liquid equilibrium. Parameters from the NRTL and UNIQUAC equations can be correlated from vapor-liquid equilibrium data6 or liquid-liquid equilibrium data9,10. The UNIFAC method can be used to predict liquid-liquid equilibrium from the molecular structures of the components in the mixture3. 

Two activity coefficient models have been developed for vapor-liquid equilibrium of electrolyte systems. The first model is an extension of the Pitzer equation and is applicable to aqueous electrolyte systems containing any number of molecular and ionic solutes. The validity of the model has been shown by data correlation studies on three aqueous electrolyte systems of industrial interest. The second model is based on the local composition concept and is designed to be applicable to all kinds of electrolyte systems. Preliminary data correlation results on many binary and ternary electrolyte systems suggest the validity of the local composition model. 

Chen, C., H. I. Britt, J. F. Boston, and L. B. Evans, "Extension and Application of the Pitzer equation for Vapor-Liquid Equilibrium of Aqueous Electrolyte Systems with Molecular Solutes," AIChE J., 1979, 25, 820. 

An application to one binary mixture of a volatile electrolyte and water will illustrate the choice of parameters H and K, an approach is proposed to represent the vapor-liquid equilibrium in the whole range of concentration. Ternary mixtures with one acid and one base lead to the formation of salts and high ionic strengths can be reached. There, it was found useful to take into account... 

None of the experimental techniques described by Bonner, however, has been capable of providing reliable vapor-liquid equilibrium data at the combined extremes of elevated temperature and reduced pressure, conditions applicable to most commercial polymer-stripping operations. This problem has been addressed by Meyer and Blanks (1982), who developed a modified isopiestic technique that could be used when solubilities are low. Although the success of this new technique was demonstrated using just polyethylene with isobutane and propane, the idea shows considerable promise for obtaining data at unusual conditions of temperature and pressure. 

The use of a dissolved salt in place of a liquid component as the separating agent in extractive distillation has strong advantages in certain systems with respect to both increased separation efficiency and reduced energy requirements. A principal reason why such a technique has not undergone more intensive development or seen more than specialized industrial use is that the solution thermodynamics of salt effect in vapor-liquid equilibrium are complex, and are still not well understood. However, even small amounts of certain salts present in the liquid phase of certain systems can exert profound effects on equilibrium vapor composition, hence on relative volatility, and on azeotropic behavior. Also extractive and azeotropic distillation is not the only important application for the effects of salts on vapor-liquid equilibrium while used as examples, other potential applications of equal importance exist as well. 

Measurements of binary vapor-liquid equilibria can be expressed in terms of activity coefficients, and then correlated by the Wilson or other suitable equation. Data on all possible pairs of components can be combined to represent the vapor-liquid behavior of the complete mixture. For exploratory purposes, several rapid experimental techniques are applicable. For example, differential ebulliometry can obtain data for several systems in one laboratory day, from which infinite dilution activity coefficients can be calculated and then used to evaluate the parameters of correlating equations. Chromatography also is a well-developed rapid technique for vapor-liquid equilibrium measurement of extractive distillation systems. The low-boiling solvent is deposited on an inert carrier to serve as the adsorbent. The mathematics is known from which the relative volatility of a pair of substances can be calculated from the effluent trace of the elutriated stream. Some of the literature of these two techniques is cited by Walas (1985, pp. 216-217). 

Several hundred plants have been installed for the dehydration of ethanol by pervaporation. This is a particularly favorable application for pervaporation because ethanol forms an azeotrope with water at 95 % and a 99.5 % pure product is needed. Because the azeotrope forms at 95 % ethanol, simple distillation does not work. A comparison of the separation of ethanol and water obtained by various pervaporation membranes and the vapor-liquid equilibrium line that controls separation obtained by distillation is shown in Figure 9.9 [40], The membranes... 

However, this technique is not applicable to any type of reaction both chemical and physical limitations to its use in chemical processes exist the main one is the necessity to achieve reasonable reaction rates in conditions of vapor-liquid equilibrium (usually at quite low temperatures and pressures). 

Many modifications of the original Redlich/Kwohg equation that appear in the literature are intended for special-purpose applications. The SRJt equation, developed for vapor/liquid equilibrium calculations, is designed specifically to yield reasonable vapor pressures for pure fluids. Thus, there is no assurance that molar volumes calculated by the SRK equation are more accurate than values given by the original Redlich/Kwong equation. 

In Chap. 6 we treated the thermodynamic properties of constant-composition fluids. However, many applications of chemical-engineering thermodynamics are to systems wherein multicomponent mixtures of gases or liquids undergo composition changes as the result of mixing or separation processes, the transfer of species from one phase to another, or chemical reaction. The properties of such systems depend on composition as well as on temperature and pressure. Our first task in this chapter is therefore to develop a fundamental property relation for homogeneous fluid mixtures of variable composition. We then derive equations applicable to mixtures of ideal gases and ideal solutions. Finally, we treat in detail a particularly simple description of multicomponent vapor/liquid equilibrium known as Raoult s law. 

The application of Eq. (10.3) to specific phase-equilibrium problems requires use of models of solution behavior, which provide expressions for G or for the Hi as functions of temperature, pressure, and composition. The simplest of such expressions are for mixtures of ideal gases and for mixtures that form ideal solutions. These expressions, developed in this chapter, lead directly to Raoult s law, the simplest realistic relation between the compositions of phases coexisting in vapor/liquid equilibrium. Models of more general validity are treated in Chaps. 11 and 12. 

Ratzsch, M. T. and H. Kehlen Application of continuous thermoldynamics to the vapor-liquid equilibrium. Z. Chem.( Leipzig) 23, 389-394(1983)... 

If the pressure in the evaporator is specified, a single call to the FLASH subprogram (which contains applicable vapor-liquid equilibrium correlations) yields the component flow rates in both product streams as well as the evaporator temperature. Suppose, however, that one of the component flow rates in one of the product streams is specified (e.g., = 65.0 mol/s) and... 

One of the main applications of the thermodynamic models is in the chemical industries which use solvent (or their mixtures) [19-22]. Two cases of the vapor-liquid equilibrium of common industrial solvent systems are discussed here. 

The simplest application of equations of state in vapor/liquid equilibrium is to the ( culation of vapor pressures P of pure liquids. Vapor pressures can of course be measured, but values are also implicit in cubic equations of state. 

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