Vapor-liquid equilibrium nonideal liquids

At 20°C and 0.073 bar, a binary liquid mixture of cyclohexane (1) and toluene (2) is in vapor-liquid equilibrium. The liquid mole fraction of cyclohexane is measured to be Xi = 0.471. Assume that the liquid phase nonideality can be represented by the two-suffix Margules equation. Answer the following questions. 

VPLQFT is a computer program for correlating binary vapor-liquid equilibrium (VLE) data at low to moderate pressures. For such binary mixtures, the truncated virial equation of state is used to correct for vapor-phase nonidealities, except for mixtures containing organic acids where the "chemical" theory is used. The Hayden-0 Connell (1975) correlation gives either the second virial coefficients or the dimerization equilibrium constants, as required. 

Calculate the temperatures and vapor compositions from the vapor-liquid equilibrium data, using the subroutine BUfiPT. Raoult s law is used in the example, but nonideality can be included by adding activity coefficient equations. Newton-Raphson convergence is used. 

Deviations from ideality often occur, and the Kt value depends not only on temperature and pressure but also on the composition of the other components of the mixture. A more detailed discussion of vapor-liquid equilibrium relationships for nonideal mixtures is outside the scope of this article. 

The properties of mixtures of ideal gases and of ideal solutions depend solely on the properties of the pure constituent species, and are calculated from them by simple equations, as illustrated in Chap. 10. Although these models approximate the behavior of certain fluid mixtures, they do not adequately represent the -behavior of most solutions of interest to chemical engineers, and Raoult s law is not in general a realistic relation for vapor/liquid equilibrium. However, these models of ideal behavior—the ideal gas, the ideal solution, and Raoult s law— provide convenient references to which the behavior of nonideal solutions may be compared. 

Experimental vapor-liquid-equilibrium data for benzene(l)/n-heptane(2) system at 80°C (176°F) are given in Table 1.8. Calculate the vapor compositions in equilibrium with the corresponding liquid compositions, using the Scatchard-Hildebrand regular-solution model for the liquid-phase activity coefficient, and compare the calculated results with the experimentally determined composition. Ignore the nonideality in the vapor phase. Also calculate the solubility parameters for benzene and n-heptane using heat-of-vaporization data. 

The vapor-liquid equilibrium (VLE) data for the three nonideal component pairs are in Table 11.1. These data come from the Vapor-Liquid... 

Consistent vapor-liquid equilibrium data are necessary to design all types of rectification devices. However, many industrially important mixtures are nonideal, particularly in the liquid phase, and predicting their equilibrium properties from fundamental thermodynamics is not possible. Thus, the correlating of experimental x-y-t and x-y-P data has developed as an important branch of applied thermodynamics. 

This study was undertaken to obtain the necessary vapor-liquid equilibrium data and to determine the distillation requirements for recovering solvent for reuse from the solvent-water mixture obtained from adsorber regeneration. Previous binary vapor-liquid equilibrium data (2, 3) indicated two binary azeotropes (water-THF and water-MEK) and a two phase region (water-MEK). The ternary system was thus expected to be highly nonideal. 

Gas solubility has been treated extensively (7). Alethods for the prediction of phase equilibria and actual solubility data have been given (8,9) and correlations of the equilibrium K values of hydrocarbons have been developed and compiled (10). Several good sources for experimental information on gas— and vapor—liquid equilibrium data of nonideal systems are also available (6,11,12). 

We conclude this discussion with one final reminder. The vapor-liquid equilibrium calculations we have shown in Section 6.4c are based on the ideal-solution assumption and the corresponding use of Raoult s law. Many commercially important systems involve nonideal solutions, or systems of immiscible or partially miscible liquids, for which Raoult s law is inapplicable and the Txy diagram looks nothing like the one shown for benzene and toluene. 

A modified local composition (LC) expression is suggested, which accounts for the recent finding that the LC in an ideal binary mixture should be equal to the bulk composition only when the molar volumes of the two pure components are equal. However, the expressions available in the literature for the LCs in binary mixtures do not satisfy this requirement. Some LCs are examined including the popular LC-based NRTL model, to show how the above inconsistency can be eliminated. Further, the emphasis is on the modified NRTL model. The newly derived activity coefficient expressions have three adjustable parameters as the NRTL equations do, but contain, in addition, the ratio of the molar volumes of the pure components, a quantity that is usually available. The correlation capability of the modified activity coefficients was compared to the traditional NRTL equations for 42 vapor—liquid equilibrium data sets from two different kinds of binary mixtures (i) highly nonideal alcohol/water mixtures (33 sets), and (ii) mixtures formed of weakly interacting components, such as benzene, hexafiuorobenzene, toluene, and cyclohexane (9 sets). The new equations provided better performances in correlating the vapor pressure than the NRTL for 36 data sets, less well for 4 data sets, and equal performances for 2 data sets. Similar modifications can be applied to any phase equilibrium model based on the LC concept. 

Data for methane/hydrocarbon mixtures are not well established. Some results can be generated through commercially available simulators like Aspen or Hysys but are somewhat questionable because of the nonidealities of these mixtures at elevated pressures. Also, the vapor-liquid equilibrium data currently available are very limited and mostly concern blends of methane with n-paraffins, which have very poor ignition characteristics in internal combustion engines. 

Various processes are used for separating components that are difficult or impossible to be separated by conventional distillation. Whether the difficulty of separation arises from the components close boiling points or their tendency to form azeotropes, the separation processes must take into account the complex vapor-liquid equilibrium relationships of the system. The system to be considered involves both the components to be separated and the separating agent that, in one way or another, enhances the desired separation. The vapor-liquid equilibria of such mixtures is highly nonideal, and it is precisely this nonideality that is capitalized on to bring about the separation. 

An extensive tabulation of azeotropes has been compilnd by Horsley.1 An older compilation is that of Lecat.2 Certain nonideal vapor-liquid equilibrium models ate useful for ptediciiag azeotropic behavior of binery systems in particular, the model of Rcoon and Prausnitz3 is usefol in this regard because it can handle the two liquid phases associated with heterogenenus azeotropes. The Horsley book also contains guidelines for the prediction of azeotropes. 

Nonideal Compute 7-groups model Vapor-liquid equilibrium data Unno el al. ... 

Be able to correlate the low-pressure vapor-liquid equilibrium data for a nonideal liquid mixture (that is. to be able to compute the conditions of vapor-liquid equilibrium and develop. r-v, T-x y, and P-x-y diagrams for nonideal mixtures using activity coefficient models (the y -cj) method) (Sec. 10.2)... 

As the first illustration of the use of these equations, consider vapor-liquid equilibrium in the hexane-triethylamine system at 60°C. These species form an essentially ideal mixture. The vapor pressure of hexane af this temperature is 0.7583 bar and that of triethylamine is 0.3843 bar these are so low that the fugacity coefficients at saturation and for the vapor phase can be neglected. Consequently, Eqs. 10.1-3 and 10.1-4 should be applicable to this system. The three solid lines in Fig. 10.1-1 represent the two species partial pressures and the total pressure, which were calculated using these equations and all are linear functions of the of liquid-phase mole fraction the points are the experimental results. The close agreement between the computations and the laboratory data indicates that the hexane-triethylamine mixture is ideal at these conditions. Note that this linear dependence of the partiaLand total pressures on mole fractions predicted by Eqs. 10.1-2 and 10.1-3 is trae only for ideal mixtures it is not true for nonideal mixtures, as we shall see in Sec. 10.2. 

Few liquid mixtures are ideal, so vapor-liquid equilibrium calculations can be more complicated than is the case for the hexane-triethylamine system, and the system phase diagrams can be more structured than Fig. 10.1-6. These complications arise from the (nonlinear) composition dependence of the species activity coefficients. For example, as a result of the composition dependence of y, the equilibrium pressure in a fixed-temperature experiment will no longer be a linear function of mole fraction. Thus nonideal solutions exhibit deviations from Raoult s law. We will discuss this in detail in the following sections of this chapter. However, first, to illustrate the concepts and some of the types of calculations that arise in vapor-liquid equilibrium in the simplest way, we will assume ideal vapor and liquid solutions (Raoult s law) here, and then in Sec. 10.2 consider the calculations for the more difficult case of nonideal solutions.. ... 

The A"-factor formulation introduced in this calculation is frequently useful in solving vapor-liquid equilibrium problems. The procedure is easily generalized to nonideal liquid and vapor phases as follows ... 

Low-Pressure Vapor-Liquid Equilibrium in Nonideal Mixtures 519... 

LOW-PRESSURE VAPOR-LIQUID EQUILIBRIUM IN NONIDEAL MIXTURES... 

Construction of Vapor-Liquid Equilibrium Diagrams for a Nonideal System... 

As another example of low-pressure vapor-liquid equilibrium, we consider the n-pentane-propionaldehyde mixture at 40.0 C. Eng and Sandler took data on this system using the dynamic still of Fig. 10.2-5. The x-y-P-T data in Table 10.2-1 and Fig. 10.2-8fl and b were obtained by them. (Such data can be tested for thermodynamic consistency see Problem 10.2-12.) As is evident, this system is nonideal and has an azeotrope at about 0.656 mole fraction pentane and 1.3640 bar. We will use these data to test the UNIFAC prediction method. 

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