Vapor liquid equilibrium nonideal solutions

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. 

Compute the Gfj parameters for the Wilson equation. General engineering practice is to establish liquid-phase nonideality through experimental measurement of vapor-liquid equilibrium. Models with adjustable parameters exist for adequately representing most nonideal-solution behavior. Because of these models, the amount of experimental information needed is not excessive (see Example 3.9, which shows procedures for calculating such parameters from experimental data). 

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. 

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 dashed lines in the figure are the predictions, at all temperatures for the acetone-water system that result from setting the binary parameter k 2 equal to zero. Note that very nonideal behavior is predicted, which shows that setting ]c 2 = 0 is not equivalent to assuming ideal solution behavior. In fact, such extreme nonideal behavior is. predicted that vapor-liquid equilibrium calculations made with the program VLMU do not even converge for acetone mole fractions less than about 0.15. 

If the top temperature is too cold and the bottom tenperature is too hot to allow sandwich conponents to exit at the rate they enter the column, they become trapped in the center of the column and accumulate there fKister. 20041. This accumulation can be quite large for trace conponents in the feed and can cause column flooding and development of a second liquid phase. The problem can be identified from the simulation if the engineer knows all the trace conponents that occur in the feed, accurate vapor-liquid equilibrium (VLE) correlations are available, and the simulator allows two liquid phases and one vapor phase. Unfortunately, the VLE may be very nonideal and trace conponents may not accumulate where we think they will. For example, when ethanol and water are distilled, there often are traces of heavier alcohols present. Alcohols with four or more carbons (butanol and heavier) are only partially miscible in water. They are easily stripped from a water phase (relative volatility 1), but when there is litde water present they are less volatile than ethanol. Thus, they collect somewhere in the middle of the column where they may form a second liquid phase in which the heavy alcohols have low volatility. The usual solution to this problem is to install a side withdrawal line, separate the intermediate component from the other components, and return the other components to the column. These heterogeneous systems are discussed in more detail in Chapter 8. 

An important first step in any model-based calculation procedure is the analysis and type of data used. Here, the accuracy and reliability of the measured data sets to be used in regression of model parameters is a very important issue. It is clear that reliable parameters for any model cannot be obtained from low-quality or inconsistent data. However, for many published experimentally measured solid solubility data, information on measurement uncertainties or quality estimates are unavailable. Also, pure component temperature limits and the excess GE models typically used for nonideality in vapor-liquid equilibrium (VLE) may not be rehable for SEE (or solid solubility). To address this situation, an alternative set of consistency tests [3] have been developed, including a new approach for modehng dilute solution SEE, which combines solute infinite dilution activity coefficients in the hquid phase with a theoretically based term to account for the nonideality for dilute solutions relative to infinite dilution. This model has been found to give noticeably better descriptions of experimental data than traditional thermodynamic models (nonrandom two liquid (NRTE) [4], UNIQUAC [5], and original UNIversal Eunctional group Activity Coefficient (UNIEAC) [6]) for the studied systems. 

VAPOR-LIQUID EQUILIBRIUM RATIOS FOR IDEAL-SOLUTION BEHAVIOR 3.1 FUGACITY OF PURE LIQUID 3.3 NONIDEAL GAS-PHASE MIXTURES 3.4... 

Such a process depends upon the difference in departure from ideally between the solvent and the components of the binary mixture to be separated. In the example given, both toluene and isooctane separately form nonideal liquid solutions with phenol, but the extent of the nonideality with isooctane is greater than that with toluene. When all three substances are present, therefore, the toluene and isooctane themselves behave as a nonideal mixture and then-relative volatility becomes high. Considerations of this sort form the basis for the choice of an extractive-distillation solvent. If, for example, a mixture of acetone (bp = 56.4 C) and methanol (bp = 64.7°Q, which form a binary azeotrope, were to be separated by extractive distillation, a suitable solvent could probably be chosen from the group of aliphatic alcohols. Butanol (bp = 117.8 Q, since it is a member of the same homologous series but not far removed, forms substantially ideal solutions with methanol, which are themselves readily separated. It will form solutions of positive deviation from ideality with acetone, however, and the acetone-methanol vapor-liquid equilibria will therefore be substantially altered in ternary mixtures. If butanol forms no azeotrope with acetone, and if it alters the vapor-liquid equilibrium of acetone-methanol sufficiently to destroy the azeotrope in this system, it will serve as an extractive-distillation solvent. When both substances of the binary mixture to be separated are themselves chemically very similar, a solvent of an entirely different chemical nature will be necessary. Acetone and furfural, for example, are useful as extractive-distillation solvents for separating the hydrocarbons butene-2 and a-butane. 

Nonideal Solutions, The final level of complexity for modeling the relationship between vapor and liquid compositions accounts for nonideal interactions in the liquid phase. The equilibrium ratio is still ased for such systems, but in this instance it is defined as... 

In 10.1 we present the basic thermodynamic relations that are used to start phase-equilibrium calculations we discuss vapor-liquid, liquid-liquid, and liquid-solid calculations. We have seen that the most interesting phase behavior occurs in nonideal solutions, but when we describe nonidealities using an ideal solution as a basis, we must select an appropriate standard state. Common options for standard states are discussed in 10.2 they include pure-component standard states and dilute-solution standard states. 

The thermodynamic model nsed is the nonrandom two liquid (NRTL), which can be used to describe vapor-liquid and liqnid-liquid equilibrium of strongly nonideal solutions. The NRTL model can handle any combination of polar and nonpolar compounds, up to very strong nonideality. In addition, many parameters for xylitol pure component were not available in the databanks of Aspen Plus and had to be acquired from the literature and from regression of experimental data (Table 12.1). 

Fifty-six isothermal data sets for vapor-liquid equilibria (VLB) have been used for 15 polymer-HSolvent binaries, 11 copolymer-nsolvent binaries and for 30 polymer-polymer-solvent ternaries to study compatibility of polymer blends. The equilibrium solubility of a penetrant in a polymer depends on their mutual compatibility. Equations based on theories of polymer solution tend to be more successful when there is some kind of similarity between the penetrant and the monomer repeat unit in the polymer, e.g., for nonpolar penetrants in polymers which do not contain appreciable polar groups. Expected nonideal behavior has been observed for systems containing hydrocarbons and poly(acrylonitrile-co-butadiene). The role of intramolecular interaction in vapor-liquid equilibria of copolymer-nsolvent systems is well documented for poly(aciylonitrile-co-butadiene) that have higher affinity for acetonitrile than do polyaciylonitrile or polybutadiene. 

We cannot construct a liquid-vapor equilibrium diagram for nonideal solutions in the simple manner illustrated in Figure 14-16. For example, vapor pressures in acetone-chloroform solutions are lower than we would predict for ideal solutions and boiling temperatures are correspondingly higher. In acetone-carbon disulfide solutions, conversely, vapor pressures are higher... 

Nitric acid is a strong electrolyte. Therefore, the solubilities of nitrogen oxides in water given in Ref. 191 and based on Henry s law are utilized and further corrected by using the method of van Krevelen and Hofhjzer (77) for electrolyte solutions. The chemical equilibrium is calculated in terms of liquid-phase activities. The local composition model of Engels (192), based on the UNIQUAC model, is used for the calculation of vapor pressures and activity coefficients of water and nitric acid. Multicomponent diffusion coefficients in the liquid phase are corrected for the nonideality, as suggested in Ref. 57. 

Figure 7.12 shows a liquid-vapor phase diagram for positive deviations from Raoult s law. Each component has a higher-than-expected vapor pressure, so the total pressure in equilibrium with the liquid solution is also higher than expected. Ethanol/benzene, ethanol/chloroform, and ethanol/water are systems that show a positive deviation from Raoult s law. Figure 7.13 shows a similar diagram, but for a solution that shows a negative deviation from Raoult s law. The acetone/chloroform system is one example that exhibits such nonideal behavior. 

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