Liquids equilibrium

There are some other applications of liquid-liquid extraction where it seems uniquely qualified as a separation technique. Many pharmaceutical products (e.g., penicillin) are produced in mixtures so complex that only liquid-liquid extraction is a feasible separation process (Seader and Henley, 2006). 

In all such operations, the solution which is to be extracted is called the feed, and the liquid with which it is contacted is the solvent. The solvent-rich product of the operation is called the extract, and the residual liquid from which solute has been removed is the raffinate (Treybal, 1980). 

Your objectives in studying this section are to be able to  

Plot extraction equilibrium data on equilateral- and right-triangular diagrams. 

Explain the difference between type I and type II extraction equilibrium behavior. 

This topic is concerned with the relations between vapor and liquid compositions over a range of temperature and pressure. Functionally, the dependence of the mol fraction y, of component i in the vapor phase depends on other variables as 

A more nearly complete expression of Kt is derived upon 

TABLE 13.1. The Soave Equation of State and Fugacity Coefficients 

Additionally usually small corrections for pressure, called Poynting factors, also belong in Eq. (13.6) and following but are omitted here. The new terms are 

Equations for fugacity coefficients are derived from equations of state. Table 13.1 has them for the popular Soave equation of state. At pressures below 5-6 atm, the ratio of fugacity coefficients in Eq. (13.8) often is near unity. Then the VER may be written 

A more rigorous expression is derived by noting that at equilibrium, partial fugacities of each component are the same in each phase, that is 

A mote nearly complete expression of K, is derived upon 

Values of the activity coefficients are deduced from experimental data of vapor-liquid equilibria and correlated or extended by any one of several available equations. Values also may be calculated approximately from structural group contributions by methods called UNIFAC and ASOG. For more than two components, the correlating equations favored nowadays are the Wilson, the NRTL, and UNIQUAC, and for some applications a solubility parameter method. The first and last of these are given in Table 13.2. Calculations from measured equilibrium compositions are made with the rearranged equation 

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The method proposed in this monograph has a firm thermodynamic basis. For vapo/-liquid equilibria, the method may be used at low or moderate pressures commonly encountered in separation operations since vapor-phase nonidealities are taken into account. For liquid-liquid equilibria the effect of pressure is usually not important unless the pressure is very large or unless conditions are near the vapor-liquid critical region. 

In vapor-liquid equilibria, if one phase composition is given, there are basically four types of problems, characterized by those variables which are specified and those which are to be calculated. Let T stand for temperature, P for total pressure, for the mole fraction of component i in the liquid phase, and y for the mole fraction of component i in the vapor phase. For a mixture containing m components, the four types can be organized in this way ... 

In liquid-liquid equilibria, the total composition and temperature are known the pressure is usually not important. 

For vapor-liquid equilibria, the equations of equilibrium which must be satisfied are of the form... 

In vapor-liquid equilibria, it is relatively easy to start the iteration because assumption of ideal behavior (Raoult s law) provides a reasonable zeroth approximation. By contrast, there is no obvious corresponding method to start the iteration calculation for liquid-liquid equilibria. Further, when two liquid phases are present, we must calculate for each component activity coefficients in two phases since these are often strongly nonlinear functions of compositions, liquid-liquid equilibrium calculations are highly sensitive to small changes in composition. In vapor-liquid equilibria at modest pressures, this sensitivity is lower because vapor-phase fugacity coefficients are usually close to unity and only weak functions of composition. For liquid-liquid equilibria, it is therefore more difficult to construct a numerical iteration procedure that converges both rapidly and consistently. 

For typical conditions in the chemical industry, the effect of pressure on liquid-liquid equilibria is negligible and therefore in this monograph pressure is not considered as a variable in Equation (2). 

The accuracy of our calculations is strongly dependent on the accuracy of the experimental data used to obtain the necessary parameters. While we cannot make any general quantitative statement about the accuracy of our calculations for multicomponent vapor-liquid equilibria, our experience leads us to believe that the calculated results for ternary or quarternary mixtures have an accuracy only slightly less than that of the binary data upon which the calculations are based. For multicomponent liquid-liquid equilibria, the accuracy of prediction is dependent not only upon the accuracy of the binary data, but also on the method used to obtain binary parameters. While there are always exceptions, in typical cases the technique used for binary-data reduction is of some, but not major, importance for vapor-liquid equilibria. However, for liquid-liquid equilibria, the method of data reduction plays a crucial role, as discussed in Chapters 4 and 6. 

Fredenslund, A., J. Gmehling, and P. Rasmussen "Vapor-Liquid Equilibria using UNIFAC," Elsevier, New York, 1977. 

Detailed and extensive information on the UNIFAC method for estimating activity coefficients with application to vapor-liquid equilibria at moderate pressures. 

Literature references for vapor-liquid equilibria, enthalpies of mixing and volume change for binary systems. 

Hirata, M., S. Ohe, and K. Nagahama "Computer-aided Data Book of Vapor-Liquid Equilibria," Elsevier, Amsterdam, 1975. 

Oellrich, L. R., J. Plocker, and H. Knapp "Vapor-Liquid Equilibria," Technical University, Institute for Thermodynamics, Berlin, 1973. 

O Connell, and R. V. Orye "Computer Calculations for Multicomponent Vapor-Liquid Equilibria," Prentice-Hall, Englewood Cliffs, N.J., 1967. 

Discusses the thermodynamic basis for computer calculations for vapor-liquid equilibria computer programs are given. Now out of date. 

Equation (4) is the )cey equation for calculation of multi-component vapor-liquid equilibria. 

Equation (6) is the Icey equation for calculation of multicomponent liquid-liquid equilibria. 

For multicomponent vapor-liquid equilibria, the equation of equilibrium for every condensable component i is... 

In the calculation of vapor-liquid equilibria, it is necessary to calculate separately the fugacity of each component in each of the two phases. The liquid and vapor phases require different techniques in this chapter we consider calculations for the vapor phase. 

At pressures to a few bars, the vapor phase is at a relatively low density, i.e., on the average, the molecules interact with one another less strongly than do the molecules in the much denser liquid phase. It is therefore a common simplification to assume that all the nonideality in vapor-liquid systems exist in the liquid phase and that the vapor phase can be treated as an ideal gas. This leads to the simple result that the fugacity of component i is given by its partial pressure, i.e. the product of y, the mole fraction of i in the vapor, and P, the total pressure. A somewhat less restrictive simplification is the Lewis fugacity rule which sets the fugacity of i in the vapor mixture proportional to its mole fraction in the vapor phase the constant of proportionality is the fugacity of pure i vapor at the temperature and pressure of the mixture. These simplifications are attractive because they make the calculation of vapor-liquid equilibria much easier the K factors = i i ... 

It is important to be consistent in the use of fugacity coefficients. When reducing experimental data to obtain activity coefficients, a particular method for calculating fugacity coefficients must be adopted. That same method must be employed when activity-coefficient correlations are used to generate vapor-liquid equilibria. 

To predict vapor-liquid or liquid-liquid equilibria in multicomponent systems, we require a method for calculating the fugacity of a component i in a liquid mixture. At system temperature T and system pressure P, this fugacity is written as a product of three terms... 

Figure 4-3. Calculated and experimental vapor-liquid equilibria.

Figure 4-4. Representation of vapor-liquid equilibria for a binary system showing moderate positive deviations from Raoult s law.

An adequate prediction of multicomponent vapor-liquid equilibria requires an accurate description of the phase equilibria for the binary systems. We have reduced a large body of binary data including a variety of systems containing, for example, alcohols, ethers, ketones, organic acids, water, and hydrocarbons with the UNIQUAC equation. Experience has shown it to do as well as any of the other common models. V7hen all types of mixtures are considered, including partially miscible systems, the... 

Figure 4-7. Vapor-liquid equilibria and activity coefficients in a binary system showing a weak minimum in the activity coefficient of methanol.

As discussed in Chapter 3, at moderate pressures, vapor-phase nonideality is usually small in comparison to liquid-phase nonideality. However, when associating carboxylic acids are present, vapor-phase nonideality may dominate. These acids dimerize appreciably in the vapor phase even at low pressures fugacity coefficients are well removed from unity. To illustrate. Figures 8 and 9 show observed and calculated vapor-liquid equilibria for two systems containing an associating component. 

Figure 4-8. Vapor-liquid equilibria for a binary system where both components solvate and associate strongly in the vapor phase.

The results shown in Table 2 indicate that UNIQUAC can be used with confidence for multicomponent vapor-liquid equilibria including those that exhibit large deviations from ideality. 

Vapor-Liquid Equilibria for Mixtures Containing One or More Noncondensable Components... 

Figure 4-12. Vapor-liquid equilibria for ethane-n-heptane at 6.9 bars. Ethane is treated as a condensable component even though its critical temperature is 305.4 K.

Figure 4-13. Vapor-liquid equilibria for the system water-nitrogen at 100 atm.

Our experience with multicomponent vapor-liquid equilibria suggests that for system temperatures well below the critical of every component, good multicomponent results are usually obtained, especially where binary parameters are chosen with care. However, when the system temperature is near or above the critical of one (or more) of the components, multicomponent predictions may be in error, even though all binary pairs are fit well. 

In multicomponent liquid-liquid equilibria,the equation of equilibrium, for every component i, is... 

Since we make the simplifying assumption that the partial molar volumes are functions only of temperature, we assume that, for our purposes, pressure has no effect on liquid-liquid equilibria. Therefore, in Equation (23), pressure is not a variable. The activity coefficients depend only on temperature and composition. As for vapor-liquid equilibria, the activity coefficients used here are given by the UNIQUAC equation. Equation (15). ... 

Liquid-liquid equilibria are much more sensitive than vapor-liquid equilibria to small changes in the effect of composition on activity coefficients. Therefore, calculations for liquid-liquid equilibria should be based, whenever possible, at least in part, on experimental liquid-liquid data. 

In the next three sections we discuss calculation of liquid-liquid equilibria (LLE) for ternary systems and then conclude the chapter with a discussion of LLE for systems containing more than three components. 

Figure 4-14. Predicted liquid-liquid equilibria for a typical type-II system shows good agreement with experimental data, using parameters estimated from binary data alone.

Figure 4-15. Effect of UNIQUAC equation modification on prediction of liquid-liquid equilibria for a type-I system containing...

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