# Wheel

While much attention has been given to the development of computer techniques for design of distillation and absorption columns, much less attention has been devoted to the development of such techniques for equipment using liquid-liquid extraction. However, regardless of the nature of the operation, few systematic attempts have been made to organize phase-equilibrium information for direct use in chemical process design. This monograph presents a systematic procedure for calculating multi-component vapor-liquid and liquid-liquid equilibria for mixtures commonly encountered in the chemical process industries. Attention is limited to systems at low or moderate pressures. Pertinent references to previous work are given at the end of this chapter. [c.1]

The possible number of liquid and vapor mixtures in technological processes is incredibly large, and it is unreasonable to expect that experimental vapor-liquid and liquid-liquid equilibria will ever be available for a significant fraction of this number. Further, obtaining good experimental data requires appreciable experimental skill, experience, and patience. It is, therefore, an economic necessity to consider techniques for calculating phase equilibria for multicomponent mixtures from few experimental data. Such techniques should require only a [c.1]

When only the total system composition, pressure, and temperature (or enthalpy) are specified, the problem becomes a flash calculation. This type of problem requires simultaneous solution of the material balance as well as the phase-equilibrium relations. [c.3]

Compilation of azeotropic data as well as other physical properties including melting and boiling points. [c.7]

Francis, A. W. "Liquid-Liquid Equilibriums," Wiley-Interscience, New York, 1963. [c.8]

A classic in its field, giving a splendid survey of solution physical chemistry from a chemist s point of view. While seriously out of date, it nevertheless provides physical insight into how molecules "behave" in mixtures. [c.9]

Design," Wiley-Interscience, New York, 1970. [c.11]

Compilation of data for binary mixtures reports some vapor-liquid equilibrium data as well as other properties such as density and viscosity. [c.12]

In Equation (13), z and <(iT refer to the monomer of species i while y is the apparent mole fraction of component i, where apparent means that dimerization has been neglected. [c.33]

Figure 5 shows fugacity coefficients for the system acetaldehyde-acetic acid at 90°C and 0.25 atm. Calculations are based on the "chemical" theory of vapor imperfection. Although the pressure is far below atmospheric, fugacity coefficients for both components are well removed from unity. Because of strong dimerization between acetic acid molecules and weak dimerization between the other possible pairs, deviations from ideality are large, much larger than one might expect at this low pressure. [c.34]

By contrast, in the system propionic acid d) - methyl isobutyl ketone (2), (fi and are very much different when y 1, Propionic acid has a strong tendency to dimerize with itself and only a weak tendency to dimerize with ketone also,the ketone has only a weak tendency to dimerize with itself. At acid-rich compositions, therefore, many acid molecules have dimerized but most ketone molecules are monomers. Acid-acid dimerization lowers the fugacity of acid and thus is well below unity. Because of acid-acid dimerization, the true mole fraction of ketone is signi- [c.35]

While vapor-phase corrections may be small for nonpolar molecules at low pressure, such corrections are usually not negligible for mixtures containing polar molecules. Vapor-phase corrections are extremely important for mixtures containing one or more carboxylic acids. [c.38]

Figure 4 shows experimental and predicted phase equilibria for the acetonitrile/benzene system at 45°C. This system exhibits moderate positive deviations from Raoult s law. The high-quality data of Brown and Smith (1955) are very well represented by the UNIQUAC equation. [c.48]

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. [c.51]

Null (1970) discusses some alternate models for the excess Gibbs energy which appear to be well suited for systems whose activity coefficients show extrema. [c.55]

Table 3 shows results obtained from a five-component, isothermal flash calculation. In this system there are two condensable components (acetone and benzene) and three noncondensable components (hydrogen, carbon monoxide, and methane). Henry s constants for each of the noncondensables were obtained from Equations (18-22) the simplifying assumption for dilute solutions [Equation (17)] was also used for each of the noncondensables. Activity coefficients for both condensable components were calculated with the UNIQUAC equation. For that calculation, all liquid-phase composition variables are on a solute-free basis the only required binary parameters are those for the acetone-benzene system. While no experimental data are available for comparison, the calculated results are probably reliable because all simplifying assumptions are reasonable the [c.61]

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. [c.61]

Unfortunately, good binary data are often not available, and no model, including the modified UNIQUAC equation, is entirely adequate. Therefore, we require a calculation method which allows utilization of some ternary data in the parameter estimation such that the ternary system is well represented. A method toward that end is described in the next section. [c.66]

To illustrate the criterion for parameter estimation, let 1, 2, and 3 represent the three components in a mixture. Components 1 and 2 are only partially miscible components 1 and 3, as well as components 2 and 3 are totally miscible. The two binary parameters for the 1-2 binary are determined from mutual-solubility data and remain fixed. Initial estimates of the four binary parameters for the two completely miscible binaries, 1-3 and 2-3, are determined from sets of binary vapor-liquid equilibrium (VLE) data. The final values of these parameters are then obtained by fitting both sets of binary vapor-liquid equilibrium data simultaneously with the limited ternary tie-line data. [c.67]

In Equation (24), a is the estimated standard deviation for each of the measured variables, i.e. pressure, temperature, and liquid-phase and vapor-phase compositions. The values assigned to a determine the relative weighting between the tieline data and the vapor-liquid equilibrium data this weighting determines how well the ternary system is represented. This weighting depends first, on the estimated accuracy of the ternary data, relative to that of the binary vapor-liquid data and second, on how remote the temperature of the binary data is from that of the ternary data and finally, on how important in a design the liquid-liquid equilibria are relative to the vapor-liquid equilibria. Typical values which we use in data reduction are Op = 1 mm Hg, = 0.05°C, = 0.001, and = 0.003 [c.68]

The method described here is based on the high degree of correlation of model parameters, in this case, UNIQUAC parameters. Thus, although a certain set of binary parameters may be best for VLE data, we are able to find other sets of binary parameters for the miscible binaries which significantly improve ternary LLE prediction while only slightly decreasing accuracy of representation of the binary VLE. Fitting ternary LLE data only, may yield unrealistic parameters that predict grossly erroneous results when used in regions not identical to those employed in data reduction. By contrast, fitting ternary LLE data simultaneously with binary VLE data, effectively provides constraints on the binary parameters, preventing them from attaining arbitrary values of little physical significance. Determination of a single set of parameters which can adequately represent both VLE and LLE is particularly important in three-phase distillation. [c.69]

[c.79]

Draper, N. R., Smith, H. "Applied Regression Analysis," John Wiley, New York (1966). [c.80]

Null, H. R., "Phase Equilibrium in Process Design," John Wiley, New York (19 70). [c.80]

Figure 3 presents results for acetic acid(1)-water(2) at 1 atm. In this case deviations from ideality are important for the vapor phase as well as the liquid phase. For the vapor phase, calculations are based on the chemical theory of vapor-phase imperfections, as discussed in Chapter 3. Calculated results are in good agreement with similar calculations reported by Lemlich et al. (1957). [c.91]

The accuracy of the calculations depends directly on the reliability of the experimental data. The correlated data presented in the Appendices were taken from standard literature sources while these data are probably reliable for most fluids, it is not possible to be certain that they are reliable for all. [c.95]

While many methods for parameter estimation have been proposed, experience has shown some to be more effective than others. Since most phenomenological models are nonlinear in their adjustable parameters, the best estimates of these parameters can be obtained from a formalized method which properly treats the statistical behavior of the errors associated with all experimental observations. For reliable process-design calculations, we require not only estimates of the parameters but also a measure of the errors in the parameters and an indication of the accuracy of the data. [c.96]

If this criterion is based on the maximum-likelihood principle, it leads to those parameter values that make the experimental observations appear most likely when taken as a whole. The likelihood function is defined as the joint probability of the observed values of the variables for any set of true values of the variables, model parameters, and error variances. The best estimates of the model parameters and of the true values of the measured variables are those which maximize this likelihood function with a normal distribution assumed for the experimental errors. [c.98]

The maximum-likelihood method, like any statistical tool, is useful for correlating and critically examining experimental information. However, it can never be a substitute for that information. While a statistical tool is useful for minimizing the required experimental effort, reliable calculated phase equilibria can only be obtained if at least some pertinent and reliable experimental data are at hand. [c.108]

Beck, J. V., Arnold, K. J., "Parameter Estimation in Engineering and Science," John Wiley Sons, New York (1977). [c.109]

Brownlee, K. A., "Statistical Theory and Methodology in Science and Engineering," 2nd ed., John Wiley and Sons, New York (1965). [c.109]

Clifford, A. A., "Multivariate Error Analysis," Halsted Press, Division of John Wiley Sons, New York (1973). [c.109]

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. [c.5]

More general forms of the Gibbs-Duhem equation have been derived to allow for variations in temperature or pressure (or both) but these are not useful for our purposes since they are not easily integrated. Equation (16) is satisfied by various simple algebraic forms relating an y to x well-ltnown examples are the Margules and van Laar equations but many others exist. The particular relation used in this work, the UNIQUAC equation, while significantly different from the equations of Margules and van Laar, is also a solution to the Gibbs-Duhem differential equation. [c.20]

Unfortunately, the ideal-gas assumption can sometimes lead to serious error. While errors in the Lewis rule are often less, that rule has inherent in it the problem of evaluating the fugacity of a fictitious substance since at least one of the condensable components cannot, in general, exist as pure vapor at the temperature and pressure of the mixture. [c.25]

To illustrate, UNIQUAC parameters were obtained for the ethanol/cyclohexane system using the extensive isothermal data of Scatchard and Satkiewicz (1964). Figure 2 shows parameters for 5, 35, and 60°C along with the confidence ellipses. These regions indicate that it is possible to choose a single value of 322 appropriate for all temperatures a single value of a2 (e.g. 1300) can be included in all three confidence ellipses, implying that in the range 5-65 C parameter a2 is temperature independent. For 3., however, there is no single value which can intercept all three confidence ellipses. Therefore, parameter a 2 must be represented by a function of temperature as shown in Table 1 where the estimated variance of the fit, a, provides a measure of how well the data are represented. The first line shows results obtained when fitting two UNIQUAC parameters, a 2 21 ii ispendent of temperature. The next two [c.45]

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 [c.48]

The acetone/chloroform system, shown in Figure 6, exhibits strong negative deviations from Raoult s law because of hydrogen bonding between the single hydrogen atom of chloroform and the carbonyl oxygen of acetone. The data of Severns et al. (1955) are well represented by the Ul IQUAC equation. [c.50]

Hougan, O. H., Watson, K. M., Ragatz, R. A., "Chemical Process Principles, 2nd ed.", John Wiley Sons, Inc., New York (1954) [c.95]

A high degree of correlation may be beneficial. When the parameters are strongly related, some linear combination of the two parameters may represent the data as well as do the individual parameters. In that case a method similar to that of Bruin and Praus- [c.104]

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