# CHAPTIR

Chapter 1 INTI DUCTION [c.1]

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]

In Chapter 2 we discuss briefly the thermodynamic functions whereby the abstract fugacities are related to the measurable, real quantities temperature, pressure, and composition. This formulation is then given more completely in Chapters 3 and 4, which present detailed material on vapor-phase and liquid-phase fugacities, respectively. [c.5]

The calculation of single-stage equilibrium separations in multicomponent systems is implemented by a series of FORTRAN IV subroutines described in Chapter 7. These treat bubble and dewpoint calculations, isothermal and adiabatic equilibrium flash vaporizations, and liquid-liquid equilibrium "flash" separations. The treatment of multistage separation operations, which involves many additional considerations, is not considered in this monograph. [c.6]

The use of Henry s constant for a standard-state fugacity means that the standard-state fugacity for a noncondensable component depends not only on the temperature but also on the nature of the solvent. It is this feature of the unsymmetric convention which is its greatest disadvantage. As a result of this disadvantage special care must be exercised in the use of the unsymmetric convention for multicomponent solutions, as discussed in Chapter 4. [c.19]

Chapter 3 discusses calculation of fugacity coefficient < ). Chapter 4 discusses calculation of adjusted activity coefficient Y fugacity of the pure liquid f9 [Equation (24)], and Henry s constant H. [c.24]

Chapter 3 THE VAPOR PHASE [c.25]

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. [c.25]

This chapter presents a general method for estimating nonidealities in a vapor mixture containing any number of components this method is based on the virial equation of state for ordinary substances and on the chemical theory for strongly associating species such as carboxylic acids. The method is limited to moderate pressures, as commonly encountered in typical chemical engineering equipment, and should only be used for conditions remote from the critical of the mixture. [c.26]

This chapter uses an equation of state which is applicable only at low or moderate pressures. Serious error may result when the truncated virial equation is used at high pressures. [c.38]

P the other terms provide corrections which at low or moderate pressure are close to unity. To use Equation (2), we require vapor-pressure data and liquid-density data as a function of temperature. We also require fugacity coefficients, as discussed in Chapter 3. [c.40]

Equations (2) and (3) are physically meaningful only in the temperature range bounded by the triple-point temperature and the critical temperature. Nevertheless, it is often useful to extrapolate these equations either to lower or, more often, to higher temperatures. In this monograph we have extrapolated the function F [Equation (3)] to a reduced temperature of nearly 2. We do not recommend further extrapolation. For highly supercritical components it is better to use the unsymmetric normalization for activity coefficients as indicated in Chapter 2 and as discussed further in a later section of this chapter. [c.40]

The words "condensable" and "noncondensable" as used here are discussed in the footnote near Equation (13) of Chapter 2. [c.40]

The most reliable estimates of the parameters are obtained from multiple measurements, usually a series of vapor-liquid equilibrium data (T, P, x and y). Because the number of data points exceeds the number of parameters to be estimated, the equilibrium equations are not exactly satisfied for all experimental measurements. Exact agreement between the model and experiment is not achieved due to random and systematic errors in the data and due to inadequacies of the model. The optimum parameters should, therefore, be found by satisfaction of some selected statistical criterion, as discussed in Chapter 6. However, regardless of statistical sophistication, there is no substitute for reliable experimental data. [c.44]

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]

In the first, both components strongly associate with themselves and with each other. In the second, only one of the components associates strongly. For both systems, representation of the data is very good. However, the interesting quality of these systems is that whereas the fugacity coefficients are significantly remote from unity, the activity coefficients show only minor deviations from ideal-solution behavior. Figures 6 and 7 in Chapter 3 indicate that the fugacity coefficients show marked departure from ideality. In these systems, the major contribution to nonideality occurs in the vapor phase. Failure to take into account these strong vapor-phase nonidealities would result in erroneous activity-coefficient parameters, a 2 21 [c.51]

As discussed in Chapter 2, for noncondensable components, the unsymmetric convention is used to normalize activity coefficients. For a noncondensable component i in a multicomponent mixture, we write the fugacity in the liquid phase [c.55]

See footnote near Equation 13 of Chapter 2. [c.57]

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. [c.63]

For all calculations reported here, binary parameters from VLE data were obtained using the principle of maximum likelihood as discussed in Chapter 6, Binary parameters for partially miscible pairs were obtained from mutual-solubility data alone. [c.64]

As indicated in Chapter 6, and discussed in detail by Anderson et al. (1978), optimum parameters, based on the maximum-likelihood principle, are those which minimize the objective function [c.67]

Enthalpies are referred to the ideal vapor. The enthalpy of the real vapor is found from zero-pressure heat capacities and from the virial equation of state for non-associated species or, for vapors containing highly dimerized vapors (e.g. organic acids), from the chemical theory of vapor imperfections, as discussed in Chapter 3. For pure components, liquid-phase enthalpies (relative to the ideal vapor) are found from differentiation of the zero-pressure standard-state fugacities these, in turn, are determined from vapor-pressure data, from vapor-phase corrections and liquid-phase densities. If good experimental data are used to determine the standard-state fugacity, the derivative gives enthalpies of liquids to nearly the same precision as that obtained with calorimetric data, and provides reliable heats of vaporization. [c.82]

For such associating vapor mixtures, the "chemical" theory is used, as discussed in Chapter 3. The derivation of Ah [c.85]

When the UNIQUAC equation (Chapter 4) is substituted into Equation (16), assuming all parameters and a to be inde- [c.87]

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]

This chapter presents quantitative methods for calculation of enthalpies of vapor-phase and liquid-phase mixtures. These methods rely primarily on pure-component data, in particular ideal-vapor heat capacities and vapor-pressure data, both as functions of temperature. Vapor-phase corrections for nonideality are usually relatively small. Liquid-phase excess enthalpies are also usually not important. As indicated in Chapter 4, for mixtures containing noncondensable components, we restrict attention to liquid solutions which are dilute with respect to all noncondensable components. [c.93]

Two generally accepted models for the vapor phase were discussed in Chapter 3 and one particular model for the liquid phase (UNIQUAC) was discussed in Chapter 4. Unfortunately, these, and all other presently available models, are only approximate when used to calculate equilibrium properties of dense fluid mixtures. Therefore, any such model must contain a number of adjustable parameters, which can only be obtained from experimental measurements. The predictions of the model may be sensitive to the values selected for model parameters, and the data available may contain significant measurement errors. Thus, it is of major importance that serious consideration be given to the proper treatment of experimental measurements for mixtures to obtain the most appropriate values for parameters in models such as UNIQUAC. [c.96]

In this chapter we present efficient calculation procedures for single-stage equilibrium separations subroutines implementing these procedures are given in Appendices F and G. While we recognize the great importance of multistage separations, it must be realized that the efficient computation of such processes requires very careful resolution of the large number of simultaneous equilibrium stages involved in a countercurrent cascade. The dominant consideration in such multistage computation procedures is usually the technique used to achieve this simultaneous solution rather than the equilibrium treatment of the stages themselves. (Goldstein and Stanfield, 1970 Holland, [c.110]

In the terms developed in Chapter 2, this latter requirement becomes [c.112]

As discussed in Chapter 3, the virial equation is suitable for describing vapor-phase nonidealities of nonassociating (or weakly associating) fluids at moderate densities. Equation (1) gives the second virial coefficient which is used directly in Equation (3-lOb) to calculate the fugacity coefficients. [c.133]

These were converted from vapor pressure P to fugacity using the vapor-phase corrections (for pure components), discussed in Chapter 3 then the Poynting correction was applied to adjust to zero pressure [c.138]

Enthalpies are evaluated directly using the methods presented in Chapter 5 and Appendices A and B. [c.295]

A step-limited Newton-Raphson iteration, applied to the Rachford-Rice objective function, is used to solve for A, the vapor to feed mole ratio, for an isothermal flash. For an adiabatic flash, an enthalpy balance is included in a two-dimensional Newton-Raphson iteration to yield both A and T. Details are given in Chapter 7. [c.319]

As illustrated here with the UNIQDAC equation, an optimum set of binary parameters can be obtained using simultaneously binary VLE data, binary LLE data, and one (or more) ternary tieline data. The maximum-likelihood principle described in Chapter 6 provides the basis for parameter estimation. The parameters obtained give good representation of ternary data for a wide variety of systems. More important, however, as outlined here, calculations based on a model for the excess Gibbs energy provide a systematic procedure for predicting VLE and LLE for systems containing more than three components. [c.79]

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