Correlation and prediction of vapor-liquid

A review is presented of techniques for the correlation and prediction of vapor-liquid equilibrium data in systems consisting of two volatile components and a salt dissolved in the liquid phase, and for the testing of such data for thermodynamic consistency. The complex interactions comprising salt effect in systems which in effect consist of a concentrated electrolyte in a mixed solvent composed of two liquid components, one or both of which may be polar, are discussed. The difficulties inherent in their characterization and quantitative treatment are described. Attempts to correlate, predict, and test data for thermodynamic consistency in such systems are reviewed under the following headings correlation at fixed liquid composition, extension to entire liquid composition range, prediction from pure-component properties, use of correlations based on the Gibbs-Duhem equation, and the recent special binary approach. 

Zudkevitch, D. Joffe, J. Correlation and Prediction of Vapor-Liquid... 

Zudkevitch, D., and J. Jaffe Correlation and Prediction of Vapor-Liquid Equilibriiun with the Redlich-Kwong Equation of State, AlChEJ., p. 496, May 1970. 

Zudkevitch, D., and Joffe, J. Correlation and prediction of vapor-liquid equilibria with the Redlich-Kwong equation of state. A. I. Ch. E. J. 16 (1970) 112. 

Application of cubic EoS in the correlation and prediction of vapor-liquid equilibria of mixtures is considered in Chapter 14. 

We now turn from the qualitative description of high-pressure phase equilibria and its measurement to the quantitative description, that is, to the correlation or prediction of vapor-liquid equilibrium for hydrocarbon (and light gas). systems, of which the ethane-propylene system is merely one example. Our interest will be only in systems describable by a single equation of state for both the vapor and liquid phases, as the case in which the liquid is described by an activity coefficient model was considered in the previous section. 

Density is defined as the mass of a substance contained in a unit volume. In the SI system of units, the ratio of the density of a substance to the density of water at I5°C is known as its relative density, while the older term specific gravity is the ratio relative to water at 60°F. Various units of density, such as kg/m, Ib-mass/fF, and g/cm, are commonly used. In addition, molar densities, or the density divided by the molecular weight, is often specified. This section briefly discusses methods of correlation of density as a function of temperature and presents the most common accurate methods for prediction of vapor, liquid, and solid density. 

Correlation and Prediction of Salt Effect in Vapor-Liquid Equilibrium... 

Generalized Correlations. A simple and reliable method for the prediction of vapor—liquid behavior has been sought for many years to avoid experimentally measuring the thermodynamic and physical properties of every substance involved in a process. Whereas the complexity of fluids makes universal behavior prediction an elusive task, methods based on the theory of corresponding states have proven extremely useful and accurate while still retaining computational simplicity. Methods derived from corresponding states theory are commonly used in process and equipment design. 

Chao-Seader Correlation. Reference was made earlier to the well known and much used Chao-Seader correlation for the prediction of vapor-liquid equilibrium for principally hydrogen-hydrocarbon systems with small amounts of CO2, H2S, O2, N2, etc. The heart of the correlation consists of several equations to represent liquid fugacity. The other two constituents, the Scatchard-Hildebrand equation for activity coefficients and the Redllch-Kwong equation for the vapor-phase nonideality, were already well established. 

Ortega, J. Espiau, F. Sabater, G. Postigo, M. Correlation and prediction of excess quantities and vapor-liquid equilibria of alkyl esters + tert-butyl alcohol experimental data for propyl esters + tert-butyl alcohol. J. Chem. Eng. Data 2006, 51, 730-742. 

Andiappan, A., and McLean, A. Y. Prediction of vapor-liquid-equilibria derivation of a new expression for vapor-liquid-correlations. Canad. J. Chem. Eng. 50 (1972) 384. 

There is always uncertainty and inaccuracy with vapor-liquid equilibrium data and correlations. Any errors in this data could mean an incorrect prediction of the location and shape of the boundary. 

The most important aspect of the simulation is that the thermodynamic data of the chemicals be modeled correctly. It is necessary to decide what equation of state to use for the vapor phase (ideal gas, Redlich-Kwong-Soave, Peng-Robinson, etc.) and what model to use for liquid activity coefficients [ideal solutions, solubility parameters, Wilson equation, nonrandom two liquid (NRTL), UNIFAC, etc.]. See Sec. 4, Thermodynamics. It is necessary to consider mixtures of chemicals, and the interaction parameters must be predictable. The best case is to determine them from data, and the next-best case is to use correlations based on the molecular weight, structure, and normal boiling point. To validate the model, the computer results of vapor-liquid equilibria could be checked against experimental data to ensure their validity before the data are used in more complicated computer calculations. 

Solutions in hand for the reference pairs, it is useful to write out empirical smoothing expressions for the rectilinear densities, reduced density differences, and reduced vapor pressures as functions of Tr and a, following which prediction of reduced liquid densities and vapor pressures is straightforward for systems where Tex and a (equivalently co) are known. If, in addition, the critical property IE s, ln(Tc /Tc), ln(PcVPc), and ln(pcVPc), are available from experiment, theory, or empirical correlation, one can calculate the molar density and vapor pressure IE s for 0.5 < Tr < 1, provided, for VPIE, that Aa/a is known or can be estimated. Thus to calculate liquid density IE s one uses the observed IE on Tc, ln(Tc /Tc), to find (Tr /Tr) at any temperature of interest, and employs the smoothing relations (or numerically solves Equation 13.1) to obtain (pR /pR). Since (MpIE)R = ln(pR /pR) = ln[(p /pc )/(p/pc)] it follows that ln(p7p)(MpIE)R- -ln(pcVpc). For VPIE s one proceeds similarly, substituting reduced temperatures, critical pressures and Aa/a into the smoothing equations to find ln(P /P)RED and thence ln(P /P), since ln(P /P) = I n( Pr /Pr) + In (Pc /Pc)- The approach outlined for molar density IE cannot be used to rationalize the vapor pressure IE without the introduction of isotope dependent system parameters Aa/a. 

The equations given predict vapor behavior to high degrees of accuracy but tend to give poor results near and within the liquid region. The compressibility factor can be used to accurately determine gas volumes when used in conjunction with a vitial expansion or an equation such as equation 53 (77). However, the prediction of saturated liquid volume and density requires another technique. A correlation was found in 1958 between the critical compressibility factor and reduced density, based on inert gases. From this correlation an equation for normal and polar substances was developed (78) ... 

Until recently the ability to predict the vapor-liquid equilibrium of electrolyte systems was limited and only empirical or approximate methods using experimental data, such as that by Van Krevelen (7) for the ammonia-hydrogen sulfide-water system, were used to design sour water strippers. Recently several advances in the prediction and correlation of thermodynamic properties of electrolyte systems have been published by Pitzer (5), Meissner (4), and Bromley ). Edwards, Newman, and Prausnitz (2) established a similar framework for weak electrolyte systems. 

To solve distillation problems involving multicomponent mixtures, vapor-liquid equilibrium data and enthalpy data are needed. The methods used to obtain these data may be classified as follows (1) the use of a single equation of state and (2) the use of multiple equations of state and/or correlations for the prediction of the liquid and vapor parts of the K values and the enthalpies. This classification was suggested by Adler et al.2 in an excellent paper on the industrial uses of equations of state. Although the first approach, the use of a single equation of state, is the more desirable, many industrial problems are encountered in which this approach is too inaccurate and the second approach is used. 

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