Vapor-liquid equilibrium data

American Petroleum Institute, Bibliographies on Hydrocarbons, Vols. 1-4, "Vapor-Liquid Equilibrium Data for Hydrocarbon Systems" (1963), "Vapor Pressure Data for Hydrocarbons" (1964), "Volumetric and Thermodynamic Data for Pure Hydrocarbons and Their Mixtures" (1964), "Vapor-Liquid Equilibrium Data for Hydrocarbon-Nonhydrocarbon Gas Systems" (1964), API, Division of Refining, Washington. 

Source for liquid-liquid and vapor-liquid equilibrium data and vapor-pressure data. 

Gmehling, J., and U. Onken "Vapor-Liquid Equilibrium Data Collection," DECHEMA Chemistry Data Ser., Vol. 1 (1-10), Frankfurt, 1977. 

Boublik "Vapor-Liquid Equilibrium Data at Normal Pressures," Pergamon, Oxford, 1968. 

Maczynski, A. "Thermodynamic Data for Technology—Verified Vapor-Liquid Equilibrium Data," Panstwowe Wydawnictwo Naukawa, Warsaw, Volume 1, 1976 Volume 2, 1978. 

Extensive compilation of vapor-liquid equilibrium data, particularly from Eastern Europe. 

Vapor-liquid equilibrium data and vapor pressure data, Vol. 2 (2a) and Vol. 4 (4b) and liquid-liquid equilibrium data, Vol. 2 (2b, 2c). 

Compilation of vapor-liquid equilibrium data data are correlated with Redlich-Kister equation (in Polish). 

Wichterle, I., J. Linek, and E. H la "Vapor-liquid Equilibrium Data Bibliography,"... 

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

Two additional illustrations are given in Figures 6 and 7 which show fugacity coefficients for two binary systems along the vapor-liquid saturation curve at a total pressure of 1 atm. These results are based on the chemical theory of vapor-phase imperfection and on experimental vapor-liquid equilibrium data for the binary systems. In the system formic acid (1) - acetic acid (2), <() (for y = 1) is lower than formic acid at 100.5°C has a stronger tendency to dimerize than does acetic acid at 118.2°C. Since strong dimerization occurs between all three possible pairs, (fij and not... 

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. 

Figure 15 shows results for a difficult type I system methanol-n-heptane-benzene. In this example, the two-phase region is extremely small. The dashed line (a) shows predictions using the original UNIQUAC equation with q = q. This form of the UNIQUAC equation does not adequately fit the binary vapor-liquid equilibrium data for the methanol-benzene system and therefore the ternary predictions are grossly in error. The ternary prediction is much improved with the modified UNIQUAC equation (b) since this equation fits the methanol-benzene system much better. Further improvement (c) is obtained when a few ternary data are used to fix the binary parameters. 

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. 

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... 

Unfortunately, many commonly used methods for parameter estimation give only estimates for the parameters and no measures of their uncertainty. This is usually accomplished by calculation of the dependent variable at each experimental point, summation of the squared differences between the calculated and measured values, and adjustment of parameters to minimize this sum. Such methods routinely ignore errors in the measured independent variables. For example, in vapor-liquid equilibrium data reduction, errors in the liquid-phase mole fraction and temperature measurements are often assumed to be absent. The total pressure is calculated as a function of the estimated parameters, the measured temperature, and the measured liquid-phase mole fraction. 

Application of the algorithm for analysis of vapor-liquid equilibrium data can be illustrated with the isobaric data of 0th-mer (1928) for the system acetone(1)-methanol(2). For simplicity, the van Laar equations are used here to express the activity coefficients. 

Vapor-Liquid Equilibrium Data Reduction for Acetone(1)-Methanol(2) System (Othmer, 1928)... 

The maximum-likelihood method is not limited to phase equilibrium data. It is applicable to any type of data for which a model can be postulated and for which there are known random measurement errors in the variables. P-V-T data, enthalpy data, solid-liquid adsorption data, etc., can all be reduced by this method. The advantages indicated here for vapor-liquid equilibrium data apply also to other data. 

VL = vapor-liquid equilibrium data MS = mutual solubility data AZ = azeotropic data... 

CHU, J.C./VAPOR-LIQUID EQUILIBRIUM DATA, ANN ARBOR, MICHIGAN (1956) ... 

UNIQUAC Binary Parameters for Noncondensable Components with Condensable Components. Parameters Obtained from Vapor-Liquid Equilibrium Data in the Dilute Region... 

Subroutine VLDTA2. VLDTA2 loads the binary vapor-liquid equilibrium data to be correlated. If the data are in units other than those used internally, the correct conversions are made here. This subroutine also reads the estimated standard deviations for the measured variables and the initial parameter estimates. All input data are printed for verification. 

DOCUMENT THE INPUT VAPOR-LIQUID EQUILIBRIUM DATA... 

Propylene oxide is a colorless, low hoiling (34.2°C) liquid. Table 1 lists general physical properties Table 2 provides equations for temperature variation on some thermodynamic functions. Vapor—liquid equilibrium data for binary mixtures of propylene oxide and other chemicals of commercial importance ate available. References for binary mixtures include 1,2-propanediol (14), water (7,8,15), 1,2-dichloropropane [78-87-5] (16), 2-propanol [67-63-0] (17), 2-methyl-2-pentene [625-27-4] (18), methyl formate [107-31-3] (19), acetaldehyde [75-07-0] (17), methanol [67-56-1] (20), ptopanal [123-38-6] (16), 1-phenylethanol [60-12-8] (21), and / /f-butanol [75-65-0] (22,23). 

A tabulation of the partial pressures of sulfuric acid, water, and sulfur trioxide for sulfuric acid solutions can be found in Reference 80 from data reported in Reference 81. Figure 13 is a plot of total vapor pressure for 0—100% H2SO4 vs temperature. References 81 and 82 present thermodynamic modeling studies for vapor-phase chemical equilibrium and liquid-phase enthalpy concentration behavior for the sulfuric acid—water system. Vapor pressure, enthalpy, and dew poiat data are iacluded. An excellent study of vapor—liquid equilibrium data are available (79). 

Additional compilations of vapor-pressure data include Boubhk, Fried, and Hala, The Vapor Pre.s.sure.s of Pure Substances, Elsevier, Amsterdam, 1984. See also Hirata, Ohe, and Nagahama, Computer Aided Data Book of Vapor-Liquid Equilibria, Kodansha/Elsevier, Tokyo, 1975 Weishaupt, Landolt-Bornstein New Series Group TV, vol. 3 Thermodynamic Equilibria of Boiling Mixtures, Springer-Verlag, Berhn, 1975 Wichterle, Linek, and Hala, Vapor-Liquid Equilibrium Data Bibliography, Elsevier, Amsterdam, 1973 suppl. 1, 1976 suppl. 2,1982. 

The analogy between equations derived from the fundamental residual- and excess-propeily relations is apparent. Whereas the fundamental lesidanl-pL-opeRy relation derives its usefulness from its direct relation to equations of state, the ci cc.s.s-property formulation is useful because V, and y are all experimentally accessible. Activity coefficients are found from vapor/liquid equilibrium data, and and values come from mixing experiments. 

Again subscript i identifies species, and J and I are dummy indicies. Values for the parameters r, qi, and (up — tip) are given by Gmehhng, Onken, and Ant (Vapor-Liquid Equilibrium Data Collection, Chemistry Data Series, vol. I, parts 1-8, DECHEMA, FrankfurUMain, 1974-1990). 

Gmehhng and Onken (Vapor-Liquid Equilibrium Data Collection, DECHEMA, Frankfurt, Germany, 1979) have reported a large collection of vapor-liqnid equilibrium data along with correlations of the resulting activity coefficients. This can be used to predict liqnid-hqnid equilibrium partition ratios as shown in Example 1. 

Gmehhng and Onken (op. cit.) give the activity coefficient of acetone in water at infinite dilution as 6.74 at 25 C, depending on which set of vapor-liquid equilibrium data is correlated. From Eqs. (15-1) and (15-7) the partition ratio at infinite dilution of solute can he calculated as follows ... 

By using vapor-liquid equilibrium data the above integral can be evaluated numerically. A graphical method is also possible, where a plot of l/(y - xj versus Xr is prepared and the area under the curve over the limits between the initial and fmal mole fraction is determined. However, for special cases the integration can be done analytically. If pressure is constant, the temperature change in the still is small, and the vapor-liquid equilibrium values (K-values, defined as K=y/x for each component) are independent from composition, integration of the Rayleigh equation yields ... 

It is essential to calculate, predict or experimentally determine vapor-liquid equilibrium data in order to adequately perform distillation calculations. These data need to relate composition, temperature, and system pressure. 

Note that good vapor-liquid equilibrium data for low pressure conditions are very scarce and difficult to locate. However, for proper calculations they are essential. See References 151 and 152 dealing with this. 

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