Multicomponent Vapor-Liquid Equilibria from Binary Data

Abstract

A D v m T A m s of calculating vaporliquid equilibria in multicomponent systems from data for the pure components and individual binaries are obvious. The relative simplicity of the experimental determination of binary data as contrasted to multicomponent data is a basic advantage. The main value of the calculation method is lost if the data required for its application become excessive or too difficult to obtain.Several types of binary data conveniently furnish activity coefficients and in some cases provide a double check on the data and their thermodynamic consistency. Such binary data are already available for many systems. They are becoming more and more available from measurements of total pressures, boiling points, azeotropic data, relative volatilities, and complete vapor-liquid equilibria. Their efficient use in calculating multicomponent systems is of prime importance.Several methods have been reported for calculating vapor-liquid equilibria. Usually vapor-liquid equilibria are calculated by liquid phase activity coefficients. The Margules (3, 7.9,22,34,45,47,57,69) and van Laar-type (4, 6 , 74, 79, 63-65, 67, 69) equations have frequently been applied to representation of the activity coefficients as a function of composition. Another method uses equations relating directly to liquid composition and relative volatilities, or vapor compositions (72, 73,23,38, 46,60).The objective of this article is to show further application of the modified van Laar-type equations ( 6 ) to the calculation of multicomponent vapor-liquid equilibria based only on data for the pure components and their binary mixtures. Phase EquilibriaComplete vapor-liquid equilibria in terms of the liquid, x,, the vapor composition, Y,, the total pressure, P, and the temperature, T , provide more than the minimum data required for a check of the thermodynamic consistency. The pressure-temperature relationship a t liquid composition x , and the vapor composition, Y,, at the corresponding x , and T . or P, provides a double check on the consistency of the data. The two are related through the activity coefficient, yt, according toand at, = r t P W r t P P 9 , = Y,x,/x,Y, (2) A method for calculating the imperfection-pressure coefficients, 0, has been described (5). For a nonpolar substance the only basic data needed are critical temperature, T,, critical pressure, P,, and vapor pressure, Po. For a polar substance a minimum of one individual constant is also required. A vapor density a t one or two temperatures can furnish the required individual constants for each polar substance. Except where special "chemical" effects are present, no binary coefficients are required to represent the imperfection-pressure coefficients for the components in the mixtures.The activity coefficients, y's, are functions of temperature and liquid compositions, 2's. While in many systems the qualitative effect of temperature on the activity coefficients is known, exact quantitative values are best derived empirically from data at more than one temperature. For ...

Excess enthalpies at 45.deg., for ternary system acetonitrile-benzene-carbon tetrachloride

“…Values of the relative densities (d254) and refractive indices (n25d) of the purified components are given in Table I. These values all lie within the ranges given by Timmer- 1 To whom correspondence should be addressed. mans (74), with the exception of the value of d254 for benzene, for which the range given is 0.8736-0.8739.…”

“…As part of an investigation of three-component behavior in which one component (acetonitrile) is highly polar, excess enthalpies or heats of mixing have been measured at 45°C for the system acetonitrile-benzene-carbon tetrachloride. Although this system is not of commercial importance in itself, acetonitrile is used as a third component in separation processes (1), and carbon tetrachloride is a possible cosolvent with it in preventing isopycnics (5). The system involving these two components with benzene was chosen for study at 45°C, since information is available on excess enthalpies at this temperature for the three binary systems (3,4, 70, 7 7) for comparison.…”

Mutual Solubility of Water and Hydrocarbons: A New Mixing Rule and the Development of a Predictive Scheme via the Cubic Two-State Equation of State

“…toluene−hexane, 49,53 and −0.0042 for cyclohexane−heptane. 50 Unfortunately, the focus of their work was the LLE of quaternary systems with an alcohol, so the low mutual solubilities in the absence of the alcohol were not accurately measured. Hence, only vapor-phase compositions were contrasted.…”

“…First, VLLE calculations were compared to the measurements of Pequenín et al − The systems were water–toluene–cyclohexane, water–toluene–hexane, and water–cyclohexane–heptane . The values of HC–HC k ij were determined from SRK correlation of the VLE experimental data: 0.0221 for toluene–cyclohexane, − 0.0117 for toluene–hexane, , and −0.0042 for cyclohexane–heptane . Unfortunately, the focus of their work was the LLE of quaternary systems with an alcohol, so the low mutual solubilities in the absence of the alcohol were not accurately measured.…”

Prediction of Vapor Compositions in Vapor-Liquid Systems

“…As Vt for distillation systems changes little with pressure, the integral in Equation 2 can be written Another way of calculating activity coefficients in multicomponent mixtures has been developed by Black (1958bBlack ( , 1959Black ( ,1963. Log 74 is given by log 7i = [ aJRJxf + 0.5 XjXkRjiRki X 3 ik( aj + aj -aJRü)]/^xsRjJ + Est (7) 3 where (3) Vi,m is the mean value of F< in the pressure range P{°t o P.…”