High Pressure Vapor-Liquid Equilibrium

In en equilibrated, multiphase mixture at temperature Tand pressure P, foreveiy component r, (he fugacity /, must be the same In all phases. Therefore, if a method is available for calculating /, for phase as a function of temperature, pressure, and the phase s composition, (hen it is possible to calculate ail equilibrium ocxnpositjoua at any desired temperature and pressure. When all phases are fluids, such a method is given by an equation of state. 

An equation of state, applicable to all fluid phases, is paitiodariy useful for phase-equilibrium calculations where a liquid phase and a vapor phase coexist at high pressures. At such conditions, conventional activity coefficients are not useful because, with rare exceptions, at least one of the mixture s components is supercritical that is, (he system temperature is above (hat component s critical temperature. In that event, one must employ special standard states for the activity coefficients of the supercritical components (see Section 1.5-2). That complication is avoided when ail fugacities are calculated front en equation of state. 

To fix ideas, consider a rtvlticomponent, two-phase (liquid-vapor) mixture where the phases are denoted, respectively, by superscripts L and V. Pressure P and temperature Tase the same in both phases. The condition of equiUbrium is given by formulation 3 of Section 1.2-5  

is (he fugacity coefficient, x is the liquid-phase mole fraction, and y is the vapor-phase mole fraction. follows that the familiar K factor is given by 

As discussed In Section 1.3-1, the fygacity confident is directly related to en integral obtained from die equation of stare. Forthe liquid-phase fugacity coefficient, at constant temperature and composition, 

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Griswold, J., D. Andres and V. A. Klein, Determination of High Pressure Vapor-Liquid Equilibria. The Vapor-Liquid Equilibrium of Benzene-Toluene," Trans. Amer. Inst. Chem. Engrs. 39, 223 (1943). 

VI. Concentrated Solutions High-Pressure Vapor-Liquid Equilibria. 170... 

The difficulties engendered by a hypothetical liquid standard state can be eliminated by the use of unsymmetrically normalized activity coefficients. These have been used for many years in other areas of solution thermodynamics (e.g., for solutions of electrolytes or polymers in liquid solvents) but they have only recently been employed in high-pressure vapor-liquid equilibria (P7). 

It is difficult to measure partial molar volumes, and, unfortunately, many experimental studies of high-pressure vapor-liquid equilibria report no volumetric data at all more often than not, experimental measurements are confined to total pressure, temperature, and phase compositions. Even in those cases where liquid densities are measured along the saturation curve, there is a fundamental difficulty in calculating partial molar volumes as indicated by... 

The correlation of Chao and Seader has been computerized and has been used extensively in the petroleum industry. It provides a useful method for estimating high-pressure vapor-liquid equilibria in hydrocarbon systems over a wide range of temperature, pressure, and composition, and presents a significant improvement over the previously used A -charts first introduced by W. K. Lewis, B. F. Dodge, G. G. Brown, M. Souders, and others (see D6) almost forty years ago. However, the Chao-Seader correlation is unreliable at conditions approaching the critical. Various extensions have been proposed (G2), especially for application at extreme temperatures. 

It is easily possible to introduce refinements into the dilated van Laar model which would further increase its accuracy for correlating activity coefficient data. However, such refinements unavoidably introduce additional adjustable parameters. Since typical experimental results of high-pressure vapor-liquid equilibria at any one temperature seldom justify more than two adjustable parameters (in addition to Henry s constant), it is probably not useful for engineering purposes to refine Chueh s model further, at least not for nonpolar or slightly polar systems. 

While the dilated van Laar model gives a reliable representation of constant-pressure activity coefficients for nonpolar systems, the good agreement between calculated and experimental high-pressure phase behavior shown in Fig. 14 is primarily a result of good representation of the partial molar volumes, as discussed in Section IV. The essential part of any thermodynamic description of high-pressure vapor-liquid equilibria must depend,... 

P8a. Prausnitz, J. M., and Chueh, P. L., Computer Calculations for High-Pressure Vapor-Liquid Equilibria. Prentice-Hall, Englewood Cliffs, New Jersey, to be published (1968). 

Shibata, S.K., and S.I. Sandler, "High-Pressure Vapor-Liquid Equilibria of Mixtures of Nitrogen, Carbon Dioxide, and Cyclohexane", J. Chem. Eng. Data, 34,419-424(1989). 

High-Pressure Vapor-Liquid Equilibria from a Corresponding States Correlation with Emphasis on Asymmetric Mixtures," I EC Process Design and Development, 1978, 17, 324. 

A New Mixing Rule for Accurate Prediction of High Pressure Vapor-Liquid Equilibria of Gas/Large n-Alkane Systems... 

In summary, based on a rigorous approximation to the quasichemical solution derived by the present authors, a generalized GC-EOS was proposed for the estimation and the prediction of properties of real pure fluids and mixtures. Its applicability was demonstrated for high pressure vapor-liquid equilibria of pure or mixed fluids. Although not shown here, we. have further results with other functional groups which indicate the extended applicability of the present method. 

In this work, the basis for a proper answer to the selectivity problem between the two cited compounds is set. For this purpose, a high-pressure vapor-liquid equilibria circulation-type apparatus was designed and constructed. Some vapor-liquid equilibria (VLE) data of the binary systems C02-limonene and C02-linalool were determined and compared with data available in the literature. The results obtained were accurately correlated by a modified SRK equation of state that avoids the use of critical constants [16]. 

Figure 1. High-pressure vapor-liquid equilibria circulation-type apparatus.

Xu, N., J. Dong, Y. Wang, and J. Shi. 1992. "High Pressure Vapor Liquid Equilibria at 293 K for Systems Containing Nitrogen, Methane and Carbon Dioxide", Fluid Phase Equil., 81 175-186. 

Plocker, U., Knapp, H., and Prausnitz, J. (1978) Ind Eng Chem Proc Des and Dev. 17, 243. Calculation of high-pressure vapor-liquid equilibria from a corresponding-states correlation with emphasis on asymmetric mixtures. 

Therefore, the scope of this chapter is to describe the results obtained using SAS with particular emphasis on the production of particles with controlled PS and PSD in the micrometric as well as in the nanometric range. We will try to understand the role of high pressure vapor-liquid equilibria (VLEs) in determining the morphology and particle size of precipitates. 

E. R. Gilliland and H. W. Scheeline High Pressure Vapor-Liquid Equilibria Propylene-Isobutane and Propane-Hydrogen Sulfide, Ind. Eng. Chem., 32 48 (1940). 

HIGH-PRESSURE VAPOR-LIQUID EQUILIBRIA USING EQUATIONS OF STATE METHOD)... 

High-Pressure Vapor-Liquid Equilibria Using Equations of State (j -(j) Method) 557... 

Measurement of high-pressure vapor-liquid equilibria... 

A solute that is a liquid at the temperature of a supercritical extraction has critical properties much closer to the supercritical fluid s critical properties than the solids discussed above. Since the mixture is somewhat less molecularly as3nranetric, the critical temperature of the supercritical fluid lies above the melting temperature of the solute. As a result, the vaporization (L2V) curve is generally the only pure solute property to be of concern on mixture P-T traces. Many literature references are available for mixtures that fall into this category, because these systems comprise the bulk of high pressure vapor-liquid equilibria research of the last century, however, most data are for hydrocarbon related systems and the current interest extends beyond these systems. A few cases of special interest will be mentioned and further information may be found in other references (4-10). 

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