Vapor-liquid equilibrium at high pressures

When we consider equilibrium between two phases at high pressure, neither phase being dilute with respect to one of the components, we can no longer make the simplifying assumptions made in some of the earlier sections. We must now realistically describe deviations from ideal behavior in both phases for each phase, the effect of both pressure and composition must be seriously taken into account if we wish to describe vapor-liquid equilibria at high pressures for a wide range of conditions, including the critical. 

Chueh, P. L. Prausnitz, J. M. Vapor-Liquid Equilibria at High Pressures ... 

To model the binary vapor-liquid equilibria at high pressure accurately, an equation-of-state approach is required. For instance, to calculate the curves in Figures 2.3-2(a) and (b) a Peng-Robinson equation with one adjustable parameter was used. This point was examined by Sandler [9]. 

Chueh, P.L. Prausnitz, J.M. (1967). Vapor-liquid equilibria at high pressures calculation of partial molar volumes in non polar liquid mixtures. AIChE., Vol.l3, pp. 1099-1107... 

Chiieh, P. L., and Prausnitz, J. M. Vapor-liquid-equilibria at high pressures. Vapor-phase fugacity coefficients in nonpolar and quantum-gas mixtures. I EC Fundamentals 6 (1967) 492. 

In vapor-liquid equilibria, it is relatively easy to start the iteration because assumption of ideal behavior (Raoult s law) provides a reasonable zeroth approximation. By contrast, there is no obvious corresponding method to start the iteration calculation for liquid-liquid equilibria. Further, when two liquid phases are present, we must calculate for each component activity coefficients in two phases since these are often strongly nonlinear functions of compositions, liquid-liquid equilibrium calculations are highly sensitive to small changes in composition. In vapor-liquid equilibria at modest pressures, this sensitivity is lower because vapor-phase fugacity coefficients are usually close to unity and only weak functions of composition. For liquid-liquid equilibria, it is therefore more difficult to construct a numerical iteration procedure that converges both rapidly and consistently. 

Thermodynamic consistency tests for binary vapor-liquid equilibria at low pressures have been described by many authors a good discussion is given in the monograph by Van Ness (VI). Extension of these methods to isothermal high-pressure equilibria presents two difficulties first, it is necessary to have experimental data for the density of the liquid mixture along the saturation line, and second, since the ideal gas law is not valid, it is necessary to calculate vapor-phase fugacity coefficients either from volumetric data for... 

Section 1.5 gives examples for vapor-liquid equilibria at ordinaiy pressures and for liquid-liquid equilibria. Section 1.6 discusses equilibria for systems containing a solid phase in addition to a liquid or gaseous phase, and Section 1.7 gives an introduction to methods for describing fluid-phase equilibria at high pressures. 

Equations of state can also be used to calculate three-phase (vapor-liquid-liquid) equilibria at high pressures the principles for doing so are the same as those used for calculating two-phase equilibria but the numerical techniques for solving the many simultaneous equations are now more complex. 

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. 

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. 

Dahl, S., Fredenslund, A., and Rasmussen, R, 1991. The MHV2 model A UNlFAC-based equation of state model for prediction of gas solubility and vapor-liquid equilibria at low and high pressures. Ind. Eng. Chem. Res., 30 1936-1945. 

Sections 9.3-9.S present the common phase behavior of binary mixtures 9.3 describes vapor-liquid, liquid-liquid, and vapor-liquid-liquid equilibria at low pressures 9.4 considers solid-fluid equilibria and 9.5 discusses common high-pressure fluid-phase equilibria. Then 9.6 briefly describes the basic vapor-liquid and liquid-liquid equilibria that can occur in ternary mixtures. This chapter describes many apparently different phase behaviors, and so we try to show when those differences are more apparent than real. The organization is intended to bring out underlying similarities, thereby reducing the number of different things to be learned. 

The vapor-liquid equilibria at pressures down to 1 mm. Hg are not greatly different from those at higher pressure. The relative volatility of a binary system may either increase or decrease as the pressure is reduced. For example, in a mixture of oleic and stearic acids, oleic is the more volatile at temperatures above 100 to 110°C., while below these temperatures it is the less volatile. For mixtures that obey Raoult s law the relative volatility generally increases as the temperature is decreased because the less volatile constituent has the higher latent heat resulting in a high temperature coefficient of vapor pressure. 

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. 

Given in the literature are vapor pressure data for acetaldehyde and its aqueous solutions (1—3) vapor—liquid equilibria data for acetaldehyde—ethylene oxide [75-21-8] (1), acetaldehyde—methanol [67-56-1] (4), sulfur dioxide [7446-09-5]— acetaldehyde—water (5), acetaldehyde—water—methanol (6) the azeotropes of acetaldehyde—butane [106-97-8] and acetaldehyde—ethyl ether (7) solubility data for acetaldehyde—water—methane [74-82-8] (8), acetaldehyde—methane (9) densities and refractive indexes of acetaldehyde for temperatures 0—20°C (2) compressibility and viscosity at high pressure (10) thermodynamic data (11—13) pressure—enthalpy diagram for acetaldehyde (14) specific gravities of acetaldehyde—paraldehyde and acetaldehyde—acetaldol mixtures at 20/20°C vs composition (7) boiling point vs composition of acetaldehyde—water at 101.3 kPa (1 atm) and integral heat of solution of acetaldehyde in water at 11°C (7). 

The discussion of the previous section was concerned with low-pressure vapor-liquid equilibria and involved the use of activity coefficient models. Here we are interested in high-pressure phase equilibrium in fluids in which both phases are describable by equations of state, that is, the cj -4> method. One example of the type of data we are interested in describing (or predicting) is shown in Fig. 10.3-1 for the ethane-propylene system. There we see the liquid (bubble point) and vapor (dew point) curves for this system at three different isotherms. At each temperature the coexisting vapor and liquid. phases have the same pressure and thus are joined by horizontal tie lines, only one of... 

It has been customary to apply an activity coefficient method to aid in the prediction of vapor-liquid equilibria of polar mixtures. At high pressures approaching the critical state of the fluid mixture, the activity coefficient method requires such thermodynamic properties as partial molar volumes or partial molar heats of solution that are very difficult,... 

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). 

An exhaustive study of high-pressure vapor-liquid equilibria has been repotted by Knapp et at., who give not only a comprehensive literanire survey but also compare calculated and observed results for many systems. In that stu, several popular equations of state were used to perform the calculations but no one equation of state emerged as markedly superior to the others. All the equations of state used gave reasonably g results provided care is exercised in choosing the all-important binary constant k,j. All the equations of state used gave poor results when mixtures were close to critical conditions. 

Roper, V. Kohayashi, R. Apparatus and procedure to measure binary total pressure at high temperature fluorene - phenanthrene vapor-liquid equilibria and data reduction by the four-suffix Margules model to obtain infinite-dilution activity coefficients Fluid Phase Equilib. 1989,47, 273-293... 

Critical Regions. At very high pressures special phenomena associated with the critical region are encountered in vapor-liquid equilibria. If the vapor pressure of a pure component is plotted vs. the temperature, a line concave upward is obtained. This line terminates at the critical point. Conditions below the line in region A, Fig. 4-1,... 

Steam Distillation Example. As an example of steam distillation, consider the separation of a mixture of two high-boiling organic acids from a small amount of nonvolatile carbonaceous material. The steam distillation is carried out at 100 C. under a total pressure of 150 mm. Hg. The organic acid mixture contains 70 and 30 mol per cent of the low- and high-boiling acids, respectively, and at 100 C. the vapor pressures of the two acids are 20 and 8 mm. Hg. It is assumed that the mixture of the two acids obeys Raoult s law and that they are immiscible with water. The nonvolatile carbonaceous material is assumed to have no effect on the vapor-liquid equilibria. It will be assumed that the vapor leaves in equilibrium with the liquid in the still, and two cases will be considered. In the first, the mixture of acids will be fed continuously to a still of small capacity, and it will be assumed that steady-state conditions have been reached in which the composition of the organic acids in the condensate is the same as in the feed. In the second... 

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