Solutions High-Pressure Vapor-Liquid Equilibria

Concentrated Solutions High-Pressure Vapor-Liquid Equilibria 

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. 

In Section II, we discussed the fugacity coefficient, which relates the vapor-phase fugacity to the total pressure and to the composition. The fugacity coefficient can be calculated exactly from an equation of state and, therefore, the problem of calculating vapor-phase fugacities reduces to the problem of 

Since Eqs. (5) and (6) are not restricted to the vapor phase, they can, in principle, be used to calculate fugacities of components in the liquid phase as well. Such calculations can be performed provided we assume the validity of an equation of state for a density range starting at zero density and terminating at the liquid density of interest. That is, if we have a pressure-explicit equation of state which holds for mixtures in both vapor and liquid phases, then we can use Eq. (6) to solve completely the equations of equilibrium without explicitly resorting to the auxiliary-functions activity, standard-state fugacity, and partial molar volume. Such a procedure was discussed many years ago by van der Waals and, more recently, it has been reduced to practice by Benedict and co-workers (B4). 

The fundamental idea of this procedure is as follows For a system of two fluid phases containing N components, we are concerned with N — 1 independent mole fractions in each phase, as well as with two other intensive variables, temperature T and total pressure P. Let us suppose that the two phases (vapor and liquid) are at equilibrium, and that we are given the total pressure P and the mole fractions of the liquid phase x, x2,. .., xN. We wish to find the equilibrium temperature T and the mole fractions of the vapor phase yu y2,. .., yN-i- The total number of unknowns is N + 2 there are N — 1 unknown mole fractions, one unknown temperature, and two unknown densities corresponding to the two limits of integration in Eq. (6), one for the liquid phase and the other for the vapor phase. To solve for these N +2 unknowns, we require N + 2 equations of equilibrium. For each component i we have an equation of the form 

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

In applying equation 33, Cpsl (the constant-pressure molar heat capacity of the stoichiometric liquid) is usually extrapolated from high-temperature measurements or assumed to be equal to Cpij of the compound, whereas the activity product, afXTjafXT), is estimated by interjection of a solution model with the parameters estimated from phase-equilibrium data involving the liquid phase (e.g., solid-liquid or vapor-liquid equilibrium systems). To relate equation 33 to an available data base, the activity product is expressed... 

Prausnitz (1,2) has discussed this problem extensively, but the most successful techniques, which are based on either closed equations of state, such as discussed in this symposium, or on dilute liquid solution reference states such as in Prausnitz and Chueh (3), are limited to systems containing nonpolar species or dilute quantities of weakly polar substances. The purpose of this chapter is to describe a novel method for calculating the properties of liquids containing supercritical components which requires relatively few data and is of general applicability. Used with a vapor equation of state, the vapor-liquid equilibrium for these systems can be predicted to a high degree of accuracy even though the liquid may be 30 mol % or more of the supercritical species and the pressure more than 1000 bar. 

The new supplementary volume is again divided into the seven chapters as used before (1) Introduction, (2) Vapor-Liquid Equilibrium (VLE) Data and Gas Solubilities of Copolymer Solutions, (3) Liquid-Liquid Equilibrium (LLE) Data of Copolymer Solutions, (4) High-Pressure Fluid Phase Equilibrium (HPPE) Data of Copolymer Solutions, (5) Enthalpy Changes for Copolymer Solutions, (6) PVT Data of Copolymers and Solutions, and (7) Second Virial Coefficients (A2) of Copolymer Solutions. Finally, appendices quickly route the user to the desired datasets. 

There are about 850 newly published referenees containing about 150 new vapor-liquid equilibrium data sets and some new tables containing classical Henry s coefficients, about 600 new liquid-liquid equilibrium data sets and some new high-pressure fluid phase equilibrium data, 10 new enthalpic data sets, 20 new data sets describing PVT-properties of polymers, and 120 new data sets with densities or excess volumes. There are also new results on second osmotic virial coefficients of about 45 polymers in aqueous solution. So, in comparison to the original handbook, the new supplementary volume contains even a larger amoimt of data and will be a useful as well as necessary completion of the origirral handbook. 

From experimental data for the ethanol-water system without salt, obtained at 700 and 760 mmHg, it can be seen that within this pressure range the effects of pressure on the equilibrium data are small enough to be within the experimental scatter. In fact, in previous works (8,11,12,13,18,19,23,24,27) there seems to be no clear difference between the equilibrium data at 700 and at 760 mmHg. Errors obtained in the determination of liquid and vapor compositions are approximately 0.05 wt % for the systems without salt. For salt-saturated systems, the same error prevails for the vapor phase, while the error is between 0.1 and 0.2 wt % for liquid phase compositions. The error for the boiling temperature is less than 0.1 °C for the systems without salt, but for saturated solutions the error is much greater from 0.2°C for nonconcentrated solutions to 3°C or more for highly concentrated solutions. 

Equation 3.28 differs from Equation 3.26 in another very fundamental way as well. While Equation 3.26 has both a low-density solution (gas phase) and a high-density solution (liquid phase) at many (T, p) combinations, Equation 3.28 has only a high-density (liquidlike) solution. In other words, the equilibrium vapor pressure of an infinite polymer chain is zero, and hence a liquid— gas phase transition is not possible for a polymer. 

When the standard states for the solid and liquid species correspond to the pure species at a pressure of 1 bar or at a low equilibrium vapor pressure of the condensed phase, the activities of the pure species at equilibrium are taken as unity at all moderate pressures. Consequently, the gas-phase composition at equilibrium will not be affected by the amount of solid or liquid present. At very high pressures, equation (2.8.1) must be used to calculate these activities. When solid or liquid solutions are present, the activities of the components of these solutions are no longer unity even at moderate pressures. In this case, to determine the equilibrium composition of the system, one needs data on the activity coefficients of the various species and the solution composition. 

The densification of boron carbide using silicon or aluminum is difficult to obtain due to the high vapor pressures of liquid silicon or aluminum at reasonable sintering temperatures, and which may hinder densification due to the formation of degassing channels and entrapment of residual gas in the closed pores. Telle and Petzow [404, 405] have demonstrated the existence of a binary equilibrium between a Bi2(B,C,Si)3 solid solution and boron-rich liquid silicon above 1560 ° C, which might be beneficial... 

This initial stage of droplet formation deserves a careful explanation. Over a flat, pure water surface at 100% relative humidity (saturation with respect to water), water vapor is in equilibrium, which means that the number of water molecules leaving the water surface is balanced by the number arriving at the surface. Molecules at water surfaces are subjected to intermolecular attractive forces exerted by the nearby molecules below. If the water surface area is increased by adding curvature, molecules must be moved from the interior to the surface layer, in which case energy is required to oppose the cohesive forces of the liquid. As a consequence, for a pure water droplet to be at equilibrium, the relative humidity has to exceed the relative humidity at equilibrium over a flat, pure water surface, or be supersaturated. The flux of molecules to and from a surface produces what is known as vapor pressure. The equilibrium vapor pressure is less over a salt solution than it is over pure water at the same temperature. This effect balances to some extent the increase in equilibrium vapor pressure caused by the surface curvature of small droplets. Droplets with high concentrations of solute can then be at equilibrium at subsaturation. 

An instrumental method described in (Booth and Bidwell, 1950 Malinin, 1962 Akolzin and Mostovenko, 1969), also used to determine salt solubility in water and hydrothermal solutions without pressure and temperature drops. In this method the solid is transferred from liquid to vapor and back by rotating the reactor or by moving solid phase. After reaching the experimental parameters a solid phase was brought into contact with liquid and then transferred to the vapor phase when equilibrium is established. After that, the reactor is cooled down rapidly. Solubility is determined both by a weight loss in solids and by chemistry of the solution, taking into account the fact that some water has vaporized at high temperatures. 

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