Vapor-liquid equilibrium partial vaporization

For systems of type II, if the mutual binary solubility (LLE) data are known for the two partially miscible pairs, and if reasonable vapor-liquid equilibrium (VLE) data are known for the miscible pair, it is relatively simple to predict the ternary equilibria. For systems of type I, which has a plait point, reliable calculations are much more difficult. However, sometimes useful quantitative predictions can be obtained for type I systems with binary data alone provided that... 

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. 

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). 

As pointed out in the previous chapter, the separation of a homogeneous fluid mixture requires the creation of another phase or the addition of a mass separation agent. Consider a homogeneous liquid mixture. If this liquid mixture is partially vaporized, then another phase is created, and the vapor becomes richer in the more volatile components (i.e. those with the lower boiling points) than the liquid phase. The liquid becomes richer in the less-volatile components (i.e. those with the higher boiling points). If the system is allowed to come to equilibrium conditions, then the distribution of the components between the vapor and liquid phases is dictated by vapor-liquid equilibrium considerations (see Chapter 4). All components can appear in both phases. 

On the other hand, rather than partially vaporize a liquid, the starting point could have been a homogeneous mixture of components in the vapor phase and the vapor partially condensed. There would still have been a separation, as the liquid that was formed would be richer in the less-volatile components, while the vapor would have become depleted in the less-volatile components. Again, the distribution of components between the vapor and liquid is dictated by vapor-liquid equilibrium considerations if the system is allowed to come to equilibrium. 

A simple model for side-rectifiers suitable for shortcut calculation is shown in Figure 11.12. The side-rectifier can be modeled as two columns in the thermally coupled direct sequence. The first column is a conventional column with a condenser and partial reboiler. The second column is modeled as a sidestream column, with a vapor sidestream one stage below the feed stage4. The liquid entering the reboiler and vapor leaving can be calculated from vapor-liquid equilibrium (see Chapter 4). The vapor and liquid streams at the bottom of the first column can then be matched with the feed and sidestream of the second column to allow the calculations for the second column to be carried out. 

The equilibrium adsorption characteristics of gas or vapor on a solid resemble in many ways the equilibrium solubility of a gas in a liquid. Adsorption equilibrium data are usually portrayed by isotherms lines of constant temperature on a plot of adsorbate equilibrium partial pressure versus adsorbent loading in mass of adsorbate per mass of adsorbent. Isotherms take many shapes, including concave upward and downward, and S-curves. Equilibrium data for a given adsorbate-adsorbent system cannot generally be extrapolated to other systems with any degree of accuracy. 

To test the validity of the extended Pitzer equation, correlations of vapor-liquid equilibrium data were carried out for three systems. Since the extended Pitzer equation reduces to the Pitzer equation for aqueous strong electrolyte systems, and is consistent with the Setschenow equation for molecular non-electrolytes in aqueous electrolyte systems, the main interest here is aqueous systems with weak electrolytes or partially dissociated electrolytes. The three systems considered are the hydrochloric acid aqueous solution at 298.15°K and concentrations up to 18 molal the NH3-CO2 aqueous solution at 293.15°K and the K2CO3-CO2 aqueous solution of the Hot Carbonate Process. In each case, the chemical equilibrium between all species has been taken into account directly as liquid phase constraints. Significant parameters in the model for each system were identified by a preliminary order of magnitude analysis and adjusted in the vapor-liquid equilibrium data correlation. Detailed discusions and values of physical constants, such as Henry s constants and chemical equilibrium constants, are given in Chen et al. (11). 

NH4NH2C00, DNH4HC03.NH3. D(NH4)2C03,NH3,and DNH4NH C00,NH3 as adjustable parameters. Experimental data and calculated results are shown in Figure 2. The average percent deviation of calculated versus measured partial pressure is 11% for CO2 and 3.9% for NH3. The same system and the same least squares objective function have been studied by Beutier and Renon (9J. Their results, on the same basis, were 16% for C02 and 5% for NH3. Edwards, et al. (10) also studied vapor-liquid equilibrium of a NH3 C02 aqueous system at 373.15°K. 

Superheated liquids are liquids which exist at temperatures above their equilibrium boiling point at the system pressure. These liquids are metastable in a thermodynamic sense, i.e., they are stable with respect to small perturbations on the system, but if the perturbation is sufficiently large, superheated liquids will partially vaporize and form a final, more stable state, usually consisting of vapor and residual liquid. 

The partial derivatives are usually assumed to be constants that are evaluated at the steadystate operating level from the vapor-liquid equilibrium data. Thus, pressure and temperature on a tray can be measured, as shown in Fig. 8.3c, and a composition signal or pressure-compensated temperature signal generated and controlled. 

Vapor pressures and Henry s Law constant, HA, measure liquid-air partitioning. Henry s Law states that the equilibrium partial pressure of a compound in the air above the air/water interface, PA, is proportional to the concentration of that compound in the water, usually expressed as the mole fraction, XA. 

The equilibrium partial pressure at the interface may be expressed in terms of vapor pressure, activity coefficient, and mole fraction at the liquid surface ... 

In this system, C = 2. If we choose a point which does not fall on the vapor-liquid equilibrium line, then all three variables must be known to describe the system. However, by choosing a point on the vapor-liquid line phases, P=2 and thus, degrees of freedom F = 2-2+2 =2. In other words, only two of the three degrees of freedom (variables) must be known. Referring to Figure 2.3b, if we have a 50/50 mole fraction solution of A and B, the mixture boils at 92°C and the vapor contains 78 mole % of B. In Figure 2.3a the dotted lines indicate the partial pressure of each of the components, that is, the equation of each line defines Raoult s law ... 

Azeotropic and Partially Miscible Systems. Azeotropic mixtures are those whose vapor and liquid equilibrium compositions are identical. Their x-y lines cross or touch the diagonal. Partially miscible substances form a vapor phase of constant composition over the entire range of two-phase liquid compositions usually the horizontal portion of the x-y plot intersects the diagonal, but those of a few mixtures do not, notably those of mixtures of methylethylketone and phenol with water. Separation of azeotropic mixtures sometimes can be effected in several towers at different pressures, as illustrated by Example 13.6 for ethanol-water mixtures. Partially miscible constant boiling mixtures usually can be separated with two towers and a condensate phase separator, as done in Example 13.7 for n-butanol and water. 

If a fluid composed of more than one component (e.g., a solution of ethanol and water, or a crude oil) partially or totally changes phase, the required heat is a combination of sensible and latent heat and must be calculated using more complex thermodynamic relationships, including vapor-liquid equilibrium calculations that reflect the changing compositions as well as mass fractions of the two phases. 

Related Calculations. This illustration outlines the procedure for obtaining coefficients of a liquid-phase activity-coefficient model from mutual solubility data of partially miscible systems. Use of such models to calculate activity coefficients and to make phase-equilibrium calculations is discussed in Section 3. This leads to estimates of phase compositions in liquid-liquid systems from limited experimental data. At ordinary temperature and pressure, it is simple to obtain experimentally the composition of two coexisting phases, and the technical literature is rich in experimental results for a large variety of binary and ternary systems near 25°C (77°F) and atmospheric pressure. Example 1.21 shows how to apply the same procedure with vapor-liquid equilibrium data. 

Again, the primary phase particles of the required substance modifica tion (material precursors) are usually very small. When seeds of the synthe sized phase are used, these primary particles are identical in size to the seeds. In the homogeneous liquid solutions or gas mixtures, the size ofpri mary particles is determined by the nucleation processes. The small size of the primary phase particles can influence considerably the chemical poten tial of the phase to be formed. For example, in the case of spherical parti cles, the chemical potential is determined by equation (1.5). Hence, the equilibrium partial pressure, p, of the saturated vapor or concentration, c of the saturated solution of the substance—for example, of the synthe sized one component phase—is determined by the Kelvin Thomson equation... 

Water molecules in an aqueous solution continually escape into a surrounding gas phase, and simultaneously water molecules condense back into the liquid phase, the two rates becoming equal at equilibrium. The gas phase adjacent to the solution then contains as much water as it can hold at that temperature and still be in equilibrium with the liquid. The partial pressure in the gas phase exerted by the water vapor in equilibrium with pure water is known as the saturation vapor pressure, P ,. 

Upon computing the bubble point of the overhead product, we find that the measured reflux temperature is well below the estimated boiling point. Thus, we choose the subcooled condenser model. The steady-state concept of the subcooled condenser often does not exist in practice. Instead, the condenser is in vapor-liquid equilibrium with the vapor augmented by a blanket of noncondensable gas (that has the effect of lowering the dew point of the overhead vapor). The subcooled condenser is a convenient work-around for steady-state models (as is needed here), but not for dynamic models. We assume a partial reboiler. 

The direct measurement of vapor-liquid equilibrium data for partially miscible mixtures such as 3-methyl-l-butanol-water is difficult, and although stills have been designed for this purpose (9, 10), the data was indirectly obtained from measurements of pressure, P, temperature, t, and liquid composition, x. It was also felt that a test of the validity of the NRTL equation in predicting the VLE data for the ternary mixtures would be the successful prediction of the boiling point. This eliminates the complicated analytical procedures necessary in the direct measurement of ternary VLE data. 

The vapor-liquid equilibrium data for the single-phase runs are graphically shown in Figure 2 where the two-phase region at 60 °C is also plotted to indicate the extent of partial miscibility at the boiling point. A line connects each pair of vapor-liquid equilibrium compositions. 

TT Then salt is added to a volatile solvent mixture, there is a salt effect—a change in the vapor-liquid equilibrium relation. This salt effect occurs because salt forms a preferential solvate with a particular component of the solvent mixture, causing a drop in partial pressure of the particular component which forms the preferential solvate. Results of the studies conducted based on this idea are reported by the author in References 1 and 2. In the past studies, the vapor-liquid equilbrium relation of the system for which formation of preferential solvate had been expected was observed, preferential solvation number was calculated based on the actually observed values, and further, salt effect was predicted based on the preferential solvate number. The author has... 

We conclude this discussion with one final reminder. The vapor-liquid equilibrium calculations we have shown in Section 6.4c are based on the ideal-solution assumption and the corresponding use of Raoult s law. Many commercially important systems involve nonideal solutions, or systems of immiscible or partially miscible liquids, for which Raoult s law is inapplicable and the Txy diagram looks nothing like the one shown for benzene and toluene. 

The OMD process can be included in the group of processes under membrane distillation [38], because it meets the terminology for membrane distillation that was decided by the expert committee at the workshop on membrane distillation in Rome in 1986 [39]. Membranes used in MD need to satisfy certain conditions For example, the membrane should be porous and should not be wetted by the process liquids no capillary condensation should take place inside the pores of the membrane the membrane must not alter the vapor-liquid equilibrium of the different components in the process liquids at least one side of the membrane should be in direct contact with the process liquid for each component the driving force of this membrane operation is partial pressure gradient in vapor phase. 

---