Phase equilibria, miscibility

Ternary-phase equilibrium data can be tabulated as in Table 15-1 and then worked into an electronic spreadsheet as in Table 15-2 to be presented as a right-triangular diagram as shown in Fig. 15-7. The weight-fraction solute is on the horizontal axis and the weight-fraciion extraciion-solvent is on the veriical axis. The tie-lines connect the points that are in equilibrium. For low-solute concentrations the horizontal scale can be expanded. The water-acetic acid-methylisobutylketone ternary is a Type I system where only one of the binary pairs, water-MIBK, is immiscible. In a Type II system two of the binary pairs are immiscible, i.e. the solute is not totally miscible in one of the liquids. 

During the 1940s, a large amount of solubility data was obtained by Francis (6, 7), who carried out measurements on hundreds of binary and ternary systems with liquid carbon dioxide just below its critical point. Francis (6, 7) found that liquid carbon dioxide is also an excellent solvent for organic materials and that many of the compounds studied were completely miscible. In 1955, Todd and Elgin (8) reported on phase equilibrium studies with supercritical ethylene and a number of... 

No other solvent extraction process other than the CO2 technology allows such a strong influence on loading, phase equilibrium, and selectivity. Unfortunately, the solubility of extracted substances in CO2 is relatively low, compared with the usual solvents which give absolute miscibility with the extracted valuable materials in most cases. The determination of solubility and solvent ratios is therefore important for the economy of the process. 

Aqueous Solubility. Solubility of a chemical in water can be calculated rigorously from equilibrium thermodynamic equations. Because activity coefficient data are often not available from the literature or direct experiments, models such as UNIFAC can be used for structure—activity estimations (24). Phase-equilibrium relationships can then be applied to predict miscibility. Simplified calculations are possible for low miscibility, however, when there is a high degree of miscibility, the phase-equilibrium relationships must be solved rigorously. 

If miscibility is significant in a binary chemical—solvent system, the calculations become more complex because the coupled nonlinear phase equilibrium expressions must be solved (10) ... 

A general formulation of the problem of solid-liquid phase equilibrium in quaternary systems was presented and required the evaluation of two thermodynamic quantities, By and Ty. Four methods for calculating Gy from experimental data were suggested. With these methods, reliable values of Gy for most compound semiconductors could be determined. The term Ty involves the deviation of the liquid solution from ideal behavior relative to that in the solid. This term is less important than the individual activity coefficients because of a partial cancellation of the composition and temperature dependence of the individual activity coefficients. The thermodynamic data base available for liquid mixtures is far more extensive than that for solid solutions. Future work aimed at measurement of solid-mixture properties would be helpful in identifying miscibility limits and their relation to LPE as a problem of constrained equilibrium. 

Phase equilibrium resulting in a UCST is the most common type of binary (liquid + liquid) equilibrium, but other types are also observed. For example, Figure 14.5 shows the (liquid + liquid) phase diagram for (xiH20 + jc2(C3H7)2NH. 7 A lower critical solution temperature (LCST) occurs in this system/ That is, at temperatures below the LCST, the liquids are totally miscible, but with heating, the mixture separates into two phases. 

Partial Miscibility in the Solid State So far, we have described (solid + liquid) phase equilibrium systems in which the solid phase that crystallizes is a pure compound, either as one of the original components or as a molecular addition compound. Sometimes solid solutions crystallize from solution instead of pure substances, and, depending on the system, the solubility can vary from small to complete miscibility over the entire range of concentration. Figure 14.26 shows the phase diagram for the (silver + copper) system.22 It is one in which limited solubility occurs in the solid state. Line AE is the (solid -I- liquid) equilibrium line for Ag, but the solid that crystallizes from solution is not pure Ag. Instead it is a solid solution with composition given by line AC. If a liquid with composition and temperature given by point a is... 

Supercritical fluids are unique solvents and reaction media due to liquid like density and gas like viscosity. Diffusion is not limited by any interface. Under ambient conditions hydrocarbons and water are nearly unmiscible. Phase equilibrium changes significantly in the supercritical region of water (Tc = 647 K, pc = 22.1 MPa). Hydrocarbons and supercritical water become miscible at any ratio, whereas supercritical carbon dioxide and hydrocarbons still have a broad miscibility gap [4],... 

Due to the fact that interfacial tension becomes zero at the critical point of the mixture, above which complete miscibility occurs, the relatively high value of interfacial tension at 30.5 MPa and 313 K (1.88 mN/m ) indicates that the system investigated in this work is still relatively far from its critical pressure. This observation is also valid for all nine temperatures investigated and agrees with the phase equilibrium measurements shown in Figure 4. 

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. 

Two early studies of the phase equilibrium in the system hydrogen sulfide + carbon dioxide were Bierlein and Kay (1953) and Sobocinski and Kurata (1959). Bierlein and Kay (1953) measured vapor-liquid equilibrium (VLE) in the range of temperature from 0° to 100°C and pressures to 9 MPa, and they established the critical locus for the binary mixture. For this binary system, the critical locus is continuous between the two pure component critical points. Sobocinski and Kurata (1959) confirmed much of the work of Bierlein and Kay (1953) and extended it to temperatures as low as -95°C, the temperature at which solids are formed. Furthermore, liquid phase immiscibility was not observed in this system. Liquid H2S and C02 are completely miscible. 

In the two-phase region, the type II(+) system has an oil-rich micellar phase in equilibrium with an excess brine phase. Surfactant is found almost exclusively in the oil-rich phase, and the concentration of surfactant in that phase can greatly exceed the concentration of surfactant in the injected chemical slug. In the type II(+) environment, the micellar phase remains miscible with the oil but is immiscible with the brine. Oil continues to be recovered by a misciblelike process. The opposite occurs if the phase environment is type II(-). The brine-rich micellar phase is immiscible with the oil phase, and oil recovery is by low IFT immiscible displacement. 

Effect of Unlike-Pair Interactions on Phase Behavior. No adjustment of the unlike-pair interaction parameter was necessary for this system to obtain agreement between experimental data and simulation results (this is, however, also true of the cubic equation-of-state that reproduces the properties of this system with an interaction parameter interesting question that is ideally suited for study by simulation is the relationship between observed macroscopic phase equilibrium behavior and the intermolecular interactions in a model system. Acetone and carbon dioxide are mutually miscible above a pressure of approximately 80 bar at this temperature. Many systems of interest for supercritical extraction processes are immiscible up to much higher pressures. In order to investigate the transition to an immiscible system as a function of the strength of the intermolecular forces, we performed a series of calculations with lower strengths of the unlike-pair interactions. Values of - 0.90, 0.80, 0.70 were investigated. 

Special consideration is given to the effect of completely miscible cosolvents such as methanol and ethanol. A new approximate method of predicting cosolvent effects is presented. The results should be useful in supplying necessary phase equilibrium data to complex computer programs for modeling transport and fate of sparingly soluble organics in the environment. 

Generally, liquid-liquid phase equilibrium (or phase separation) occurs only over certain temperature ranges, bounded above by the upper consolute or upper critical solution temperature, and bounded below by the lower consolute or lower critical solution temperature. These critical solution temperatures are indicated on the liquid-liquid phase diagrams given here. All partially miscible mixtures should exhibit either one or both consolute temperatures however, the lower consolute temperature may be obscured by the freezing of the mixture, and the upper consolute temperature will not be observed if it is above the bubble point temperature of the mixture, as vaporization will have instead occurred. ... 

The prerequisite of all types of extraction processes is the existence of a large miscibility gap between raffinate and extract. The thermodynamic principles of phase equilibrium are dealt with in Chap. 2. An extensive collection of liquid-liquid equilibria is given in the Dechema Data Collection (Sorensen and Arlt 1980ff). Volume 1 contains data of miscibility gaps of binary systems. Phase equilibrium data (miscibility gaps and distribution equilibrium) of ternary and quaternary mixtures are listed in volumes 2-7. 

---