Binary Phase Diagrams

Liquid-liquid mutual solubilities in partially miscible systems change with temperature at a given pressure. Whether the solubilities increase or decrease can be due to a number of factors including hydrogen bonding. When one species H-bonds and the other does not, then as the temperature is raised and hydrogen bonds are broken, the fluids become more “similar,” and the LLE region decreases in size. The fluids can become miscible before the boiling point as shown in Fig. 19.12 on page 804 for methanol + cyclohexane. The liquid-liquid envelope is the dome in the figure. The temperature where the liquids become totally miscible is known as the upper critical solution temperature (UCST). Pressure affects the VLE curve, but has virtually no effect on the liquid phases or LLE. Thus, as the pressure is lowered, the VLE shifts to lower temperatures, and the VLE curve will overlap the LLE curve, giving a diagram similar to Fig. 16.2B on page 616, insets (e) and (f). For other systems that differ more greatly in vapor pressure, an azeotrope may not appear in the VLE and the diagram will appear as in Fig. 16.2A on page 616, insets (b) and (c).

When VLE is predicted by process simulators, the common default settings check for only one liquid phase. The result can be the odd diagrams as in Fig. 11.10 on page 435. How do we resolve such diagrams? Consider the T-x-y diagram in Fig. 14.5(a) for ethyl acetate + water generated using UNIQUAC parameters in the ASPEN Plus database. By default, ASPEN Plus models VLE; the dotted line is vapor and the dashed line is liquid. The solid line and dots have been added manually. Note the L^β is in equilibrium with the left V branch all the way from 373 K to the two left-most dots. Likewise the L^α is in equilibrium with the right V branch all the way from the pure ethyl acetate boiling point to the two rightmost dots. The horizontal line is the VLLE condition because both L branches are simultaneously in equilibrium with the center V dot, and thus they are also in equilibrium with each other. The liquid compositions are at the outside dots and the vapor composition in this case is given by the center dot. This state is known as a heteroazeotrope because two liquid phases co-exist at the azeotrope condition. The odd loops below this VLLE temperature are not equilibrium states and are discarded. Fig. 14.5(b) is a comparison of experimental data with the diagram generated by specifying that the process simulator check for VLLE, though the dotted LLE lines are added manually to show the general type of expected behavior. Note how the lower loops are eliminated. The horizontal line method is easy to apply manually to any diagrams that you may generate.

Figure 14.5. (a) VLE predictions of ethyl acetate + water as predicted by literature parameters in ASPEN using UNIQUAC. The horizontal line and the dots have been added manually. (b) The correct phase behavior after specifying to check for VLLE. Note that the liquid-liquid envelope is sketched by hand based on general behavior that may be expected, not predicted, but the two liquid compositions at the bubble temperature are at the ends of the horizontal VLLE line. Data from Ellis, S. R. M.; Garbett, R. D. 1960. Ind. Eng. Chem. 52:385-388; Reichl, A.; et al, 1998. Fluid Phase Equil. 153:113–134; Lee, L.-S.; et al. 1996. J. Chem. Eng. Japan 96:427–438.