Preliminary Indications of VLLE

Recall from Section 10.7 that azeotropes occur at x=y, where a maximum or minimum appears in all the plots. Also note that the bubble and dew lines do not cross, but they touch at the azeotrope composition. Occasionally when a P-x-y or T-x-y diagram is generated in a Stage III calculation, the diagram can look very odd. The two-parameter fit in Fig. 11.5 was generated using A₁₂ = 1.99, A₂₁ = 1.09 as fitted in Example 11.5. Suppose, due to a slight calculation error or programming typo, we generated a diagram using parameters A₁₂ = 2.99, A₂₁ = 1.09. The predicted phase diagram and y-x diagram would look like those shown in Fig. 11.10.

Figure 11.10. Phase diagram calculations for the 2-propanol + water system at 30°C compared with data cited in Example 11.2. The parameters where selected as described in the text to illustrate how a numerical error can result in thermodynamically unstable loops. Note the dew line has a has a loop and the maximum in the bubble line is not at the azeotropic condition. Note in the y-x plot that the coexistence curve has maxima and minima. These calculated conditions are indicative of LLE as discussed in the text, though the experiments do not show LLE.

The behavior of the lines using these parameters actually predicts that two liquid phases exist. However, the diagram requires additional modification before coexisting compositions and the vapor-liquid-liquid equilibria (VLLE) can be read from the diagram. It is important to understand that the diagram has been generated assuming that only one liquid phase exists. Though we started the discussion by assuming that a parameter calculation error resulted in predictions, all systems that exhibit VLLE will have similarly odd diagrams when only one liquid phase is assumed to exist. This assumption is the default in common process simulators such as ASPEN Plus and ChemCAD because the calculations are faster when the simulator can avoid checking for two phases. When working with simulators, you should check the phase diagrams to see if liquid-liquid phase behavior exists and you should understand where to change the simulator settings to calculate liquid-liquid behavior when it exists. Within this chapter, you should be ready to recognize that such diagrams are indicative of two liquid phases. Also recall that a T-x-y diagram qualitatively resembles an inverted P-x-y, so peculiar loops appear on a T-x-y diagram if a similar situation exists. When models incorrectly predict VLLE behavior that we know to be incorrect, we need to check our calculations. We learn how to rigorously characterize VLLE phase diagrams and how to eliminate the loops in Chapter 14.