Phase equilibria nonideal miscibility

The compositions of the vapor and liquid phases in equilibrium for partially miscible systems are calculated in the same way as for miscible systems. In the regions where a single liquid is in equilibrium with its vapor, the general nature of Fig. 13.17 is not different in any essential way from that of Fig. I2.9< Since limited miscibility implies highly nonideal behavior, any general assumption of liquid-phase ideality is excluded. Even a combination of Henry s law, valid for a species at infinite dilution, and Raoult s law, valid for a species as it approaches purity, is not very useful, because each approximates real behavior only for a very small composition range. Thus GE is large, and its composition dependence is often not adequately represented by simple equations. However, the UNIFAC method (App. D) is suitable for estimation of activity coefficients. 

In Fig. 9.26, the thermodynamic equilibrium, solid-liquid phase diagram of a binary (species A and B) system is shown for a nonideal solid solution (i.e., miscible liquid but immiscible solid phase). The melting temperatures of pure substances are shown with Tm A and Tm B. At the eutectic-point mole fraction, designated by the subscript e, both solid and liquid can coexist at equilibrium. In this diagram the liquidus and solidus lines are approximated as straight lines. A dendritic temperature T and the dendritic mass fractions of species (p)7(p)s and (p)equilibrium partition ratio kp is used to relate the solid- and liquid-phase mass fractions of species (p)7(p)J and (p)f/(p)f on the liquidus and solidus lines at a given temperature and pressure, that is,... 

If the top temperature is too cold and the bottom tenperature is too hot to allow sandwich conponents to exit at the rate they enter the column, they become trapped in the center of the column and accumulate there fKister. 20041. This accumulation can be quite large for trace conponents in the feed and can cause column flooding and development of a second liquid phase. The problem can be identified from the simulation if the engineer knows all the trace conponents that occur in the feed, accurate vapor-liquid equilibrium (VLE) correlations are available, and the simulator allows two liquid phases and one vapor phase. Unfortunately, the VLE may be very nonideal and trace conponents may not accumulate where we think they will. For example, when ethanol and water are distilled, there often are traces of heavier alcohols present. Alcohols with four or more carbons (butanol and heavier) are only partially miscible in water. They are easily stripped from a water phase (relative volatility 1), but when there is litde water present they are less volatile than ethanol. Thus, they collect somewhere in the middle of the column where they may form a second liquid phase in which the heavy alcohols have low volatility. The usual solution to this problem is to install a side withdrawal line, separate the intermediate component from the other components, and return the other components to the column. These heterogeneous systems are discussed in more detail in Chapter 8. 

Whereas in the vapor-liquid equilibrium calculation at low pressures, the model is only used to correct for the nonideality of the liquid phase, the results for liquid-liquid equilibrium calculations and even whether a demixing is calculated or not, is completely determined by the model used. Therefore, liquid-liquid calculations are always much more challenging for any model. Figure 7 demonstrates the ability of PC-SAFT to model also liquid-liquid demixing in polymer systems with high accuracy. The calculations are performed for the system pol5q)ropylene/ -pentane at three different temperatures. Although only temperature-independent pure-component and binary parameters were used, the experimental data can be described very well and the model even correctly captures the temperature dependence of the miscibility gap. 

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