Bubble and Dew Point Calculations

We have concluded, thus, our discussion of the activity coefficient and are ready to consider its use in solving vapor-liquid equilibrium problems. 

The typical such problems are presented in Table 13.1 and involve - as seen in Section 13.6 - bubble point (B.P.) and dew point (D.P.) calculations. (An other common VLE problem, requires the so-called flash calculation. It involves often high pressures and is considered, therefore, in the next Chapter.) 

We discussed bubble and dew point calculations for ideal solutions in Examples 13.2 through 13.7. And in Examples 13.9 and 13.11 we carried out B.P. pressure calculations for nonideal solutions assuming, however, vapor phase ideality. 

We proceed now with a discussion of the more general case nonideal liquid and nonideal vapor phases. Notice that the type of calculation involved depends on the information given, as described in Table 13.1. 

The approach to calculations in this more general case is the same with 

---

For bubble and dew-point calculations we have, respectively, the objective functions... 

Estimating the unknown but required starting values of conditions and compositions is an important and sensitive part of these calculations. The composition of the feed is always known, as is the composition of one of the two phases in bubble and dew point calculations. With the Chao-Seader, Grayson-Streed, and Lee-Erbar-Edmister methods, it is possible to assume that both phases have the composition of the feed for the first trial. This assumption leads to trouble with the Soave-Redlich-Kwong, the Peng-Robinson and the Lee-Kesler-Ploecker... 

This modified Raoult s law was used for data reduction in Sec. 11.6. Bubble- and dew-point calculations made with Eq. (11.74) are, of course, somewhat simpler than those shown by Figs. 12.12 through 12.15. Indeed, the BUBL P calculation yields final results in a single step, without iteration. The additional assumption of liquid-phase ideality (yk - 1), on the other hand, is justified only infrequently. We note that yk for ethanol in Table 12.1 is greater than 8. 

Once you have a Txy diagram like that of Figure 6.4-1, bubble- and dew-point calculations become trivial. To determine a bubble-point temperature for a given liquid composition, go to the liquid curve on the Txy diagram for the system pressure and read the desired temperature from the ordinate scale. (If you are not sure why this works, go back and consider again how the curve was generated.) You can then move horizontally to the vapor curve to determine the composition of the vapor in equilibrium with the given liquid at that temperature. 

Bubble- and dew-point calculations are useful to determine saturation conditions for liquid and vapor streams, respectively. It is important to note that when vapor-liquid equilibrium is established, the vapor is at its dew point and the liquid is at its bubble point. 

Two important problems are the bubble and dew point calculations, obtained by zeroing V and I, respectively, while the duty Q is unknown. 

Similar solutions can be obtained for all of the bubble and dew point calculations. We are now ready to consider several examples. See Highlight 7.5. 

Use in carrying out bubble and dew point calculations that provide the numerical answers for the relationship between the two phases. 

We return then to the general vapor-liquid equilibrium problem and discuss how the activity coefficient is used in solving it. We will see that this is accomplished through the so-called bubble and dew point calculations. 

We proceed now to use bubble and dew point calculations in the following Examples that represent typical applications of vapor-liquid equilibrium to distillation column design. 

Details for bubble and dew point calculations are given by Van Ness and Abbott (1982) and by Prausnitz et al (1980), who also present the appropriate computer subroutines. (The last book is a must for anyone involved in such calculations). They can be also easily developed using the subroutines of Appendix E. 

Bubble and dew point calculations are presented in the next two Examples with the simplest approach, the use of K values from Eqs 14.5.1 through 14.5.5. They can be also carried out with the computer subroutines, using the SRK EoS, given by Daubert (1985), that can be easily adapted to other EoS and for bubble point pressure calculations, using the EoS of Chapter 10, with the Program VLEEOS presented in Appendix E, which can be easily modified to perform B.P. temperature calculations. 

---