1. Chapter 14-Part VII
Applications of VLLE

2. problem
Toluene (1) and water (2) are essentially immiscible as liquids. Determine the dew point T and the composition of the first drop of liquid formed when vapor mixtures of these species with mole fractions z1 = 0.2 and z1 =0.7 are cooled at constant P of kPa. What is the bubble point T and the composition of the last bubble of vapor in each case?

4. Let’s first find T* Since the liquids are immiscible, x1b =1, x2a =1
We solve the equation to find T*, using Antoine equations
T*= 84.3 oC
Then y1* = x1b P1sat/P = 0.444
Therefore, one of the z1 is at the left and the other at the right of y1*

5. For z1 < y1*  the first liquid is pure 2

6. Lets write the VLE equations
For the first composition, y1 = 0.2, solve for T
T=93.85 oC

7. For z1 > y1*  the first liquid is pure 1

8. Again, write VLE equations
Now, use the first equation with y1 =0.7 and solve for T
T=98.49 oC
Note that the bubble point temperature is T*
and the mole fraction of the last vapor is y1*

9. Second problem
Consider a binary system of species 1 and 2 in which the liquid phase exhibits partial miscibility. In the regions of miscibility, the excess Gibbs free energy at a particular temperature is expressed by the equation:
The vapor pressures of the pure species are 75 kPa and 110 kPa respectively (comp. 1 and 2). Prepare a P-x-y diagram for this system at the given temperature

10. What type of diagram do we expect?

11. Lets find the solubility limits
For the simple GE model, the activity coefficient equations are:
For LLE and this model, because the solubility curves
are symmetric about x1 = 0.5, see equation E in example 14.5
Solve for x1a = 0.224; and x1b = 0.776
(only because the model is symmetric!!!)

12. Now find the 3-phase equilibrium point
P* =160.7 kPa
y1* =0.405
Now draw the actual diagram

13. Calculate VLE in the 2-phase regions
First solve for P (for increasing x1b values) and for the corresponding y1
Similar procedure for the a-V equilibrium

14. Third problem
The system water (1)-n-pentane (2)-n-heptane (3) exists as a vapor at kPa and 100oC with mole fractions z1 = 0.32, z2 = 0.45, z3 = The system is slowly cooled at constant P until it is completely condensed into a water phase (b) and a hydrocarbon phase (a) . Assuming that the two liquid phases are immiscible, that the vapor phase is an ideal gas, and that the HCs obey Raoult’s law, determine: a) the dew-point T of the mixture and the composition of the first condensate.

15. Calculate dew point T and liquid composition assuming the hydrocarbon layer (a) forms first:
Only two components in the HC phase (a phase) :
components 2 and 3; VLE for the HC phase
Since there are 3 unknowns Tdew 1, x2a and x3a, we need only 3 equations,
Use the last three because the first is a combination of the 2nd and 3rd
Solve for Tdew 1 ; x3a ; x2a

16. Calculate dew point T assuming the water layer (b) forms first:
x1b =1
Solve for Tdew 2;
Tdew 2 = oC
Then Tdew 1 =65.12 oC; Tdew 2 = oC
Since we are cooling, we will find Tdew 2 first, the water layer will form first

17. Next step explanation
In the previous two slides we determined which phase condenses first.  In
the vapor phase the compositions were z1, z2, and z3. We found out that water condenses first.
Next, we have a system that has vapor (water, C5 and C7) coexisting with a liquid water phase (pure water). 
Now we want to find out at what temperature the second phase is going to condense. 
The vapor composition has changed because some water is being condensed,
but the HC components have not condensed yet, so for them,
their compositions must be in the same ratio as the original:
y2/y3 = z2/z3, at the temperature where the first drop of HC phase shows up.

18. b) What is the temperature at which the second layer forms
6 equations and 6 unknowns
y1, y2, y3, T dew 3, x2a, x3a
y1= 0.24, y2 =0.503, y3 =0.257,
T dew 3 = oC, x2a = 0.21, x3a = 0.79

19. Last step Finally (next slide) we calculate the bubble temperature
where we have the two phases
with their final liquid compositions, (x1 = 1 for the water phase),
x2=z2/(z2+z3) and x3=z3/(z2+z3) for the HC phase, and we can calculate the composition of the last vapor.

20. c) Calculate bubble point given the total molar composition of the two phases
Find T (bubble point) = oC
And compositions of the last bubble of vapor