1. Goal 1: Design a flash drum
How big should the drum be?
What height should the nozzle be?
What T and P should the drum be?
What T and P should the feed be?

2. Vapor-liquid equilibrium (VLE)
Consider a binary (i.e., 2-component) system with 2-phases:
What do we know?
yA + yB = 1 xA + xB = 1
yA ≠ xA
Tvap, Pvap
yA, yB
Tliq, Pliq
xA, xB
At equilibrium: Tvap = Tliq
Pvap = Pliq
Gibbs’ Phase Rule:
degrees of freedom = # components (C) - # phases (P) + 2
For a binary, 2-phase system: 2 – = 2
We can specify only 2 intensive variables (all others are fixed, by VLE)

3. Specify P and T
2 graphs in one:
T vs. xA
T vs. yA
superheated vapor
subcooled liquid
2-phase
region
saturated vapor line
saturated liquid line TA xA • • yA •
A subcooled liquid feed of composition zA, heated to temperature TA, will separate spontaneously into 2 phases, of composition xA and yA
Lecture 2 ends in the middle of this slide zA •
Figure 2-3 Temperature-composition diagram for ethanol-water
From Separation Process Engineering, Third Edition by Phillip C. Wankat (ISBN: ) Copyright © 2012 Pearson Education, Inc. All rights reserved.

4. Boiling point, dew point, bubble point
Pure liquids have a boiling point; mixtures have a boiling range, delimited by their bubble point and dew point.
1. Consider a sub-cooled binary liquid that is 40 mol% ethanol.
What is its bubble point?
What is the composition of the first bubble?
dew point
2. Consider a superheated binary vapor that is 40 mol% ethanol.
What is its dew point?
What is the composition of the first drop?
boiling
range
bubble point
xE,initial
yE,initial
3. What is the boiling range of this mixture?
Figure 2-3 Temperature-composition diagram for ethanol-water
From Separation Process Engineering, Third Edition by Phillip C. Wankat (ISBN: ) Copyright © 2012 Pearson Education, Inc. All rights reserved.

5. Useful definitions
Boiling/bubble point Tbp: temperature at which the average liquid molecule has just enough kinetic energy to escape from the surface of the liquid into the gas phase
Recall that kinetic energy follows a Boltzmann distribution, so molecules with higher than average kinetic energy can still escape from the surface at T < Tbp, by evaporation
Saturated liquid: a liquid at its boiling/bubble point
Dew point Tdp: temperature at which the average vapor molecule has just enough kinetic energy to condense
Saturated vapor: a vapor at its dew point
Vapor pressure: pressure at which the liquid and vapor phase are in equilibrium at a given temperature
Azeotrope: a constant-boiling mixture, i.e., a mixture that behaves like a single component

6. How much liquid and vapor will the flash drum produce?
F, L and V are extensive variables
mass balance method total mass balance (TMB): F = L + V component mass balance (CMB): F zA = L xA + V yA rearrange:
OR inverse lever-arm method • L M V
isotherm
For a given F, we can now compute L and V.

7. Specify P and one composition (xA)
y=x
VLE line always lies above y=x line if plotted for the more volatile component
For a binary system at constant P, if one composition (xA or yA) is chosen, all others are fixed:
T incr.
K = yE/xE
volatility = K = K(T, P, zi)
≈ K(T)
VLE line
VLE:
K = yA/xA
mole balance:
xA + xB = 1
yA + yB = 1
azeotrope: K = 1.0
how can we “break” an azeotrope?
Figure 2-2 McCabe-Thiele diagram for ethanol-water
From Separation Process Engineering, Third Edition by Phillip C. Wankat (ISBN: ) Copyright © 2012 Pearson Education, Inc. All rights reserved.

8. Specify two of (P, T, volatility)
pure compound T´ P´
K > 1
Consider a pure compound:
• for a given P, find Tbp (i.e., K = 1)
• for a given T, find P0 (i.e., K = 1)
• for a given P, T, find K
K > 1 prefers vapor phase
K < 1 prefers liquid phase
Tbp P0
pressure
total
K = 1.0
temperature T* P*
K < 1
DePriester Chart
Don’t extrapolate beyond the range of the chart.

9. Figure 2-11 Modified DePriester chart (in S. I
Figure Modified DePriester chart (in S.I. units) at low temperatures
(D. B. Dadyburjor, Chem. Eng. Prog.,85, April 1978; copyright 1978, AIChE; reproduced by permission of the American Institute of Chemical Engineers)
volatility
At 2000 kPa, what is the boiling point of ethane?
At 15 °C, what is the saturated vapor pressure of isobutane?
At 0 °C and 500 kPa, what is the volatility of n-hexane?
At 2000 kPa, what is the boiling point of ethane? -6 °C
At 15 °C, what is the saturated vapor pressure of isobutane? 250 kPa
At 0 °C and 500 kPa, what is the volatility of n-hexane? 0.006
From Separation Process Engineering, Third Edition by Phillip C. Wankat (ISBN: ) Copyright © 2012 Pearson Education, Inc. All rights reserved.

10. Using data from vapor pressure tables
Raoult’s Law ideal liquid: non-ideal liquid:
activity coefficient
Dalton’s Law
ideal gas:
non-ideal gas:
fugacity coefficient

11. Bubble point calculation for multi-component mixtures
Trial-and-error method Given the composition of a subcooled liquid and PTOTAL, find Tbp and (yi)bp VLE: mole balance:
Algorithm:
Pick a temperature T and find the corresponding Ki(T) values for each component
Calculate the yi value for each Ki(T)
Check to see if Syi = 1
If not, pick a new temperature, repeat
How to pick a temperature? How to pick the next temperature?

12. To achieve rapid convergence:
Initial guess: (weighted average of boiling points of pure components)
Next guess:
pick a reference component (A)
find Tnext using DePriester Chart

13. Dew point calculation for multi-component mixtures
Trial-and-error method Given the composition of a superheated vapor and PTOTAL, find Tdp and (xi)dp VLE: mole balance:
Algorithm:
Pick a temperature T and find the corresponding Ki(T) values for each component
Calculate the xi value for each Ki(T)
Check to see if Sxi = 1
If not, pick a new temperature and repeat
Lecture 3 ends here

14. Relative volatility volatility relative volatility
strong function of temperature
volatility
not a strong function of temperature; often assumed independent
relative volatility
for a binary system, substitute and rearrange:

15. Bubble point calculation using relative volatility
definition of relative volatility:
solve for yi:
sum:
solve for Kref:
Algorithm:
given a solution composition (xi values), find relative volatilities (ai values), then
1. guess Tinitial
2. calculate Kref
3. find T = Tbp corresponding to Kref

16. Ex.: Finding Tbp using relative volatilities
Find the bubble point of a mixture of n-pentane (xP = 0.3), n-hexane (xX = 0.3) and n-heptane (xH = 0.4), at 1 atm total pressure. Find the composition of the first vapor bubble.
Designate n-pentane as the reference. At 71 °C, KP = 2.8.
Find Tbp corresponding to KP = 2.0 (read from DePriester Chart): Tbp = 58 °C
Check: