### GE 115, Section 11

```CBE 417
“Chemical Engineering Equilibrium
Separations”
Lecture: 9
28 Sep 2012
1
Overview
•McCabe-Thiele graphical technique (binary systems)
•Condensers
•Reboilers
• Binary Shortcut Methods
• AspenPlus:
o Shortcut methods: DSTWU
• Efficiencies
•Introduction to multicomponent distillation
2
Problem Solving Exercise
3
Problem Solving Exercise
4
McCabe Thiele: Total Condenser
y1 V1
1
0.9
LO
D
0.8
xD
y1
Ya
0.7
xD
1
0.6
Y=X
0.5
x1
x0.4
y2
D
2
R
1
0.3
x2
0.2
y3
0.1
3
0
0
0.1
0.2
0.3
0.4
Xa
0.5
0.6
0.7
0.8
0.9
1
x3
y4
5
McCabe Thiele: Partial Condenser
yD
D
y1 V1
1
0.9
LO
0.8
x0
Ya
0.7
xO
y1
1
0.6
Y=X
0.5
x1
x0.4
y2
D
2
R
1
0.3
x2
0.2
y3
0.1
3
0
0
0.1
0.2
0.3
0.4
Xa
0.5
0.6
0.7
0.8
0.9
1
x3
y4
6
McCabe Thiele: Partial Condenser
Why consider using a partial condenser?
• Desire vapor distillate?
• Need to control temperature in the column?
Concept:
o control distillation column temperatures
by controlling the operating pressure.
o Condenser design / column opn. P
o Minimum desirable condenser
temperature is ~ 49 oC (120 oF).
o Construction of column more expensive
at higher pressures (i.e. > 14.8 bar [200
psig])
o Bottoms T too high (decomposition or Tc
approached)
• Running a partial condenser lowers the
column operating pressure (i.e. don’t have to
fully condense the distillate product
yD
D
y1 V1
LO
x0
xO
y1
1
x1
y2
2
x2
y3
3
x3
y4
7
McCabe Thiele: Partial Condenser
8
McCabe Thiele:
Reboilers
9
Effect of Different Reflux Ratios
• Before we saw that..
• increasing reflux resulted in an enrichment of vapor stream
in the “lighter” component
35
N [number equil. stages]
30
25
20
15
10
5
0
1
1.2
1.4
1.6
1.8
R/Rmin
10
Effect of Different Reflux Ratios
• Increase R --- cost effect??
\$30,000
Steam Costs [\$/yr; 1991]
\$180,000
\$25,000
\$160,000
\$140,000
\$20,000
\$120,000
\$100,000
\$15,000
\$ steam
\$80,000
\$ water
\$60,000
\$10,000
\$40,000
\$5,000
Cooling Water Costs [\$/yr; 1991]
\$200,000
\$20,000
\$0
\$0
1
1.2
1.4
R/Rmin
1.6
1.8
11
Effect of Different Reflux Ratios
Rmin  Ropt  R
R = factor * Rmin
1.05 
Ropt
Rmin
 1.50
12
Tie Together
• Found using McCabe-Thiele (knowing xD , xB , & feed condition):
o Nmin (at total reflux)
o Rmin (at infinite number of stages)
• If given actual R (or choose by R = factor * Rmin ) can find:
oN
o NF (optimum feed stage number)
Suggests there is a relation between N, Nmin, and Rmin.
13
Gilliland Correlation
61 Data points over ranges:
1.
2.
3.
4.
5.
6.
No. components: 2 to 11
q : 0.28 to 1.42
P : vacuum to 42.4 bar
 : 1.11 to 4.05
Rmin : 0.53 to 9.09
Nmin : 3.4 to 60.3
Molokanov Eqn:
 1  54.4 X  X  1 
Y  1  exp
 0.5 
 11 117.2 X  X 
14
Binary Shortcut Methods
McCabe-Thiele is good at showing procedure and helping explain concepts for
binary distillation. It can be extended to multiple feeds and side draws
(Wankat).
When consider multicomponent mixtures, McCabe-Thiele is not quite as
useful. However, having some shortcut methods to aid in final column
design is useful.
Minimum number of stages: Fenske Equation
N min
 xD 1  xB 
ln 

1

x
x
D
B 
 
ln 
- binary; total condenser;  ~ constant
   Dist  Bot or   Dist  Feed Bot 
1
3
15
Binary Shortcut Methods
Minimum reflux ratio: Underwood Equation
 DxD
D1  xD 
 Fz   F 1  z  
Lmin  F
F 

F
 1
- binary; assumes rectifying line intersects eq. line at feed line;  ~ constant
Rmin
Lmin

D
R = factor * Rmin
Approximate number of equilibrium stages (N): Gilliland correlation
16
Binary Shortcut Methods
Optimum feed stage location (NF): Kirkbride Equation
N R  1  z F   xB  B 



 
N S  z F  1  xD   D 


2
0.206
- binary; approximate result
17
Binary Shortcut Methods
18
Summary Binary Shortcut Methods (FUG)
Fenske Equation
N min
 xD 1  xB 
ln 

1

x
x
D
B 
 
ln 
   Dist  Bot or   Dist  Feed Bot 
Underwood Equation
Rmin
Lmin

D
Gilliland correlation (Nequil)
Kirkbride Equation (NF(opt))
1
3
 DxD
D1  xD 
 Fz   F 1  z  
Lmin  F
F 

F
 1
R = factor * Rmin
2

 1  z F   xB  B 
NR



 
N S  z F  1  xD   D 


0.206
19
Overview
• Questions on homework??
• McCabe-Thiele graphical technique (binary systems)
•Condensers
•Reboilers
• Binary Shortcut Methods
• AspenPlus:
o Shortcut methods: DSTWU