### CBE_417

```CBE 417
“Unit Operations”
Lecture: 3
7 Sep 2012
1
Overview
• Introduction
• UO course overview
• Equilibrium Stage separations
• What are “Unit Operations”
• Brief thermodynamics review
• Binary flash with energy balance
• Multicomponent flash
2
V
L
fˆi  fˆi
Vapor Liquid Equilibrium (VLE)
Vapor phase: good; liquid phase: good for
HC or moderate – high pressures
(compressible liquid phase)
V
L
y i P ˆi  x i P ˆi
V
sat
sat
y i P ˆi  x i  i Pi  i P .C .
V
y i P ˆi  x i H i
Typical simplifications:
Ideal vapor phase
Ideal liquid phase
Typically used for liquid phase
fugacity calculations
Used for special cases (like gases
dissolving into liquid phase)
ˆi  1
y i P  x i  i Pi
i 1
y i P  x i Pi
V
sat
sat
Raoult’s Law
3
Phase Equilibrium (Alternate Form VLE)
Historically, when estimates were done by hand:
y i  K i xi
4
Phase
Equilibrium
(Recommendations)
5
Phase Equilibrium (Alternate Form VLE)
Historically, when estimates were done by hand:
y i  K i xi
K i  K i T , P , all x i 
Sometimes the K values are nearly composition independent
“hand” techniques of design/solution have used DePriester Charts
(hydrocarbons):
6
DePriester
Chart
P = 2 bar
T = 100 oC
Isobutane
others….
7
ln K 
aT 1
T
2

aT 2
T
 a T 6  a P 1 ln P 
aP2
P
2

aP3
DePriester
P
(equation fit)
with T [  ] R & P [  ] psia
o
8
V
L
fˆi  fˆi
Vapor Liquid Equilibrium (VLE)
V
L
y i P ˆi  x i P ˆi
V
sat
sat
y i P ˆi  x i  i Pi  i P .C .
V
y i P ˆi  x i H i
Vapor phase: good; liquid phase: good for
HC or moderate – high pressures
(compressible liquid phase)
Typically used for liquid phase
fugacity calculations
Used for special cases (like gases
dissolving into liquid phase)
Equations of state models
Activity coefficient models
9
Equations of State Models
10
Phase
Equilibrium
(Recommendations)
11
Activity Coefficient Models
12
Activity
Coefficient
Models
13
Activity
Coefficient
Models
14
Activity
Coefficient
Models
15
CBE 417
“Unit Operations”
Lecture: 4
10 Sep 2012
16
Overview
• Introduction
• UO course overview
• Equilibrium Stage separations
• What are “Unit Operations”
• Brief thermodynamics review
• Binary flash with energy balance
• Multicomponent flash
17
Activity Coefficient Models
18
Phase
Equilibrium
(Recommendations)
Mixtures to model:
•
•
•
•
•
•
•
•
MeOH – water
EtOH – water
propanol – water
n-butanol – water
n-butane – n-pentane
benzene – toluene
acetic acid – propionic acid
CO2 – toluene (high P)
19
Other Equilibrium Diagrams:
P – T diagram
20
PT Equilibrium Diagram:
http://www.dlr.de/vt/en/Portaldata/29/Resources/dokumente/CO2GasphaseDiagrams_Goos_Riedel_Zhao_Blum2010_GHGT_webnew.pdf
21
Other Equilibrium Diagrams:
P = 1.013 bar
T = various oC
Benzene - Toluene
Y vs X diagram
T vs X or Temp vs Composition
22
Other Equilibrium Diagrams:
23
Y vs X
Diagram
(LLE)
24
Effect of Pressure:
25
Effect of Pressure:
26
Other Equilibrium Diagrams:
27
Overview
• Brief thermodynamics review
• Binary Flash with energy balance
•Sequential solution
•Simultaneous solution
• Multicomponent Flash
28
Binary Flash
F V  L
Overall mole balance
mole balance on a
mole balance on b
equilibrium eqn for a
ya
V
Z a F  y aV  x a L
Za & F
Z b F  y bV  x b L
xa
L
ya P  xa P
sat
a
sat
mole balance on a
xa 
ZaF 
Za
sat
a
V   L 
  
P F  F 
P
x a Pa
P
 by F & solve for x a
V  xa L
xb 
Zb
sat
V   L 
  
P F  F 
Pb
29
x
Flash separation:
i
Binary Flash
ya
1
V
Za
1
sat
a
V   L 
  
P F  F 

P
Specify:
a = n-pentane
b = n-hexane
Z a  0 .5
T  90 C
sat
V   L 
  
P F  F 
Pb
Za & F
xa
L
Find: V frac , x a , y a
T ,Za & P
sat
 4 . 707 bar
V frac ,  ??
sat
 1 . 888 bar
Vfrac 0.471 V/F
P
3.000 bar
functi 1.89Eon
08
Xa
0.394
Xb
0.606
Ya
0.619
Yb
0.381
Pa
Pb
V frac  V
F
L frac  L
F

P  3 bar
Zb
 f
 1  V frac  q
30
Binary Flash
ya
F V  L
Overall mole balance
V
Z a F  y aV  x a L
mole balance on a
mole balance on b
Z b F  y bV  x b L
equilibrium eqn for a
y a P  xa a P
Za & F
xa
L
sat
a
x a  a Pa
sat
mole balance on a
xa 
ZaF 
Za
 aP
sat
a
P
V   L 
  
F  F 
P
 by F & solve for x a
V  xa L
xb 
Zb
 b Pb
sat
P
V   L 
  
F  F 
31
x
Flash separation:
1
i
Binary Flash
ya
1
V
Za
 aP
sat
a
P
Specify:
a = n-pentane
b = n-hexane
Z a  0 .5
T  90 C

P  3 bar
V   L 
  
F  F 

Zb
 b Pb
sat
P
T ,Za & P
sat
 4 . 707 bar
sat
 1 . 888 bar
Pa
Pb
V   L 
  
F  F 
Find: V frac , x a , y a
 a  f  x a , xb , T 
 b  f  x a , xb , T 
Za & F
xa
L
V frac ,  ??
  a Pasat  V   L  
Z a  xa 
      0
 P  F   F 
y a P  x a  a Pa
sat
0
32
Binary Flash
ya
Graphical Solution:
V
Z a F  y aV  x a L
mole balance on a
ya   xa
solve for ya
V
F
 f
or
L
F
q
L
V
 Za
Za & F
F
xa
V
L
 (1  f ) 
1
ya   
 xa    Z a
f


 f 
“Operating Line”
33
Binary Flash
Graphical:
1
ya
 (1  f ) 
1
ya   
 xa    Z a
f


 f 
V
Za & F
Equilibrium curve
0.9
xa
y=x
0.8
L
0.7
Solution!
Ya
0.6
0.5
0.4
What if f is unknown, but T
is known?
Za
0.3
0.2
0.1
0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Xa
1
Limits:
f =0
f =1
34
Binary Flash Energy Balance
Q flash
ya
T feed
V
P feed
T in
HV
P&T
QH
Pin F , Z a
Za & F
xa
hf
hL
L
EB on CV:
F h f  Q flash  V H V  L h L
h f  Z a C Pa T Feed  T ref   Z b C Pb T Feed  T ref
L
L
h L  x a C Pa T  T ref   x b C Pb T  T ref
L

L
H V  y a  a (T ref )  C Pa T  T ref
V

  y 
b

(T ref )  C Pb T  T ref
b
V

35
Other Equilibrium Diagrams:
36
Alternative Thermodynamics
Older (hand methods):
ya  K a xa
yb  K b xb
Relative Volatility (VLE):
ya 
 ab 
Ka

Kb
ya / xa
yb / xb

Raoult’s law
*
Pa
*
Pb
 ab x a
1  x a  ab  1 
Aside (couple with MB)
1  f 
f
 ab

1  f 
Za 
Za
 1 x   ab 
  ab  1
0
 xa 
f
f 
f

2
a
37
Separation Factor or Relative Volatility
*
 ab 
Pa
*
Pb
38
Effect of Pressure:
39
Constant Relative Volatility?
1
0.9
0.8
Y MeOH
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.2
0.4
0.6
0.8
1
X MeOH
40
Alternative Thermodynamics
Ki with multicomponent flash: y i  K i x i
xi 
Into MB:
x
i
1
1





Zi


 V   L 
Ki    
  F   F 



Zi
V   L 
Ki    
F  F 


Zi






K
f

1

f
 i

Sequential solution: suggestions p 35-37 (Rachford-Rice Eqn)
Simultaneous solution technique: suggestions p 40-43
41
Sizing Flash Drums
u perm  K drum
h total
 L  V
L
 3 to 5
D
V
V
( mol )

u perm Ac  V
Mw
V
42
Simulators
Flash input:
Sensitivity Analysis:
Design Spec:
43
Questions?
44
```