Transcript CBE_417_H - South Dakota School of Mines and Technology

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
fˆiV  fˆi L
Vapor Liquid Equilibrium (VLE)
Typical simplifications:
Ideal vapor phase
Ideal liquid phase
ˆiV  1
i 1
3
Phase Equilibrium (Alternate Form VLE)
Historically, when estimates were done by hand:
yi  Ki xi
•Seader & Henley (2006)
4
Phase
Equilibrium
(Recommendations)
5
Phase Equilibrium (Alternate Form VLE)
Historically, when estimates were done by hand:
yi  Ki xi
Ki  Ki T , P, all xi 
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
aT 1 aT 2
aP 2 aP 3
ln K  2 
 aT 6  aP1 ln P  2 
T
T
P
P
with T [] o R & P [] psia
DePriester
(equation fit)
8
Other Equilibrium Diagrams:
P = 1.013 bar
T = various oC
Benzene - Toluene
9
Other Equilibrium Diagrams:
10
Effect of Pressure:
11
Effect of Pressure:
•Seader & Henley (2006)
12
Other Equilibrium Diagrams:
13
Overview
• Brief thermodynamics review
• Binary Flash with energy balance
•Sequential solution
•Simultaneous solution
• Multicomponent Flash
14
Binary Flash
F V  L
Overall mole balance
mole balance on a
Z a F  yaV  xa L
mole balance on b
Zb F  ybV  xb L
equilibrium eqn for a
mole balance on a
ya
V
Za & F
L
ya P  x P
sat
a a
xa Pasat
Za F 
V  xa L
P
Za
xa  sat
Pa  V   L 
  
P F F
xa
 by F & solve for xa
Zb
xb  sat
Pb  V   L 
  
P F F
15
Flash separation:
x
i
Binary Flash
ya
1
V
Za
Zb
1  sat
 sat
Pa  V   L  Pb  V   L 
  
  
P F F
P F F
Specify:
a = n-pentane
b = n-hexane
Z a  0.5
T  90 C
P  3 bar
T , Za & P
Za & F
xa
L
Find:
V frac , xa , ya
Pasat  4.707bar
V frac ,  ??
Pbsat  1.888bar
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
V frac  V
F
L frac  L
F
 f
 1  V frac  q
16
Binary Flash
Overall mole balance
F V  L
mole balance on a
Z a F  yaV  xa L
mole balance on b
Zb F  ybV  xb L
equilibrium eqn for a
ya P  x  P
V
Za & F
 P
sat
a a
P
Za
V   L 
  
F F
xb 
xa
L
sat
a a a
xa a Pasat
mole balance on a Z a F 
V  xa L
P
xa 
ya
 b Pbsat
P
 by F & solve for xa
Zb
V   L 
  
F F
17
Flash separation:
1
 a Pasat
P
Specify:
a = n-pentane
b = n-hexane
Z a  0.5
T  90 C
P  3 bar

x
i
Binary Flash
ya
1
V
Za

sat
 V   L   b Pb
  
P
F F
T , Za & P
Zb
V   L 
  
F F
Find:
Za & F
xa
L
V frac , xa , ya
V frac ,  ??
  a Pasat
Z a  xa 
 P
 V   L 
      0
 F   F 
Pasat  4.707bar
Pbsat  1.888bar
 a  f xa , xb , T 
 b  f xa , xb , T 
ya P  xa a Pasat  0
18
Binary Flash
ya
Graphical Solution:
V
mole balance on a
Za & F
L
F
y a   xa  Z a
V
V
solve for ya
V
 f
F
Z a F  yaV  xa L
or
L
q
F
xa
L
 (1  f ) 
1
ya   
xa    Z a

 f 
f
“Operating Line”
19
Binary Flash
Graphical:
1
ya
 (1  f ) 
1
ya   
xa    Z a

 f 
f
V
Za & F
Equilibrium curve
0.9
y=x
0.8
xa
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
20
Binary Flash Energy Balance
Q flash
T feed
ya
Pfeed
V
Tin
HV
P &T
Pin F , Z a
QH Z a & F
hf
xa
L
EB on CV:
hL
F h f  Q flash  V HV  L hL
L
TFeed  Tref  ZbCPbL TFeed  Tref 
hf  ZaCPa
L
T  Tref  xbCPbL T  Tref 
hL  xaCPa

 

V
T  Tref   yb b (Tref )  CPbV T  Tref 
HV  ya a (Tref )  CPa
21
Other Equilibrium Diagrams:
22
Alternative Thermodynamics
ya  K a xa
Older (hand methods):
yb  K b xb
Raoult’s law
Relative Volatility (VLE):
Ka
y /x
 ab 
 a a
Kb
yb / xb
Pa*
 *
Pb
 ab xa
ya 
1  xa  ab  1
Aside (couple with MB)
1  f  
f


Za 
Za
1 f 
  ab  1  xa 
0
ab  1 x   ab 
f
f 
f

2
a
23
Separation Factor or Relative Volatility
 ab
Pa*
 *
Pb
24
Effect of Pressure:
•Seader & Henley (2006)
25
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
26
Alternative Thermodynamics
Ki with multicomponent flash:
yi  Ki xi
Into MB:
x
i
1
Zi
xi 
V   L 
Ki     
F F






Zi
Zi
  
1 

V
L




K
f

1

f




K

 i






i
  F   F  
Sequential solution: suggestions p 35-37 (Rachford-Rice Eqn)
Simultaneous solution technique: suggestions p 40-43
27
Sizing Flash Drums
u perm  K drum
htotal
 3to 5
D
V
( mol )
V

 L  V
L
u perm Ac V
MwV
28
Simulators
Flash input:
Sensitivity Analysis:
Design Spec:
29
Questions?
30