Transcript CBE_417 - South Dakota School of Mines and Technology

CBE 417
“Unit Operations”
Lecture: 5
12 Sep 2012
1
Overview
• Brief thermodynamics review
• Binary flash with energy balance
• Multicomponent flash
Separation Factor (eqn 1-4; Seader et.al.)
Ci(1)
SPij 
Ci( 2 )
C (j1)
C (j 2 )
Relative Volatility (eqn 2-21; Seader et.al.)
yi
 ij 
Ki
xi

K j yj
xj
2
Other Equilibrium Diagrams:
P = 1.013 bar
T = various oC
Benzene - Toluene
Y vs X diagram
T vs X or Temp vs Composition
3
Other Equilibrium Diagrams:
4
Y vs X
Diagram
(LLE)
5
Effect of Pressure:
6
Effect of Pressure:
•Seader & Henley (2006)
7
Other Equilibrium Diagrams:
8
Overview
• Brief thermodynamics review
• Binary Flash with energy balance
•Sequential solution
•Simultaneous solution
• Multicomponent Flash
9
Binary Flash
F V  L
Overall mole balance
mole balance on a
Z a F  yaV  xa L
mole balance on b
Z b F  ybV  xb L
equilibrium eqn for a
mole balance on a
ya
V
Za & F
L
y a P  xa P
sat
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
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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  4.707 bar
V frac ,  ??
Pbsat  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
V frac  V
F
L frac  L
F
 f
 1  V frac  q
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Binary Flash
Overall mole balance
ya
F V  L
mole balance on a
Z a F  yaV  xa L
mole balance on b
Z b F  ybV  xb L
equilibrium eqn for a
y a P  xa  P
Za & F
xa
L
sat
a a
xa a Pasat
mole balance on a Z a F 
V  xa L
P
Za
xa 
 a Pasat  V   L 
  
P F F
V
 by F & solve for xa
Zb
xb 
 b Pbsat  V   L 
  
P F F
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Flash separation:
x
i
Binary Flash
ya
1
V
Za
Zb
1

sat
 a Pa  V   L   b Pbsat  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
Find:
V frac , xa , ya
Za & F
xa
L
V frac ,  ??
Pasat  4.707 bar
Pbsat  1.888 bar
 a  f xa , xb , T 
 b  f xa , xb , T 
  a Pasat  V   L 
Z a  xa 
      0
 P  F   F 
ya P  xa a Pasat  0
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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”
14
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
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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 
h f  Z aCPa
L
T  Tref  xbCPbL T  Tref 
hL  xaCPa




V
T  Tref   yb b (Tref )  CPbV T  Tref 
HV  ya a (Tref )  CPa
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Other Equilibrium Diagrams:
17
Alternative Thermodynamics
y a  K a xa
Older (hand methods):
yb  K b xb
Raoult’s law
Relative Volatility (VLE):
 ab
Ka
y /x

 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
18
Separation Factor or Relative Volatility
Pa*
 ab  *
Pb
19
Effect of Pressure:
•Seader & Henley (2006)
20
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
21
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
22
Sizing Flash Drums
u perm  K drum
htotal
 3to 5
D
V
( mol )
V

 L  V
L
u perm Ac V
MwV
23
Simulators
Flash input:
Sensitivity Analysis:
Design Spec:
24
Questions?
25