L3b-1 sy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urba Ideal CSTR Design Eq with X A : Review: Design Eq & Conversion BATCH SYSTEM: FLOW SYSTEM: Ideal Batch Reactor Design Eq with X A : Ideal SS PFR Design Eq with X A : Ideal SS PBR Design Eq with X A : n j ≡ stoichiometric coefficient; positive for products, negative for reactants D a d C a c B a b A fed A moles reacted A moles X A A 0 A j 0 j j X N N N n j A 0 A j j 0 T j T X N N N N n A 0 A j 0 j j X F F F n j A 0 A j j 0 T j T X F F F F n r X F V A A 0 A V r dt dX N A A 0 A A X 0 A A 0 A V r dX N t A A 0 A r dV dX F A X 0 A A 0 A r dX F V ' r dW dX F A A 0 A A X 0 A A 0 A ' r dX F W
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L3b-1
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
Ideal CSTR Design Eq
with XA:
Review: Design Eq & ConversionD
ad C
ac B
ab A
fed A moles reacted A moles XA
BATCHSYSTEM: A0Aj0jj XNNN
jA0A
jj0TjT XNNNN
FLOW SYSTEM: A0Aj0jj XFFF
jA0A
jj0TjT XFFFF
rXF
VA
A0A
Vr dt
dXN AA
0A Ideal Batch Reactor Design Eq with XA:
AX
0 A
A0A Vr
dXNt
AA
0A rdV
dXF Ideal SS PFR Design Eq with XA:
AX
0 A
A0A r
dXFV
'rdWdXF A
A0A Ideal SS PBR
Design Eq with XA:
AX
0 A
A0A 'r
dXFW
j≡ stoichiometric coefficient; positive for products, negative
for reactants
L3b-2
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
Review: Sizing CSTRsWe can determine the volume of the CSTR required to achieve a specific conversion if we know how the reaction rate rj depends on the conversion Xj
AA
0ACSTR
A
A0ACSTR X
rFV
rXFV
Ideal SS CSTR
design eq.
Volume is product of FA0/-rA and XA
• Plot FA0/-rA vs XA (Levenspiel plot)
• VCSTR is the rectangle with a base of XA,exit and a height of FA0/-rA at XA,exit
FA 0 rA
X
Area = Volume of CSTR
X1
V FA 0 rA
X1
X1
L3b-3
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
FA 0 rA
Area = Volume of PFR
V 0
X1FA 0 rA
dX
X1
Area = VPFR or Wcatalyst, PBR
dX'r
FW
1X
0 A
0A
Review: Sizing PFRs & PBRsWe can determine the volume (catalyst weight) of a PFR (PBR) required to achieve a specific Xj if we know how the reaction rate rj depends on Xj
Aexit,AX
0 A
0APFR
exit,AX
0 A
A0APFR dX
rF
V r
dXFV
Ideal PFR design eq.
• Plot FA0/-rA vs XA (Experimentally determined numerical values) • VPFR (WPBR) is the area under the curve FA0/-rA vs XA,exit
Aexit,AX
0 A
0APBR
exit,AX
0 A
A0APBR dX
rFW
rdXFW
Ideal PBR
design eq.
dXr
FV
1X
0 A
0A
L3b-4
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
Numerical Evaluation of Integrals (A.4)Simpson’s one-third rule (3-point):
2102X
0XfXf4Xf
3hdxxf
hXX 2
XXh 0102
Trapezoidal rule (2-point):
101X
0XfXf
2hdxxf
01 XXh
Simpson’s three-eights rule (4-point):
32103X
0XfXf3Xf3Xfh
83dxxf
3XXh 03
h2XX hXX 0201
Simpson’s five-point quadrature :
432104X
0XfXf4Xf2Xf4Xf
3hdxxf
4XXh 04
L3b-5
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
Review: Reactors in Series2 CSTRs 2 PFRs
CSTR→PFR
VCSTR1 VPFR2
VPFR2VCSTR1
VCSTR2
VPFR1
VPFR1
VCSTR2
VCSTR1 + VPFR2
≠ VPFR1 + CCSTR2
PFR→CSTR
A
A0r-
F
i j
CSTRPFRPFR VVV
If is monotonically
increasing then:
CSTRi j
CSTRPFR VVV
L3b-6
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
Chapter 2 Examples
L3b-7
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
Need to evaluate at 6 pts, but since there is no 6-pt rule, break it up
0
01 0
3
AA .
A,outCSTR AF XV Xr
Total volume for configuration 2: 58 dm3 + 173 dm3 = 231 dm3
X1=0.3FA0, X0 X2=0.8
Config 2
CSTR30. 583 0193 dmV
A0PFR2 A
A
0.8
0.3
FV dX
r
PFRV ... . 263 263 34217 34 3 3
8 33 2482193 694
0 08 57
0 30 5
3 point rule 4 point rule
3173 dm
PFR2CSTR1
0.A0 A0
PF0.3
R2 A AA
05
.
.
5
8
A0
F FV dX dX
r r
Must evaluate as many pts as possible when the curve isn’t flat
L3b-13
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
ACSTRA
AV XC
r
0
0
CSTRA
AA
V Cr X
00
For a given CA0, the space time needed to achieve 80% conversion in a CSTR is 5 h. Determine (if possible) the CSTR volume required to process 2 ft3/min and achieve 80% conversion for the same reaction using the same CA0. What is the space velocity (SV) for this system?
space time holding time mean residence h V time
0
5
=5 h 0=2 ft3/min
ftmin h hV min
3 60 52 3V ft 600
VSV
0 1Space velocity:
-1hSV . h
0 2
51 1
Notice that we did not need to solve the CSTR design equation to solve this problem.Also, this answer does not depend on the type of flow reactor used.
XA=0.8
ACSTR A
AFr XV
0 A
ACSTR
A
Cr
V X
0
0
00
V V
L3b-14
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
XA,exitPFR
AA
X AA,in
CV dXr
0
0
A product is produced by a nonisothermal, nonelementary, multiple-reaction mechanism. Assume the volumetric flow rate is constant & the same in both reactors. Data for this reaction is shown in the graph below. Use this graph to determine which of the 2 configurations that follow give the smaller total reactor volume.
FA0, X0X1=0.3
X2=0.7
Config 2
X1=0.3FA0, X0 X2=0.7
Config 1
ACSTR A,out A,in
AV X Xr
C 0
0
Shown on graph
XA,exitPFRn A
AA,in
AX
V dXFr
0
CSTRA
AA
V XrF
0
• Since 0 is the same in both reactors, we can use this graph to compare the 2 configurations
• PFR- volume is 0 multiplied by the area under the curve between XA,in & XA,out
• CSTR- volume is 0 multiplied by the product of CA0/-rA,outlet times (XA,out - XA,in)
L3b-15
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign.
A product is produced by a nonisothermal, nonelementary, multiple-reaction mechanism. Assume the volumetric flow rate is constant & the same in both reactors. Data for this reaction is shown in the graph below. Use this graph to determine which of the 2 configurations that follow give the smaller total reactor volume.
FA0, X0X1=0.3
X2=0.7
Config 2
X1=0.3FA0, X0 X2=0.7
Config 1
• PFR- V is 0 multiplied by the area under the curve between XA,in & XA,out
• CSTR- V is 0 multiplied by the product of CA0/-rA,outlet times (XA,out - XA,in)
Config 1 Config 2
Less shaded areaConfig 2 (PFRXA,out=0.3 first, and CSTRXA,out=0.7 second) has the smaller VTotal