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Lecture 6
Chemical Reaction Engineering (CRE) is the field that studies the rates and mechanisms of chemical reactions and the design of the reactors in which they take place.
2
Lecture 6 – Tuesday 1/29/2013
Block 1:
Mole Balances
Block 2:
Rate Laws
Block 3:
Stoichiometry
Block 4:
Combine Review of Blocks 1, 2 and 3 Examples : Undergraduate Reactor Experiments CSTR PFR BR Gas Phase Reaction with Change in the Total Number of Moles
3 Review Lecture 2
Building Block 1:
in terms of conversion, X
Mole Balances
Reactor
Batch
Differential
N A
0
dX dt
r A V
Algebraic
t
Integral
N A
0
X
0
dX
r A V
X CSTR
V
F A
0
X
r A
PFR
F A
0
dX dV
r A
F A
0
dX dW V
F A
0 0
X dX
r A W
F A
0 0
X dX
r
A
X t W
4 Review Lecture 3
Building Block 2: Rate Laws
Power Law Model:
r A
kC
A C B
α
order in A 2
A
B
3
C β
order in B Overall Rection Order
α
β
A reactor follows an elementary rate law if the reaction orders just happens to agree with the stoichiometric coefficients for the reaction as written.
e.g. If the above reaction follows an elementary rate law
r A
k A C
2
A C B
2nd order in A, 1st order in B, overall third order
5 Review Lecture 4
Building Block 3: Stoichiometry
6 Review Lecture 5
Building Block 4: Combine
Review Lecture 5 Building Block 4: Combine 7
8
Today’s lecture
Example for Liquid Phase Undergraduate Laboratory Experiment (CH 2 CO) 2 O + H 2 O 2CH 3 COOH A + B 2C Entering Volumetric flow rate Acetic Anhydride Water Elementary with k’ v 0 = 0.0033 dm 7.8% (1M) 3 /s 92.2% (51.2M) 1.95x10
-4 dm 3 /(mol.s) Case I Case II CSTR PFR V = 1dm 3 V = 0.311 dm 3
9
Today’s lecture
Example for Gas Phase : PFR and Batch 2NOCl 2A 2NO + Cl 2 2B + C Calculation Pure NOCl fed with C NOCl,0 = 0.2 mol/dm 3 elementary rate law with k = 0.29 dm 3 /(mol.s) follows an Case I Case II PFR with v 0 = 10 dm3/s Find space time, 𝜏 with X = 0.9 Find reactor volume, V for X = 0.9
Batch constant volume Find the time, t, necessary to achieve 90% conversion. Compare 𝜏 and t.
10 Part 1: Mole Balances in terms of Conversion
Algorithm for Isothermal Reactor Design 1.
Mole Balances
and Design Equation 2.
3.
Rate Laws Stoichiometry 4.
5.
Combine Evaluate A. Graphically (Chapter 2 plots) B. Numerical (Quadrature Formulas Chapter 2 and appendices) C. Analytical (Integral Tables in Appendix) D. Software Packages (Appendix- Polymath)
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CSTR Laboratory Experiment Example: CH 3 CO 2 + H 2 0 2CH 3 OOH
C A
0 1
M C B
0 51 .
2
M
X ?
V
0 1
dm
3 3.3
10 3
dm
3
s
A + B 2C CSTR :
V
F A
0
r A X
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CSTR Laboratory Experiment 2) Rate Law:
r A
k A C A C B
3) Stoichiometry: A B F A0 F A0 Θ B C 0 -F A0 X -F A0 X 2F A0 X F A =F A0 (1-X) F B =F A0 (Θ B -X) F C =2F A0 X
13 CSTR Laboratory Experiment
C A
F A
F A
0 1 0
X
C A
0 1
X
C B
F A
0
B
0
X
C A
0
B
X
B
51 .
2 1 51 .
2
C B
C A
0 51 .
2
X
C A
0 51 .
2
C B
0
14 CSTR Laboratory Experiment
r A
' 0
C A
0 1
k X
kC A
0 1
X
V
C
0
A
0
kC A
0 1
X X
V
0 1
kX
X
V
0 1
kX
X
X
1
k
k X
3 .
03 4 .
03 0 .
75
15
PFR Laboratory Experiment A + B 2C 0 .
00324
dm
3
s
0.311
dm
3
1) Mole Balance:
dX dV
r A F A
0
X
?
2) Rate Law:
r A
kC A C B
3) Stoichiometry:
C A
C A
0 1
X
C B
C B
0
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PFR Laboratory Experiment 4) Combine:
r A
k
'
C B
0
C A
0 1
X
kC A
0 1
dX dV
kC A
0
C
1
A
0 0
X
X
1
dX
X
k
0
dV
ln 1 1
X X
1
e
k
k
kd
V
0 0 .
311
dm
0 .
00324
dm
3 3 sec 96 .
0 sec
k
0 .
01
s
1
X
0 .
61
17
Gas Flow PFR Example 0 2 NOCl 2 NO + Cl 2 2A 2B + C 10
dm
3
s T
T
0
P k
0 .
29
dm
3
mol
s
P
0
X
0.9
C A
0 0 .
2
mol L V
?
1) Mole Balance:
2) Rate Law:
dX dV
r A F A
0
r A
kC A
2
18`1
Gas Flow PFR Example 3) Stoichiometry: (Gas Flow) 4) Combine:
C A
0 1
X
C
A
0 1 1
X X
A
r A
B + ½C
kC A
2 1 0 1
X dX dV
C
2
kC A
0
A
0 0
X
2 1 1 2
X
X
2 2
X
0 1 1
X X
2 2
dX
V
0
kC A
0 0
dV
kC A
0 0
V
kC A
0
Gas Flow PFR Example
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kC A
0 2 1 1
X
2
X
1 1 2
X X
y A
0 1 2 1 2
kC A
0 17 .
02 17 .
02
kC A
0 294 sec
V
V
0 2940
L
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Constant Volume Batch Example Gas Phase 2A 2B + C t=?
1) Mole Balance:
2) Rate Law:
dX dt
r A V
0
N A
0
N A
0
r A V
0
r C A
0
A
r A
kC A
2 3) Stoichiometry: (Gas Flow)
V
V
0
C A
r A
N A
0 1
V
0
kC
2
A
0 1
X
X
C A
0 1 2
X
Constant Volume Batch Example
21
4) Combine:
dX dt
2
kC A
0 1
X
2
C A
0
kC A
0 1
X
2
dX
kC A
0 1
X
2
dt
1
dX X
2
kC A
0
dt
1 1
X
kC A
0
t t
155 sec
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Heat Effects Isothermal Design Stoichiometry Rate Laws Mole Balance
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