Lecture 2
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.
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Lecture 2 – Tuesday 1/10/2011
 Review of Lecture 1
 Definition of Conversion, X
 Develop the Design Equations in Terms of X
 Size CSTRs and PFRs given –rA= f(X)
 Conversion for Reactors in Series
 Review the Fall of the Tower of CRE
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Reactor
Batch
Differential
3
Integral
t
dN A
 rAV
dt
NA

N A0
dN A
rAV
NA
t
FA 0  FA
V 
rA
CSTR
PFR
Algebraic
dFA
 
rA
dV
V
FA

FA 0
FA
dFA
drA
V
Homework Problem Solution
Given the following information, Find V
dm 3
0  10
min
CA 0
FA 0   0CA 0

Liquid phase
4
  0
FA   0CA
V ?


dm 3
   0  10
min
CA  0.1CA 0
FA  CA
(1) Mole Balance:
FA 0  FA 0CA 0  0CA 0 CA 0  CA 
V


rA
rA
rA
(2) Rate Law:
rA  kC A
(3) Stoichiometry:
CA 
5
FA


FA
0
(4) Combine:
V
 0 CA 0  CA 
kCA
(5) Evaluate:
CA  0.1CA 0
10dm3
CA 0  0.1CA 0  101  0.1

3
V  min

dm
1
0.23min

0.1CA 0  0.230.1
900
V
 391 dm3
2.3
6
Consider the generic reaction
a AbB
 c C  d D
ChooselimitingreactantA as basis of calculation
b
c
d
A B
 C  D
a
a
a
Define conversion, X
molesA reacted
X
molesA fed
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 Moles A   Moles A  Moles A
rem aining  initially   reacted 

 
 

NA
 N A0
 N A0 X
dNA  0  N A0 dX
dN A
dX
  N A0
 rAV
dt
dt
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dN A
rAV

d
N A0
t 0 X 0
t t X  X
Integrating
X
dX
t  N A0 
 rAV
0
The necessary t to achieve conversion X.
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Steady State
dNA
0
dt
Well Mixed
FA 0  FA
V 
rA

 r dV  r V
A
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
A
 Moles A
 Moles A   Moles A
leaving   entering  reacted 



 

FA

FA0
 FA0 X
FA0  FA   rA dV  0
V
FA 0  FA 0  FA 0 X 
FA0 X
V
 rA
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
rA
CSTR volume necessary to achieve conversion X.
dFA
 rA
dV
FA  FA0  FA0 X
Steady State
dFA  0  FA0 X
dX  rA

dV FA0
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V 0 X 0
V V X  X
Integrating
X
FA0
V 
dX
 rA
0
PFR volume necessary to achieve conversion X.
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Reactor
Differential
Algebraic
Integral
X
X
Batch
N A0
V
CSTR
PFR
dX
t  N A0 
 rAV
0
dX
  r AV
dt
dX
FA 0
 rA
dV 
t
FA 0 X
rA
X
V  FA0 
0
dX
 rA
X
PBR
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
dX
FA 0
 rA
dW
X
W  FA 0 
0
dX
 rA
W
Reactor Sizing
Given –rA as a function of conversion, -rA= f(X), one
can size any type of reactor. We do this by constructing
a Levenspiel plot. Here we plot either (FA0/-rA) or
(1/-rA) as a function of X. For (FA0/-rA) vs. X, the
volume of a CSTR and the volume of a PFR can be
represented as the shaded areas in the Levenspiel Plots
shown as:
FA0
 g( X )
 rA
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FA 0
rA
X


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FA 0
Area = Volume of CSTR
rA
 FA0 
 X 1
V  
  rA  X 1
X1
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Area = Volume of PFR
FA 0
rA
V
X1


18
X1
0
FA 0 

d X
rA 
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Numerical Evaluations of Integrals
 The integral to calculate the PFR volume can be evaluated using
method as Simpson’s One-Third Rule: (See Appendix A.4)
 1
FA0
x
4
1 
dX 
FA0 




r
3

r
(
0
)

r
(
X
/
2
)

r
(
X
)
A
A
A
A


0
X
V 
1
 rA ( X 2 )
1
 rA
1
 rA ( X 1 )
1
 rA (0)
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0
X1
X2
Other numerical methods are:
 Trapezoidal Rule (uses two data
points)
 Simpson’s Three-Eight’s Rule (uses
four data points)
 Five-Point Quadrature Formula
Given: rA as a function of conversion, one can also design any
sequence of reactors in series by defining X:
total moles of A reacted up to point i
Xi 
moles of A fed to first reactor
Only valid if there are no side streams.
Molar Flow rate of species A at point i:
FAi  FA0 X i
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Reactor 1:
FA1  FA0  FA0 X1
FA0  FA1 FA0  FA0  FA0 X 1  FA0 X 1
V1 


 rA1
 rA1
 rA1
FA 0
 rA
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V1
X1
X
Reactor 2:
X2
FA0
V2  
dX
 rA
X1
V2
FA0
 rA
X1
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X
X2
Reactor 3:
FA2  FA3  rA3V3  0
FA0  FA0 X 2   FA0  FA0 X 3   rA3V3  0
V3 
FA 0 X 3  X 2 
rA 3
V3
FA 0
 rA
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X1
X
X2
X3
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Space time τ is the time necessary to process 1 reactor volume
of fluid at entrance conditions.

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V
0
KEEPING UP
 The tower of CRE, is it stable?
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Reaction Engineering
Mole Balance
Rate Laws
These topics build upon one another.
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Stoichiometry
Heat Effects
Isothermal Design
Stoichiometry
Rate Laws
Mole Balance
CRE Algorithm
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Mole Balance
Rate Laws
Be careful not to cut corners on any of the
CRE building blocks while learning this material!
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Heat Effects
Isothermal Design
Stoichiometry
Rate Laws
Mole Balance
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Otherwise, your Algorithm becomes unstable.
End of Lecture 2
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