# Plain PowerPoint ```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.
1
Lecture 2 – Tuesday 1/15/2013
 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
2
Review Lecture 1
Reactor Mole Balances Summary
The GMBE applied to the four major reactor types
(and the general reaction AB)
Reactor
Differential
Algebraic
Integral
NA
Batch
dN
dt
A
N A0
CSTR
PFR
V 
dF A
dV

t
 r AV
dN
 rA
NA
A
rAV
FA 0  FA
 rA
FA
V 

FA 0
FA
dF A
dr A

3
PBR
dF A

dW
FA
 rA
t
W 

FA 0
dF A
V
FA
rA
W
Review Lecture 1
CSTR – Example Problem
Given the following information, Find V
 0  10 dm
3
C A0
FA0   0C A0
Liquid phase

  0
FA   0C A
4
   0  10 dm
min
V ?
C A  0 . 1C A 0
FA  C A
3
min
Review Lecture 1
CSTR – Example Problem
(1) Mole Balance:
V 
FA0  FA
 rA

 0C A0   0C A
(2) Rate Law:
 r A  kC A
(3) Stoichiometry:
CA 
5
FA


FA
0
 rA

 0 C A 0  C A 
 rA
Review Lecture 1
CSTR – Example Problem
(4) Combine:
V 
 0 C A 0  C A 
kC A
(5) Evaluate:
C A  0 . 1C A 0

10 dm
V 
V 
6
3
C A 0  0 . 1C A 0 
min
0 . 23 min

900
2 .3
1
0 .1C 
 391 dm
A0
3

10 1  0 . 1
0 . 23 0 . 1
dm
3
Define conversion, X
Consider the generic reaction:
aAbB
 c C  d D
Chose limiting reactant A as basis of calculation:
A 
b
a
B

c
C
a
Define conversion, X
X 
moles A reacted
moles A fed
7
d
a
D
Batch
 Moles A   Moles A   Moles A 

 


remaining
initially
reacted

 
 

NA
dN
A
dN
A
dt
8

N A0
 0  N A 0 dX
  N A0
dX
dt
 r AV

N A0 X
Batch
dN A

dt
r AV
t 0
X 0
N A0
t t
X  X
Integrating,
X
t  N A0 
0
dX
 r AV
The necessary t to achieve conversion X.
9
CSTR
Consider the generic reaction:
aAbB
 c C  d D
Chose limiting reactant A as basis of calculation:
A 
b
a
B

c
C
a
Define conversion, X
X 
moles A reacted
moles A fed
10
d
a
D
CSTR
dN
dt
Well Mixed
11

0
FA 0  FA
V 
r
A
 rA
A
dV  rAV
CSTR
 Moles A 
 Moles A   Moles A 

  


 leaving 
 entering   reacted 
FA

FA0  FA 
V 
V 
12

FA 0 
FA0
r
A

FA0 X
dV  0
F A 0  F A 0 X 
 rA
FA0 X
 rA
CSTR volume necessary to achieve conversion X.
PFR
dF A
dV
 rA
FA  FA0  FA0 X
dF A  0  F A 0 X
dX
dV
13

 rA
FA0
PFR
V 0
X 0
V V
X  X
Integrating,
X
V 
FA0
r
0
dX
A
PFR volume necessary to achieve conversion X.
14
Reactor Mole Balances Summary
in terms of conversion, X
Reactor
Differential
Algebraic
Integral
X
X
Batch
N A0
dX
dt
  r AV
0
V 
CSTR
PFR
t  N A0 
FA 0
  rA
dV

 r AV
t
FA 0 X
 rA
X
dX
dX
V 

F A 0 dX
 rA
0
X
15
PBR

FA 0
dX
dW
X
  rA
W 

0
F A 0 dX
 r A
W
Levenspiel Plots
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
 rA
16
 g(X )
Levenspiel Plots
FA 0
 rA
X

17

CSTR
FA 0
Area = Volume of CSTR
rA
 FA0 
 X1
V  


r
A X

1
X1
18
PFR
19
Levenspiel Plots
20
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)
X
V 
1
r
0
 rA ( X 2 )
FA0
A
dX 
 1

4
1
FA0 



3

r
(
0
)

r
(
X
/
2
)

r
(
X
)
A
A
 A

x
1
 rA
1
 rA ( X 1 )
1
 rA ( 0 )
21
0
X1
X2
Other numerical methods are:
 Trapezoidal Rule (uses two
data points)
 Simpson’s Three-Eight’s
Rule (uses four data points)
Formula
Reactors in Series
Given: rA as a function of conversion, one can also
design any sequence of reactors in series by defining
X:
Xi 
total moles of A reacted up to point i
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  FA 0  FA 0 X i
22
Reactors in Series
23
Reactors in Series
Reactor 1:
F A1  F A 0  F A 0 X 1
V1 
F A 0  F A1
 r A1
FA 0
 rA
24

FA0  FA0  FA0 X 1 
 rA1
V1
X1
X

FA0 X 1
 r A1
Reactors in Series
Reactor 2:
X2
V2 
FA0
r
X1
dX
A
V2
FA0
 rA
X1
25
X2
X
Reactors in Series
Reactor 3:
F A 2  F A 3  rA 3V 3  0
 F A 0  F A 0 X 2    F A 0  F A 0 X 3   rA 3V 3
V3 
0
F A 0 X 3  X 2 
 rA 3
V3
FA 0
 rA
26
X1
X
X2
X3
Reactors in Series
27
Reactors in Series
Space time τ is the time necessary to process 1
reactor volume of fluid at entrance conditions.
 
28
V
0
KEEPING UP
 The tower of CRE, is it stable?
29
Reaction Engineering
Mole Balance
Rate Laws
These topics build upon one another.
30
Stoichiometry
Heat Effects
Isothermal Design
Stoichiometry
Rate Laws
Mole Balance
CRE Algorithm
31
Mole Balance
Rate Laws
Be careful not to cut corners on any of the
CRE building blocks while learning this material!
32
Heat Effects
Isothermal Design
Stoichiometry
Rate Laws
Mole Balance
33