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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.
Lecture 2
1
Lecture 2
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
Chapter 2
Reactor Differential Algebraic Integral
The GMBE applied to the four major reactor types
(and the general reaction AB)
V FA 0 FA
rA
CSTR
Vrdt
dNA
A
0
A
A
N
N A
A
Vr
dNtBatch
NA
t
dFA
dV rA
A
A
F
F A
A
dr
dFV
0
PFR
FA
V
dFA
dW r A
A
A
F
F A
A
r
dFW
0
PBRFA
W3
Reactor Mole Balances Summary
Review Lecture 1
4
CSTR – Example Problem
000
0
3
0 mindm 10
AA
A
CF
C
AA
AA
CF
CC
0
3
0
1.0
mindm 10
0
FA 0CA
Liquid phase
V ?
Given the following information, Find V
Review Lecture 1
5
CSTR – Example Problem
(1) Mole Balance:
A
AA
A
AA
A
AA
r
CC
r
CC
r
FFV
000000
AA kCr
(2) Rate Law:
(3) Stoichiometry:
0AA
A
FFC
Review Lecture 1
6
CSTR – Example Problem
(4) Combine:
V 0 CA 0 CA
kCA
(5) Evaluate:
3
0
1
00
3
0
1.023.0
1.0110
1.0min23.0
1.0min
10
1.0
dmC
CCdm
V
CC
A
AA
AA
3 3913.2
900dmV
Review Lecture 1
Define conversion, X
7
D d C c B b A a
Consider the generic reaction:
D a
d C
a
c B
a
b A
Chose limiting reactant A as basis of calculation:
fedA moles
reactedA moles X
Define conversion, X
Chapter 2
Batch
8
Vrdt
dXN
dt
dN
dXNdN
XNNN
reacted
AMoles
initially
AMoles
remaining
AMoles
AAA
AA
AAA
0
0
00
0
Chapter 2
Batch
9
X
A
AVr
dXNt
0
0
Integrating,
The necessary t to achieve conversion X.
XXtt
Xt
0 0
0
A A
A
dN r V
dt N
Chapter 2
CSTR
10
D d C c B b A a
Consider the generic reaction:
D a
d C
a
c B
a
b A
Chose limiting reactant A as basis of calculation:
fedA moles
reactedA moles X
Define conversion, X
Chapter 2
CSTR
11
dNA
dt 0Steady State
VrdVr AA
Well Mixed
V FA 0 FA
rA
Chapter 2
CSTR
12 CSTR volume necessary to achieve conversion X.
V FA 0 FA 0 FA 0X
rA
A
A
r
XFV
0
XFFF
reacted
AMoles
entering
AMoles
leaving
AMoles
AAA 00
00 dVrFF AAA
Chapter 2
PFR
13
AA r
dV
dF
XFFF AAA 00
0A
A
F
r
dV
dX
XFdF AA 00Steady State
Chapter 2
PFR
14
XXVV
XV
0 0
PFR volume necessary to achieve conversion X.
dXr
FV
X
A
A
0
0
Integrating,
Chapter 2
Reactor Differential Algebraic Integral
V FA 0X
rA
CSTR
FA 0
dX
dV rA
X
A
A
r
dXFV
0
0PFR
Vrdt
dXN AA 0
0
0
X
A
AVr
dXNtBatch
X
t
FA 0
dX
dW r A
X
A
A
r
dXFW
0
0PBR
X
W15
Reactor Mole Balances Summaryin terms of conversion, X
Chapter 2
Levenspiel Plots
16
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:
)(0 Xgr
F
A
A
Chapter 2
Levenspiel Plots
17
FA 0
rA
X
Chapter 2
FA 0
rA
X 1
Area = Volume of CSTR
10
1
Xr
FV
XA
A
18
CSTR
Chapter 2
19
PFR
Chapter 2
20
Levenspiel Plots
Chapter 2
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
)2/(
4
)0(
1
30
0
0
XrXrrF
xdX
r
FV
AAA
A
X
A
A
21
Other numerical methods are:
Trapezoidal Rule (uses two
data points)
Simpson’s Three-Eight’s
Rule (uses four data points)
Five-Point Quadrature
Formula
)(
1
2XrA
)(
1
1XrA
)0(
1
Ar
Ar
1
0 1X 2X
Chapter 2
Given: rA as a function of conversion, one can also
design any sequence of reactors in series by defining
X:
reactorfirst tofedA of moles
ipoint toup reactedA of moles total Xi
Only valid if there are no side streams.
22
Reactors in Series
Molar Flow rate of species A at point i:
0 0Ai A A iF F F X
Chapter 2
23
Reactors in Series
Chapter 2
Reactor 1:
1001 XFFF AAA
1
10
1
1000
1
101
A
A
A
AAA
A
AA
r
XF
r
XFFF
r
FFV
24
V1
A
0A
r
F
X1X
Reactors in Series
Chapter 2
Reactor 2:
dXr
FV
X
X A
A
2
1
02
25
V2
A
A
r
F
0
X1X 2X
Reactors in Series
Chapter 2
0
0
33300200
3332
VrXFFXFF
VrFF
AAAAA
AAA
V3 FA 0 X3 X2
rA 3
26
V3
A
0A
r
F
X 3X1X 2X
Reactors in Series
Reactor 3:
27
Reactors in Series
Space time τ is the time necessary to process 1
reactor volume of fluid at entrance conditions.
V
0
28
Reactors in Series
Chapter 2
KEEPING UP
The tower of CRE, is it stable?
29
Chapter 2
Reaction Engineering
Mole Balance Rate Laws Stoichiometry
These topics build upon one another.
30
Algorithm
Mole Balance
Rate Laws
Stoichiometry
Isothermal Design
Heat Effects
31
CRE Algorithm
Algorithm
Mole Balance
32
Be careful not to cut corners on any of the
CRE building blocks while learning this material!
Rate Laws
Algorithm
Mole Balance
Rate Laws
Stoichiometry
Isothermal Design
Heat Effects
33
Otherwise, your Algorithm becomes unstable.
Algorithm
End of Lecture 2
34
