Dr. G. N. Rameshaiah,
Ph. D. (IITM)
Professor
Department of Chemical Engineering
E-mail: gnrameshaiah@rediffmail.com
Mobile: +09180 8277126901
Phone: +91 080 26622130-35, Extn.6027
1
• Period of time: 39 hr
• Text Book:
• Chemical Reaction Engineering 3rd
edition by Octave Levenspiel (English)
• Chemical Engineering Kinetics 3rd
edition by J. M. Smith (English)
2
3
• References:
1. Elements of Chemical Reaction
Engineering 4th edition by H. Scott Fogler
(English)
2. Chemical and Catalytic Reaction Engineering
by James J. Carberry (English)
3. Reactor Analysis and Design 2nd edition by
G.F.Froment & K.B.Bischoff (English)
4
Chapter 1 Overview of Chemical
Reaction Engineering
• 1.1 The importance of chemical reaction
5
6
• 1.2 Classification of Reaction
7
• 1.3 Variables Affecting the Rate of
Reaction
• In homogeneous systems, Temperature,
Pressure and Composition
• In heterogeneous systems, besides T, P &C,
mass & heat transfer some times play
important roles.
8
• 1.4 Definition of Reaction Rate
• If the rate of change in number of moles of
component i due to reaction is dNi/dt, the
rate of reaction is defined as follows:
Based on unit volum e of reacting fluid :
1 dN i
mole i formed
ri 

volume of fluid time
V dt
Based on unit mass of solid in fluid - solid system
1 dN i
mole i formed
ri 

mass of solid time
W dt
9
Based on unit interfacia l surface in two - liquid system
or based on unit surface of solid in gas - solid systems :
1 dN i mole i formed
ri

surface time
S dt
Based on unit volum e of solid in gas - solid systems :
1 dN i
mole i formed
ri

volume of solid time
Vs dt
Based on unit volum e of reactor, in diferent from the
rate based on unit volum e of fluid,
1 dN i
mole i formed
ri

volume of reactor time
Vr dt
10
• Relationship in-between these definitions:
 volume 
 mass

 surface 

ri  
ri  
ri
 of fluid 
 of solid 
 of solid 
 volume 
 volume of 

ri 
ri
 of solid 
 reactor 
or Vri  Wri  Sri VS ri Vr ri
11
• 1.5 Speed of Chemical Reaction
• 1 sec to 3yr----With such a large ratio, of
course the design of reactors will be quite
different in these cases.
12
13
14
15
16
17
18
19
Chapter 2 Kinetics of
Homogeneous Reaction
• Simple Reactor types
20
• The Rate Equation
• Suppose a single-phase reaction
aA  bB  rR  sS
• The most useful measure of reaction rate for
reactant A is then
21
• The rates of reaction of all materials are
related by:
 rA  rB rR rS

 
a
b
r
s
• Experience shows that the rate of reaction is
influenced by the composition and the
energy of the material.
• Energy means temperature, light intensity,
magnetic field intensity etc. Ordinarily we
only need to consider the temperature.
22
• 2.1 Concentration-dependent term of rate
equation
• Single and Multiple Reaction
• When a single stoichiometric equation and
single rate equation are chosen to represent
the progress of the reaction, we have a
single reaction.
A  B or A  B  R  S
23
• When more than one stoichiometric
equation is chosen to represent the observed
changes, then more than one kinetic
expression is needed to follow the changing
composition of all the reaction components,
and we have multiple reactions.
24
25
• Elementary and Non-elementary Reactions
ABR
• If we postulate that the rate-controlling
mechanism involves the collision or
interaction of a single molecule of A with a
single molecule of B, then the number of
collisions of molecules A with B is
proportional to the rate of reaction.
26
• But at given temperature the number of
collisions is proportional to the
concentration of reactants in the mixture;
hence the rate of disappearance of A is
given by:
 rA  kCACB
• Such reaction in which the rate equation
corresponds to a stoichiometric equation are
called elementary reaction.
27
• When there is no direct correspondence
between stoichiometry and rate, then we
have non-elementary reaction.
• A very famous example of non-elementary
reaction is that between hydrogen and
bromine.
H 2  Br2  2 HBr
k1 H 2 Br2 
rHBr 
k2  HBr /Br2 
1/ 2
28
• Molecularity and Order of Reaction
• Molecularity of an elementary reaction is
the number of molecules involved in the
reaction, and this has been found to have the
values of one, two, or occasionally three.
• Note that the molecularity refers only to an
elementary reaction.
29
 rA  kCAaCBb ......CDd
a  b  .......  d  n
• Where a, b,......d are not necessarily related
to the stoichiometric coefficients. We call
the powers to which the concentrations are
raised the order of the reaction.
• Above reaction is
• a th order with respect to A
• b th order with respect to B
• nth order overall
30
Order of Reaction
31
• Rate constant k
• In a rate expression  rA  kCAaCBb ......CDd
• the dimensions of rate constant k for nthorder reaction are
time concendration 
1
1 n
• For a first order reaction, it becomes
time
1
32
• Representation of an elementary reaction
• Any measure equivalent to concentration
can be used to express a rate, for example:
 rA  kPAa PBb ......PDd
• Whatever measure we use leaves the order
unchanged; but it will affect the rate
constant k .
33
• Elementary reactions are often represented
by an equation showing both the
molecularity and the rate constant.
k
• A reaction 2 A 
2 R represents a
bimolecular irreversible reaction with
second-order rate constant k1, implying that
the rate of reaction is
1
 rA  rR  k1C A2
But : A  R implying :  rA  rR  k1C A
k1
34
Consider a reaction : B  2 D  3T
-rB  k B C B C
2
D
-rD  k D C B C
rT  k T C B C
2
D
2
D
1
1
From the stoichiome try : -rB  - rD  rT
2
3
1
1
k B  k D  kT
2
3
35
• Equation A+2B=3T does not tell us which k
values we are referring.
• There is an ambiguity here.
• So to eliminate any possible confusion,
write the stoichiometric equation followed
by the complete rate expression, and gives
the units of the rate constant.
36
• Representation of a Non-elementary
Reaction
N 2  3 H 2  2 NH 3


N 2 H 2  2
NH 3 
rNH  k1
 k2
2
3
NH 3 
H 2  2
3
3
• This nonmatch shows that we must try to
develop a multistep reaction model to
explain the kinetics.
37
• Kinetic models for Non-elementary
Reaction
• Free radicals
• Transition Complexes
• Molecular intermediants
• We have learnt from the
Physical Chemistry
The kinetic equations of all non-elementary
reactions are determined by experiments.
38
• 2.2 Temperature Dependent Term of a rate
equation
• From the collision and transition state
E
theories : k  k T m e RT , 0  m  1
0
• Because the exponential term is so much
more temperature-sensitive than preexponential term, the variation of the latter
with temperature is effectively masked, and
E
we have in effect
RT
k  k0 e
39
• Activation Energy and Temperature Dependency
• 1. From Arrhenius’ law, a plot of ln k vs 1/T gives
a straight line, with large slop for large E and
small slop for small E.
• 2. Reaction with high activation energies are very
temperature-sensitive.
• 3. Any given reaction is much more temperaturesensitive at a low temperature.
• 4 From the Arrhenius’ law, the value of the
frequency factor k0 does not affect the temperature
sensitivity.
40
41
42
43
• 2.3 Searching for a Mechanism
The more we know about what is
occurring during reaction, what the reacting
materials are, and how they react, the more
assurance we have for proper design. This is
the incentive to find out as much as we can
about the factors influencing a reaction within
the limitation of time and effort set by the
economic optimization of the process．
44
There are three areas of investigation of a
reaction, the stoichiometry, the kinetics, and
the mechanism. In general,
the stoichiometry is studied first, and when
this is far enough along,
the kinetics is then investigated.
With empirical rate expressions available, the
mechanism is then looked into.
In any investigative program considerable
feedback of information occurs from area to
area.
45
• Although we cannot delve into the many
aspects of this problem, a number of clues
that are often used in such experimentation
can be mentioned．
• Some simple examples are ignored.
• Consider two alternative paths for a simple
reversible reaction. If one of these paths is
preferred for the forward reaction， the
same path must also be preferred for the
reverse reaction. This is called the principle
of microscopic reversibility.
46
•Consider, for example, the forward reaction of
2 NH 3  N 2  3 H 2
•At a first sight this could very well be an
elementary bimolecular reaction with two molecules
of ammonia combining to yield directly the four
product molecules. From this principle, however, the
reverse reaction would then also have to be an
elementary reaction involving the direct combination
of three molecules of hydrogen with one of nitrogen.
Because such a process is rejected as improbable，
the bimolecular forward mechanism must also be
rejected．
47
For parallel mechanism
the reaction rate
dependents on the
temperature sensitive
one.
For series mechanism
the reaction rate
dependents on the
temperature insensitive
one.
48
• 2.4 Predictability of Reaction Rate From
Theory
• We can never tell beforehand whether the
predicted rate will be in the order of
magnitude of experiment or will be off by a
factor of 106. therefore, for engineering
design, this kind of information should not
be relied on and experimentally found rates
should be used in all cases.
49
Chapter 3 Interpretation of
Batch Reactor Data
• A rate equation characterizes the rate of
reaction, and its form may either be
suggested by theoretical consideration or
simply be the result of an empirical curvefitting procedure. In any case, the value of
the constants of the equation can only be
found by experiment; predictive methods
are inadequate at present.
50
• In this chapter, we may learn how to make a
rate equation by batch reactor data.
• The determination of the rate equation is
usually a two-step procedure; first the
concentration dependency is found at fixed
temperature and then the temperature
dependency of the rate constants is found,
yielding the complete rate equation.
51
• 3.1 Constant-volume Batch Reactor
• Actually means constant-density reaction
system--most liquid-phase reaction and gasphase reaction occurring in a constantvolume bomb.
52
Analysis of Total Pressure Data Obtained in a Constantvolume System
Here, x occurs at first time, it means the degree of reaction.
53
54
55
• The Conversion
• Suppose that NA0is the initial amount of A
in the reactor at time t=0, and that NA is the
amount present at time t. Then the
conversion of A in the constant volume
system is given by
N A0  N A
NA V
CA
XA 
 1
 1
N A0
N A0 V
C A0
dC A
dX A  
C A0
56
• Integral Method of Analysis Data
The Integral method of analysis always puts a
particular rate equation to the test by integrating
and comparing the predicted C versus t curve with
the experimental C versus t data. If the fit is
unsatisfactory, another rate equation is guessed and
tested．It should be noted that the integral method
is especially useful for fsimple reaction types
corresponding to elementary reactions．
itting
57
58
59
60
61
62
What’s happen when M=1?
• For the second order reaction with equal
initial concentrations of A and B, or for the
reaction
63
64
65
66
Empirical Rate Equations of nth Order
• When the mechanism of reaction is not
known, we often attempt to fit the data with
an nth-order rate equation of the form
dC A
 rA  
 kCAn
dt
• which on separation and integration yields
C1An  C1Aon  n  1kt
n 1
67
• Here, we have presented the procedure of
how to use the integral method. Reaction of
other orders may be done similarly.
68
69
70
71
72
73
74
75
76
• Irreversible Reaction in Parallel
A  R
k1
A  S
k2
dC A
 rA  
 k1C A  k2C A  k1  k2 C A
dt
dCR
rR 
 k1C A
dt
dCS
rS 
 k 2C A
dt
77
• To find the k values, the three differential
equations should be used.
• First one is simple:
CA
 ln
C A0
 k1  k2 t
• Divide the second one by third one and
integrate:
rR dCR k1


rS dCS k2
CR - CR0 k1

CS - CS0 k2
• Combining k1+k2 and k1/k2, we can get both
k1 and k2.
78
• Typical concentration-time curves shown
below:
79
80
• Homogeneous Catalyzed Reaction
A  R
k1
A  C  R  C
k2
 dC A 

  k1C A
 dt 1
 dC A 

  k2C ACC
 dt  2
The reaction would
proceed even without a
catalyst present and the
rate of the catalyzed
reaction is directly
proportional to the
catalyst concentration.
dC A

 k1C A  k2C ACC  k1  k2CC C A
dt
81
• On integration, noting that the catalyst
concentration remains unchanged.
CA
 ln
  ln 1  X A   k1  k2CC  t  kobservedt
C A0
82
• Autocatalytic Reaction
A R  R R
dC A
 rA  
 kCACR
dt
The total number of moles of A and R
remain unchanged as A is consumed
C0  C A  CR  C A0  CR 0  constant
CR  C0  C A
dC A
 rA  
 kCA C0  C A 
dt
83
dC A
1  dC A
dC A 
  kdt

  

C A C0  C A 
C0  C A C0  C A 
C A0 C0  C A 
CR CR 0
ln
 ln
 C0 kt  C A0  CR0 kt
C A C0  C A0 
C A C A0
84
85
• Irreversible Reaction in series
k1
k2
A 
R 
S
dC A
 rA  
 k1C A
dt
dC R
rR 
 k1C A  k 2C R
dt
dCS
rS 
 k 2C R
dt
With the initial conditions : C A  C A0 , C R 0  0 and CS 0  0
dC A
CA
Integrate
 k1C A we get  ln
 k1t or C A  C A0 e -k1t
dt
C A0
86
• Substitute CA into:
dC R
rR 
 k1C A  k 2C R
dt
dC R
 k 2C R  k1C A0 e  k1t
I .C.
dt
 k1 
C A0 e  k2t  e  k1t
C R  
 k1  k 2 

t  0 , CR 0  0

No straight line available
Noting that there is no change in total number of moles :
C A0  C A  C R  CS
87
dC R
 k 2C R  k1C A0 e  k1t
I .C.
dt
dC R
dC R
  k 2C R
 k 2 dt
dt
CR
t  0 , CR 0  0
ln C R  k 2t  C
C R  C t e  k2t
dC R
dC t   k 2t
 C t  k 2 e  k2t 
e
dt
dt
dC t   k2t
 k 2t
C t  k 2 e 
e  k 2C t e  k 2t  k1C A0 e  k1t
dt
k1C A0 k2  k1 t
dC t 
 k 2  k1 t
 k1C A0 e
C t  
e
C
dt
k 2  k1
 k1C A0 k2  k1 t
  k 2t
C R  
e
 C e
I .C. t  0 , C R 0  0
 k 2  k1

 k1C A0 k2  k1 t k1C A0   k2t
k1C A0
e
C
C R  
e

k 2  k1
k 2  k1 
 k 2  k1
CR 

k1C A0  k2t
e  e  k1t
k1  k 2

88
Cs  C A0  C A0 e
 k1t
 k1 
 k1t
 k 2t



C A0 e  e

 k1  k 2 




 k1   k1t
 k1t
 k 2t

 e  e
Cs  C A0 1  e  

k

k
1
2






 k1  k 2  k1t  k1   k1t

 k 2t

 e  e
Cs  C A0 1 
e  

k

k
k

k
1
2
 1 2





1
 k1t
 k 2t 

Cs  C A0 1 
k2e  k1e
 k1  k 2



89
When k 2  k1

C S  C A0 1  e
It is similar to
C A0  C A  C A0  C A0 e
 k1t

 k1t

 C A0 1  e
 k1t
first order irreversib le reaction 

It means that the rate is determined by
the first step.
If the product is R, almost all the reactant
become to by - product.
90
When k1  k 2

C S  C A0 1  e
 k 2t

The speed is governed by k 2 , the lower step.
For any number of reaction in series it is the
lowest step that has the greatest influence on
the overall reaction rate.
Anyhow,no matter how large k1 is , as long as
the time long enough, R will finally convert to S.
91
92
The maximum C R :
  k1 

 k 2t
 k1t
C A0 e  e 
d  

k

k
dC R
 1 2



0
dt
dt
We get :

 k2 
ln  
k1 
1

t max C R 

klog mean k 2  k1

 k1 
C R max  C A0  
 k2 
k2
k 2  k1
93
  k1 

 k 2t
 k1t
C A0 e  e 
d  
dC R
 k1  k 2 

 0

dt
dt

k2
 k  k t
 e 2 1 opt
k1
ln

k2
 k 2  k1 topt
k1
 k1 
C A0 e  k 2t  e  k1t
substitute to C R  
 k1  k 2 

 k 2 e  k 2t  k1e  k1t  0
k2
ln
k1
topt 
k 2  k1

k
k
ln 2
ln 2 

k1
k1 


k

k
2
1
 k1 


k1
 k 2t opt
 k1t opt
k 2  k1
k 2  k1






C R max  
C
e

e

C
e

e
A0
A0




 k1  k 2 
 k1  k 2  





94
e
k
k
 2 ln 2
k 2  k1 k1


k
  2 
k

k
 k 2  2 1 
e
ln  
 k1 
 k2 
  
 k1 

k 
  2 
 k 2  k1 


k 
k 

  2 
  1  
 k1    k 2  k 2  k1   k 2  k2  k1  
C A0   
C R max  
  

=1
 k1  k 2    k1 
 k1 





k 
k
k 
  2  
  1  2  
 k1   k 2  k2  k1    k 2  k2  k1 k 2  k1  
C A0  
C R max  
1   

 k1  k 2   k1 
  k1 



 k1   k 2    k 2 
1    C A0  
C R max  


 k1  k 2   k1    k1 
 k1 
C R max  C A0  
 k2 
 k2 


k

k
 2 1

k 
  2 
 k 2  k1 
=1
95
• For a longer chain of reactions, say
A  R ST  U
96
• First-Order Reversible Reaction


A  R K C  K  equilibriu m constant
k2
k1
Starting with a concentration ratio M  CR 0 /C A0
the rate equation is
dC A dCR
dX A

 C A0
 k1C A  k2CR
dt
dt
dt
 k1 C A0  C A0 X A   k2 CR 0  C A0 X A 
 k1 C A0  C A0 X A   k2 MC A0  C A0 X A 
97
dC A
At equilibriu m
0
dt
k1 C A0  C A0 X A   k2 MC A0  C A0 X A   0
k1 MC A0  C A0 X Ae M  X Ae


 KC
k2
C A0  C A0 X Ae
1  X Ae
1  X Ae
k2  k1
Substitute to
M  X Ae
dX A
 k1 1  X A   k2 M  X A 
dt
dX A k1 M  1
 X Ae  X A 

dt
M  X Ae
98
• Remember the value of KC comes from
thermodynamics, with high accuracy.
• The definition of KC is KC=CRe/CAe , depend
on the stoichiometric equation, no matter
what reaction order it is. Therefor, when the
reaction is in equilibrium, there must
dC
dC
A
A
be
 0 , but when we find
 0 from
dt
dt
kinetics, i.e., from reaction rate expression,
the result is not reliable.
99
• With conversions measured in terms of XAe,
this may be looked as a pseudo first-order
irreversible reaction which on integration
gives

XA
0
t k M  1
dX A
 1
dt
0 M  X
X Ae  X A
Ae

 C A  C Ae 
XA 
M 1
 

 ln  1 
k1t   ln 
X Ae  M  X Ae

 C A0  C Ae 
100
101
• Comparing first order reversible and
irreversible reactions, we can find the the
irreversible reaction is only a special case of
reversible one when CAe=0 or XAe=1 or
KC=∞.
Another special case is CR0  0,
M 0
M 1
1
k1
X Ae

and

M  X Ae X Ae
k2 1  X Ae
k1
X Ae 
k1  k2
 C A  C Ae 

k1  k2 t   ln 
 C A0  C Ae 
102
103
For orders other than
one or two,integration
of the rate equation
becomes cumbersome.
The search for an
adequate rate equation
is best done by the
differential method.
104
• Reaction of Shifting Order
AR
dC A
k1C A
with  rA  

dt
1  k 2C A
At high CA , The reaction is zero order with rate constant k1/k 2
At low CA , The reaction is first order with rate constant k1
105
106
m
A
m
A
k1C
k1C
 rA 
or  rA 
n
n
1  k 2C A
1  k2C A 
Might be treated with similar procedure.
107
• Differential Method of Analysis of Data
The differential method of analysis deals
directly with the differential rate equation to
be tested, evaluating all terms in the equation
including the derivative dCi/dt, and testing
the goodness of fit of the equation with
experiment.
108
Just like
integral
method
109
110
111
112
113
0.25
0.24
Could you figure out the slopes point by point?
0.23
0.22
0.21
CA
0.20
0.19
0.18
0.17
0.16
0.15
0
1
2
3
4
5
6
7
8
t
114
•3.2 Varying-Volume Batch Reactor
•A capillary tube with a movable bead
•Using for micro-processing field
•Following the movement of bead with time is
much simpler than following concentration
change.
115
A 
VX A 1  VX A 0
VX A 0
Expansion factor -
V0
V0  initial volume of the
reactor
V  the volume at time t
V-V0
dV
V  V0 1  ε A X A  X A 
dX A 
V0 ε A
V0 ε A
For example :
A  4R
4 1
starting with pure reactant A :  A 
3
1
52
starting with 50% inert :  A 
 1.5
2
116
Therefore,  A accounts for both the reaction
stoichiometry and the presence of inert.
At any cases : N A  N A0 1-X A  C A  C A0 1-X A 
Varing Volume :
N A0 1-X A 
NA
1-X A
CA 

 C A0
V
V0 1  ε A X A 
1 εA X A
CA
1-X A

C A0 1  ε A X A
1 - C A C A0
XA 
1   A C A C A0
117
dN A
 rA  
N A  N A0 1  X A  dN A   N A0 dX A
Vdt
V  V0 1  ε A X A 
In term of conversion  X  :
N A0 dX A
C A0
dX A
 rA 

V0 1  ε A X A dt 1  ε A X A  dt
In term of volumeV  :
N A0 dX A
N A0 dV
 rA 

V0 1  ε A X A dt
V V0 ε A dt
C A0 dV C A0 d ln V 
 f C A 
 rA 

Vε A dt
εA
dt






V

V
1

ε
X

0
A
A 


V-V0
XA 

V
ε


0 A


dV
 dX A 



V
ε
0 A


118
The reaction rate means the change of amount
of reactant A ( N A ) with time in unit volum e,
dN A
definition 
 rA  
Vdt
but the value of reaction rate is determined by
the concentrat ion of reactant A (C A ).
 rA  f C A 
may be kC  determinat ion 
n
A
If we have some methods to make the concentrat ion
of reactant A go up (for example, distillati on,
membrane separation ) when it is reacted, we can keep
the reaction rate unchanged or even accelerate d .
119
Differential method of
Replaced with
Analysis
 C A0 dV 

log 10 
 Vε A dt 
The procedure is same
as constant-volume
situation except that
we replace
dC A
n
kCA  
 rA with
dt
C A0 dV
C A0 d ln V 
or
Vε A dt
εA
dt
120
• Integral Method of Analysis
• Only a few of the simpler rate forms integrate to
give manageable V vs. t expressions.
• Zero-Order Reactions
dN A
d  N A  in varying
 rA  
k
note : rA   

Vdt
dt  V  volume
For constant volume
N A is variable
For varying volume both N A and V are variables
C A0 d ln V 
 rA 
k
N A has been replaced by V .
εA
dt
121
Integratin g gives :
t  0,V  V0 
C A0 V
ln
 kt
ε A V0
122
• First-Order Reactions
C A  C A0 1  X A 
dN A C A0 dV
 rA  

 kCA
Vdt Vε A dt
1-X A
For C A  C A0
1 εA X A
C A0 dV
1 X A
so
 kCA0
Vε A dt
1 εA X A
Replacing X A by V  V0 1  ε A X A 
dV
 k V0 A  V  V0 
t  0,V  V0
dt

V 
  kt and ΔV  V-V0
Integrating gives :  ln 1 
 V0 A 
123
124
• Second-Order Reaction
• For a bimolecular-type second-order
reaction
2 A  products or
A  B  products with C A0  C B 0
The rate is given by
C A0 dV
2
2  1 X A 

 rA 
 kCA  kCA0 
V A dt
1  A X A 
2
125
• Treating it by the same way as first-order
reaction: replacing XA by V and integrating
gives 1   V

V 
  kCA0t
  A ln 1 
V0 A  V
 V0 A 
A
126
C A0 dV
2  1 X A 

 kCA0 
 AV dt
1  A X A 
2
Replace X A with V
C A0 dV
2  V0 A  V  V0  V0 A  

V  V0 1   A X A 
 kCA0 
 AV dt
V V0


kCA0
VdV
dt 
For left side :
2
A
V0 1   A   V 
2
 V0 1   A   V0 1   A   V dV
VdV

2
V0 1   A   V 
V0 1   A   V 2

V0 1   A  
1

dV integrate :

dt  

2 
A
 V0 1   A   V V0 1   A   V  
V0 1   A 
kCA0
 ln V0 1   A   V  

t C
t  0,V  V0
V0 1   A   V
A
kCA0
 ln V0 A  
1  A
A
C
127
ln V0 1   A   V  
V0 1   A 
kC
1  A
 A0 t  ln V0 A  
V0 1   A   V
A
A
 V 1   A   V 
V0 1   A 
1   A kCA0
 
ln  0


t
V0 A
A
A

 V0 1   A   V
 V0 1   A   V 

V 
  ln 1 
 V  V  V0 
First item : ln 
V0 A


 V0 A 
V0 1   A 
V 1   A   V  V
V
Second item :
 0
 1
V0 1   A   V
V0 1   A   V
V0 1   A   V
Therd item :
1  A
A
 1
1
A

V 
V
1 kCA0
 
Put togather : ln 1 


t
A
 V0 A  V0 1   A   V  A

V   AV  V0 1   A   V  kCA0
 
ln 1 

t
 A V0 1   A   V 
A
 V0 A 

V  V 1   A 
 
 A ln 1 
 kCA0t
 V0 A  V0 A  V
128
• For all rate forms (varying volume) other
than zero-, first-, and second-order the
integral method is not valid.
• 3.3 Temperature and reaction rate
129
130
131
132
Summery of Chapter 3
• This chapter is about how to make rate
equation from batch reactor data.
• The two methods can be employed, integral
and differential.
• Computer is a useful tool.
133
Chapter 4
Introduction to Reactor Design
• The aim of reactor design is to determine
the size and type and method of operation
for a given job.
• Equipment in which homogeneous reaction
are effected can be one of three general
types: the batch, the steady-state flow, and
the unsteady-state flow or semibatch reactor.
134
135
• The starting point for all design is the
material balance
136
• Where the composition within the reactor is
uniform, the accounting may be made over
the whole reactor.
• Where the composition is not uniform, it
must be made over a differential element of
volume and then integrated across the
whole reactor for the appropriate flow and
concentration condition.
137
• In non-isothermal operations energy
balances must be used in conjunction with
material balances.
138
Symbols
139
• Relationship between CA and XA
There are two related measures of the extent
of reaction, CA and XA.
• However, the relationship between CA and
XA is often not obvious but depends on a
number of factors.
• This leads to three special cases.
140
For the reaction aA  bB  rR, with i nert iI
141
142
143
144
145
146
Chapter 5
Ideal Reactor for a Single Reaction
• Three ideal reactors: Batch Reactor Plug
Flow Reactor Mixed Reactor
• In this chapter we develop the performance
equation for a single fluid reacting in the
three ideal reactors
147
• Batch reactor
• The reactants are initially
charged into a container,are
well mixed, and left to react
for a certain period. This is
an unsteady-state operation
where composition changes
with time, but at any instant
the composition throughout
the reactor is uniform.
Batch reactor
148
• Plug Flow Reactor
• The flow of fluid through the reactor is
orderly with no element of fluid overtaking
or mixing. There must be no mixing or
diffusion along the flow path. The necessary
and sufficient condition for plug flow is for
the residence time in the reactor to be the
same for all elements of fluid.
PFR
149
• Mixed Reactor
• In this reactor the
contents are well
stirred and uniform
throughout. The exit
stream from this
reactor has the same
composition as the
fluid within the reactor.
CSTR
150
• 5.1 Ideal Batch Reactor
• Make a material balance for any component
A:
151
dX A
 rA V  N A0
dt
t  N A0 
XA
0
dX A
 rA V
This equation may be simplified for a number of situation
Constant Density  A  0  :
Compare with :
t  C A0 
XA
0
C A dC
dX A
A
 
C A0  r
 rA
A
dN A
 rA  
Vdt
For all reactions in which t he volume changes propotionally
with conversion,
XA
XA
dX A
dX A
t  N A0 
 C A0 
0
0
 rA V0 1   A X A 
 rA 1   A X A 
152
153
• Space-Time and Space-Velocity
• Just as the reaction time t is the natural
performance measure for a batch reactor, so
are the space-time and space-velocity the
proper performance measures of flow
reactor.
• Space-time:
 time required to process one 

1 
    reactor volume of feed measured   time 
s 

at
specified
condition


154
•Space-velocity:
 number of reactor volume of 

1 
s    feed at specified condition which   time 1
 

can
be
treated
in
unit
time




Thus, a space-velocity of 5hr-1 means that five
reactor volumes of feed at specified condition
are being fed into the reactor per hour. A
space-time of 2 min means that every 2 min
one reactor volume of feed at specified
conditions is being treated by reactor.
155
 moles A entering 

volume of reactor 
1 C A0V  volume of feed 
 

s
FA0
 moles A entering 


time


V
reactor volume
 
v0 volumetric feed rate
Note above is under actual feed condition
For  and s, the relation between actual and standard
condition is given by
1 C A0V
C A0 1 C A0
  


s
FA0
C A0 s C A0
156
• 5.2 Steady-state mixed flow reactor
• Select reactant A for consideration
157
At steady-state,the
volume of reactor
doesn’t change.
158
159
160
161
• For a first-order reaction
XA
C A0  C A
k 

1 XA
CA
• For varied density
V  V0 1   A X A 
X A 1   A X A 
k 
1 XA
For  A  0
CA
1 XA

CA0 1   A X A
For any  A
• For second-order constant density -rA=kCA2
C A0  C A
k 
C A2
-1  1  4 kC A0
or C A 
2kτ
162
• when  A  0 what is the real stay time
(holding time) t?
• Because CSTR reactor is operated in outlet
condition, the stay time can be got by the
reactor volume divided by outlet volumetric
flow rate.
V
V

t


vout v0 1   A X A  1   A X A 
• But this is occasionally happened, for most
CSTR operated with liquid.
163
164
165
166
• Using component A leads the same result
V C A0  C A
 
v
 rA
1
6   0.2
2
v
 2liter / min 
1.4  1.1
• So 1[liter/min] for each feed stream
167
•5.3 Steady-state plug flow reactor
In a plug flow reactor the
composition of the fluid
varies from point to point
along a flow path,
consequently, the balance
for a reaction component
must be made for a
differential element of volume dV.
168
169
• Integrate for whole reactor
X A dX
dV
A

0 FA0 0  rA
V
Thus
or
X Af dX
V

A


0
FA0 C A0
 rA
X Af dX
V VC A0
A
 
 C A0 
0
v0
FA0
 rA
X Af dX
V
A
M ore general :

X Ai  r
FA0
A
or
for any ε A
dX A
  C A0 
X Ai  r
A
X Af
170
Constant Density ε A  0 
CA
X A  1
C A0
dC A
and dX A  
C A0
X Af dX
V

1 C Af dC A
A




0
FA0 C A0
 rA
C A0 C A 0  rA
X Af dX
C Af dC
V
A
A
   C A0 
 
0
CA0  r
v0
 rA
A
171
172
173
• Comparing the batch expressions with plug
flow expressions we find:
1. For systemsof constant density, the performance
equations are identical,  for plug flow is equivalent
to t for the batch reactor, and the equations can be
used interchang eably.
2. For systemsof changing density there is no direct
correspondence between the batch and the plug flow
equations and the correct equation must be used for
each particular situation. In this case the performance
equations cannot be used interchang eably.
174
175
176
• Holding time and space time for flow
reactor
Holding time :
XA
dX A
 mean residence time  C A0 
For PFR
0


 rA 1   A X A 
t   of flowing material  
XA


C A0
For CSTR
in the reactor


 rA 1   A X A 
time 
Space time :
 time needed to 

 V C A0V
   treat one reactor   

FA0
 volume of feed  v0


dX A
For PFR
0
 rA 
time 
XA
C A0
For CSTR
 rA
C A0 
XA
when ε A  0 τ  t
177
Holding time :
For CSTR, the reaction
V

t

v0 1   A X A  1   A X A  volume changes suddenlly
t  C A0 
XA
0
dX A
 rA 1   A X A 
For PFR, the reaction
volume changes gradually
when ε A  0 τ  t
178
Popcorn
Popper
179
180
Summery of Chapter 5
• Three kinds of ideal reactor and their
performance equation
• Space time and holding time
181
http://websites.umich.edu/~essen/html/byconc
ept/lectures/frames.htm
182