Reaction Engineering

CHE505: REACTION ENGINEERING II
1.1
Catalysts
1.2
Steps in Heterogeneous
Catalytic Reactions
1.3
Rate Limiting
Steps
1.4
Temperature Dependence
of Catalytic Reaction
Rates
1.5
Langmuir-
Hinshelwood
Kinetic
1.6
Designing
Catalytic
Reactors
1.7
Deactivation
of Catalyst

Reactor  Pellet  Catalyst pore  Catalyst particle
Length of Scales

CPE624: ADVANCED CHEMICAL REACTION ENGINEERING
A  B )

Steps in Heterogeneous Catalytic Reaction........
Adsorption
Surface reaction
Desorption

CAb = concentration of reactant
A in bulk fluid
CAs = concentration of reactant
A at external catalyst
surface
CAx = concentration of reactant
A within the pellet
Concentration Gradients in Catalytic Reactor

Reactant Ab in the bulk
of the flowing fluid must
migrate through a
boundary layer over the
pellet at the external
surface of the pellet.
It must then migrate
down pores within the
pellet to find surface
sites where it adsorbs
and reacts to form B,
STEPS INVOLVED ARE:
which then reverses the process to wind up in the flowing fluid,
where it is carried out of the reactor
r” = k”CAs

1. EXPLAIN EACH PROCESS
INVOLVE IN CATALYSIS
STEPS REACTIONS.
2. ILLUSTRATE EACH STEP IN
A CATALYTIC REACTION BY
DIAGRAMS

(and the concept of overall rate of reaction)
 Typically, rate limiting step is the rate of the slowest step in the
mechanism (slowest step among the 7 heterogeneous catalytic steps).
 This rate limiting step governs the overall rate of the reaction.
 Classification of steps
1. Mass Transfer/transport related steps (1,2,6 and 7)
2. Reaction Kinetic related steps (3,4 and 5)

(and the concept of overall rate of reaction (cont..))
 Then there are two cases:
– Mass Transfer /transport limitations
– Reaction Kinetic limitations
 If any of steps 3, 4 or 5 is slower than steps 1,2,6 and 7, transport
or mass transfer or diffusion steps do not affect the overall rate of
the reaction. The reaction is said to be under reaction kinetic
limitation or reaction kinetic regime/region, and free from mass
transfer/transport limitation.
 If any of steps 1,2,6 or 7 is slower
than steps 3, 4 and 5, reaction
kinetics does not affect the overall
rate of reaction. The reaction is
said to be under mass
transfer/transport limitation or
mass transfer/transport
regime/region, and free from
reaction kinetics limitation.

(and the concept of overall rate of reaction (cont..))
The structures and concentration profiles of reactant near and
in a catalyst particle might look as illustrated in Figure 7-9.
For the reactant to migrate into the particle, there must be a
concentration difference between the flowing bulk fluid CAb, the
concentration at the external surface CAs, and the concentration
within the pellet CA(x).
We write the
concentration within the
pellet as CA(x), indicating
that it is a function of
position x, which will be
different for different
geometries, as we will
consider later

How do we know whether the reaction rate is
reaction limited (reaction control) or external mass
transfer limited (external mass transfer control)??
First, let’s recall on mass transfer
coefficient…

Mass transfer correlations for gases....
If there is a concentration difference of A between two
locations 1 and 2, then
JA = kmA (CA1 – CA2)
JA is the mass transfer flux, [mol/s.m2]
km is the mass transfer coefficient, [mol/(s·m2)/(mol/m3), or m/s]
CA1-CA2, concentration difference [mol/m3].
)
( 2
1 A
A
A
mA
C
C
J
k



Mass transfer coefficient can be defined through the
Sherwood number:
l is length and DA is the diffusion coefficient of A
[convective mass transfer rate]
[diffusive mass transfer rate]
Shl =
A
mA
l
D
l
k
Sh 
l
D
Sh
k A
l
mA 
Then kmA can be defined:

Sherwood numbers for several geometries:
1. Flow over a flat plate
2. Flow over a sphere
3. Flow through a tube
4. Flow over a cylinder
5. Tube banks and packed spheres
6. Heat transfer

For flow over a flat plate of length L.......
 Flow is laminar if ReL < 105,
3
1
2
1
Re
66
.
0 Sc
Sh L
L 
 Flow is turbulent if ReL > 105,
3
1
8
.
0
Re
036
.
0 Sc
Sh L
L 

 The Reynolds number is
 Schmidt SC number
u is the velocity
v is the kinematic viscosity
DA the diffusivity of
species A, both of which
have units of length2/time.
 For gases, SC =1

2. Flow over a sphere
 Important geometry in catalyst spheres, liquid drops, gas
bubbles, and small solid particles
 The characteristic length is the sphere diameter D
 In the limit of slow flow over a sphere ShD = 2.0, and
this corresponds to diffusion to or from a sphere
surrounded by a stagnant fluid.
  4
.
0
3
2
2
1
Re
06
.
0
Re
4
.
0
0
.
2 Sc
Sh D
D
D 



3. Flow through a tube
 the characteristic length is the tube diameter D
 Flow is laminar if ReD < 2100,
 Flow is turbulent if ReD > 2100,
3
8

D
Sh
3
1
8
.
0
Re
023
.
0 Sc
Sh D
D 

4. Flow over a cylinder
 The transition from laminar to turbulence depends on
position around the cylinder
 Flow is laminar if ReD < 4,

For gasses, we usually
assume Schmidt
Number, Sc = 1

Is it reaction limited or mass transfer
limited??
To answer this question, we consider the simplest example:
a nonporous catalyst (where reactions occur only on the
external surface of the catalyst pellet)

The reaction occurs only on the external surface of a pellet -
only the external surface is reactive (e.g: non porous pellets)
ASSUMPTION AND CONSIDERATION.
Steady state assumption: there is no accumulation on the
surface:
[rate of transport to surface] = [rate of reaction at surface]
As
As
Ab
mA C
k
R
r
R
C
C
k
R "
4
"
4
)
(
4 2
2
2


 


For a first-order irreversible reaction on a single spherical pellet
of radius R, the total rate of reaction on the external surface of
the pellet is:

As
As
Ab
mA C
k
R
r
R
C
C
k
R "
4
"
4
)
(
4 2
2
2


 


Transport
The rate of reaction on the pellet with surface area is equal
to the rate of mass transfer from the bulk fluid to the surface
2
4 R

Ab
mA
As
mA
As
As
As
mA
Ab
mA
As
As
Ab
mA
As
As
Ab
mA
C
k
C
k
C
k
C
k
C
k
C
k
C
k
C
C
k
C
k
R
C
C
k
R








"
"
"
)
(
"
4
)
(
4 2
2

  
 














mA
Ab
As
mA
Ab
mA
As
Ab
mA
mA
As
k
k
C
C
k
k
C
k
C
C
k
k
k
C
"
1
"
"

Eliminate from the rate expression and solve for the rate to
yield
As
C
Ab
eff
mA
Ab
As
C
k
k
k
C
k
r
C
k
r
'
'
"
1
"
"
"
"












The reaction rate has an effective rate constant:










mA
eff
k
k
k
k
"
1
"
'
'

If k” << kmA, then..... 









mA
eff
k
k
k
k
"
1
"
'
'
LIMITING CASES:
 
  Ab
Ab
C
k
C
k
r "
0
1
"
" 


 Reaction limited
If kmA << k” then.....
Ab
mAC
k
r 
"
Mass transfer limited

As the temperature is varied in a reactor, we should
expect to see the rate-controlling step vary.

At sufficiently low temperature, reaction rate is small
and overall rate is reaction limited.
As temperature
increases, pore diffusion
becomes controlling and
at sufficiently high
temperature, external
mass transfer might
limit the process.

Irving Langmuir
1881 - 1957
Nobel Prize 1932
1915
Langmuir Isotherm
1927
Kinetics of Catalytic
Reactions
Cyril Norman
Hinshelwood
1897 - 1967
Nobel Prize 1956

7 Steps of Heterogeneous Catalysis

 Adsorption
 Surface Reaction
 Desorption
 Determining the rate limiting step (is the adsorption rate or
surface reaction rate or desorption rate the rate limiting
step?)
 Developing/Postulate the overall rate law for the
heterogeneous reaction (assuming the reaction is free from
external mass transfer and internal diffusion limitations)
 Comparing the postulated overall rate law to experimental
data

ADSORPTION

Adsorption is a physical or chemical phenomenon by
which the molecules present in a liquid or a gas attach to
the surface of a solid.
WHAT IS ADSORPTION????
Surface means both external and internal surface
The substance on which surface adsorption occurs is
termed as the adsorbent, and the substance which
adsorbed from the bulk phase is known as the adsorbate
Depending on the force of attraction, adsorption is
mainly two types: (1) Physical adsorption (Physisorption)
and (2) Chemical adsorption (Chemisorption).

The adsorption phenomenon comes from the existence of non-
compensated forces of a physical nature on the surface of the
solid.
WHY DOES SOLID SUBSTANCE ADSORB?
Adsorbate
Adsorbent
Adsorbate
All the bonding requirements of the
constituent atoms of the material
are filled by other atoms in the
material.
However, atoms on the surface of
the adsorbent are not wholly
surrounded by other adsorbent
atoms and therefore can attract
adsorbates.

H
H
Pt Pt Pt
H H
O
O
O O
Pt Pt Pt Pt Pt Pt Pt Pt Pt Pt
H
O
H
Adsorption theory

Physical adsorption is a phenomenon which takes place purely due
to the van der Waals forces of attraction.
PHYSICAL ADSORPTION (PHYSISORPTION)
It is a reversible phenomenon.
Because of very weak force of
attraction, the physical adsorption
cannot bring to any change of
chemical structure of the adsorbent
and adsorbate
It can be compared with the
condensation of vapour of
liquids onto the solid surface

Chemical adsorption is adsorption which results from chemical bond
formation (strong interaction) between the adsorbent and the
adsorbate in a monolayer on the surface.
CHEMICAL ADSORPTION (CHEMISORPTION)
Example: Organic compound get adsorbed on the solid surface
with chemical bond formation.
Chemical bond

ADSORPTION ISOTHERM
S = active site
A = atom; molecule; atomic combination
A.S = one unit of species A adsorbed on site S
Ct = total molar concentration of active sites
per unit mass of catalyst.
Cv = molar concentration of vacant sites
Pi = partial pressure of species, i in gas
phase (atm)
Ci.s = surface concentration of sites occupied
by species, i (g.mol/g.cat)

Adsorption of A on a site S is represented by:
Adsorption of A and B on a site S is represented by:
Site balance:
S
A
S
A 


S
B
S
A
v
t C
C
C
C 
 


A B

ADSORPTION ISOTHERM
Isotherms  the amount of gas adsorbed on a solid at
different pressures but at one temperature.
A model system was proposed then, the isotherm obtain
from the model is compared with the experimental data
shown on the curve.
If the curve predicted by the model agrees with the
experimental data, the model may reasonably described
what is occurring physically in the real system.

ADSORPTION MECHANISM
It depends on the surface.
The equation can be considered as an elementary
reaction in order to determine the rate law.
Rate of attachment – molecules adsorb on vacant site,
the rate is proportional to the concentration of vacant
site, Cv. rA  Cv
Rate of detachment – detachment of molecules from the
surface, the rate is proportional to the concentration of
sites occupied by molecules, Ci.s. rD  Ci.s

ADSORPTION ISOTHERM: 2 MODELS
Molecular or nondissociated adsorption (e.g., CO).
Dissociative adsorption (e.g., C and O).
S
CO
S
CO 


S
O
S
C
S
CO 



 2

ADSORPTION MECHANISM
Net rate of adsorption = rate of attachment to the
surface – rate of detachment from the surface
Assumption to obtain Langmuir Isotherm:
Surface of catalyst
Adsorption system.

EXAMPLE (NONDISSOCIATED ADSORPTION)
Consider the adsorption of carbon monoxide molecule:
S
CO
S
CO 


 The rate of attachment of carbon monoxide molecules to the
active site on the surface is proportional to the number of
collisions that these molecules make with a surface active site
per second.
 The collisions rate is proportional to the partial pressure, PCO.

 Carbon monoxide molecules adsorb only on vacant sites and
the rate of attachment is proportional to the concentration of
vacant sites, Cv.
 Thus, the rate of attachment to the surface is proportional to
the partial pressure and the concentration of vacant sites
S
CO
S
CO 



C
P
k CO
A

attachment
of
Rate

Rate of detachment - detachment of CO molecules from
the surface usually proportional to the concentration of
sites occupied by the adsorbed molecules (e.g., CCO.S).
Rate of adsorption is equal to the rate of molecular
attachment to the surface minus the rate of detachment
from the surface
S
CO
AC
k 


detachment
of
Rate
S
CO
A
CO
A
AD C
k
C
P
k
r 


 

Adsorption equilibrium constant
A
A
A k
k
K 
 /









 
A
S
CO
CO
A
AD
K
C
C
P
k
r 
kA  independent of temperature
k_A  increases exponentially with increasing temperature
KA  decreases exponentially with increasing temperature

Site balance:
S
CO
v
t C
C
C 


At equilibrium,
CO
v
A
S
CO P
C
K
C 

CO
A
t
CO
A
S
CO
P
K
C
P
K
C



1
Solve CCO.S in terms of constant and partial pressure. Thus,

EXAMPLE (DISSOCIATED ADSORPTION)
Consider the isotherm for carbon monoxide adsorbing as
atom.
Two adjacent vacant active site are required.
The rate of attachment is proportional to the product of
partial pressure of CO and square of the vacant site
concentration.
The rate of detachment is proportional to the product of
the occupied site concentration.
Rate of attachment = kAPCOCv
2
Rate of detachment = k-ACC.SCO.S

Thus, the net rate of adsorption:
S
C
S
O
A
v
CO
A
AD C
C
k
C
P
k
r 



 2
rAD = kA PCOCv
2
-
CO×SCC×S
KA
æ
è
ç
ö
ø
÷
Site balance:
S
O
S
C
v
t C
C
C
C 
 



At equilibrium,
Consider CC.S = CO.S. Solve CO.S in terms of constant and
partial pressure. Thus
S
O
S
C
A
v
CO
A C
C
k
C
P
k 



2
2
1
2
1
)
(
2
1
)
(
CO
A
t
CO
A
S
O
P
K
C
P
K
C




EXERCISE 1
Write a rate law and Langmuir isotherm based on the
adsorption reaction below:
a) I + S IS
b) W + S WS

SURFACE REACTION MODEL
The rate of adsorption of species A onto solid surface
S
A
S
A 











 
A
S
A
v
A
A
AD
K
C
C
P
k
r
The reactant that has been adsorbed onto the surface
will react in a number of ways
 Single site
 Dual site
 Eley-Rideal mechanism

SURFACE REACTION MODEL
SINGLE SITE
MECHANISM
DUAL SITE
MECHANISM
ELEY-RIDEAL
MECHANISM

SINGLE SITE MECHANISM
Surface reaction with single site mechanism
Only the site on which reactant is adsorbed is involved in
reaction
The reaction mechanism is elementary in each step, thus
the rate law:
S
A
S
A 











 

S
S
B
S
A
S
S
K
C
C
k
r
A B
S
B
S
A 



DUAL SITE MECHANISM
Surface reaction may be dual site mechanism
The adsorbed reactant interacts with another site
(occupied/unoccupied ) to form the product.
Adsorbed A react with an adjacent vacant site to yield a
vacant site and adsorbed product site.
S
S
B
S
S
A 













 

S
v
S
B
v
S
A
S
S
K
C
C
C
C
k
r
A B

Reaction between two adsorbed species
S
D
S
C
S
B
S
A 















 



S
S
D
S
C
S
B
S
A
S
S
K
C
C
C
C
k
r
A
B D
C
Reaction of two species adsorbed on different types of
sites S and S’
S
D
S
C
S
B
S
A 





 '
' 








 



S
S
D
S
C
S
B
S
A
S
S
K
C
C
C
C
k
r '
'
A
B D
C

ELEY-RIDEAL MECHANISM
The reaction between an adsorbed molecule and molecule
in the gas phase
)
(
)
( g
g D
S
C
B
S
A 













 

S
D
S
C
B
S
A
S
S
K
P
C
P
C
k
r
A C
B D

EXERCISE 2
Based on surface reaction below :
i) Sketch the reaction on the conceptual model
ii) Write down the rate law of surface reaction

DESORPTION
The products of the surface reaction adsorbed on the
surface are subsequently desorbed into the gas phase.
The rate of desorption:
S
C
S
C 











 
DC
v
C
S
C
D
DC
K
C
P
C
k
r
Desorption equilibrium constant is
reciprocal of adsorption
equilibrium constant.
KDC =
1
KC
 𝑟𝐷𝐶 = 𝑘𝐷 𝐶𝐶.𝑆 − 𝐾𝐶𝑃𝐶𝐶𝑉

The adsorption isotherm of A in the presence of
adsorbate B is:
EXAMPLE
CA×S =
KAPACt
1+ KAPA + KBPB
When the adsorptions of A and B are 1st order, the
desorption are also 1st order, and, both A and B are
adsorbed as molecules.

RATE LIMITING STEP
The rates of adsorption, surface reaction and desorption
series are equal to one another at steady state.
Rate limiting or rate controlling is one of the particular
step in the series.
In determining the step limiting in overall rate of
reaction, Langmuir-Hinshelwood approach was used.

RATE LIMITING STEP
 Assuming a sequence of steps in the reaction.
Langmuir-Hinshelwood approach
 Choose the mechanisms either as molecular or atomic
adsorption and single or dual site reaction
 By assuming all steps are reversible, rate laws are
written for the individual steps
 Rate limiting steps is postulated. Steps that are not
rate limiting are used to eliminate all coverage
dependent terms.

STEPS IN A LANGMUIR HINSHELWOOD KINETIC
MECHANISM
 Adsorption  Surface Reaction  Desorption
There is no accumulation of reacting species on the
surface, therefore the rates of each step in the sequence
are all equal.
D
S
AD
C r
r
r
r 


 '
Cv or Cc∙s in the rate law must be replaced with
measurable quantities.

STEPS IN A LANGMUIR HINSHELWOOD KINETIC
MECHANISM
 Adsorption Rate Limiting D
S
A k
k
k ,

 Surface Reaction Rate Limiting D
A
S k
k
k ,

 Desorption Rate Limiting S
A
D k
k
k ,


Question 3(a): Exam Q June 2012
EXERCISE
The catalytic reaction of was carried out in a differential
reactor. The reaction is controlling by the surface reaction
and is irreversible. The surface reaction is reacted through the
Eley-Rideal mechanism, and the rate expression is rs=ksCA∙SPB.
The adsorption and desorption step are reversible. Suggest
the reaction mechanism steps for the above reaction. Prove
that the overall rate law can be expressed as:
-rA
'
=
kPAPB
1+ KAPA + KCPC
(13 marks)

EXERCISE
t-Butyl alcohol (TBA) was produced by the liquid phase
hydration (W) of isobutene (I) over an Amberlyst-15 catalyst.
The system is normally a multiphase mixture of hydrocarbon,
water and solid catalyst. The reaction mechanism is:
Determine a rate law :
 If the surface reaction is rate limiting.
 If the adsorption of isobutene is limiting

ADDITION OF INERTS
Example: A → B (surface reaction rate limiting)
S
I
S
I
S
B
S
B
S
B
S
A
S
A
S
A












I
I
B
B
A
A
A
A
P
K
P
K
P
K
kP
r





1
'
If KIPI >> 1, KA &KB,
I
I
A
A
P
K
kP
r 
 '

ADDITION OF INERTS
The rate is reduced by species I. It shows that the inert
can strongly inhibit the reaction of A.
Inert blocks the sites on which A must adsorb to react
and lowers its coverage to a small value, therefore inhibit
the reaction

TEMPERATURE DEPENDENCE
Specific reaction rate, k will follow an Arrhenius
temperature dependence and increase exponentially
with temperature.
The adsorption of all species on the surface is exothermic.
The adsorption equilibrium constant, K, will decreases as
the temperature increases.





 

RT
E
k
k R
R
R exp
0

TEMPERATURE DEPENDENCE
Example: A → B (surface reaction limited)









RT
E
K
K
j
j
j exp
0
ER is the activation energy for surface reaction.
Ej is the heat of adsorption of species j.
B
B
A
A
A
A
P
K
P
K
kP
r




1
'
As the temperature increases, KA & KB decrease resulting
less coverage of the surface by A and B.

Question 2(b) April 2011
EXERCISE

Reaction Engineering

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