Catalytic Reaction Engineering (CRE)

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Catalytic conversion process
Catalytic Reaction Engineering (CRE)
Kinetics Catalytic reactions
selection and design
Minimum cost of
overall process
• Examples reactor systems
Reactants
• Description ideal reactors
Reactor
Energy
• batch, CSTR and plug flow
• Catalytic kinetics
?
Process
requirements
• Effects of catalyst properties
• mass and heat transfer
• Labscale reactors - performance testing
• purpose
• criteria
Ammonia oxidation
2NH3 + 2O2  NO + 3H2O
•Maximum selectivity
•maximum conversion
•ease of scale-up
•high throughput
•low pressure drop
•…….
Desired products
Undesired products
Unconverted reactants
•Intrinsically safe
•WRAP
•…….
Environment
& Safety
Pt-Rh gauzes – various structures
‘Bispin’
Ammonia oxidation reactors
Economics
Installation
wire-mesh gauze
Pd – gauze (Pt entrapment)
‘Warp knitted’
Fixed bed reactors
Aromatization – Amoco Ultrafining
Hexane Benzene + 3H2
Spherical reactor
Fixed bed
Pressure drop
Endothermal
Hydrotreating
adiabatic
Methanol synthesis Isothermal reactor
(Linde type)
FTS – Multi-tubular reactor
G
L
•
•
•
•
•
•
Maximum weight = 900 tonnes
Diameter = 6 m
Height = 20 m
8000 tubes
Reactor productivity = 300 tonnes
MD/day
Cooling by steam generation: water
evaporation
Reactors in series
adiabatic
Fischer-Tropsch synthesis I - Secunda
nCO + 2nH2  -(CH2)n- + nH2O
Sasol Slurry Phase Distillate
(waxes)
Bubble column slurry reactor
•
•
•
•
Fine catalyst particles ~ 50m
2500 bbl/day production
Diameter 5m, height 22 m
Cooling by steam generation:
water evaporation
Steam reforming -
Catalytic cracking
CH4 + H2O  3 H2 + CO
CO + H2O  H2 + CO2
Heavy feedstock  Lighter
Products (gasoline) + coke
Catalyst deactivation
~50 m particles
Batch – CSTR reactor
Batch – CSTR reactors
2200 l
stirrer motor
Hand holes for
reactor charging
Liquid
Gas-liquid
Gas-liquid-solid
cooling/heating
tube/jacket
agitators
100 l
Cryo-reactor
Fermentation - biocatalysis
Bioreactors – waste water teatment
Beer brewing
Aerobic reactors
Catalytic process
Slow stirring
Research
facility
Diesel - Johnson Matthey CRT
Environmental – Automotive TWC
gases
Monolith wall
Pre-oxizider
porous
support
NO +O2  NO2
Wall-flow monolith
NO2 + C  CO2 + NO
Exhaust
gas inlet
active
component
Low pressure drop
NO, CO, HC removal
Pt-Rh/Al2O3 catalyst
Solids, gases
Separator
Bifunctional catalysis
Gas distributor
Exhaust
gas outlet
Microreactors
Excellent heat removal
Higher selectivities
CVD reactors - semiconductors
Multiwafer reactors
Selective oxidation
Hot-wall
Cold-wall
Home appliances
Reaction coupling – SMART reactor
ABB
Ethylbenzene dehydrogenation H 118 kJ/mol
Tefal Azura
Matsumoto et al., 1993
US 5266543
Elimination heat exchanger,
hot piping & steam superheater
Higher conversion per pass (80%)
Lower energy consumption
G
packed bed
Reactor supermarket
methanol
(Krishna)
G
Catalytic reactors
L
methanol,
i-butene,
n-butene
membrane reactor
fluid bed
MTBE
catalytic distillation
reactor
Riser
circulating
fluid bed
G
multitubular
trickle
bed
slurry
reactor
L
bunker
G
L reactor
Cat
G
Cat
cyclone
G
Cat
stirred tank
• What to choose?
• How to design?
Ideal reactor types
Catalytic Reaction Engineering (CRE)
Discontinuous
Continuous
• Examples reactor systems
• Description ideal reactors
• batch, cstr and plug flow
• Effects of catalyst properties
• mass and heat transfer
Continuous stirred
tank reactor (CSTR)
• Labscale reactors
• purpose
• criteria
c
T
• Tutorials – application/illustration
Plug flow reactor
(PFR)
Batch reactor
c(z)
T(z)
c(t)
T(t)
• Biocatalytic reactor engineering
How to describe these?
Gas/Liquid/Solid
Fixed
Trickle-bed
Bed
Monolith
The Chemical Engineer’s tool
Reactors
Slurry
Mechanically
agitated
Bubble
column
Input
2 kg/s
3 mol A /s
Steady state
Production ?
Output
??
??
Accumulation ?
Input - Output + Production = Accumulation
units: mol/s
Steady state = 0
Rate definitions - units
Water-tap: Liquid volume in bucket
In chemistry usually: mol A / m3 s
unsteady state
or transient
steady state
m3reactor ,m3catalyst ???
m3reactor
 mol / s 
 m 3 reactor 


rW
kg catalyst
 mol / s 
 kg catalyst 


rVp
m3particle
 mol / s 
 m3 particle 


rV
t=0
Vliquid  tap  t
Vliquid  Vbucket
per
In mass balance
Rate definitions - units
RV ,A   A  rV
(CSTR)
Molar balance
In - Out + Production = Accumulation
V  rV  Vp  rVp  W  rw
 mol / s 
 m3 particle 


Continuous (flow) stirred tank reactor
Isothermal
In mass balance unit: mol A / s
 mol / s 
 m 3 reactor 


 mol A 
 s 


 mol / s 
 kg catalyst 


FA0
FA0  FA  RW  W  0
Introduce X = conversion FA  FA0 (1  X A )
FA 0  X A
 RW
W
rW,W
cA0
cA
rate expression
stoichiometric coefficient
+ products
- reactants
FA
W
X
 A
FA0
RW
‘space time’
Design equation CSTR
Continuous (flow) stirred tank reactor
Graphical interpretation
(CSTR)
Relationship between CA0 and CA??
W
X
 A
FA0
RW
W
X
 A
FA0
RW
FA0
FA
‘space time’
A
A= -1
rW,W
Area
CSTR operates here
1
rW
Order of reaction?
2 CSTRs in series??
Batch reactor type
cA 
c A0
1  kw 1 0
space
time
Isothermal
Molar balance
In - Out + Production = Accumulation
d V  c A 
dc

V  A
dt
W  c A0
FA0
Plug flow reactor (PFR)
In - Out + Production = Accumulation
dN A
0  0  RW ,A  W 
dt
kw 1 0
1  kw 1 0
0 
cA
zero order?
negative order?
XA
XA 
cA0
n>0
Molar balance
.......
rW  k1  cA  k1  cA0  1  X A 
CSTR
W  1
 XA


 FA0  rW
1st order reaction
FA  FA  dFA   RW ,A  dW  0
dt
dW
FA0
rW
FA
dc A W  RW ,A

dt
V
FA+dFA
FA  FA 0 (1  X )
dFA  FA 0 dX
rW,W,V
c A  c A0 (1  X A )
dX A
1 W
RW ,A

dt
c A0 V
B 
W
t
V
dX A
FA0
 RW ,A
dW
‘batch
space-time’
XA
cA
0
X
dX A
 RW ,A
d W FA0 
A
1 W
1
t 
dX
c A0 V
R
W ,A
0
Design equation Batch reactor
cA0
‘space time’
W
X
A
W
1

dX
FA0
RW ,A
0
(integral)
Reactor characteristics: CSTR versus PFR
Reactor design equations
W 


 FA0 
Area=
B 
Batch
r,V,W
PFR
CSTR
XA
W
dX
t  c A 0 
V
R
W ,A
0
similarity !
A
dX
W  c A0
 c A 0 
R
FA0
W ,A
0
1
rW
1
rW
PFR
CSTR
X
FA0
r(X,z)
FA0
0 
Plug flow
FA
FA
Which one is most efficient???
simplicity
Similar conditions:
• W/F PFR < CSTR
positive orders
• W/F PFR > CSTR
negative orders
• CSTR operates at lowest reactant concentrations
• PFR at maximum local concentrations
RW ,A   A  rW
FA0  V  c A0
Series reaction - Profiles
most efficient: PFR or CSTR??
A
kw1
2s-1
Q
Series reaction - max. yields
Maximum yields
kw2
1.0
P
1s-1
1.00
Plug flow/Batch
CSTR
0.80
n<0
n>0
X
W  c A0
0 
 c A 0 A
RW ,A
FA0
CSTR
r,W
XA
XA
YQ,max
0.8
0.6
Ci
P
0.60
0.4
0.40
CSTR
PFR
 k

YQ,max   w 2  1
k
 w1

2
kw 2
 k  kw 1  kw 2
YQ,max   w 2 
 kw 1 
Q
0.2
0.20
A
0.00
0.00
0.50
1.00
0 / kgcat
1.50
2.00
m-3 s-1
Max. yield PFR>CSTR
(n>0)
0.0
10-6
10-5
10-4
10-3
10-2
10-1
k2/k1
kw2
/kw1
100
101
102
103
Tutorial 1
A second order reaction A  R has been studied in a Berty-reactor,
a CSTR suited for the investigation of solid catalysed reactions. The
following data are available:
V=1l
W = 3 g catalyst
cA0 = 2.0 mol/l
cA = 0.5 mol/l
v = 1 l h-1
Tutorial 2 - Batch conversion sucrose
At room temperature sucrose can be hydrolysed by the enzyme
sucrase:
sucrose  products
Starting with an initial sucrose concentration of 1.0 mmol/l and an
enzyme concentration of 0.01 mmol/l the following data have been
obtained in a batch reactor. Concentrations have been determined by
using polarized light.
1.0
a. Determine the value of the rate constant and give its dimension
b. How much catalyst is needed to obtain 80% conversion in a packed
bed reactor at a volume flow rate of 1000 l/h and an inlet
concentration cA0 = 1 mol/l ?
0.8
Verify that the data can be represented
well by a kinetic expression of the
Michaelis-Menten type:
0.6
0.4
r 
k cs cE 0
M  cs
0.2
0.0
Determine the parameters k and M
0
2
4
6
t
8
10
12
Ideal reactor types
Catalysis Engineering: Questions
Do you ever:
Discontinuous
Continuous
•
•
•
Measure and compare activities of catalysts for reactions?
Compare catalyst selectivities? For what purpose?
How? What does your reactor look like?
•
•
•
How do you define your catalyst activity ?
Perform kinetic studies?
How would you define reaction rate and how to determine it ?
•
•
What do you think plays a role in your measurements?
Are you sure you get the information you want?
Continuous stirred
tank reactor (CSTR)
c
T
Plug flow reactor
(PFR)
c(z)
T(z)
Batch reactor
c(t)
T(t)
How to describe these?
Phenomena in catalytic reactor
Reactor design equations
(fluid-solid)
Reactor level
X
Batch
r,V,W
A
W
dX
 B  t  c A 0 
V
R
W ,A
0
Plug flow
0 
A
W  c A0
dX
 c A 0 
FA0
RW ,A
0
CSTR
0 
X
W  c A0
 c A 0 A
RW ,A
FA0
PLUG FLOW
similarity !
MIXING
DISPERSION
VELOCITY PROFILE
X
FA0
r(X,z)
FA0
FA
FA
r,W
simplicity
DIFFUSION
REACTION
TRANSPORT PHENOMENA
Particle level
Temperature and concentration profiles
within catalyst particle
Three-phase catalytic process
How would they qualitatively be??
Catalyst
Liquid
Gas
T
T
c
c
Exothermal
Gas concentration
profile
Endothermal
Rates different from rate at bulk conditions
How to handle ?
Catalytic reactor design equation
External mass transfer - isothermal
plug-flow, steady state
conversion i
r obs
stoichiometric coefficient i
dX i
  i    rW  
d W F0 i 
deactivation function
film layer around particle
cb

real rate r (cs )

rate at c b r (cb )
intrinsic rate
cs
‘space time’
‘catalyst effectiveness’
Use:
effective rate

effective rate
rate at c b ,Tb
How to determine cs ?
Isothermal - external mass transfer
In - Out + Production = Accumulation
cb
cs
mass transfer rate
to particle:
=
reaction rate
in particle:
mol/s
mol/s
Isothermal first order - external mass transfer
Ap  k f cb  cs 
A
kv c s  p k f c b  c s 
Vp
=
film layer
Vp  rv cs 
rv  kv c
kf a '
1
cs 
cb 
cb
k
k f a ' kv
1 v '
kf a
cs
a' 
Effective rate:
Ap  k f cb  cs 
=
Vp  rv cs 
cb
Ap
Vp
1
 1
1 
 c b
rvobs  

 k f a' k v 
rate determined by
physical resistance and by
chemical resistance
or:
mass transfer flux
(mol/s.m2)
rate per particle volume
(mol/s.m3p)
Limits?
rvobs 
1
k c   e rv ( c b )
kv v b
1
a' k f
a ' k f  kv
Mass transfer control
a ' k f  kv
Kinetic control
L/S, G/S, L/L reaction systems
Isothermal - internal mass transport
Slab-type catalyst
Effective diffusivity porous media
only fraction  open
for diffusion
combined to
 ‘tortuosity’
tortuous path
longer
Flux direction
N  Deff
dc
dx
Diffusion and reaction
Concentration profile
Reaction rate profile
component gradient
in flux direction
Profiles?
Effectiveness factor
Deff 

D

gradient dc/dx
direction
Isothermal - internal mass transport
Slab
Mass balance, steady state difusion & reaction
1st order irreversible: De
x
cosh( )
L
c  cs
cosh( )
Solution:

1.0
0
L
d 2c
 kv c  0
dx 2
c/ci
e x  e x
2
e x  e x
cosh( x ) 
2
sinh( x )
1

tanh( x ) 
cosh( x ) coth( x )
sinh( x ) 
4.0
3.0
2.0
sinh' ( x )  cosh( x )
0.1
0.8
x+dx x
Some mathematics - Hyperbolic functions
1.0
tanh
cosh' ( x )  sinh( x )
0.6
1.0
L
0.4
2.0
kv
Deff
‘Thiele
modulus’
0.2
0.0
1.0
0.8
0.6
0.4
0.2
x  0 .3
1.0
1.5
2.0
x
x 3
 0
 
tanh( x )  1
Catalyst effectiveness
Effectiveness factor- experimental
Post et al. AIChE-J 35(1989)1107
Vp
 rv (c,T )dV
observed rate
 0
rate at external surface conditions rv (c s ,Ts )  Vp
Fischer Tropsch synthesis
n CO + m H2
Slab:
0.5
cosh( x )  1  x 2 2  1
0.0
x/L
Limits?
0.0
0.0
sinh( x )  tanh( x )  x
10.0
i 
sinh
cosh
i 
CnH2(m-n) + n H2O
tanh 
2

1st order irrev.
Limits:
1
0
i  1

i 
1

Co,Zr/SiO2 catalyst
H2/CO=2
21 bar
473-513 K
dp= 0.38-2.6 mm spheres
rv=kvpH2

(zero order CO)
1

0.1
0.1
1
3
0.1
0.1
1

10
10
Foam structures
Classical catalyst particles
Monoliths - cell density
Generalizations - isothermal - internal
 L
Geometry
200 cpsi
400 cpsi
600 cpsi
Kinetics
kv
Deff
i  1

i 
Vp
Ap

1
a'
Sphere:
1.80/0.27 mm
1890 m2/m3
 = 0.72
1.27/0.16 mm
2740 m2/m3
 = 0.76
1.04/0.11 mm
3440 m2/m3
 = 0.8
Use:
 L
kv
De

R
2
R
L
3
1

cylinder
slab
sphere
nth order:
LL
Cylinder: L 
L
0
Slab:
L???
 n21 c i n 1
1

tanh 

0.1
0.1
1

10
What’s observed?
Controlling regimes
extraparticle limitation, first order kinetics
'
rvobs
,p  a kf cb
• Kinetic control
rvobs  rv (cb )
• Diffusion control
(internal)
rvobs  i  rv (c b ) 
• Mass transfer control
(external)
rvobs  e rv (cb )  a' k f cb
rv (c b )
a' 

1
L
LL
R
Cylinder: L 
2
R
Sphere: L 
3
Slab:
a' 
1
dp
External mass transfer increases at increasing linear velocity
From literature
kf  u 0.6 0.7
• dependent of u, dp
• first order
• no activation energy
• How to determine in which regime?
• What do we observe?
What’s observed?
intraparticle limitation
Post et al AIChE-J 35(1989)1107
Observed temperature behaviour
Bernardo & Trimm Carbon 17(1979)115
0.1
kvobs
Catalysed steam gasification coke on Ni catalyst
Limiting case: ‘Falsified kinetics’
dp/mm
0.38
Ni
activation energy: Eatrue/2
C + H2O
CO + H2
5
Ea(kJ/mol)
0.01
0
1.4
0.001
1.90
1.95
2.00
robs    rchem 
2.05
rchem


1
n 1
k v De c s
L
2.10
1000/T
wide pore silica spheres
effect dp
reaction order (n+1)/2
• p(H2O)=26 kPa
• thermobalance
• coked catalyst:
Ni/Al2O3
1
r(obs)
2.4
61
1
0.75
164
0.1
0.6
order n
0.01
0.9
1.0
1.1
1.2
1000/T
particle size dependent
Tutorial 8
1.3
1.4
Summary dependencies rv,obs
Isothermal - external mass transfer
strong mass transport limitations
Catalyst effectiveness:
Internal mass transfer:
robs 
rchem


e 
1
n 1
k v De c i
L
depends on: 1/L, (n+1)/2 reaction order, Eaapp= ½Eatrue
r (c ,T )  Vp  c s
observed rate
 v s s

rate at bulk fluid conditions rv (c b ,Tb )  Vp  c b
Observable quantity: Ca 



n
robs
a ' k f (c b  c s ) (c b  c s )
c


 1 s
a' k f c b
a' k f c b
cb
cb
10
External mass transfer:
robs  a ' kf cb 
-1
un
cb
Lm
e  1  Ca
depends on: L, flow rate, 1st reaction order, Eaapp= 0
e  1  Ca
0.5
1
n
e
1
n=
0.1
Criterion:
2
 e  1 0.05
How to check if limitations are present ?
Kinetics unknown
0.01
0.001
0.01
Kinetics unknown
5%deviation
Ca < 0.05/n
Diffusion control?
Criteria - experimental verification
r
1
Ca
effectiveness cannot be calculated
v ,obs
 1  0.05
Criterion: r
v ,chem
0.1
Weisz-Prater:
effectiveness cannot be calculated
  i  2 
observed rate L2 robs

'diffusion rate' Decs
observed rate
External transfer:
Ca 
slab
rv ,obs
0.05

a' k f c b
n
Ap
Vp
particle properties
(nth order)
cylinder
1
sphere
reaction order
a' 
 n21 
i
Criterion:
mass transfer coefficient
0.1
0.1
1
i2
10
i G2 
rv ,obs  L2
Deff  c i
 n  1

  0.15
 2 
When temperature effects?
Effect temperature rise
5%Criterion
How much increases rate constant ?
 E  T
 
k (Ti )
  T
 exp  a   b  1   exp  b 
k (Tb )
RT
T
b  i
 

  Tb  T
 

 
Prater numbers
k(Ti)/k(Tb)
1.5
External transfer:
Tb=500 K
1.4
Ea(kJ/mol):
A few degrees
already critical !
120
1.3
80
Internal transfer:
1.2
 i  s i  2 
2
40
1.1
1.0
e 
 e  bCa  0.05
0
2
4
6
8
e
i
10-104 gas-solid
10-4-0.1 liquid-solid
 0.05
i 
E
b  a
RTb
10
T / K
(  H )k f c b
hTb
De (  H )cs
eTs
0-0.3 (exothermal)
10-20
Criterion 0.05

 
 1 

Ca
1

e

 

e  1  Ca  exp  b 
n

1
External gradient criterion more
severe than internal criterion
 e  bCa  0.05
External transfer:
Temperature and concentration profiles
Temperature gradient in catalyst bed
Ea
R Tw
Largest T-gradient
in film layer
T
T
c
c
Exothermal
rt
2
eff ,b Tw
r 
criterion bed T - gradient
 t 
criterion film T - gradient particle  rp 
1   b  1  b   1 
8
2

  p,eff
 b,eff
1 dp 
  0.05
Bi w d t 
  s 2 (1   b ) 

  1
 
8

 
temperature gradient in bed always develops first !
Endothermal
Largest c-gradient
inside particle
 H r  rv ,obs
Summary:
T  grad bed  T  grad ext  c  grad int , T  grad int  c  grad ext
Tutorials
• Tutorials #6, 7 & 10
Screening
Laboratory performance testing catalysts
Kinetic studies
n
tio
iz a
tim
Op
Preparation
Combinatorial
stage
Quantification
stage
Reaction network
Kinetics
Increasing:
• time
• money
• reality
Catalyst testing & Kinetic studies
Stability tests
Scale-up
How to obtain intrinsic performance data?
solid catalysts
Choose a well-defined reactor
Information wanted
– Ideal type: CSTR, plug flow,..
– Dimensions: L, dt, dp, shape
– Hydrodynamics
 Intrinsic reaction rate data
 Not obscured by parasitic phenomena
• Flow distribution
• Wetting, contact phases
 reactor characteristics
 mass and heat transport phenomena
Avoid undesired gradients
 particle – reactor scale
– C and T gradients on a particle scale
– C and T gradients on the reactor scale
 user manipulations
 catalyst misbehaviour
 deactivation/fouling
For
•
•
Comparison activities and selectivities
Kinetic modeling
Starting point for example
How ?
Rateobserved
 1 0.05
Rateideal
Laboratory Reactors
PFR
CSTR
–
–
–
–
Proper comparison - Selectivity
simple
yields conversion data, not rates
deactivation noted directly
small amounts of catalyst needed
catalysts of different activity
different product yields
kinetic selectivity = 2
A
k1
2s-1
k2
Q
1s-1
1.00
– direct rate data from conversions
– larger amounts of catalyst and flows needed
– deactivation noted directly
FBR
– non-ideal behaviour
– continuous handling of solids possible
TGA
– limited to weight changes
– careful date interpretation needed
– often mass-transfer limitations
Plug flow/Batch
0.80
Ci
P
0.60
0.40
Batch
P
Q
0.20
A
0.00
0.00
– yields conversion and selectivity data quickly over large range
– Easy to change feed
– catalyst deactivation hard to detect
0.50
1.00
1.50
2.00
k / s-1
Compare selectivities at similar conversion levels !
Important checks
Particle level 5% criteria – ‘Observables’
‘Ten commandments of catalyst testing’ - Dautzenberg
Particle criteria:
Bed citeria:
External temperature rise
Internal mass transfer
Carberry
Weisz-Prater
Temperature rise
Flow velocity profile
Plug flow - dilution
Mears
•
External (film) gradients
Ca 
– Concentration
– Temperature
•
rv ,obs
a ' kf cb

0.05
n
 E a   (  H r )  k f  c b   rv ,obs 


  0.05
h  Tb
 R  Tb  
  k f  a ' c b 
 b   e  Ca  
Internal (particle) gradients
– Concentration (Weisz-Prater)
– Temperature
i 2 
rv ,obs  L2  n  1 

 0.15
Deff  c s  2 
 Ea    Hr   Deff  cs   rv ,obs  L2 
  
  0.1
  
p,eff Ts
 R Ts  
  Deff  cs 
 s  i i 2  
Packed bed reactor - assumptions
Diagnostic tests mass transport limitations
ideal
real life
1. Particle size variation
egg-shell catalysts?
observed rate
particle size
2. Flow rate variation at constant space time!
XA,1
XA,2
plug flow
isothermal
XA,3
X
W1
W2
equal res,,T
W3
FA0,1
FA0,1
FA0,2
FA0,2
FA0,3
FA0,3
Catalyst bed size
Practical catalyst: often dp = ~1 - 3 mm
Moreover, velocity profiles
 Dt

 dp
Lb 8n  1 

 ln

dp Pep  1 x 
Pep 

X
 
0.03

X =0.8
n =1
u  dp
Dax
L > 25-75 mm
radial
temperature
gradient
 res varies
 10
X
   33
 d p  dp
T varies
Impact on observed conversion levels
Temperature rise in catalyst bed
Mears:
Reaction
heat production vs. conduction
Wall effect
heat transfer vs. conduction
  H  rvobs  rt2  1   b 1  b   E a



 RTw
er Tw


Effective thermal
bed conductivity
~ 1 J/s.m2K
Dt > 25 –75 mm
velocity
profile
“dispersion” analogous to diffusion
Dax “Dispersion coefficient”
 Dt  Dt
Criterion:
Axial dispersion
axial
dispersion
rp
 1
 8  r Bi
t
w


  0.05

Activation energy
Biot wall number
~ 0.8-10
b = fraction inert
diluent
Generally most severe temperature criterion
‘large’ reactor needed
What to do ?
Bed dilution - bypassing ?
Catalyst testing - Bed dilution
decoupling hydrodynamics and kinetics
Berger, Perez et al.
App.Catal.227(2002)321
Chem.Eng.Sci. 57(2002)4921
Chem.Eng.J. 90(2002)173
inhomogeneous distribution
catalyst by-passing
Diluent
Bed dilution (e.g. SiC)
• Hydrodynamics determined by
Do not:
• dilute too much
• use too high conversion
small particles (wetting, velocity)
• Longer bed, larger L/dp
• Testing of real catalyst particles
• Better heat conduction
• Larger heat transfer area
• Less heat produced per volume
Heat
transfer
area
Criterion:
 b  xobs
 

 1 b  2
Real particle
Lb/dp>~50
Dt/dp>~10-15
or
-5
160
Range I
-6
140
Eaapp / kJ mol-1
Practical example
Effect of Catalyst/Diluent Distribution in
Decomposition of N2O
137 kJ mol-1
120
non-porous
non-porous
quartz
quartz
-7
100
-8
-9
-10
Range II
80
60
40
20
-11
0
1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50
-3
-1
10 T / K
-1
Achieve a homogeneous mixture
of catalyst and diluent !
Catalyst
Diluent

  0.05

1

k obs =
ln  1
(Wcat /FN2O,0) pN2O,0 1-xN O

2 
ln(kobs)
inhomogeneous distribution
 dp

 Lbed
(= deviation rate constant less than 5%)
Dt/dp<4
Bed dilution: detrimental?
catalyst by-passing?
b = fraction inert diluent
Range I
Range II
Heat effects in packed-bed reactor
Coated wall reactor
T-profiles
Poor heat transfer
• in bed
• to wall h  50 W
Heat production/
consumption
2
mK
Cooling-heating:
• Reaction coupling
• Heat exchange
• through wall
• no wall
• Evaporation
Improvements:
• foams (ceramic,
metal)
• catalytic coatings
h  10 4
Better heat removal
W
m 2K
Exothermal reactions
oxidation
hydrogenation
But:
Velocity profile?
Concentration gradients?
• forced flow
radial
axial
Monoliths, microreactors, kinetic studies
G.Kolios et al. Chem.Eng.Sci. 57(2002)1505
TCR, UOP
Coated wall – flow patterns
Coated wall reactors
Porous catalytic walls
support washcoat
• Monoliths
Flow pattern
Flow pattern
Pe ' 
Concentration
profile
Criteria
X CWR 
0.16
0.23  nPe '
u0 L  R 
DA,rad  L 
mm size
• Microreactors
2
Concentration
profile
X CWR 
1.48
1.04  nPe '
0.05-0.2 mm
• Kinetic studies
5-15 mm
R.J. Berger & F. Kapteijn Ind. Eng. Chem. Res. 46 (2007) 3863
Ind. Eng. Chem. Res. 46 (2007) 3871
Redlingshöfer et al.
Ind.Eng.Chem.Res.41(2002)1445-1453
CSTR – fixed bed
Internally mixed
Alternative reactors for multiphase
kinetics measurements
Externally mixed
Batch – Liquid phase systems – fixed bed
Robinson-Mahoney
Berty-type
Carberry-type
Gas
Liquid
Recirculation reactor
300 ml (turbine)
Flat blade basket
SISR
Pitched blade basket
Alternative reactors for multiphase
kinetics measurements
Alternative reactors for multiphase kinetics
measurements
(Semi-) batch – G-L-S systems
In/out
Bentrod
Swinging capillary reactor
Capillary
Fixed
point
Heating
+ =
Turbine Reactor
Screw Impeller Stirred Reactor
F.Kapteijn and J.A.Moulijn,
Laboratory testing of solid catalysts in: Handbook of Heterogeneous Catalysis
Wiley-VCH Verlag, Weinheim, 2008, p. 2019-2045
S.Tajik et al., Meas.Sci.Technol. 1(1990)815
Monolithic Stirrer Reactor
Mn-oxide/Alumina H2O2 decomposition
Principles Catalyst Performance Testing
Down scale as far as possible
–
–
–
–
–
–
–
Lower cost equipment
Less material consumption
Lower utility demands
Safer
Less labour
Less synthesis effort
More options to test
Do not mimic industrial reactor
• Output industrial reactor: $$$$ or €€€€
• Output laboratory reactor: knowledge
I.Hoek et al. Chem.Engng.Sci. 59 (2004) 4975-4981
R.K.Edvinsson-Albers et al. AIChE J. 44 (1998) 2459-2464
No Dinky Toy / Matchbox approach!
Scaling down steps
N. van der Puil
N. van der Puil
Six-flow equipment
Observations
• Mainly fixed bed and batch slurry systems
applied
Sie, AIChE-J. 1996
Manhour per reactor hour
• Massive parallelization
2
Pilot plant
(non-automated)
• Cost reduction
1
Bench scale
0.5
(non-automated)
• Used for
– Catalyst screening 0.1
– Catalyst performance
– Kinetic studies
Plug flow - parallelization
FEED CONTROL
ANALYSIS
REACTOR
P
MFC
Diesel soot
FTS
N2O, NOx
HDS
MFC
VENT
MFC
MFC
MFC
SV
MFC
MFC
Bench scale
(semi-automated)
MFC
Microflow
(automated)
BPC
MFC
BPC
parallellization
0.01
1960 1970 1980 1990 2000
‘Workhorse’ in catalyst testing
Year
Pérez et al. Catal. Today 60(2000)93
N2O/NOx decomposition set-up
FAo
FAo
FAo
FAo
FAo
FAo
FAo
(a)
(b)
x1
FAo
x2
x3
x4
FAo
(c)
x1
FAo
dp1
increasing
particle size
FAo
dp5
x1
x1
GC
NDIR
GC
MS, NOx
FAo
W2
x2
FAo
W3
x3
FAo
W4
x4
W5
x5
FAo5
FAo1
increasing
flow rate
(d)
W1
o
Wi / FAi
constant
W5
x1
x5
x5
x



x5
x1

x5
• FischerFischer-Tropsch
• Soot abatement
• CFC, Automotive
• SCR
FAo
W1
x5
x
Other systems:
FAo






dp1
dp5
FA0,1
Particle size
FA0,5
Flow rate
reference
catalyst
Commercial developments
Commercial developments
Nelleke van der Puil, dec. 2008
Nelleke van der Puil, dec. 2008
Kinetics
Commercial developments
Procuring rate data laborious task
conversion vs.
space time W/F
temperature
partial pressures / concentrations
Improve speed:
• PC controlled equipment
• Six-flow set-up (parallel reactors)
• Temperature scanning
• Sequential experimental design
Don’t forget:
Nelleke van der Puil, dec. 2008
stable catalyst, blank runs, duplicates, criteria
Catalysis Engineering: Questions
Chapters 3 and 8
Do you ever:



Measure and compare activities of catalysts for reactions?
Compare catalyst selectivities? For what purpose?
How? What does your reactor look like?



How do you define your catalyst activity ?
Perform kinetic studies?
How would you define reaction rate and how to determine it ?


What do you think plays a role in your measurements?
Are you sure you get the information you want?
Kinetics of catalysed reactions
Kinetics of catalysed reactions
Structure
Batch
CSTR
Plug flow
Kinetics of Catalysed Reactions
Catalysis
Reactor engineering
Ideal reactors
 Kinetics
 Reactor theory
 Experimental aspects
– Interpretation
– Reactors
– Interfering phenomena
• Mass transfer
• Diffusion
• Dispersion
• Criteria
 Problems/questions
Transport
phenomena
Reaction models
Kinetics
Heat & Mass
Behaviour single
particle
Non-ideal reactors
 Why Reaction Kinetics
 Derivation rate expressions
 Simplifications
– Rate determining step
– Initial reaction rate
 Limiting cases
– Temperature dependency
– Pressure dependency
 Examples
Catalytic Reactor
Kinetics of catalysed reactions
Kinetics of catalysed reactions
Utilization of kinetic data for
different chemical industry sectors
Utilization of kinetic data in industry
Questionnaire 1997
(a) Chemical Companies
Bos et al. Appl.Catal. A160 (1997) 185-190
Mechanistic
Research
6%
Catalyst
Development
29%
Other
1%
Process
Development
34%
Mechanistic
Research
8%
Catalyst
Development
26%
Other
1%
Catalyst
Development
56%
www.eurokin.tudelft.nl
Process
Development
15%
Catalyst
Development
15%
Process
Optimisation
28%
Other
0%
Batch reactor
CA
design
process start-up and control
process development and improvement
selection reaction model
CA
CA
r=k
r = kcA
 General relationship
r = kcn, n ~2
t
r  f ( pi ,.......T , NT , k i ,........., K i ,......, K eq )
 Often used
CA
t
CA
t
r=k
r = k(cA-cp/Keq)
m
j

Process
Development
56%
Mechanistic
Research
1%
Rate data, Examples A  P
 Rate expressions in principle crucial for
r  kp p
– power rate models
– models based on elementary processes
sNT k 2K AK B2 pA  pB2 / K eq
r 
1  K A pA  K B pB 2
• extrapolation more reliable
• intellectually process better understood
Process
Optimisation
37%
Kinetics of catalysed reactions
Rate expressions
n
i
Process
Development
30%
(d) Engineering Companies
Mechanistic
Research
12%
Process
Optimisation
17%
Mechanistic
Research
2%
Catalyst
Development
27%
Other
4%
(c) Catalyst Companies
Process
Optimisation
30%
Kinetics of catalysed reactions
Kinetics of catalysed reactions
Process
Development
34%
Process
Optimisation
31%
Other
0%
–
–
–
–
(b) Oil Companies
r = kcA

t
Rate equation??
Kinetics of catalysed reactions
t
Does power rate equation fit?
If so, n = ??
Role of catalyst?
Rate expression – Catalysed reaction
forward rate
backward
Success frequency
 Concentrating reactants
adsorption/complexation
 Providing alternative reaction path
catalyst selectivity
other activation energy barrier
affect rate
r  k   c Aads  s B  k   cCads  s C
rate constant
amount of A adsorbed
chance of adjacent B adsorbed
 But:
– other components adsorb, too
block ‘active sites’
– fixed number of ‘active sites’
affect rate
affect rate
Note:
• cgas and cads differ
• ratios components differ
other form rate expression expected
Kinetics of catalysed reactions
Kinetics of catalysed reactions
Simple example: reversible reaction
A
B
Elementary processes
 Rate expression follows directly from rate equation
‘Elementary processes’
A

r
r1
r1
A*
r
2
r2
B
r  r1  r1  k1  p A  NT  *  k 1  NT  A
3
r3
r  r2  r  2  k 2 N T  A  k  2 N T  B
B*
r  r3  r3  k 3 NT  B  k 3 pB NT  *
‘Langmuir adsorption’
Eliminate unknown surface occupancies
How many unknowns, when the overall rate is known?
Kinetics of catalysed reactions
Kinetics of catalysed reactions
Elementary processes contd.
Algebraic eqs.
Quasi-equilibrium / rate determining step
1 * A B
 Site balance:
d A
0
dt
d B
0
dt
 Steady state assumption:
r1
r1  r2
r-1
r2  r3
r2
r-2
 Rate expression:
rate determining
r3
r 
NT k1k 2 k 3 ( pA  pB / K eq )
(.....)  (......) pA  (......) pB
r-3
Microkinetics
Michaelis-Menten
‘quasi-equilibrium’
r
with :
K eq  K1K 2K 3
r = r2 - r-2
Very simple case, nevertheless quite complex equation
Kinetics of catalysed reactions
Kinetics of catalysed reactions
Rate expression, contd.
Rate expression - r.d.s.
Substitution:
Rate determining step:
r  r2  r2  k 2 NT K1p A  *  k 2 NT p B * / K3
r  r2  r2  k2 NT  A  k 2 NT  B
r  k 2 NT K1  *  p A  k 2 p B / k 2 K1K3 
Eliminate unknown occupancies
where:
Quasi-equilibrium:
r1  r1
So:
 A  K1p A   *
k1 p A NT  *  k 1 NT  A
with: K1 
k1
k 1
Unknown still *
p
 B  B  *
K3
Kinetics of catalysed reactions
p 
Keq  K1K2 K3   B 
 p A eq
Kinetics of catalysed reactions
Other rate determining steps
Rate expression, contd.
Adsorption r.d.s
Site balance:
1   *   A   B   *  1  K1p A  p B / K 3 
* 

k1 NT p A  pB / Keq

1  1  1 / K2 pB / K3
1
1  K1p A  pB / K3 
Surface reaction r.d.s.
Finally:
r
r
‘lumped’

k 2 NT K1 p A  p B / Keq
1  K1p A  pB / K3 
r
‘lumped’


k 2 NT K1 p A  p B / Keq
1  K1p A  pB / K3 

Desorption r.d.s.
r

k 3 NT K1K2 p A  p B / Keq
1  1  K2 K1p A

Rule of thumb: Generally surface reaction r.d.s.
Kinetics of catalysed reactions
Kinetics of catalysed reactions
Thermodynamics
Initial rate expressions
Equilibrium constant
 Forward rates
 Product terms negligible
Reaction entropy

RT ln K eq  G (T )   H (T )  T S
o
o
o

Adsorption
Reaction enthalpy
r  k 'p0A
  i Gfo,i (T )
i
ln K A 
Adsorption entropy, <0
(J/mol K)
S
H

R
RT
o
T1
atm-1
Kinetics of catalysed reactions
T2
Data sources: Handbooks, API, JANAF
Chemsage, HSC, YAW’s Handbook
pA
Kinetics of catalysed reactions
T2
T3
Adsorption enthalpy,<0
(J/mol)
r  k'
T1
T1
r0
Desorption
high p
low p
Adsorption constant
o
Surface
k 'p0A
r
1 KA p0A
T3
pA
T2
T3
pA
Langmuir adsorption
Multicomponent adsorption / inhibition
 Uniform surface (no heterogeneity)
 Discrete number of sites
 No interaction between adsorbed species
Langmuir adsorption
Irving Langmuir
1881 - 1957
Nobel Prize 1932
A+*
A*
1.0
A 
0.8
A 
K A pA
1  K A pA
100


KA /bar -1
10
0.6
K 1p A
1  K 1p A   K i p i
1.0
0.4
0.2
Inhibitors
0.1
0
0
0.2
0.4
0.6
0.8
1.0
pA /bar
Kinetics of catalysed reactions
Kinetics of catalysed reactions
Surface occupancies
Langmuir adsorption model
 Generally used
Empty sites
Occupied by A
* 
A 
1
1  K1p A  pB / K3 
K1p A
1  K1p A  pB / K3 
1
 KB
K3
–
–
–
–
Simplification (uniform, no interactions)
although nonlinear, mathematically simple
simple physical interpretation
rather broadly applicable
• multicomponent adsorption
 S o H o 
• non-uniform surfaces

K A  exp

RT 
 R
– ‘compensation effect’
– very weak and strong sites do not contribute much
to the rate
Occupied by B
B 
Kinetics of catalysed reactions
pB / K3
1  K1p A  pB / K3 
• for microporous media (activated carbons) often
not satisfactory
Kinetics of catalysed reactions
N2O decomposition over ZSM-5 (Co,Cu,Fe)
Effect of CO on N2O decomposition
Kapteijn et al. J.Catal.167(1997)256-265
1.0
Cu-ZSM-5 (673 K)
2N2 + O2
CO + O*
CO2 + *
CO + * 
Kinetic model
1.
2.
0.8
CO* (Cu+)
X(N2O)
2 N2 O
0.6
Fe-ZSM-5 (673 K)
0.4
0.2
N2O + *  N2 + O*
N2O + O* N2 + O2 + *
Co-ZSM-5 (693 K)
0.0
0.0
0.5
1.0
1.5
molar CO/N2O ratio
CO removes oxygen from surface
so ‘enhances’ step 2, oxygen removal
Rate expression
r
k1 NT pN 2O
k2 
1  k1
no oxygen inhibition
1st order
Kinetics of catalysed reactions
now observed: rate of step 1
increase: ~2, >3, >100
Kinetics of catalysed reactions
Dissociative adsorption
Dissociative adsorption
O2 + 2*
r1 = k1 NT pN2O
2O*
Gerhard Ertl
Nobel laureate
Chemistry 2007
H2 + 2*
2H*
K p 
1  K p 
0.5
H 
Lower pressures:
K p 

1 K p 
H2
H2
H2
0.5
H2
0.5
O
O2
O2
O2
0.5
Two adjacent sites needed
O2
STM oxygen on Ru
Two adjacent sites needed
Kinetics of catalysed reactions
Kinetics of catalysed reactions
2.0
Initial rates - CO hydrogenation over Rh
Koerts, Van Santen et al.
Langmuir-Hinshelwood/Hougen-Watson models
(LHHW)
Irving Langmuir
Cyril Norman Hinshelwood
(1881 – 1957) Nobel Prize 1932
(1897 – 1967) Nobel Prize 1956
Kinetic model
1.
2.
CO + *  CO*
CO* + *  C* + O*
For: A+B
(r.d.s.)
includes NT, k(rds)
800
r 
600
Rate
Initial rate
r0  sNT k 2 CO   *
C+D
pApB-pCpD/Keq
( kinetic factor )  ( driving force )
400
( adsorption term ) n
200
r0 
sk 2 NT KCO pCO
 1  KCO pCO 
molecular: KApA
dissociative: (KApA)0.5
0
2
0.2
Oc
cu
0.6
pa
nc
y(
-)
= 0, 1, 2...
number species in
and before r.d.s.
600
0.4
550
500
450
0.8
1.0
400
(K)
ture
pera
Tem
Leonor Michaelis
Kinetics of catalysed reactions
Terminology
Heterogeneous catalysis
Kinetics
Langmuir-Hinshelwood 1916/20
Linearization rate expression
Biocatalysis
Michaelis-Menten 1913
rmax
Rate expression
Maud Menten
(1879-1916)
Kinetics of catalysed reactions
(1875-1949)
Vmax
k NT K A pA
r 
1 K A pA
adsorption constant
v
kE 0 c A
K M c A
kE 0 c A
v
K M c A
Hougen-Watson
Lineweaver-Burke
Catalytic centre
‘active site’
enzyme
=Vm
1/v
Michaelis constant
Linearization
1 KM 1
1



v kE 0 c A kE 0
Intercept
= 1/Vm
Slope = KM/Vm
=-1/KM
Turnover number
Turnover frequency
Number of turnovers
Kinetics of catalysed reactions
k (s-1)
r
NTsurface
1/cA
(s-1)
number molecules converted/number complexes
Kinetics of catalysed reactions
• Lineweaver-Burke
• Hougen-Watson
Enzyme Catalysis
Terminology
Biocatalysis
Heterogeneous catalysis
Reactants
Molecules
Biocatalysis
Heterogeneous Catalysis
1. Irreversible inhibition
2. Competitive inhibition
Substrates
1. Catalyst poisoning (irrev.)
2. Competitive adsorption
or inhibition
k2
Reactor
performance
CSTR, autoclave
Residence time, space time
Chemostat, fermentor
Flow rate
Dilution rate
S + E  ES  E + P
I + E  EI
3. Non-competitive inhibition 3. Co-adsorbed intermediates
change active sites
(‘modifiers’)
k2 depends on intermediate
concentration
Affect activity and selectivity
k2’
S + E  ES E + P
I + E  EI
Kinetics of catalysed reactions
v
Kinetics of catalysed reactions
What about observed:
reaction order
activation energy ?
Determination:
Reaction order - Activation energy
slope = -Eaobs/R
K A pA  1
ln r
ln r
r 
limiting cases?
ln pi
1/T
 ln r
 ln pi
Eaobs
 ln r

R
 1 T 
Kinetics of catalysed reactions
r 
k 2 NT K A p A
1 K A p A  K B pB 
Reaction order ?
k 2 NT K A p A
1

 K A p A  K B pB 
k 2 NT K A pA
1  K B pB 
r  k 2NT
K A pA  1
LHHW models ?
r 
rate expression
slope = order ni
ni 
k 2' E0 cS
K M'  cS
Activation energy ?
depend strongly on occupancy!
vary during reaction
Svante Arrhenius
(1859 – 1927)
Nobel Prize 1903
General:
Kinetics of catalysed reactions
nA  1   A
nB   B
Try it yourself
Eaobs  E a 2  1   A  H A   B H B
Tutorial 13
Selective hydrogenation benzaldehyde
r 
Surface reaction r.d.s.
700
Concentration / mol/m3
Limiting cases - forward rates
600
Benzaldehyde
Benzyl alcohol
r  k 2 NT
1. Strong adsorption A
500
k 2 NT K A p A
1 K A p A  K B pB 
400
A#*
k#+
300
kbarrier
k#200
Toluene
Ea2 H#
Eaobs
100
A*
0
0
5000
10000 15000
Time / s
20000
25000
B*
Kinetics of catalysed reactions
Kinetics of catalysed reactions
Limiting cases - forward rates
Surface reaction r.d.s.
r 
k 2 NT K A p A
Surface reaction r.d.s.
1 K A p A  K B pB 
3. Strong adsorption B
r  k 2 NT K A p A
2. Weak adsorption
Limiting cases - forward rates
k 2 NT K A p A
r 
1 K A p A  K B pB 
r 
k 2 NT K A p A
K B pB
Eaobs =Ea2+ HA HB
A#*
A#*
Eaobs =Ea2+ HA
A(g)+ * +B(g)
HA
Ea2
A(g)+*
 HA
A*
HB
 HR
B(g)+*
 HB
A(g)+B*
B*
Kinetics of catalysed reactions
Kinetics of catalysed reactions
A*
Ea2
Cracking of n-alkanes over ZSM-5
n-Alkanes cracking
J. Wei I&EC Res.33(1994)2467
Energy diagram
200
Initial state
Ea2
100
kJ/mol
0
-100
-200
0
negative!?
Transition state
A+*
Eaobs
Ea,obs
Hads
HA
5
Ea2
r0  k 2 K A p A
10
15
20
B*,C*
E aobs  E a 2   H A
Carbon number
A*
Adsorbed state
Kinetics of catalysed reactions
Kinetics of catalysed reactions
Dual site reaction :
A+B
C
Observed temperature behaviour
• T higher
coverage lower
• Step highest Ea increased most
Change in r.d.s.
adsorption r.d.s.
A + *

A*
B + *

B*
A* + B*

C* + *

C + *
C*
ln robs
r  k3  NT  A  sB  k 3  NT C  s *
desorption r.d.s.
4 unknowns, 4 equations
r 
1/T
Ea,observed depends on T, because of change r.d.s.
Kinetics of catalysed reactions
(r.d.s.)
Kinetics of catalysed reactions
k3 s NT K1K 2  pA pB  pC / K eq 
1  K1pA  K 2 pB  pC / K 4 
2
More than one reactant (no product inhibition)
Dual site reaction, contd.
e.g. hydrogenation, oxidation
• One-site models
r  r3  r3  s  NT k 3 A B  k 3 C * 
r  kNT  AB 
dual site reaction
r  kNT s A B 
• Two-site
Number of neighbouring sites (here: 6)
kNT K AK AB pA pB
1  K A pA (1  K AB pB )
single site reaction
models
r  kNT s  A B 
different sites
• Number
kNT s K A pA K B pB
(1  K A pA  K B pB )2
kNT s K A pA K B pB
(1  K A pA ) (1  K B pB )
of sites conditions dependent
NT 0 K A pA 
12
NT 
Kinetics of catalysed reactions
1  K
pA 
12
A

optimal surface concentrations
optimal adsorption strengths
Kinetics of catalysed reactions
Reaction kinetics, summary
Further kinetics
 Langmuir adsorption

– uniform sites, no interaction adsorbed species,
finite number of sites, multicomponent
 Rate expressions derivation
r
series of elementary steps
steady state assumption, site balance
quasi-equilibrium / rate determining step(s)
initial rates (model selection)
p le
sim
–
–
–
–

 LHHW models
– inhibition, variable reaction order, activation
energy


mechanism
Kinetics of catalysed reactions
kinetics
Microkinetics
– Keep all elementary processes
• Estimate theoretically pre-exponentials
(statistical physics) and activation
energies (molecular modeling, DFT) or
from experimental work (TPD)
• Active site concentration and limited
number of constants estimated from
experimental rate data
Single event modeling
– Complex reaction schemes reduced to finite
number of single events
– Detailed composition feed required
– Further as microkinetics
Transient operation
– Active site concentration and rate constant
decoupled
Include lateral interactions, surface reconstruction,
dependency catalyst properties on exposed
environment
Kinetics of catalysed reactions
AppCatA342(2008)3–28
Concepts of Modern
Catalysis and Kinetics.
I. Chorkendorff,
J.W. Niemantsverdriet
2003
WILEY-VCH Verlag
GmbH & Co. KGaA,
Weinheim
Hydrodesulphurization kinetics
Sie, AIChE-J 42(1996)3498
Example HDS vacuum gasoil
2.2
2.0
1/S-1/S0 (1/wt.%)
Examples kinetics
Gasoil
CoMo-alumina
trickle flow
L=0.2-0.4 m
1.8
• Apparent second order behaviour
r = kcS2
• H2S inhibits strongly
1.6
1.4
1.2
1.0
0.8
0.6
0.4
2.0
0.2
concentration
0.0
1.5
0.0
c
conversion
0.1
0.2
0.3
0.4
0.5
1/LHSV (h)
1.0
fast decrease followed
by slow decrease
0.5
0.0
0.0
0.2
0.4
0.6
0.8
1.0
bed length
Second order silly, what is wrong??
Kinetics of catalysed reactions
Kinetics of catalysed reactions
Composition oil fractions
Vacuum gasoil
Sulphur compounds
R
R
S S
R
Thiophene
Benzthiophene
S
Three lump model: first order reactions
Simulated model data:
2nd order
k=10 m3/mol.s
c0=2 mol/m3
Thioethers
R
S
0
Dibenzthiophene
5
10
15
20
25
30
Three lump model:
1st orders
k1=36.1 s-1
c01=1.23
k2=16.0 s-1
c02=0.59
k3=7.5 s-1
c03=0.18
2.0
sum
concentration
S
Simulated profiles - HDS reactivity lumping
1.5
1
1.0
2
3
0.5
Simulated distillation b.p.
0.0
0.0
S
0.2
0.4
0.6
0.8
1.0
bed length
S
R
Kinetics of catalysed reactions
R
Substituted
dibenzthiophene
complex mixtures
different reactivities
lumping
Three lump model adequate
Inhibition through LHHW models
Kinetics of catalysed reactions
Which groups lumped?
model studies
0.6
N2O decomposition
Effect of CO on N2O decomposition
1.0
Cu-ZSM-5 (673 K)
CO + O*
CO2 + *
CO + * 
CO* (Cu+)
X(N2O)
0.8
0.6
Fe-ZSM-5 (673 K)
0.4
0.2
Co-ZSM-5 (693 K)
0.0
0.0
0.5
1.0
1.5
2.0
molar CO/N2O ratio
CO removes oxygen from surface
so ‘enhances’ step 2, oxygen removal
now observed: rate of step 1
r1 = k1 NT pN2O
increase: ~2, >3, >100
Kinetics of catalysed reactions
Kapteijn et al. J.Catal.167(1997)256-265
Kinetics of catalysed reactions
Effect of CO on N2O decomposition
rate without CO
Apparent activation energies N2O decomposition
CO/ N2O = 2
rate with CO
Apparent activation energies (kJ/mol)
kN p
r  1 T N 2O
1  k1 k 2 
ratio = 1 + k1/k2
So k1/k2 = :
Kinetics of catalysed reactions
1
Co
>2
Cu
>100 Fe
r  k1 NT pN 2O
only N2O
Co
and:  O *
 O* 
k k
 1 2
1  k1 k 2
0.5
>0.7
>0.99
CO/N2O=2
115
Cu
138
187
Fe
165
78
Co,
Fe
r  k1 NT p N 2O
Cu
r
Kinetics of catalysed reactions
110
k1 NT p N 2O
k N p
 1 T N 2O
k 2  KCO pCO 
KCO pCO
1  k1
E aobs  E a 1
E aobs  E a1  HCO
Apparent activation energies N2O decomposition
N2O decomposition over ZSM-5 (Co,Cu,Fe)
CO/ N2O = 0
Kapteijn et al. J.Catal. 167(1997)256
1.0
Apparent activation energies (kJ/mol)
Co
110
r
Fe
r  k 2 NT p N 2O
833 K
Oxygen inhibition model
115
Cu
138
187
Fe
165
78
k1 NT pN 2O
k2 
Co,
Cu
1.
2.
3.
E
1  k1
obs
a
0.6
793 K
Cu-ZSM-5
Fe-ZSM-5
0.4
Co-ZSM-5
N2O + * 
N2O + O*
O2 + * 
N2 + O*
N2 + O2 + *
*O2
0.2
733 K
688
773 K
0.0
0
2
4
6
8
10
p(O2) / kPa
 m ix( E a 1, E a 2 )
Rate expression
r
E aobs  E a 2
Kinetics of catalysed reactions
k1 NT p N 2O
k 2  K3 pO 2 
1  k1
Kinetics of catalysed reactions
Catalysed N2O decomposition over oxides
N2O decomposition over Mn2O3
Winter, Cimino
Rate expressions:
Kinetic model
strong O2 inhibition
0.5

k obs pN 2O
1   pO 2 K 3 
0.5

N2O + * 
N2O* 
2 O*

1.
2.
3.
2
r 
2N2 + O2
1st order
p N 2O
 pO 
Yamashita & Vannice J.Catal.1996
2 N2 O
r  k obs  p N 2O
r  k obs 
moderate inhibition
r 
k 2 NT K 1 p N 2O
1 K p
1 N 2O
= Explain / derive =
Kapteijn et al. Appl.Catal.B: Env. 9 (1996) 25-64
N2O*
N2 + O*
2* + O2
Rate expression
Also: orders 0.5-1
water inhibition
Kinetics of catalysed reactions
743 K
0.8
CO/N2O=2
X(N2O)
only N2O
Kinetics of catalysed reactions
  pO 2 K 3 
0.5

N2O decomposition over Mn2O3
N2O decomposition over Mn2O3
Yamashita & Vannice J.Catal.1996
Yamashita & Vannice J.Catal.1996
Kinetic model
order N2O ~0.78
Oxygen inhibition
Values
0.4
r / 10-6 mol.s-1.g-1
0.3
0.2
2.0
4.0
6.0
8.0
k 2 NT K 1 p N 2 O
0 .5
N 2O  pO 2 K 3 
1  K p
1

10.0
= Thermodynamically consistent =
= Explain =
Kinetics of catalysed reactions
Kinetics of catalysed reactions
Effect reaction kinetics - batch operation
A+B
Kinetic coupling between catalytic cycles
irreversible
C+D
Bifunctional catalysis: Reforming
cA=cB
KA=KB
KD small
kK A K B c A c B
1  K A c A  K B c B  K C cC  K D c D 
2
Isomerization n-pentane: n-C5 -> i-C5
KA=10
KC=1
Pt-function:
n-C5 -> n-C5=
surface diffusion
1.0
conversion
r 
S 3  109 J/mol K
pO2 / kPa
r 
 N2O*

N2 + O*
 2* + O2
H 3  92 kJ/mol
638 K
623 K
608 K
598 K
0.0
0.0
N2O + *
N2O*
2 O*
Rate expression
Ea2  130 kJ / mol
648 K
0.1
H1  29 kJ/mol
S1  38 J/mol K
pN2O = 10 kPa
Eaobs= 96 kJ/mol
1.
2.
3.
Acid function:
n-C5= -> i-C5=
Pt-function:
i-C5= -> i-C5
KA=KC= 1
0.8
low concentration
close proximity
surface diffusion
0.6
KA=KC= 0.1
0.4
KA=1
KC=100
0.2
0.0
Kinetics of catalysed reactions
0
20
40
60
80 100 120 140 160 180 200
time
Coupled catalytic cycles on different sites
Strong product inhibition
Kinetics of catalysed reactions
See tutorial
NIOK course December 2009
Tutorial 1
A second order reaction A  R has been studied in a Berty-reactor, a CSTR suited for
the investigation of solid catalysed reactions. The following data are available:
v = 1 l h-1
V=1l
W = 3 g catalyst
cA0 = 2.0 mol/l
cA = 0.5 mol/l
a. Determine the value of the rate constant and give its dimension
b. How much catalyst is needed to obtain 80% in a packed bed reactor at a volume
flow rate of 1000 l/h and an inlet concentration cA0 = 1 mol/l ?
Tutorial 2
At room temperature sucrose can be hydrolysed by the enzyme sucrase:
sucrose  products
Starting with an initial sucrose concentration of 1.0 mmol/l and an enzyme
concentration of 0.01 mmol/l the following data have been obtained in a batch reactor.
Concentrations have been determined by using polarized light.
c mmol/l
0.84
0.68
0.53
0.38
t (h)
1
2
3
4
c mmol/l
0.27
0.16
0.09
0.04
t (h)
5
6
7
8
c mmol/l
0.018
0.006
0.0025
t (h)
9
10
11
Verify that the data can be represented well by a kinetic expression of the MichaelisMenten type:
r 
k cS c E 0
cS  M
with M the Michaelis constant
Determine the parameter values in this rate expression.
Tutorial 3
a. External mass transfer limitations can be verified by the Carberry number, Ca.
1. How would you calculate Ca
2. What are the limiting values of Ca, and why?
3. Give the physical interpretation of Ca
b. Pore diffusion limitations in porous catalysts can be verified by the Thiele modulus .
1. Give  for a first order irreversible reaction and dimensions of the parameters
2. What is the physical meaning of 2 ?
3. Give the relation between the catalysts effectiveness  and  for the limits of
 approaching 1 and approaching 0.
4. To be able to calculatate  the kinetics of the reaction has to be known. If the
kinetics are unknown give two ways to be able to check the presence or
absence of pore diffusion limitations.
5. What is the effect on the observed reaction rate if one increases the dispersion
of the active phase of a catalyst by a factor of two, while one operates in a
strongly pore diffusion controlled regime? Motivate your answer.
Tutorial 4
For a first order catalysed gas-phase decomposition reaction under chemically
controlled conditions the following data have been reported:
rv = 10-6 mol s-1 (cm3cat)-1
cA = 10-5 mol cm-3 @ 1 bar, 673 K
De = 10-7 m2 s-1
Which maximum particle diameter of a spherical catalyst may still be used without
diffusional disguise?
Tutorial 5
A conversion rate of 8 mol s-1 is being observed for the isothermal gas phase
decomposition of a component A in a catalyst bed of 0.5 m3 with a porosity  b =0.4 at
600 K and at pA = 1 bar. The spherical catalyst particles have a diameter of 15 mm. In
this case De = 2·10-6 m2 s-1.
Are diffusion limitations present? Motivate your answer. Use the correct units.
Tutorial 6
The data in the table below have been produced in a Berty reactor, a type of CSTR for
heterogeneous catalysts with internal recirculation of the fluid. The isothermal reaction
conditions were identical in all runs. What can you tell about transport limitations and
catalyst porosity ?
Run no.
1
2
3
4
Wcat
1
4
1
4
dp
1
1
2
2
FA0
1
4
1
4
Recycle rate
High
Very high
Very high
High
rvobs
4
4
3
3
Tutorial 7
A first order catalysed decomposition has been studied in a labscale reactor. Use the
data below to answer the following questions.
a. Has external mass transfer been interfering ?
b. Are diffusional disguises present ?
c. Do temperature differences exist over the gasfilm or within the particle?
Data:
Catalyst
dp
De
e
kf
h

cb
rvobs
Gasfilm
Reaction
=
=
=
=
=

=
=
2.4
mm
1.4·10-8
m2 s-1
-1 -1 -1
0.45 J m s K
0.083 m s-1
46
J m-2 s-1 K-1
 kJ mol-1
20
mol m-3 (@ 1 bar, 609 K)
27
mol s-1 m-3cat
Tutorial 8
The Fischer-Tropsch reaction has been studied by Post et al. (AIChE-J. 35 (1989) 1107)
using a wide-pore silica supported cobalt based catalysts (spherical particles). The
reaction can be described as a first order
0.1
irreversible reaction in the hydrogen partial
pressure. They calculated an observed first
dp/mm
order rate constant at different temperatures
obs
and for different particle diameters, as
kv
0.38
indicated in the graph.
0.01
2.4
0.001
1.90
1.95
2.00
1000/T
1.4
2.05
2.10
A particle size dependency has been observed
and the temperature dependency decreases
with increasing particle size.
Explain these phenomena and by first deriving
an expression for the observed reaction rate
under extreme diffusion limitations.
Tutorial 9
For the irreversible conversion of a component A into a product the following data are
available: 1 g catalyst, kw = 10-3 m3 min gcat , cA0 = 3 mol m-3 and v= 10-3 m3 min-1.
Calculate the (averaged) exit conversion for an ideal plug flow reactor for the cases a-c.
Do the same for a ten times lower catalyst activity.
a. For an undiluted catalyst bed
b. For the catalyst homogeneously diluted with the same volume
of inert particles
c. Same as for b., but now the catalyst and inert particles form two
parallel beds in the reactor (see drawing)
Tutorial 10
In a thermobalance the catalysed oxidation of four char samples has been studied to
investigate the effect of the catalyst precursor (copper salts) on the catalytic activity. a
schematic diagram of the thermobalance used is given below, together with the observed
reaction rate R (mg C per h and per mg C initially present).
a. One observes at a certain temperature for each catalyst a strong increase in
reactivity and it becomes nearly constant at even higher temperatures. The authors
explain this by a changing mode of catalytic action, ‘from a non-wetting to a
wetting mode’.
Give your explanation for this constant level.
b. Why is this level about the same for all samples ?
c. Explain the increase in apparent activation energy with increasing temperature in
the intermediate temperature regime.
gas flow
RT (mg/h mgi)
10
cooling
water
sample in
ceramic
cup
1.0
heating
coil
thermocouple
0.1
1.40
1.45
1.50
1.55
1.60
1000/T (K-1)
Thermobalance
Tutorial 11
The first order irreversible decomposition of N2O into O2 and N2 has been studied in an
internally recirculated reactor (Berty type). Under isothermal and kinetically controlled
conditions (700 K) the observed conversion amounts to 0.7. The following additional
data are available. Total flow rate 200 ml/min, amount of catalyst 1 gram, stainless steel
reactor, internal reactor volume 100 ml, feed concentration N2O 40 * 10-6 mol/l.
Furthermore, the reaction is not affected by other components that may be present.
Design a packed bed reactor that has to convert 2000 ppm N2O (80 *10-6 mol/l) in a
stack gas for 90% and a total flow rate of 24000 Nm3/h, i.e. calculate the weight of
catalyst needed and the reactor volume needed for the following situation: similar
temperature as the Berty reactor, isothermal operation, catalyst effectiveness 0.8 and
100 kg catalyst fits into 1 m3 reactor volume (monolithic catalyst). All volumetric
dimensions given are identical in this problem.
Hint: Use the design equations for the reactors.
Tutorial 12
Hosten and Froment studied the isomerization of n-pentane to i-pentane in the presence
of hydrogen over a bifunctional Pt-Al2O3 catalyst. Globally first a dehydrogenation
takes place over the metallic function, followed by an isomerization over the acidic
alumina sites and finally a hydrogenation of the i-pentene takes place over Pt.
The reaction sequences can be given as:
Dehydrogenation
1) A + *
2) A* + *
3) H2*
4) M*
Isomerization
5) M + #
6) M#
7) N#
Hydrogenation
8) N + *
9) H2 + *
10) N* + H2*
11) B*
 A*
 M* + H2*
 H2 + *
M+*
 M#
 N#
N+#
 N*
 H2 *
 B* + *
B+*
a. Derive a rate expression for this reaction where step 6. is rate determining.
b. The overall reaction rate is found pressure independent. Is that in agreement with
your result?
Tutorial 13
For the catalytic decomposition of alcohols into alkenes and water the following results
have been obtained:
Alcohol
n-propanol
iso-propanol
n-butanol-1
High pressure
172
163
184
Ea (kJ/mol)
Low pressure
119
109
117
Difference
53
54
67
Under all conditions water is adsorbed much stronger at the catalyst than the other two
components. The apparent (observed) activation energy, obtained from an Arrheniusplot of ln(r) versus 1/T , is significantly different for high and low pressure conditions.
The backward reaction is negligible in all cases and a single-site kinetic model can be
assumed for this reaction.
1. Demonstrate by means of a kinetic analysis what the physical meaning of the
constant difference of about 58 kJ/mol is.
2. Is it logical that this difference is about the same for all three alcohols?
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