Chap 03 Masters
Transcript of Chap 03 Masters
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Catalysis Engineering - Kinetics
Catalytic Reaction Kinetics
Why Catalytic Reaction Kinetics ?
Derivation rate expressions
Simplifications
– Rate determining step
– Initial reaction rate
Limiting cases
– Temperature dependency
– Pressure dependency Examples
Catalysis Engineering - Kinetics
Reactor design equation - Packed bed
ν η = ⋅ ⋅i i W dF
r dW
stoichiometric coefficient i
catalyst effectiveness
rate expression
Molar flow i
‘bed coordinate’
Dimension of rate?
Catalysis Engineering - Kinetics
Rate expression
A + B C + D
Catalyst
How much detail ?
A + B + * AB* * + C + D
A + B [intermediates] C + D
etc.
overall rate expression?
.....),,,,( catalyst K k T pf r eqi
=
conditions
rate constant(s) thermodynamics
Catalysis Engineering - Kinetics
Rate expression – Gas phase reaction
2C B A c k c c k r ⋅−⋅⋅= −+
forward ratebackward
chance to success
amount of A × chance to meet B
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Catalysis Engineering - Kinetics
Role of catalyst?
Concentrating reactants
adsorption/complexation
Providing alternative reaction path
catalyst selectivity
other activation energy barrier
But:
– other components adsorb, too
block ‘active sites’ – fixed number of ‘active sites’
rate constant
affect rate
affect rate
affect rate
other form rate expression expected other form rate expression expected
Catalysis Engineering - Kinetics
Rate vs. pressure/concentration ?
rate
mol/s.gcat
pressure / kPa
• fixed number of active sites
• mono & bimolecular reactions
Catalysis Engineering - Kinetics
Rate expression – Catalysed reaction
C
ads
C B
ads
Asc k sc k r θ θ ⋅⋅−⋅⋅=
−+
forward ratebackward
chance to success
amount of A adsorbed
chance of adjacent B adsorbed
Note:
• cgas and cads differ • ratios components differ
Catalysis Engineering - Kinetics
Kinetics
Rate expressions in principle crucial for
– design
– process start-up and control
– process development and improvement
– selection reaction model
Often used in catalysis
– power rate models
– models based on elementary processes
• extrapolation more reliable
• intellectually process better understood
m
j
n
i p pk r ⋅⋅=
( )222
2
1
/
BB A A
eqB AB AT
pK pK
K p pK K k sN r
++
−=
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Catalysis Engineering - Kinetics
Simple example: reversible reaction
A B
A B
A* B*
‘Elementary processes’
‘Langmuir adsorption’
monomolecular
e.g. isomerization
Catalysis Engineering - Kinetics
Elementary processes
Rate expression follows from rate equation
r r r k p N k N A T T A= − = −− −1 1 1 1θ θ *
r r r k N k N T A T B= − = −− −2 2 2 2θ θ
r r r k N k p N T B B T = − = −− −3 3 3 3θ θ *
Eliminate unknown surface occupancies
Catalysis Engineering - Kinetics
Site balance:
(3.5)
Steady state assumption:
(3.6-7)
Rate expression:
(3.9)
Elementary processes contd.
1= + +θ θ θ * A B
0
0
=
=
dt
d
dt
d
B
A
θ
θ
321
321
:with
(......)(......)(.....)
)/(
K K K K
p p
K p pk k k N r
eq
B A
eqB AT
=
++
−=
Microkinetics
Michaelis-Menten
Algebraic eqs.
Catalysis Engineering - Kinetics
Quasi-equilibrium / rate determining step
r 1
r 2
r 3
r -1
r -2
r -3
r
rate determining
‘quasi-equilibrium’
r = r 2 - r -2
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Catalysis Engineering - Kinetics
Rate expression - r.d.s.
r r r k N k N T A T B= − = −− −2 2 2 2θ θ Rate determining step:
Eliminate unknown occupancies
Quasi-equilibrium:
r r k p N k N A T T A1 1 1 1= =− − θ θ *
So: θ θ
θ θ
A A
BB
K p K k
k p
K
= ⋅ =
= ⋅
−
1 11
1
3
*
*
with:
Catalysis Engineering - Kinetics
Rate expression, contd.
Substitution:
{ }
r r r k N K p k N p K
r k N K p k p k K K
T A T B
T A B
= − = −
= −
− −
−
2 2 2 1 2 3
2 1 2 2 1 3
θ θ
θ
* *
*
/
/
K K K K p
peq
B
A eq
= =
1 2 3where:
Unknown still θ *
Catalysis Engineering - Kinetics
Rate expression, contd.
Site balance:
{ }1 1 1 3= + + = ⋅ + +θ θ θ θ * * / A B A BK p p K
( )θ *
/= + +11 1 3K p p K A B
Finally:
{ }( )
r k N K p p K
K p p K
T A B eq
A B
= −
+ +
2 1
1 31
/
/
Catalysis Engineering - Kinetics
Surface occupancies
Empty sites
Occupied by A
Occupied by B
( )θ B
B
A B
p K
K p p K =
+ +
/
/3
1 31
( )θ A
A
A B
K p
K p p K =
+ +1
1 31 /
( )θ *
/=
+ +
1
1 1 3K p p K A B
BK K
=3
1
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Catalysis Engineering - Kinetics
Other steps rate determining
Adsorption r.d.s
Surface reaction r.d.s.
Desorption r.d.s.
{ }( )
r k N K p p K
K p p K
T A B eq
A B
= −
+ +
2 1
1 31
/
/
{ }( )
r k N K K p p K K K p
T A B eq
A
= −+ +
3 1 2
2 11 1/
{ }( )
r k N p p K
K p K
T A B eq
B
= −
+ +
1
2 31 1 1
/
/ /
Rule of thumb:Generally surface reaction r.d.s.Catalysis Engineering - Kinetics
Thermodynamics
Equilibrium constant
Adsorption constant
Reaction entropy
Reaction enthalpy
Adsorption enthalpy,
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Catalysis Engineering - Kinetics
Langmuir adsorption model
Generally used – although nonlinear, mathematically simple
– simple physical interpretation
– rather broadly applicable
• multicomponent adsorption
• non-uniform surfaces
– ‘compensation effect’
– very weak and strong sites do not contribute much
to the rate
• for microporous media (activated carbons) often
not satisfactory
Catalysis Engineering - Kinetics
Dissociative adsorption
H 2 + 2* 2H*
( )( )
θ H H H
H H
K p
K p=
+
2 2
2 2
0.5
0.5
1
Two adjacent sites needed
Catalysis Engineering - Kinetics
Initial rate expressions
Forward rates
Product terms negligible
r k p A='
0 r k p
K p A
A A
=+
'0
01r k = '
Adsorption Surface Desorption
r 0
T1
T2
T3
p A p A p A
T1
T2
T3
T1
T2
T3
See tutorial Catalysis Engineering - Kinetics
Dual site reaction :
A + B C
A + * ↔ A*
B + * ↔ B*
A* + B* ↔ C* + *
C* ↔ C + *
(r.d.s.)
{ }2421
213
/1
/
K p pK pK
K p p pK K N sk r
C B A
eqC B AT
+++
−=
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Catalysis Engineering - Kinetics
Dual site reaction, contd.
{ }*3333 θ θ θ θ C B AT k k N sr r r −− −⋅=−=
Number of neighbouring sites (here: 6)
Catalysis Engineering - Kinetics
More than one reactant
• One-site models
• Two-site models
e.g. hydrogenation, oxidation
dual site reaction
single site reaction
• Number of sites conditions dependent
)1(1 B AB A A
B A AB AT ABT
pK pK
p pK K kN kN r
++== θ
2)1( BB A A
BB A AT B AT
pK pK
pK pK skN skN r
++== θ θ
)1()1( BB A A
BB A AT B AT
pK pK
pK pK skN skN r
++== •∗θ θ
( )( ){ }21
21
0
1 A A
A AT T
pK
pK N N
+=
different sites
optimal surface concentrationsoptimal adsorption strengths
Catalysis Engineering - Kinetics
Langmuir-Hinshelwood/Hougen-Watson models
(LHHW)
r k ine tic fa ctor d rivin g fo rce
adsorpt ion term=
⋅( ) ( )
( )n
includes N T , k (rds)
For: A+B C+D
p A pB-pC pD /K eq
molecular: K A p Adissociative: (K A p A)
0.5 = 0, 1, 2...
number species in
and before r.d.s.
Catalysis Engineering - Kinetics
What about observed: reaction order activation energy ?
Determination:
i
i p
r n
ln
ln
∂
∂=
ln r
ln pi
slope = order ni
ln r
1/T
slope = -E aobs /R
T
r RT E obsa
∂
∂=
ln2
LHHW models ? ( )r
k N K p
K p K pT A A
A A B B
=+ +
2
1
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Catalysis Engineering - Kinetics
Reaction order - Activation energy
( )
r k N K p
K p K p
T A A
A A B B
=
+ +
2
1
rate expression
Reaction order
Activation energy
BB
A A
n
n
θ
θ
−=
−= 1
( ) BB A Aaobsa H H E E ∆−∆−+= θ θ 12
• depend strongly on occupancy!
• vary during reaction
limiting cases?
Catalysis Engineering - Kinetics
Limiting cases - forward rates
Surface reaction r.d.s.( )
r k N K p
K p K pT A A
A A B B
=+ +
2
1
1. Strong adsorption A
r k N T = 2
E E aobs
a= 2
A*
B*
A* #
E a2
Catalysis Engineering - Kinetics
Limiting cases - forward rates
2. Weak adsorption
r k N K pT A A= 2
Surface reaction r.d.s.( )
r k N K p
K p K pT A A
A A B B
=+ +
2
1
E E H aobs
a A= +2 ∆
A*
A(g) + *
A* #
E a2
Catalysis Engineering - Kinetics
Limiting cases - forward rates
3. Strong adsorption B
r k N K pK p
T A A
B B
= 2
Surface reaction r.d.s.( )
r k N K p
K p K p
T A A
A A B B
=+ +
2
1
E E H H aobs
a A B= + −2 ∆ ∆
A* #
B* + A
B+*+AE a2
A*
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Catalysis Engineering - Kinetics
Cracking of n-alkanes over ZSM-5J.Wei I&EC Res.33(1994)2467
A A pK k r 20 =
Aaobsa H E E ∆+= 2
Carbon number
negative!?E a2
E aobs
∆H A
kJ/mol
200
100
-200
-100
0
0 5 10 15 20
Catalysis Engineering - Kinetics
n-Alkanes cracking
Energy diagram
Initial state Transition state
Adsorbed state
A + *
∆H adsE a2
E a,obs
A* B*,C*
Catalysis Engineering - Kinetics
Observed temperature behaviour
• T higher coverage lower • Highest E a most favoured
Change in r.d.s.
1/T
ln r obs
desorption r.d.s.
adsorption r.d.s.
Catalysis Engineering - Kinetics
Catalytic reaction kinetics, summary
Langmuir adsorption
– uniform sites, no interaction adsorbed species,
finite number of sites, multicomponent
Rate expression derivation
– series of elementary steps
– steady state assumption, site balance
– quasi-equilibrium / rate determining step(s)
– initial rates (model selection)
LHHW models
– inhibition, variable reaction order, activationenergy
s i m p
l e r
mechanism kinetics
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Catalysis Engineering - Kinetics
Hydrodesulphurization kinetics
Sie, AIChE-J 42(1996)3498
• Apparent second order behaviour
• H2S inhibits strongly
Example HDS vacuum gasoil
0.0 0.1 0.2 0.3 0.4 0.5 0.6
1/LHSV (h)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
1 / S - 1 / S 0
( 1 / w t . % )
Gasoil CoMo-aluminatrickle flow L=0.2-0.4 m
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.5
1.0
1.5
2.0
bed length
c
concentration
conversion
fast decrease followed by slow decrease
Catalysis Engineering - Kinetics
Composition oil fractions
S
S
SR R
S
RS S
R
R S R
0 5 10 15 20 25 30
Vacuum gasoil
Simulated distillation b.p.
Sulphur compounds
Thioethers
ThiopheneBenzthiophene
Dibenzthiophene
Substituteddibenzthiophene
complex mixtures
different reactivities
⇒lumping
Catalysis Engineering - Kinetics
Simulated profiles - HDS reactivity lumping
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.5
1.0
1.5
2.0
bed length
c o n c e n t r a t i o n
Three lump model: first order reactionsSimulated model data:2 nd order
k=10 m3 /mol.sc 0 =2 mol/m
3
Three lump model:
1st orders
k 1=36.1 s-1 c 01=1.23
k 2 =16.0 s-1 c 02 =0.59
k 3=7.5 s-1 c 03=0.18
sum
1
2
3
Three lump model adequateInhibition through LHHW models Which groups lumped?
⇒model studiesCatalysis Engineering - Kinetics
Kinetic coupling between catalytic cycles
Bifunctional catalysis: Reforming
Isomerization n-pentane: n-C5 -> i -C5
Pt-function: n-C5 -> n-C5=
surface diffusion
Acid function: n-C5= -> i -C5=
surface diffusion
Pt-function: i -C5= -> i -C5
Coupled catalytic cycles on different sites
low concentrationclose proximity
See tutorial
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Catalysis Engineering - Kinetics
Initial rates - CO hydrogenation over Rh
Van Santen et al.
Kinetic model 1. CO + * ↔ CO*
2. CO* + * → C* + O* (r.d.s.)
r sN k T CO0 2= ⋅θ θ *
{ }
r sk N K p
K p
T CO CO
CO CO
02
2
1
=
+
Initial rate
0.2
0.40.6
0.8
1.0
O c
c u p a n c y ( - ) 400
450500
550
600
T e m p e r a t
u r e ( K )
0
200
400
600
800
R a t e
Catalysis Engineering - Kinetics
Catalysis Engineering - Kinetics
Catalysed N2O decomposition over oxides
Winter, Cimino
Rate expressions:
( )( )r
k p
p K
obs N O
O
=+
2
21 3
0.5
r k pobs N O= ⋅ 2
( )r k p
pobs
N O
O
= ⋅ 2
2
0.5
1st order
strong O2 inhibition
moderate inhibition
Also: orders 0.5-1
water inhibition
= Explain / derive =
Catalysis Engineering - Kinetics
N2O decomposition over Mn2O3
2 N 2 O 2N 2 + O2
Vannice et al. J.Catal. 1996
Rate expression
( )( )r
k N K p
K p p K
T N O
N O O
=+ +
2 1
1 3
0.5
2
2 21
Kinetic model1. N 2 O + * ↔ N 2 O* 2. N 2 O* → N 2 + O*
3. 2 O* ↔ 2* + O2
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Catalysis Engineering - Kinetics
N2O decomposition over Mn2O3Vannice et al. 1996
0.0 2.0 4.0 6.0 8.0 10.0
pO2
/ kPa
0.0
0.1
0.2
0.3
0.4
r / 1 0 - 6 m o l . s - 1 . g
- 1
Oxygen inhibitionorder N 2 O ~0.78
E aobs= 96 kJ/mol
648 K
638 K
623 K 608 K
598 K
= Explain =
pN2O = 10 kPa
Catalysis Engineering - Kinetics
N2O decomposition over Mn2O3Vannice et al. 1995
Kinetic model
1. N 2 O + * ↔ N 2 O*
2. N 2 O* → N 2 + O*
3. 2 O* ↔ 2* + O2
Rate expression
( )( )5.03112
22
2
1 K p pK
pK N k r
OON
ON T
++=
Values
E a2 130= kJ / mol
KJ/mol109S
kJ/mol92
3
3
=∆
=∆H
KJ/mol38S
kJ/mol29
1
1
−=∆
−=∆H
= Thermodynamically consistent =
Catalysis Engineering - Kinetics
Ethanol dehydrogenationFranckaerts &Froment
C 2 H 5 OH ↔ CH 3CHO + H 2
Model:
1. A + * ↔ A*
2. A* + * ↔ R* + S* (r.d.s.)
3. R* ↔ R + *
4. S* ↔ S + *
= Derive rate expression =
Cu-Co cat.
Catalysis Engineering - Kinetics
Initial rates - linear transformation
Full expression
Initial rate
After rearrangement
{ }{ }
r k s N K p p p K
K p K p K p
T A A R S eq
A A R R S S
= −
+ + +
2
21
/
{ }r
k K p
K p
A A
A A
0 21
=+
p
r k K
K
k K p A
A
A
A
A
0
1= + ⋅
y a b x = + ⋅linear form:
linear least squares fit
trends, positive parameters
Ethanol dehydrogenation
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Catalysis Engineering - Kinetics
Kinetic studies
( ) ( )oi i i
i o
i
i
F W
x r r
F W d
dx
⋅−=⇒⋅−=
ν ν
Rate equation
= model selection =
= rate parameters =
Differential reactor:• plug flow, low conversion
• CSTR
Take care catalyst
effectiveness = 1 !
Integral reactor
Catalysis Engineering -Kinetics
Model selection
Mechanistic information
Initial rate measurements
Fit data on rate expressions (non-linear least squares)
Best model:
– low SSR (sum of squares of residuals)
– no trending in residuals
– parameters significant
– parameters obey thermodynamics
– ‘linearization’
Catalysis Engineering - Kinetics
Data fitting - Parameter estimation
Linear least squares - straightforward
Nonlinear least squares methods:
– Simplex / Powell etc. (iterative)
– Levenberg-Marquardt (gradient)
( )O F Min x x
x f k K
obs calc
i
calc j
. .
(.... , ...)
= −
=
∑2
with:
to be estimated
= initial parameters values needed =
Catalysis Engineering -Kinetics
Model selection
Divergence rival models
Experimental design (sequential)
po
rate
model 1
model 2
experimental range
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Catalysis Engineering - Kinetics Catalysis Engineering - Kinetics
N2O decomposition over ZSM-5 (Co,Cu,Fe)
2 N 2 O 2N 2 + O2
Kapteijn et al. 11th ICC,1996
Rate expression
( )r k N p
k k T N O
= +1
1 2
2
1
Kinetic model
1. N 2 O + * → N 2 + O*
2. N 2 O + O* → N 2 + O2 + *
no oxygen inhibition
Catalysis Engineering - Kinetics
N2O decomposition over ZSM-5 (Co,Cu,Fe)Kapteijn et al. 11th ICC,1996
Rate expression
( )r
k N p
k k K pT N O
O
=+ +
1
1 2 3
2
21
Oxygen inhibition model
1. N 2 O + * → N 2 + O*
2. N 2 O + O* → N 2 + O2 + *
3. O2 + * ↔ *O2
0 2 4 6 8 10
p(O2) / kPa
0.0
0.2
0.4
0.6
0.8
1.0
X
( N 2
O )
Fe-ZSM-5
Co-ZSM-5
Cu-ZSM-5
743 K
833 K
793 K
733 K
688
773 K
Catalysis Engineering -Kinetics
Effect of CO on N2O decomposition
0.0 0.5 1.0 1.5 2.0
molar CO/N2O ratio
0.0
0.2
0.4
0.6
0.8
1.0
X ( N 2
O )
Co-ZSM-5 (693 K)
Cu-ZSM-5 (673 K)
Fe-ZSM-5 (673 K)
CO removes oxygen from surface
so ‘enhances’ step 2, oxygen removal
now observed: rate of step 1 r 1 = k 1 N T pN2O
increase: ~2, >3, >100
CO + O* → CO2 + *
CO + * ↔ CO* (Cu+)
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Catalysis Engineering - Kinetics
Effect of CO on N2O decomposition
rate without CO rate with CO
r k N pT N O= 1 2
So k 1 /k 2 = : 1 Co
>2 Cu>100 Fe
ratio = 1 + k 1 /k 2 and:21
21*
1 k k
k k O
+=θ
θ O* = 0.7
>0.9>0.99
( )211
12
k k
pN k r ON T
+=
Catalysis Engineering -Kinetics
Apparent activation energies N2O decompositionCO/ N2O = 2
Cu ( )r
k N p
k k K p
k N p
K pT N O
CO CO
T N O
CO CO
=+ +
≈1
1 2
12 2
1
Co,
Fe
r k N pT N O= 1 2
E E aobs
a= 1
E E H aobs
a CO= +1 ∆
Apparent activation energies (kJ/mol)
onl y N2O CO /N2O=2
Co 110 115
Cu 138 187
Fe 165 78
Catalysis Engineering - Kinetics
Apparent activation energies N2O decompositionCO/ N2O = 0
Co,Cu
Fe
( )r
k N p
k k T N O=
+1
1 2
2
1
r k N pT N O= 2 2E E a
ob sa= 2
E E E aobs
a a= mix( )1 2,
Apparent activation energies (kJ/mol)
on ly N2O CO /N2O=2
Co 110 115Cu 138 187
Fe 165 78
Catalysis Engineering -Kinetics
Kinetic coupling between catalytic cyclesadsorption effect on selectivity
Hydrogenation: butyne -> butene -> butane
A1 A2 A3
butyne and butene compete for the same sitesbut: K 1 >> K 2resulting high selectivity for butene (desired) possible
even when k 2 > k 1
since:
22
112,1
K k
K k S =
Meyer and Burwell (JACS 85(1963)2877) mol%:
2-butyne 22.0
cis-2-butene 77.2
trans-2-butene 0.7
1-butene 0.0
butane 0.1