Catalysis and Catalysts - Kinetics Catalytic Reaction Kinetics Why catalytic reaction kinetics Derivation rate expressions Simplifications –Rate.

Catalysis and Catalysts - Kinetics

Catalytic Reaction KineticsCatalytic Reaction Kinetics

Why catalytic reaction kinetics Derivation rate expressions Simplifications

– Rate determining step– Initial reaction rate

Limiting cases– Temperature dependency– Pressure dependency

Examples


Reactor design equationReactor design equation

dx

d W Fri

ii

stoichiometric coefficient i

catalyst effectiveness

rate expression

conversion i

‘space time’


Simple example: reversible reaction A B

Simple example: reversible reaction A B

A B

A*

B*

‘Elementary processes’

‘Langmuir adsorption’

1

2

3A + * A*

k1

k-1

A* B*k-2

k2

B* B + *k3

k -3

1.

2.

3.


Elementary processesElementary processes

Rate expression follows from rate equation:

At steady state:

1 1 1 1 A T * 1 T Ar r r k p N k N

2 2 2 2 T A 2 T Br r r k N k N

3 3 3 3 T B 3 B T *r r r k N k p N

Eliminate unknown surface occupancies

1 2 3r r r r


Site balance:(7.5)

Steady-state assumption:(7.6-7)

Rate expression:(7.9)

* A B1

A

B

d0

dd

0d

t

t

T 1 2 3 A B eq

eq 1 2 3A B

( / )with:

(.....) (......) (......)

N k k k p p Kr K K K K

p p

Elementary processes contd.Elementary processes contd.


Quasi-equilibrium / rate-determining stepQuasi-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


Rate expression r.d.s.Rate expression r.d.s.

2 2 2 T A 2 T Br r r k N k N

Rate determining step:

Eliminate unknown occupancies

Quasi-equilibrium:

1 1 1 A T * 1 T A r r k p N k N

So:

1A 1 A * 1

1

BB *

3

with: k

K p Kk

p

K


Rate expression, contd.

Substitution:

2 2 2 T 1 A * 2 T B * 3

2 T 1 * A B eq

/

/

r r r k N K p k N p K

r k N K p p K

B

eq 1 2 3A eq

pK K K K

p

where:

Unknown still *


Rate expression, contd.

Site balance:

* A B * 1 A B 31 1 /K p p K

*1 A B 3

1

1 /K p p K

Finally:

T 2 1 A B eq

1 A B 3

/

1 /

N k K p p Kr

K p p K


Adsorption r.d.s

Surface reaction r.d.s.

Desorption r.d.s.

T 2 1 A B eq

1 A B 3

/

1 /

N k K p p Kr

K p p K

T 3 1 2 A B eq

2 1 A

/

1 1

N k K K p p Kr

K K p

T 1 A B eq

2 B 3

/

1 1 1/ /

N k p p Kr

K p K

Other rate-determining stepsOther rate-determining steps


Langmuir adsorptionLangmuir adsorption

Uniform surface (no heterogeneity) Constant number of identical sites Only one molecule per site No interaction between adsorbed species

A + * A*

A AA

A A1

K p

K p

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

0.1

100

10

1

pA (bar)

KA (bar-1)


Equilibrium constant

Adsorption constant

Reaction entropy

Reaction enthalpy

Adsorption enthalpy,<0(J/mol)

Adsorption entropy, <0(J/mol K)

atm-1

oooeq STTHTGKRT )()(ln

)(, TGi

oifi

0 0

ln A AA

S HK

R RT

ThermodynamicsThermodynamics


Multicomponent adsorption / inhibitionMulticomponent adsorption / inhibition

Langmuir adsorption

A A

A A I I1A

K p

K p K p

Inhibitors


Dissociative adsorptionDissociative adsorption

H2 + 2* 2H*

2 2

2 2

0.5

H H

H 0.5

H H1

K p

K p

Two adjacent sites needed


Langmuir-Hinshelwood/Hougen-Watson models (LHHW)

Langmuir-Hinshelwood/Hougen-Watson models (LHHW)

rkinetic factor driving force

adsorption term

( ) ( )

( )n

includes NT, k(rds)

For: A+B C+D

pApB-pCpD/Keq

molecular: KApA

dissociative: (KApA)0.5 = 0, 1, 2number of species in r.d.s.


Verwerking p. 11 t/m 13


Initial rate expressionsInitial rate expressions

Forward rates Product terms negligible

0 T 1 A0r N k p T 2 A A0

0A A01

N k K pr

K p0 T 3r N k

r0

T1

T2

T3

pA0pA0 pA0

T1

T2

T3

T1

T2

T3

Adsorption Surface reaction Desorption

(K2 and KApA0 >>1)


Ethanol dehydrogenationEthanol dehydrogenationFranckaerts &Froment

C2H5OH CH3CHO + H2

Model:

1. A + * A*2. A* + * R* + S* (r.d.s.)3. R* R + *4. S* S + *

= Derive rate expression =

Cu-Co cat.


Initial rates - linear transformationInitial rates - linear transformation

Full expression

Initial rate

After rearrangement

2 T A A R S eq

2

A A R R S S

/K

1

k s N K p p pr

K p K p K p

A A

0 2 T2

A A

with1

k K pr k k sN

K p

A AA

0 A A

1p Kp

r k K k K

y a b x linear form:

linear least squares fittrends, positive parameters

Ethanol dehydrogenation


Initial rates - CO hydrogenation over RhInitial rates - CO hydrogenation over RhVan Santen et al.

Kinetic model

1. CO + * CO*2. CO* + * C* + O* (r.d.s.)

0 T 2 CO *r sN k

2 T CO CO

0 2

CO CO1

sk N K pr

K p

Initial rate

0.2

0.4

0.6

0.8

1.0

Occupancy (-) 400450

500550

600

Temperature (K)

0

200

400

600

800

Ra

te


*A *A# *Bk-#

k+# kbarrier

Verwerking p. 18 t/m21

Temperature and Pressure DependenceTemperature and Pressure Dependence


Limiting cases - forward ratesLimiting cases - forward rates


2 T A A

A A B B1

k N K pr

K p K p

1. Strong adsorption A

2 Tr k N

obsa a2E E

A*

B*

A* #

Ea2


2. Weak adsorption

2 T A Ar k N K p

obsa a2 AE E H


2 T A A

A A B B1

k N K pr

K p K p

A*

A(g) + *

A* #

Ea2

HA



3. Strong adsorption B

2 T A A

B B

k N K pr

K p

obsa a2 A BE E H H


2 T A A

A A B B1

k N K pr

K p K p

A* #

B* + A

B + *+ AEa2

A*- HB

HA



Cracking of n-alkanes over ZSM-5J. Wei I&EC Res.33(1994)2467

Ea2

Eaobs

HA

Carbon number

kJ/mol

200

100

-200

-100

0

0 2 A Ar k K p

obsa a2 AE E H


Observed temperature behaviourObserved temperature behaviour

1/T

ln robs

desorption r.d.s.

adsorption r.d.s.

•T higher coverage lower•Highest Ea most favoured

Change in r.d.s.


Pt-catalysed dehydrogenation of methylcyclohexane:

M T + H2

Two kinetic significant steps:* + M ....T* T + *

mari

no inhibition by e.g. benzeneT* much higher than equilibrium with gas phase T

‘Kinetic Coupling’ two kinetically significant steps

‘Kinetic Coupling’ two kinetically significant steps


Heat of adsorption

Rate

Sabatier principle - Volcano plotSabatier principle - Volcano plot


Langmuir adsorption– uniform sites– no interaction adsorbed species– constant number of sites

Rate expression– series of elementary steps– steady state assumption – site balance– quasi-equilibrium / rate determining step(s)– initial rates

simpler

mechanism kinetics

SummarySummary


Catalysed N2O decomposition over oxidesWinter, Cimino

Rate expressions:

rk p

p Kobs 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 0.5-1water inhibition

= Explain / derive =


N2O decomposition over Mn2O3

2 N2O 2N2 + O2

Vannice et al. 1995

Rate expression

rk N K p

K p p KT N O

N O O

2 1

1 3

0.52

2 21

Kinetic model

1. N2O + * N2O*2. N2O* N2 + O*3. 2 O* 2* + O2



Vannice et al. 1995

Oxygen inhibitionorder N2O ~0.78

Eaobs= 96 kJ/mol

= Explain =

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

mol

.s-1.g

-1648 K

638 K

623 K608 K

598 K

pN2O = 10 kPa



Vannice et al. 1995

Kinetic model

1. N2O + * N2O*2. N2O* N2 + O*3. 2 O* 2* + O2

Rate expression

5.031

12

22

2

1 KppK

pKNkr

OON

ONT

Values

Ea2 130 kJ / mol

K J/mol 109S

kJ/mol 92

3

3

H

K J/mol 38S

kJ/mol 29

1

1

H

= Thermodynamically consistent =


N2O decomposition over ZSM-5 (Co,Cu,Fe)

2 N2O 2N2 + O2

Kapteijn et al. 11th ICC,1996

Rate expression

rk N p

k kT N O

1

1 2

2

1

Kinetic model

1. N2O + * N2 + O*2. N2O + O* N2 + O2 + *

no oxygen inhibition


N2O decomposition over ZSM-5 (Co,Cu,Fe)Kapteijn et al. 11th ICC,1996

Rate expression

rk N p

k k K pT N O

O

1

1 2 3

2

21

Oxygen inhibition model

1. N2O + * N2 + O*2. N2O + O* N2 + 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

2O

)

Fe-ZSM-5

Co-ZSM-5

Cu-ZSM-5

743 K

833 K

793 K

733 K

773 K

688K


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

2O

)

Co-ZSM-5 (693 K)

Cu-ZSM-5 (673 K)

Fe-ZSM-5 (673 K)

CO removes oxygen from surfaceso ‘enhances’ step 2, oxygen removal

now observed: rate of step 1 r1 = k1 NT pN2O

increase: ~2, >3, >100

CO + O* CO2 + *

CO + * CO* (Cu+)


Effect of CO on N2O decomposition

rate without CO rate with CO

r k N pT N O 1 2

So k1/k2 = : 1 Co>2 Cu>100 Fe

ratio = 1 + k1/k2 and:21

21* 1 kk

kkO

O* 0.7>0.9>0.99

21

1

12

kk

pNkr ONT


Apparent activation energies N2O decompositionCO/ N2O = 2

Cu rk 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 Eaobs

a 1

E E Haobs

a CO 1

Apparent activation energies (kJ/mol)

only N2O CO/N2O=2

Co 110 115

Cu 138 187

Fe 165 78


Apparent activation energies N2O decompositionCO/ N2O = 0

Co,Cu

Fe

rk N p

k kT N O

1

1 2

2

1

r k N pT N O 2 2 E Eaobs

a 2

E E Eaobs

a amix( )1 2,

Apparent activation energies (kJ/mol)

only N2O CO/N2O=2

Co 110 115

Cu 138 187

Fe 165 78


Complex kineticsHDN of Quinone over NiMo/Al2O3 (Prins & Jian, Zurich)

Kinetic scheme

Q THQ1 OPA PB

THQ5 DHQ PCHA

PCH

PCHE

N N

NN

NH2

NH2

Purpose: Kinetics of reactionEffects functions Ni and MoAddition role of P


Complex kinetics

Subscheme research: HDN of OPA

OPA PB

PCHA PCHPCHE

NH2

NH2

Not observedintermediate,not significant


Complex kineticsHDN of OPA

Derived global scheme:

OPA PB

PCHPCHE

k3

k5

k6

k1

NH2 How can this ‘direct’ stepbe rationalised?


Complex kineticsHDN of OPA (Jiang & Prins)

Reaction modelling

space time (cs)

0 10 20 30 40 50 60

0.0

0.2

0.4

0.6

0.8

1.0

0

1

2

3

4

5

OPA NiMo one site model 370C

Par

tial p

ress

ure

(kP

a)

Par

tial p

ress

ure

(kP

a)

OPA

PBPCHE

PCH

strong adsorptionN-containg species

plug flow reactor

excellent fit


Complex kineticsHDN of OPA

OPA + *

OPA* PB + *

PCHA* PCHA + *

PCHE* PCHE + *

PCH + *

HCs not adsorbed(weakly compared to N-s)

Only traces foundFast reactionsteps

slow

The direct route to PCH

Competitive parallel steps

Other hydrogenation functional sites ?

Direct globalroutes

kb

ka

kc

kd ke


Rate expressions•Steady state assumption•Site balance (one site)•Strong adsorption N-species

r

k k K p

kk k

K p K pOPA

a b OPA OPA

a

c dOPA OPA NH NH

1 1

3 3

r

k kk k

K p k p

kk k

K p K pPCH

a d

a dOPA OPA e PCHE

a

c dOPA OPA NH NH

1 1

3 3

parallel reactions

direct routefrom PCHE

Q: explain zero order OPA



‘Kinetic coupling’two steps kinetically significant

Decomposition of ammonia over Mo (low p, high T)

2NH3 -> N2 + 3H2

Steps: 2NH3 + * -> 2N* + 3H2

2N* -> N2

surface concentration N much higher than equilibriumwith N2 pressure

‘fugacity of N* corresponds with virtual fugacity N2


Virtual fugacity, kinetic coupling

Aromatization light alkanes over zeolite

Alkanes -> Aromatics + Hydrogen

• Cracking yields high H*, so high fugacity H*• H* not in equilibrium with H2

-> low aromatics selectivity

Addition of Ga provides escape route for H*

Kinetic coupling used to increase reaction selectivity for aromatics

zeolite: alkane -> 2H* + .....Ga: 2H* -> H2


Kinetic coupling between catalytic cycleseffect on selectivity

Hydrogenation: butyne -> butene -> butane A1 A2 A3

butyne and butene compete for the same sitesbut: K1 >> K2 resulting high selectivity for butene (desired) possibleeven when k2 > k1

since:22

112,1 Kk

KkS

Meyer and Burwell (JACS 85(1963)2877) mol%:2-butyne 22.0cis-2-butene 77.2trans-2-butene 0.71-butene 0.0butane 0.1


Kinetic coupling between catalytic cycleseffect on selectivity

Bifunctional catalysis: Reforming

Isomerization n-pentane: n-C5 -> i-C5

Pt-function: n-C5 -> n-C5=

surface diffusionAcid function: n-C5= -> i-C5=

surface diffusionPt-function: i-C5= -> i-C5

Catalytic cycles on different catalysts

Affect selectivity:• modify surface (change adsorption properties)• modify fluid phase (change adsorption properties)

benzene hydrogenation M. Soede

low concentrationclose proximity


Competitive adsorption Selective hydrogenation aromaticsCompetitive adsorption

Selective hydrogenation aromatics

S.Toppinen,Thesis 1996S.Toppinen,Thesis 1996

0 2 4 6 8 10

space time / min.g.ml-1

0

5

10

15

20

25

30

conc

entr

atio

n / w

t.%

CH3

CH3

CH3

CH2

CH3

CH3

H3C CH3

Ni-alumina trilobe catalyst3 mm particles40 bar H2

125oCsemi-batch reactor

Ni-alumina trilobe catalyst3 mm particles40 bar H2

125oCsemi-batch reactor

•Consecutive conversion behaviour•rate constants ~ similar•adsorption constants decrease

•Consecutive conversion behaviour•rate constants ~ similar•adsorption constants decrease

Propose a rate expression to account for this effectPropose a rate expression to account for this effect


Partial benzene hydrogenationPartial benzene hydrogenation

Ru-catalyst - clusters of crystallites Slurry reaction, elevated pressures Water-salt addition increases selectivity

+ + 2 H2 H2

RuSalt-water

Adsorption / Desorption properties affectedAdsorption / Desorption properties affected


Dual site models:A + B C

A + * A*

B + * B*

A* + B* C* + *

C* C + *

(r.d.s.)

2

421

213

/1

/

KppKpK

KpppKKNskr

CBA

eqCBAT


Surface occupanciesSurface occupancies

Empty sites:

Occupied by A:

Occupied by B:

B 3

B1 A B 3

/

1 /

p K

K p p K

1 A

A1 A B 31 /

K p

K p p K

*1 A B 3

1

1 /K p p K


Dual site models, contd.

*3333 CBAT kkNsrrr

Number of neighbouring sites (here: 6)

Catalysis and Catalysts - Kinetics Catalytic Reaction Kinetics Why catalytic reaction kinetics Derivation rate expressions Simplifications –Rate.

Documents

r rate

expression initial rate

rate equation

step r

step initial reaction

p b p c p d

b c d p

s surface reaction