Chap 03 Masters

8/20/2019 Chap 03 Masters

1/15

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


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?


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


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


2/15


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


Rate vs. pressure/concentration ?

rate

mol/s.gcat

pressure / kPa

• fixed number of active sites

• mono & bimolecular reactions


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


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

++

−=


3/15


Simple example: reversible reaction

A B

A B

A* B*

‘Elementary processes’

‘Langmuir adsorption’

monomolecular

e.g. isomerization


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


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.


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


4/15


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:


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 *


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

/

/


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


5/15


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,


6/15


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


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


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

+++

−=


7/15


Dual site reaction, contd.

{ }*3333 θ θ θ θ C B AT k k N sr r r −− −⋅=−=

Number of neighbouring sites (here: 6)


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


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.


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


8/15


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?


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



2. Weak adsorption

r k N K pT A A= 2


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



3. Strong adsorption B

r k N K pK p

T A A

B B

= 2


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*


9/15


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


n-Alkanes cracking

Energy diagram

Initial state Transition state

Adsorbed state

A + *

∆H adsE a2

E a,obs

A* B*,C*


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.


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


10/15


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


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


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


11/15


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



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 =


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


12/15


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


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 =


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.


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


13/15


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’


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 =


Model selection

Divergence rival models

Experimental design (sequential)

po

rate

model 1

model 2

experimental range


14/15

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


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


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+)


15/15


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

+=


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


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


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

Chap 03 Masters

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