Tutorial lecture on Interplay between reactivity and

Interplay between reactivity and transport phenomena in heterogeneous catalysis

Matteo Maestri

July 23, 2013 Conversationshaus - Norderney, Germany

Tutorial lecture on

Chemical reactor The reactor is the device within which the physicochemical transformations are caused. It can assume various shapes and modes of operations and be operated in a number of possible environments of pressure and temperature.

(images from internet)

Heterogeneous catalytic reactor

B A

REACTOR

CATALYST SUPPORT: ACTIVE SITES ARE DEPOSITED WITHIN THESE POROUS SOLIDS

Heterogeneous catalytic reactions by their nature involve a separate phase of catalyst embedded in a phase of

reacting species.

Film diffusion

Pore diffusion

Adsorption/ desorption

Boundary layer

Porous catalyst

Active sites

Chemical reaction

1

4

7

2 6

3 5

The way to the active sites

B A

B* A*

Film diffusion

Pore diffusion


Boundary layer

Porous catalyst

Active sites

Chemical reaction

1

4

7

2 6

3 5


B A

B* A*

Film diffusion

Pore diffusion


Boundary layer

Porous catalyst

Active sites

Chemical reaction

1

4

7

2 6

3 5


B A

B* A*

The observable reaction rate may differ

substantially from the intrinsic rate of

chemical transformation under bulk fluid

phase conditions.

Catalysts at work

Film diffusion

Pore diffusion

Adsorption/desorption

Boundarylayer

Porouscatalyst

Active sites

Chemical reaction

1

4

7

2 6

3 5

BA

BA

B A

How do transport phenomena and distribution of residence times in the reactor affect the observed reaction rate?

Outline

1) Effect of the distribution of the contact times in the reactor on the observed reaction rate

2) Inter-phase and intra-phase transport phenomena and their impact on the observed reaction rate

3) Show-case: effect of transport phenomena on catalyst reactivity

4) Take-home messages

Reactivity (for this talk)

3 [mol/m / ]Ar kc s=

A → B

0 exp Ek kRT

= −

A

B

E

Reaction coordinate

Outline





How long molecules stay in the reactor?

PLUG-FLOW-REACTOR: all molecules have same residence time and concetrations vary only along the length of the tubular reactor.

CONTINUOUS-FLOW STIRRED TANK REACTOR: due to vigorous agitation, the reactor contents are well mixed, so that effluent composition equals that in the tank

Residence time distribution in PFR

Time

INLET

0

x

V

Q


Time Time

INLET OUTLET

0

x

V

Q


Time Time

OUTLET INLET

0

x

V/Q

V

Q

Residence time distribution in CSTR

Time Time

INLET OUTLET

0

x

V

Q


Time Time

INLET OUTLET

0

x

V

Q


Time Time

INLET OUTLET

0

x

V

Q

V/Q

PFR Vs.CSTR reactor

Time

Time

Time

OUTLET

PFR

CSTR

INLET

PFR Vs.CSTR reactor

Time

Time

Time

OUTLET

PFR

CSTR

INLET

Does RTD affect the observed reactivity?

Do I have to expect different reactivity

even if I am running the reaction at constant

T, P and same inlet composition?

Effect of RTD on observed reaction rate 3 [mol/m / ]Ar kc s=A → B

Q = 10 m3/s cA,0=1 kmol/m3

V = 5 m3 k = 5 s-1 @ T = 500K – P = 1 atm

PLUG FLOW REACTOR

Every “small” element travels along the reactor without mixing with the rest

VQ

τ =

We want to run the reaction isothermally and pressure drops are negligible

V V+dV IN-OUT+PROD = ACC

0A A AV V dVQc Qc kc dV

+− − =


Q = 10 m3/s cA,0=1 kmol/m3

V = 5 m3 k = 5 s-1 @ T = 500K – P = 1 atm

PLUG FLOW REACTOR

Every “small” element travels along the reactor without mixing with the rest

Mass balance equation:

AA

dc kcdτ

= − ,0 exp( )A Ac c kτ= − ,0

,0

91%A A

A

c cc

χ−

= =

VQ

τ =



Q = 10 m3/s cA,0=1 kmol/m3

V = 5 m3 k = 5 s-1 @ T = 500K – P = 1 atm

Mixing is so fast that concentration of every species is uniform and homogeneous in the reactor

VQ

τ =

CONTINUOUS STIRRED TANK REACTOR (CSTR)


IN-OUT+PROD = ACC

,0 0A A AQc Qc kc V− − =


Q = 10 m3/s cA,0=1 kmol/m3

V = 5 m3 k = 5 s-1 @ T = 500K – P = 1 atm

Mass balance equation:

,0 0A A Ac c kcτ− − = ,0

1A

A

cc

kτ=

+


Mixing is so fast that concentration of every species is uniform and homogeneous in the reactor

VQ

τ =

CONTINUOUS STIRRED TANK REACTOR (CSTR)

,0

,0

71%A A

A

c cc

χ−

= =


Q = 10 m3/s cA,0=1 kmol/m3

V = 5 m3 k = 5 s-1 @ T = 500K – P = 1 atm

CSTR PFR

,0

,0

71%A A

A

c cc

χ−

= =,0

,0

91%A A

A

c cc

χ−

= =


Outline





Inter- and Intra-phase transport phenomena

3 [mol/m / ]Ar kc s=A → B

CA CA

CA,S

Catalytic slab

Interphase transport phenomena


CA CA

CA,S

Catalytic slab

L



CA CA

CA,S

L AA

DkL

= ( ),A A A SN k C C= −

,A Sr kC=

INTRINSIC REACTION RATE

MASS TRANSPORT RATE

Catalytic slab

Catalytic slab


CA CA

CA,S

L AA

DkL

= ( ),A A A SN k C C= −

,A Sr kC=


MASS TRANSPORT RATE

( ), ,A S A A A SkC V k C C S= −

Catalytic slab


CA CA

CA,S

L AA

DkL

= ( ),A A A SN k C C= −

,A Sr kC=


MASS TRANSPORT RATE

( ) ( )*, , ,A S A A A S A A A S

SkC k C C k C CV

= − = −

Catalytic slab


CA CA

CA,S

L AA

DkL

= ( ),A A A SN k C C= −

,A Sr kC=


MASS TRANSPORT RATE

,

*11

A AA S

A

C CC k Dak

= =++

Interphase transport phenomena ,

*11

A AA S

A

C CC k Dak

= =++

1

, *

*

1 1

1A

obs A S A obs AA

A

Cr kC k C k Ck k kk

−

= = = + = +

Da << 1 Da>>1

obs Ar kC= *obs A Ar k C=

CHEMICAL REGIME MASS TRANSFER REGIME

Effect on observable reaction rate

Da<<1 Da >> 1

obs Ar kC= *obs A Ar k C=

CHEMICAL REGIME MASS TRANSFER REGIME

0 expobsEk k k

RT− = =

*

00expobs A

Ek k kRT

− → = =

*0

0expobs AEk k kRT

− → = =

Transport coefficient has very weak dependence on temperature

Catalytic slab

Intraphase transport phenomena

CA CA

CA,S

L AA

DkL

= ( ),A A A SN k C C= −

, ( )A Sr kC g y= =

MASS TRANSPORT RATE

WE CONSIDER NOW THE POSSIBILITY THAT TRANSPORT WITHIN THE SLAB CAN BECOME LIMITING

, ( )A SC f y=

Catalytic slab


CA CA

CA,S(y)

L

y y+dy

( ) ( ) ( ) 0eff effA AA A A

y y dy

dC y dC yD S D S kC y Sdydy dy +

− − − − =

Catalytic slab


CA CA

CA,S(y)

L

2

2

( ) ( )eff AA A

d C yD kC ydy

= 0

,

0

( )

A

A A S

dCdy

C y L C

=

= =

Intraphase transport phenomena 2

2

( ) ( )eff AA A

d C yD kC ydy

= 0

,

0

( )

A

A A S

dCdy

C y L C

=

= =

( ) ,

cosh( )

coshA A S

yLC y C

φ

φ

=

eff

A

k reaction rateLD diffusion rate

φ = ≈where:

THIELE MODULUS

Intraphase concentration gradients

So what?

At what extent am I using the catalyst?

( ),

( )tanhA

obs V

S A S

kC V dVRR kC V

φη

φ= = =

∫


( ),

( )tanhA

obs V

S A S

kC V dVRR kC V

φη

φ= = =

∫

For high values of Thiele modulus (internal mass transfer limitations):

1ηφ

→

, , ,1 1 1 eff

Aobs S S A S A S obs A S

DR R R kC kC k CL k

ηφ φ

= = = = =

1 1effeffA

obs ADk k D k

L k L

= =


0

1 1 exp

exp

effeff obsA

obs A obsEDk k D k k

L k L RT

Ek kRT

= = = − = −

2obsEE =

Interplay between kinetic and transport

1/T

Rat

e of

reac

tion,

log

scal

e

EslopeR

= −

CHEMICAL REGIME

0 exp Ek kRT

= −

INTRINSIC ACTIVATION ENERGY (dashed line)

OBSERVED ACTIVATION ENERGY (solid line)


1/T

Rat

e of

reac

tion,

log

scal

e

EslopeR

= −

2EslopeR

= −

CHEMICAL REGIME INTRAPHASE MASS

TRANSFER REGIME

0 exp Ek kRT

= −




1/T

Rat

e of

reac

tion,

log

scal

e

EslopeR

= −

2EslopeR

= −0slope →


TRANSFER REGIME

INTER MASS TRANSFER

REGIME

0 exp Ek kRT

= −




1/T

Rat

e of

reac

tion,

log

scal

e

EslopeR

= −

2EslopeR

= −0slope →


TRANSFER REGIME

INTER MASS TRANSFER

REGIME

Homogeneous reaction

0 exp Ek kRT

= −



Outline





Annular Reactor

Annular reactor

Laminar flow ⇒ negligible pressure drops

High GHSV ⇒ 106 – 107 Nl/Kgcat/h

⇒ distance from chemical equilibrium

Small annular gap (0.5 mm) and thin catalyst layers

Regular geometry (easy modeling)

Thermal equilibrium across the section of the ceramic tube

Isothermal conditions are easily reached (efficient heat dissipation by

radiation, dilution)

M. Maestri, A. Beretta, T. Faravelli, G. Groppi, E. Tronconi, D.G. Vlachos, Chemical Engineering Science, 2008

Combustion of a fuel-rich H2 over Rh catalyst in an annular reactor (*)

0

0,2

0,4

0,6

0,8

1

1,2

0 100 200 300 400 500 600

O2

Conv

ersi

on [%

]

Temperature [°C]

Annular reactor - experiments

1

4

7

2 6

3 5

Governing equations

B A

Fluid Phase

Solid Phase

B A

multiRegion

Governing equations

( )ρ ω αΓ ∇ = − Ω =, 1,...,het

k mix k cat kcatalytick NG

ω∇ = 0k inert

( )∇ = ,inert

T g t T

( )λ α=

∇ = − ∆∑ 1

NRhet het

cat j jcatalyticj

T H r

Catalytic walls

Non-catalytic walls

( )= ,inert

T f t T

1. H2+2Rh(s)=>2H(s) 2. 2H(s)=>H2+2Rh(s) 3. O2+2Rh(s)=>2O(s) 4. 2O(s)=>O2+2Rh(s) 5. OH(s)+Rh(s)=>H(s)+O(s) 6. H(s)+O(s)=>OH(s)+Rh(s) 7. H2O(s)+Rh(s)=>H(s)+OH(s) 8. H(s)+OH(s)=>H2O(s)+Rh(s) 9. H2O(s)+O(s)=>2OH(s) 10. 2OH(s)=>H2O(s)+O(s) 11. OH+Rh(s)=>OH(s) 12. OH(s)=>OH+Rh(s) 13. H2O+Rh(s)=>H2O(s) 14. H2O(s)=>H2O+Rh(s) 15. H+Rh(s)=>H(s) 16. H(s)=>H+Rh(s) 17. O+Rh(s)=>O(s) 18. O(s)=>O+Rh(s)

Detailed microkinetic models

M. Maestri, Microkinetic analysis of complex chemical processes at surface, in “New strategy for chemical synthesis and catalysis”, Wiley-VCH (2012)

θσ ∂= Ω =

∂ 1,...,heti

cat i i NSt

Adsorbed (surface) species

Identification of the calculation domain

Cylindrical symmetry 2D domain Lower computational

effort

Fluid and solid regions

M. Maestri, A. Beretta, T. Faravelli, G. Groppi, E. Tronconi, D.G. Vlachos, Chemical Engineering Science, 2008


0

0,2

0,4

0,6

0,8

1

1,2

0 100 200 300 400 500 600

O2

Conv

ersi

on [%

]

Temperature [°C]

Annular reactor

No resistances in the porous washcoat


0

0,2

0,4

0,6

0,8

1

1,2

0 100 200 300 400 500 600

O2

Conv

ersi

on [%

]

Temperature [°C]

Annular reactor

No resistances in the porous washcoat


0

0,2

0,4

0,6

0,8

1

1,2

0 100 200 300 400 500 600

O2

Conv

ersi

on [%

]

Temperature [°C]

Model results

multiRegion


0

0,2

0,4

0,6

0,8

1

1,2

0 100 200 300 400 500 600

O2

Conv

ersi

on [%

]

Temperature [°C]

multiRegion

Model results

,0,000

,002,000

,004,000

,006,000

,008,000

,010,000

,012,000

,014,000

,016,000

0 10 20 30 40 50

O2 m

ass f

ract

ion

Catalytic Layer Width [μm]

0.000E+00

05E-04

10E-04

15E-04

20E-04

25E-04

30E-04

35E-04

40E-04

0 10 20 30 40 50

O2 m

ass f

ract

ion


0E+00

1E-04

2E-04

3E-04

4E-04

5E-04

6E-04

7E-04

8E-04

0 10 20 30 40 50

O2 m

ass f

ract

ion


0E+00

1E-05

2E-05

3E-05

4E-05

5E-05

6E-05

7E-05

8E-05

9E-05

0 10 20 30 40 50

O2 m

ass f

ract

ion


373 K 423 K

523 K 823 K

0E+00

2E-03

4E-03

6E-03

8E-03

1E-02

1E-02

0 10 20 30 40 50

O2 m

ass f

ract

ion


373 K 423 K 523 K 823 K

Different controlling regimes at different T

Intraphase gradients

0

0,2

0,4

0,6

0,8

1

1,2

0 100 200 300 400 500 600

O2

Conv

ersi

on [%

]

Temperature [°C]

Interphase gradients

150°C

400°C

500°C

H2 mole fraction

[0-0.04] [0-0.10] [0-0.05]

O2 mole fraction H2O mole fraction

0

0,2

0,4

0,6

0,8

1

1,2

0 100 200 300 400 500 600

O2

Conv

ersi

on [%

]

Temperature [°C]

Outline





Take-home messages 1) Physical transport may have a strong influence on the rate of the overall

process and may introduce additional dependences on the operating conditions

2) The observable reaction rate may differ substantially from the intrinsic rate of the chemical transformation under bulk fluid phase composition

A A A A A*

A* A*

A* 0

x

Chemical regime Internal mass transfer regime

Internal/External mass transfer

regime

Fully external mass transfer regime

TEMPERATURE

Take-home messages 1) Physical transport may have a strong influence on the rate of the overall

process and may introduce additional dependences on the operating conditions

2) The observable reaction rate may differ substantially from the intrinsic rate of the chemical transformation under bulk fluid phase composition

3) You need to be aware of such interplay and related effects in order to: 1) understand what you are measuring 2) understand what you are comparing 3) scale-up properly and successfully your reaction 4) force your catalyst to the desired observed functionality

(selectivity €€€!! – safe operation)

4) Reactivity measurement is intrinsically a multiscale phenomenon: make sure you minimize the effect of transport (dilution, temperature, geometry)

A first-principles approach to CRE

Time

Leng

th

MICROSCALE making and breaking of

chemical bonds

MESOSCALE Interplay among the

chemical events

MACROSCALE Reactor engineering and

transport phenomena CFD

Electronic structure theory

kMC

Thank you for your attention!

www.catalyticfoam.polimi.it

Politecnico di Milano Raffaello, The school of Athens, 1509, Apostolic Palace, Roma

[email protected]

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Tutorial lecture on Interplay between reactivity and