from a detailed model of porous catalytic washcoat to the ... · from a detailed model of porous...

From a detailed model of porous catalytic washcoatto the effective model of entire catalytic monolith

Conference MODEGAT, Bad Herrenalb, September 14, 2009

Institute of Chemical Technology, Prague, Czech Republic

From a detailed model of porous catalytic washcoat

to the effective model of entire catalytic monolith

Petr Kočí, Vladimír Novák, František Štěpánek, Miloš Marek, Milan Kubíček

http://www.vscht.cz/monolith



catalytic sites,metal crystallites

(e.g. Pt)

~ 1-10 nm

porouswashcoat

(e.g. -Al2

O3

)

~ 10-100 m

monolith channelsd ~1 mmL ~ 10 cm

wall(metal foil

or ceramics)

~ 100 m

Catalytic monolith reactor



Multiple scales in catalytic monolith reactor

catalyticmonolith~ 10 cm

channelwith catalytic washcoat on the wall~ 1 mm

porouscatalyticwashcoat~ 10 m

meso-porous-Al2

O3with dispersed Pt particles~ 100 nm

macro-scale

micro-scale nano-scale

Kočí et al., 2006



L0 z

inlet gas outlet gasck

(z), T(z)

wall• heat accumulation & conduction• no reactions

kC kH

flowing gas• convection• mass & heat transfer

0

c*k

(z,r)(z,r)r

T*(z)

T*(z)

ck

(z) T(z)

porous washcoat• diffusion –

often not considered• adsorption, surface reactions• heat accumulation & conduction

Deff

Monolith channel

Güthenke

et al., 2007



flowing gasmass balance )()()(),( *

C

kkkk cc

εazk

zuc

ttzc

catalytic surfacemass balance

J

jjjm

m

m Rt

tz1

,,

,cap

νΨ1),(

flowing gasenthalpy balance

)()(),( *Hpp TTazk

zTcu

ttzTc

+ respective boundary & initial conditions

Standard mathematical model of a monolith channel -

1D washcoat

washcoat poresmass balance

J

jjjkkkC

k Rcc-εak

ttzcε

1,

**

* .ν)(1

),(

solid phaseenthalpy balance

)(1

),(

*

1R,2

*2*

***

TTak

RHzT

ttzTc

H

J

jjjzp

Güthenke

et al., 2007



flowing gasmass balance )()()(),( *

C

kkkk cc

εazk

zuc

ttzc

washcoat poresmass balance

J

jjjk

kk RrcD

ttrzcε

1,2

*2eff

** ),,( ν

catalytic surfacemass balance

J

jjjm

m

m Rt

trz1

,,

,cap

1),,( νΨ

flowing gasenthalpy balance

)()(),( *Hpp TTazk

zTcu

ttzTc

solid phaseenthalpy balance

)(1),(

d),(

*H

1 0,R2

*2*z

**p

*

TTatzk

rRHazT

ttzTc

J

j rjj

Mathematical model of a monolith channel -

2D (1D+1D) washcoat

+ respective boundary & initial conditionsGüthenke

et al., 2007



10 m (SEM)

•

macropores

(d ~ 1 m, void space among

the supporting material micro-particles)• mesopores

(d ~ 10 nm, pores inside

the supporting material micro-particles)

Complex porous structure: Overall effective diffusion coefficient

Deff

? 10-7

– 10-6

m2/s

Porous structure of the washcoat -

bimodal pore size distribution

220 nm (TEM)

macropores(black)

mesoporous-Al2

O3 (grey)CeO2

(white)

noble metalsPt crystallites(several nm)

Starý et al., 2006;

Kočí et al., 2006, 2007; Novák

et al., 2009



Computer reconstruction of porous catalyst from 2D images

2DSEMor TEMimage

binaryimage

0 5 10 15

0

0.2

0.4

0.6

0.8

1RRxRy

Autocorrelationfunction

R(u),pore-size distribution,particle-size distribution

30

m

3Drecon-structedmedium

Generation

of 3D medium:a) mechanistic(particles packingand sintering), orb) stochastic(Gaussian fields,simulated annealing)

Image processing,thresholding

Kosek et al., 2005



•

Phase function Z: R3

{0,1}Z(x) = 1 x

pore space

Z(x) = 0 x

solid

•

Phase volume fractions

=

Z(x)

… porosity

•

Auto-correlation function

RZ

(u) = (Z(x+u) -

)·(Z(x) -

)

/ (Z(x) - )2

•

Minkowski functionals–

Mean curvature

–

Gaussian curvature

•

Cord-length distribution function, etc.

u

RZ (u)

Lc

l

f(l)

Characterization of porous structure

Kosek et al., 2005



Direct reconstruction of 3D porous structurefrom X-ray microtomography

Scanning of the sample from different angles, superposition of the projections.

Advantage: Non-invasive method, 3D image of the porous medium obtained

Disadvantage: lower resolution than classical 2D SEM/TEM

Fig: 3D scanned cordierite substrate sample.

120 μm.

Novák et al., 2009



Two scales in catalytic monolith washcoat: micro and nano

catalyticmonolith~ 10 cm

channelwith catalytic washcoat on the wall~ 1 mm

porouscatalyticwashcoat~ 10 m

meso-porous-Al2

O3with dispersed Pt particles~ 100 nm

micro-scale nano-scale

Kočí et al., 2006



Reconstruction of porous Pt/-Al2

O3

catalyst on nano-scale

single -Al2

O3nano-particle

set of Pt nano-particles

cluster of -Al2

O3nano-particles

system of packed-Al2

O3

nano-particles

Pt/-Al2

O3

nano-systemwith discretised meso-

pores and Pt particles

5. Random Pt insertion onto-Al2

O3

surface (into available pores).

1. Defined -Al2

O3

nano-

particles (size, shape).2. -Al2

O3

agglomeration.

3. Random packing of -Al2

O3

nano-particles and/or clusters.4. Defined Pt nano-particles (size).

Kočí et al., 2009



Reconstruction of porous Pt/-Al2

O3

catalyst on micro-scale

Pt/-Al2

O3

micro-system= washcoat section with discretised macro-pores

1. Pt/-Al2

O3

nano-system (meso-porous structure, distribution of Pt nano-particles).

3. Random packing of Pt/-Al2

O3

micro-

particles with defined overlap (sintering level).

Pt/-Al2

O3

micro-particle= simplified representation

of the nano-system

Pt/-Al2

O3nano-system

2. Simplification of the nano-system into the form of defined Pt/-Al2

O3

micro-particle (size, shape, effective Pt concentration, mean internal meso-pore diameter).

Kočí et al., 2009



Evaluation of local pore sizes and local diffusivitiesLocal pore size determines local diffusivity(Knudsen diffusion). How to evaluate effective local pore size in general porous medium?

Maximum sphere inscription (MSI) methodMap of local pore sizes -> map of local diffusivities.Validation of MSI method –

comparison with molecular dynamics simulations.

Novák et al., 2009



Typical pore-size distributions in reconstructed Pt/-Al2

O3

Nano-scale model Micro-scale model

Real catalyst sample

(measured by mercury porosimetry)

Kočí et al., 2009



gas mass balances:

Mathematical model of mass & heat transport and reactionsin spatially 3D reconstructed porous catalyst(nano-

and micro-scale)

surface mass balances:

enthalpy balance:

Kočí et al., 2007, 2009



Mathematical model

boundary conditions:

test case reaction kinetics: CO oxidation on Pt/Al2

O3( * = active Pt site)

Kočí et al., 2007, 2009



CO concentration profile in Pt/-Al2

O3

nano-system

System size 0.1×0.1×0.1 m3. The delimited zones with zero CO concentration correspond tosolid -Al2

O3

nano-particles. The Pt particles (4 nm) are displayed in dark grey.Active CPt

= 184 mol/m3, T

= 653 K.

Kočí et al., 2009



Effects of Pt particles sizesSystem size 0.1×0.1×0.1 m3, constant total amount of Pt, vol. frac. Pt = 0.0013

CPt

.........

concentration of active Pt sites

............

Pt dispersionNPt

.........

number of active Pt sitesKočí et al., 2009



Profiles of the CO concentration and reaction rate.T = 240 °C, 3 and 1 m particles 1:16, sintering =0.15, M

= 18.1 %, CPt

= 50 mol/m3.Catalyst section size 10x10x10 m3.

CO oxidation in porous Pt/Al2

O3

catalyst –

micro-scale modelCO concentration CO reaction rate

Kočí et al., 2006, 2007



CO concentration profiles.3 and 1 m particles 1:16, sintering =0.15, M

= 18.1 %, CPt

= 50 mol/m3

Effect of temperature on internal concentration gradients

T = 220 °C T = 260 °C

Kočí et al., 2006, 2007



Dependence of effectiveness factoron temperature and catalyst morphology on micro-scale

= 10 m, active CPt

= 50 mol/m3, small:large Al2

O3

micro-particles ratio = 8

Kočí et al., 2007



Dependence of macropores surface density aM,hydraulic diameter dh

and macroporosity M

on the mixing ratio of the 1 and 3 m Al2

O3

micro-particles

Kočí et al., 2006, 2007



CO reaction rate profile in Pt/-Al2

O3

micro-systemLocal representation of entire washcoat layer ( = 30 m)

System size 30×10×10 m3,micro-scale model.Empty space = macro-pores.Packed spherical Pt/-Al2

O3

micro-particleswith diameters 1 m and 3 m,small:large

particles ratio 32,sintering level =0.15.Internal meso-pores d=10 nm.Active CPt

=50 mol.m−3

(uniform distribution),yO2

bnd=2 %, yCObnd=0.5 %, Tbnd=220°C.

Kočí et al., 2009



Calculated average reaction rates and effectiveness factorsfor a model Pt/-Al2

O3

catalytic washcoat

( = 30 m)

System size 30×10×10 m3, micro-scale model. Packed spherical Pt/-Al2

O3

micro-particleswith diameters 1 m and 3 m (small:large

particles ratio 32), sintering level =0.15.Internal meso-pores d=10 nm, active CPt

=50 mol.m−3, yO2bnd=2 %.

The calculated table of effective reaction rates for actual washcoat

structure can be used for evaluation of local reaction rates in the standard 1D model of monolith channel. -> Multi-scale model

Kočí et al., 2009



Multi-scale model –

simulated

CO light-off curve

Catalytic monolith 400 cpsi, L

= 10 cm, washcoat = 30 m, active CPt

= 50 mol/m3.SV = 60 000 h-1, yCO

in

= 0.3 %, yO2in

= 2 %.

Kočí et al., 2009



Multi-scale model –

Simulated CO light-off curveEffect of washcoat

macropores

sintering level

Catalytic monolith 400 cpsi, L

= 10 cm, washcoat = 30 m, active CPt

= 50 mol/m3.SV = 120 000 h-1, yCO

in

= 0.3 %, yO2in

= 2 %.Kočí et al., 2009



SummaryKočí et al., 2009

Kočí et al., 2009



Summary

Methodology and models for detailed simulations of reaction-transport processes in porous catalyst layer (washcoat) were discussed:

3D digital reconstruction of porous catalyst, based on 2D SEM/TEM images and 3D microtomopgraphy.

Evaluation of local pore sizes and diffusivities.

Solution of reaction-diffusion problem in heterogeneous 3D system.

Dependence of catalyst performance on its structure (-Al2

O3

and Pt particle sizes, sintering level, pore-size distribution, porosity).

Multi-scale approach –

the volume-averaged parameters calculated in the nano-

and micro-system used as input parameters for simulations at the full scale (entire monolith reactor).



References

P. Kočí, V. Novák, F. Štěpánek, M. Marek, M. Kubíček: Multi-scale modelling of reaction and transport in porous catalysts, Chemical Engineering Science (2009), in press, http://dx.doi.org/10.1016/j.ces.2009.06.068

V. Novák, F. Štěpánek, P. Kočí, M. Marek,

M. Kubíček: Evaluation of local pore sizes and transport properties in porous catalysts, Chemical Engineering Science (2009), in press, http://dx.doi.org/10.1016/j.ces.2009.09.009

P. Kočí, F. Štěpánek, M. Kubíček, M. Marek: Modelling of micro/nano-scale concentration and temperature gradients in porous supported catalysts, Chemical Engineering Science 62 (2007) 5380-

5385, http://dx.doi.org/10.1016/j.ces.2006.12.033

A. Güthenke, D. Chatterjee, M. Weibel, B. Krutzsch, P. Kočí, M. Marek, I. Nova, E. Tronconi: Current status of modeling

lean exhaust gas aftertreatment

catalysts in "Advances in Chemical Engineering vol. 33: Automotive Emission Control", pp. 103-211, ed. G. B. Marin, ISBN: 978-0-12-373900-1.

Elsevier (2007).

P. Kočí, F. Štěpánek, M. Kubíček, M. Marek: Meso-scale modelling of CO oxidation in digitally reconstructed porous Pt/ γ-Al2O3 catalyst, Chemical Engineering Science 61 (2006) 3240-3249, http://dx.doi.org/10.1016/j.ces.2005.12.008

J. Kosek, F. Štěpánek, M. Marek: Modelling

of

transport and

transformation

processes

in porous

and

multiphase

bodies, in Advances

in Chemical

Engineering

30 (2005) 137. Elsevier

2005.

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Institute of Chemical Technology, Prague, Czech Republic

From a detailed model of porous catalytic washcoat

to the effective model of entire catalytic monolith

Petr Kočí, Vladimír Novák, František Štěpánek, Miloš Marek, Milan Kubíček


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