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
From a detailed model of porous catalytic washcoatto the effective model of entire catalytic monolith
Conference MODEGAT, Bad Herrenalb, September 14, 2009
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
From a detailed model of porous catalytic washcoatto the effective model of entire catalytic monolith
Conference MODEGAT, Bad Herrenalb, September 14, 2009
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
From a detailed model of porous catalytic washcoatto the effective model of entire catalytic monolith
Conference MODEGAT, Bad Herrenalb, September 14, 2009
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
From a detailed model of porous catalytic washcoatto the effective model of entire catalytic monolith
Conference MODEGAT, Bad Herrenalb, September 14, 2009
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
From a detailed model of porous catalytic washcoatto the effective model of entire catalytic monolith
Conference MODEGAT, Bad Herrenalb, September 14, 2009
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
From a detailed model of porous catalytic washcoatto the effective model of entire catalytic monolith
Conference MODEGAT, Bad Herrenalb, September 14, 2009
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
From a detailed model of porous catalytic washcoatto the effective model of entire catalytic monolith
Conference MODEGAT, Bad Herrenalb, September 14, 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
From a detailed model of porous catalytic washcoatto the effective model of entire catalytic monolith
Conference MODEGAT, Bad Herrenalb, September 14, 2009
•
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
From a detailed model of porous catalytic washcoatto the effective model of entire catalytic monolith
Conference MODEGAT, Bad Herrenalb, September 14, 2009
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
From a detailed model of porous catalytic washcoatto the effective model of entire catalytic monolith
Conference MODEGAT, Bad Herrenalb, September 14, 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
From a detailed model of porous catalytic washcoatto the effective model of entire catalytic monolith
Conference MODEGAT, Bad Herrenalb, September 14, 2009
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
From a detailed model of porous catalytic washcoatto the effective model of entire catalytic monolith
Conference MODEGAT, Bad Herrenalb, September 14, 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
From a detailed model of porous catalytic washcoatto the effective model of entire catalytic monolith
Conference MODEGAT, Bad Herrenalb, September 14, 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
From a detailed model of porous catalytic washcoatto the effective model of entire catalytic monolith
Conference MODEGAT, Bad Herrenalb, September 14, 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
From a detailed model of porous catalytic washcoatto the effective model of entire catalytic monolith
Conference MODEGAT, Bad Herrenalb, September 14, 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
From a detailed model of porous catalytic washcoatto the effective model of entire catalytic monolith
Conference MODEGAT, Bad Herrenalb, September 14, 2009
Mathematical model
boundary conditions:
test case reaction kinetics: CO oxidation on Pt/Al2
O3( * = active Pt site)
Kočí et al., 2007, 2009
From a detailed model of porous catalytic washcoatto the effective model of entire catalytic monolith
Conference MODEGAT, Bad Herrenalb, September 14, 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
From a detailed model of porous catalytic washcoatto the effective model of entire catalytic monolith
Conference MODEGAT, Bad Herrenalb, September 14, 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
From a detailed model of porous catalytic washcoatto the effective model of entire catalytic monolith
Conference MODEGAT, Bad Herrenalb, September 14, 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
From a detailed model of porous catalytic washcoatto the effective model of entire catalytic monolith
Conference MODEGAT, Bad Herrenalb, September 14, 2009
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
From a detailed model of porous catalytic washcoatto the effective model of entire catalytic monolith
Conference MODEGAT, Bad Herrenalb, September 14, 2009
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
From a detailed model of porous catalytic washcoatto the effective model of entire catalytic monolith
Conference MODEGAT, Bad Herrenalb, September 14, 2009
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
From a detailed model of porous catalytic washcoatto the effective model of entire catalytic monolith
Conference MODEGAT, Bad Herrenalb, September 14, 2009
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
From a detailed model of porous catalytic washcoatto the effective model of entire catalytic monolith
Conference MODEGAT, Bad Herrenalb, September 14, 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
From a detailed model of porous catalytic washcoatto the effective model of entire catalytic monolith
Conference MODEGAT, Bad Herrenalb, September 14, 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
From a detailed model of porous catalytic washcoatto the effective model of entire catalytic monolith
Conference MODEGAT, Bad Herrenalb, September 14, 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
From a detailed model of porous catalytic washcoatto the effective model of entire catalytic monolith
Conference MODEGAT, Bad Herrenalb, September 14, 2009
SummaryKočí et al., 2009
Kočí et al., 2009
From a detailed model of porous catalytic washcoatto the effective model of entire catalytic monolith
Conference MODEGAT, Bad Herrenalb, September 14, 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).
From a detailed model of porous catalytic washcoatto the effective model of entire catalytic monolith
Conference MODEGAT, Bad Herrenalb, September 14, 2009
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.
More at
http://www.vscht.cz/monolith
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