reinhard schomäcker institut für chemie der technischen
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Institut für Chemie
Block Course “Reactivity and Catalysis”How to get to the active site ?
Mass Transfer in Heterogeneous Catalysis
Reinhard SchomäckerInstitut für Chemieder Technischen Universität Berlin
For more details see: Roland Dittmeyer and Gerhard EmigSimultaneous Heat and Mass Transfer and Chemical Reaction, chapter 6.3 in Handbook of Heterogeneous Catalysis Eds. G. Ertl, et.alWiley-VCH, Weinhein, 2007
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Institut für Chemie
Block Course “Reactivity and Catalysis”How to get to the active site ?
Molecular Level: e.g. Langmuir-Hinshelwood Kinetics
A B
AA
AAA pK
pK
+=
1θ
( )21 BBAA
BBAABA
pKpK
pKpKkkr
++== θθ
AdsorptionReactionDesorption
= sequential steps
pA= partial pressure near surface
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Institut für Chemie
Block Course “Reactivity and Catalysis”How to get to the active site ?
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Institut für Chemie
Block Course “Reactivity and Catalysis”How to get to the active site ?
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Institut für Chemie
Block Course “Reactivity and Catalysis”How to get to the active site ?
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Institut für Chemie
Block Course “Reactivity and Catalysis”How to get to the active site ?
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Institut für Chemie
Block Course “Reactivity and Catalysis”How to get to the active site ?
Pressure drop in a fixed bed
ud p
L= 1
32
2
η∆
2
1150
1)(
−=
εεεF
( ) L
pdu k
ηεε ∆−
=2
2
3
01150
1 ( ) 202
1Re u
d
Lp
k
ρλ=∆
( ) ( )Re
Re3001
3
2
εελ −= ( ) ( )
+−−= 5,3)1(3001
3 ReRe
εε
ελ
laminar laminar und turbulent, Ergun-Gl.
( )εη
ε 02 u
L
pdFu k =∆=
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Institut für Chemie
Block Course “Reactivity and Catalysis”How to get to the active site ?
Sequential steps:
Pressure driven flow,Film diffusion,Pore diffusion
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Institut für Chemie
Block Course “Reactivity and Catalysis”How to get to the active site ?
Steps of Heterogeneous Reaction
1. Diffusion of reactant to catalyst
2. Transport of reactant within catalyst pores
3. Adsorption of reactant on catalyst surface
4. Reaction
5. Desorption of products from catalyst surface
6. Transport of products out of catalyst pores
7. Diffusion of products away from catalyst
Transport and reaction occure simultaneously(at a catalyst under steady state conditions)
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Institut für Chemie
Block Course “Reactivity and Catalysis”How to get to the active site ?
Impact of mass transfer limitation
k > D k < D
Feed Feed
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Institut für Chemie
Block Course “Reactivity and Catalysis”How to get to the active site ?
Mass Transport and Heterogeneous Catalysis
PrinciplesSurface layer
catalyst
Concentration profile
fluid phase
Influence of mass transport on the temperature dependance of het. catalysis
Mass transportinfluence
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Institut für Chemie
Block Course “Reactivity and Catalysis”How to get to the active site ?
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Institut für Chemie
Block Course “Reactivity and Catalysis”How to get to the active site ?
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Institut für Chemie
Block Course “Reactivity and Catalysis”How to get to the active site ?
Time Scales in a Reactor
residence time τ = VR/VF
Mixing time Θ
Time constant of reaction = CM,0/R0
Time constant of diffusion = R2/De
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Institut für Chemie
Block Course “Reactivity and Catalysis”How to get to the active site ?
Description of pore diffusion
cgradDj −=→
A
→j
cgrad
D wg = 1
2Λ
Λ =
=
k T
p
wk T
m
B
B
2
8
2πσ
π
Average free path length
Average molecular velocity
Dg ~ T1,5 und Dg ~ 1/p
1. Fick`s Law
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Institut für Chemie
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a) Diffusion in pores dp >> λ
D Deff g= ετ
b) Knudsen – Diffusion dp = λ
D Dd
weff Kp= =ε
τετ
1
2 2
DK ~ T0.5
c) Intermediate range
D
D D
eff
g K
=+
11 1
ετ
N2, X
N2, X =?
N2
Wicke-Kallenbach-Experiment
porousmaterial
cDj xexgrad−=
→
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Institut für Chemie
Block Course “Reactivity and Catalysis”How to get to the active site ?
Simultaneous reaction and pore diffusion in a sperical particle
temporal change changes of material changes causedof materials within = amount by transport + by reactionsvolume element
dV
dcdt
dV j do r dVi
Vi i
V∫ ∫ ∫= − +( )
r rν ( )∫ ∫=
r r rj do div j dV
V
dc
dtdiv j ri
i i= − +→
ν
one dimensional
Spherical geometry
div jd j
dzz
→=
div jR
d
dRR jR
→= 1
22( )
Mass balance
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Institut für Chemie
Block Course “Reactivity and Catalysis”How to get to the active site ?
01
22= − +
R
d
dRR j ri R i( ) ν Mass balance of sperical particle
in steady state
Solution of mass balance and description of average reaction rate
Dd c
dR R
dc
dRk ceff
n( )2
2
2+ = with r= kcn and ν=-1
c R R c
dc
dR R
( )= =
==
0 0
0 0
Φ0 00
1
=−
Rkc
D
n
eff
renormalized parameter= Thiele-Modulus
c R cR
R
RR
( )sinh( )
sinh= 0
0 00
0
Φ
Φ
radial concentration profilwithin sperical pellet
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Institut für Chemie
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k > D
k < D
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Institut für Chemie
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0RReffss dR
dcDAVr
=
= r = rhet
rR
Dc
Rhet effo= −3
10 0
0
0
(tanh
)Φ
Φ
r k chom = 0 Reaction without mass transport limitation
η = = −r
rhet
hom
3 1 1
0 0 0Φ Φ Φ(tanh
) Effectiveness factor
Thiele-Modul
Po
ren
wir
kun
gsg
rad
0
0,2
0,4
0,6
0,8
1
0 5 10 15 20
effe
ctiv
enes
sfa
cto
r
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Institut für Chemie
Block Course “Reactivity and Catalysis”How to get to the active site ?
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Institut für Chemie
Block Course “Reactivity and Catalysis”How to get to the active site ?
η ≈ 3
0Φ
r k cR
D
kk c k chet
effeff= = =3 3
00
00 0Φ
k D keff eff≅ E E Eeff D= +1
2( )
Influence of pore diffusion on effectiverate constant
Influence of temperature
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Institut für Chemie
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Film diffusion und Reaction
ms
mol3
*
&n S Dc c
Diff aW= −0
δ
n S c c mitD
Diff a W
.( ),= − =β β
δ0
rV
dn
dti
i= 1 1
νr
S
dn
dtSi a
i= 1 1
ν
ms
mol2
*
r r a k k a mit aS
VS Sa= = =, :
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Institut für Chemie
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)()( 0
.
WSaWa crSccSn =−= β
Discussion of a first order reaction with rs=kscw
ß(c0-cw) = kscw
cc
kWS
=+0β
β
Border cases:
ks << ß cw =c0 ( no layer formation)c0 cw
ks >> ß cw 0 c0
cw
≈
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Institut für Chemie
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0,0 ckck
kckr effS
S
SWSS =
+==
ββ
1 1 1
k kS eff S,
= +β
k a ka
k k a
eff S eff
s
= =+
=+
, 1 11
1 1β β
Calculation of eff. volume related rate constant
1 1 1
k a keff
= +β η
dspheredd
Particle volumea
6
63
2
=== ππParticle surface
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Institut für Chemie
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Temperature dependance:
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Institut für Chemie
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< 1
Generalized Thiele-Modulus
Criterion with mesasurable data only: Weisz-Modul
Criteria to exclude mass transfer limitations
T h i e le - M o d u l
Po
ren
wir
kun
gsg
rad
0
0 , 2
0 , 4
0 , 6
0 , 8
1
0 5 1 0 1 5
effe
ctiv
enes
sfa
cto
r
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Institut für Chemie
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Experimental check
for pore diffusion for film diffusion
Reduce particle sizedecreaseφincreaseη το 1
Decrease reactor diameter
at constantτ, Τ, ci
τ=VR/Vf
increase u = Vf/q
at constantτ, Τ, ci
increase ß = D/δ
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Institut für Chemie
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Institut für Chemie
Block Course “Reactivity and Catalysis”How to get to the active site ?