Mass Transfer in Heterogeneous Catalysis - How to get to ... · PDF fileInstitut für Chemie How to get to the active site ? Block Course “Reactivity and Catalysis” Mass Transfer

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Block Course Reactivity and Catalysis How to get to the active site ?
Mass Transfer in Heterogeneous Catalysis - How to get to the active site?
Reinhard Schomcker Institut fr Chemie der Technischen Universitt Berlin
For more details see: Roland Dittmeyer and Gerhard Emig Simultaneous Heat and Mass Transfer and Chemical Reaction, chapter 6.3 in Handbook of Heterogeneous Catalysis Eds. G. Ertl, et.al Wiley-VCH, Weinhein, 2007

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Molecular Level: e.g. Langmuir-Hinshelwood Kinetics
A B
AA
AAA pK
pK+
=1
( )21 BBAABBAA
BA pKpKpKpKkkr
++==
Adsorption Reaction Desorption
= sequential steps
pA= partial pressure near surface

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Why so different geometries?

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= VR/VF
= VR/q uF

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Pressure drop in a fixed bed
u d pL
=132
2
2
11501)(
=
F
( ) Lpdu k
=
2
2
3
0 11501 ( ) 202
1Re udLpk
=
( ) ( )Re
Re 3001 32
= ( ) ( )
+
= 5,3)1(3001 3 ReRe
laminar laminar und turbulent, Ergun-Eq.
( )
02 uLpdFu k ==
channel

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Sequential steps: Pressure driven flow, Film diffusion, Pore diffusion

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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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Impact of mass transfer limitation
k > D k < D
Feed Feed

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Mass Transport and Heterogeneous Catalysis Principles Surface layer
catalyst
Concentration profile
fluid phase
Influence of mass transport on the temperature dependance of het. catalysis
Mass transport influence

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Time Scales in a Reactor
residence time = VR/VF Mixing time
Time constant of reaction = CM,0/R0 Time constant of diffusion = R2/De

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Description of pore diffusion
cgradDj =
A
j
cgrad
D wg =12
=
=
k Tp
w k Tm
B
B
2
8
2
Average free path length
Average molecular velocity
Dg ~ T1,5 und Dg ~ 1/p
1. Fick`s Law

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a) Diffusion in pores dp >>
D Deff g=
b) Knudsen Diffusion dp =
D Ddweff K
p= =
12 2
DK ~ T0.5
c) Intermediate range
D
D Deff
g K
=+
11 1
Tortuosity XL

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a) Diffusion in pores dp >>
D Deff g=
b) Knudsen Diffusion dp =
D Ddweff K
p= =
12 2
DK ~ T0.5
c) Intermediate range
D
D Deff
g K
=+
11 1
N2, X
N2, X =?
N2
Wicke-Kallenbach-Experiment
porous material
cDj xex grad=

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Simultaneous reaction and pore diffusion in a sperical particle
temporal change changes of material changes caused of materials within = amount by transport + by reactions volume element
dV
dcdtdV j do r dVi
Vi i
V = +( )
( ) =
j do div jdV
V
dcdt
div j ri i i= +
one dimensional
Spherical geometry
div j d jdzz
=
div jR
ddR
R jR=12
2( )
Mass balance

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0 122= +
RddR
R j riR i( ) Mass balance of sperical particle in steady state
Solution of mass balance and description of average reaction rate
D d cdR R
dcdR
k ceffn( )
2
22
+ = with r= kcn and =-1
c R R cdcdR R
( )= =
==
0 0
0 0
0 001
=
R kcD
n
eff
renormalized parameter = Thiele-Modulus
c R c RR
RR( )
sinh( )
sinh= 0
0 00
0
radial concentration profil within sperical pellet

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k > D
k < D

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0RReffss dRdcDAVr
=
= r = rhet
rRD c
Rhet effo=
3 10 0
0
0(tanh
)
r k chom = 0 Reaction without mass transport limitation
= = rrhet
hom
3 1 1
0 0 0 (tanh
) Effectiveness factor
Thiele-Modul
Porenwirkungsgrad
0
0,2
0,4
0,6
0,8
1
0 5 10 15 20
effe
ctiv
enes
s fac
tor

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3
0
r k cR
Dkk c k chet eff eff= = =
3 3
00
00 0
k D keff eff E E Eeff D= +12( )
Influence of pore diffusion on effective rate constant
Influence of temperature

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Film diffusion und Reaction
msmol
3*
n S D c cDiff a W=0
n S c c mit DDiff a W.
( ),= = 0
rVdndtii=
1 1
rSdndtS i ai=
1 1
msmol
2*
r r a k k a mit a SVS Sa= = =, :

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)()( 0.
WSaWa crSccSn ==
Discussion of a first order reaction with rs=kscw
(c0-cw) = kscw
c ckW S
=+0
Border cases:
ks > cw 0 c0
cw

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0,0 ckckkckr effS
S
SWSS =+==
1 1 1k kS eff S,
= +
k a k a
k k a
eff S eff
s
= =+
=+
, 1 11
1 1
Calculation of eff. volume related rate constant
1 1 1k a keff
= +
dsphere d d
Particle volume a 6
6 3
2 = = =
Particle surface

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Temperature dependance:

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< 1
Generalized Thiele-Modulus
Criterion with mesasurable data only: Weisz-Modulus
Criteria to exclude mass transfer limitations
Thiele-Modul
Poren
wirku
ngsgrad
0
0,2
0,4
0,6
0,8
1
0 5 10 15 20
effe
ctiv
enes
s fa
ctor

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Experimental check
for pore diffusion for film diffusion
Reduce particle size decrease
increase 1
Decrease reactor diameter
at constant , , ci
=VR/Vf increase u = Vf/q
at constant , , ci
increase = D/

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Mass Transfer in Heterogeneous Catalysis - How to get to ... · PDF fileInstitut für Chemie How to get to the active site ? Block Course “Reactivity and Catalysis” Mass Transfer