10.37 Chemical and Biological Reaction Engineering, Spring 2007
Prof. William H. Green
Lecture 22: Combined Internal & External Transport Resistances
Packed Bed Reactor Æ use PFR equation
dFi
= Ari eff
dz
z=0
z=L
Figure 1. Packed Bed Reactor
ri eff ≠ ri chem
ri eff = Ωri chem
Æ
if Ω ≈ 1 ?
if Ω 1 ?
( Ω > 1 ) –weird
BL:
δ
porous
catalyst
particle
dp
Figure 2. Porous Catalyst Particle
Biot Number:
Bi ∼
external heat transfer resistance
internal heat transfer resistance
Mass transfer Biot Number:
Cite as: William Green, Jr., course materials for 10.37 Chemical and Biological Reaction Engineering,
Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology.
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Bim =
kc d p
where kc ∼
D fluid
eff
Dinside
D
diameter
Bim = efffluid
Dinside
δ
δ
Mears’ Test:
rA′ (observed) ρb R p n
if
kc C A bulk
< 0.15
where n ≡ order of rxn
then C Ab ≈ C As (no external diffusion limitation) Æ i.e. no changing
concentration across the boundary layer
Similarly,
if
ΔH rxn rA′′ (observed or theory) ρb R p Ea
h fluid RT 2
< 0.15 then Tb ≈ Ts (text: Eqn. 12-63)
rAno external diff. limit vs. rAobserved
[>]
Weisz-Prater:
if
rA′ (observed) ρc R p 2
eff
Dinside
C A bulk
(text: Eqn. 12-61)
1
then you can neglect internal diffusion limitations, i.e. C As ≈ C Ab ≈ C A ( r = 0)
1000
η
Ea ∼ 30 RTs
β = 0.6
100
ΔH rxn
Ea
10
1
.1
1
10
.1
ΔH rxn > 0
100
0⎫
⎬ temp. dep. & exothermic
0 ⎭
φ1
ΔH rxn = 0
or Ea = 0
Figure 3. (text: Figure 12-7)
10.37 Chemical and Biological Reaction Engineering, Spring 2007
Prof. William H. Green
Lecture 22
Page 2 of 3
Cite as: William Green, Jr., course materials for 10.37 Chemical and Biological Reaction Engineering,
Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology.
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β=
−ΔH rxn DeC As
eff
where De ≡ Dinside and kt ≡ heat conductivity
ktTs
⎛ ∂Ci ⎞
eff
kc ( Ci ,b − Ci , s ) = − Dinside
⎜
⎟
⎝ ∂r ⎠ r = R
= ∫ ri dV .
kc Ci
r=R
⎛ ∂Ci ⎞
eff
− Dinside
= kc Ci , bulk
⎜ ∂r ⎟
⎝
⎠ r =R
⎛ ∂Ci ⎞
⎜ ∂r ⎟ = 0
⎝
⎠ r =0
if no significant external diffusion limit: Ci
r =R
≈ Ci , bulk
rA ≈ −k C A
e − Ea
RT
rAeff ≈ f (k ) C A
fit to:
Aeff e− Ea
eff
RT
.
(text: Table 12-1)
10.37 Chemical and Biological Reaction Engineering, Spring 2007
Prof. William H. Green
Lecture 22
Page 3 of 3
Cite as: William Green, Jr., course materials for 10.37 Chemical and Biological Reaction Engineering,
Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology.
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