10.37 Chemical and Biological Reaction Engineering, Spring 2007
Prof. William H. Green
Lecture 21: Reaction and Diffusion in Porous Catalyst (cont’d)
This lecture covers: Packed bed reactors
dFA
= ArAeff
dz
A
products
Deff (actual is very complicated)
Figure 1. Packed Bed Reactor
Void Fraction
φ ~.5
C A ( x j , ym , zl )
j = 1,30
m = 1,30
l = 1,30
(points)
(11-21)
Di ∇ 2Ci − U ⋅∇Ci + ri fluid = 0 Å in the fluid
Di
∂Ci
∂nˆ
+ ri surface = 0
i=1, N species
fluid
(boundary condition for the above)
surface
Ergun’s Eq.:
(4-22)
dP
G 1−φ
=−
dz
ρ gc Dp φ 3
where P =
ρ RT
,
ρU z =
⎡150 (1 − φ ) μ
⎤
+ 1.75G ⎥
⎢
Dp
⎢⎣
⎥⎦
G
A
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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∂FA
= ArAeff
∂z
rAeff = (effectiveness factor )rAC Ab ( z )
(
)
Ω C Ab ( z ) (or η internal)
area
total
Ω≡
∂Fi
= Ari eff = AΩri ideal
∂z
Actual rate of reaction
Rate if
ri ideal [=]
(rAeff )
C A = C Abulk ( z ), and T = Tbulk everywhere
mol
vol. s
⎛ wt. of catalyst in reactor ⎞
ri ideal = ri′ ⎜
⎟
V reactor
⎝
⎠
ri = ri′ ρc (1 − φ )
⎛ surface area of cat. ⎞
= ri′′ ⎜
⎟ ρ c (1 − φ )
wt. cat.
⎝
⎠
ac / m particle
m2
[=] Sa + (macroscopic surface area, visual)
g
FA = ν C A = AUC A (some approximation)
Dispersion
dC A
d 2C A
1 dFA
= +U
− Da
A dz
dz
dz 2
hope this is 0!
Figure 2. Flow over a sphere
10.37 Chemical and Biological Reaction Engineering, Spring 2007
Prof. William H. Green
Lecture 21
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.
Downloaded on [DD Month YYYY].
(
)
kc ac C Ab − C As = η ( C As ) rA particle ( C As ) V p
Dinside
∂ 2C A
+ rA ( C A (r ) ) = 0
∂r 2
∂C A
=0
∂r r =0
kc C A r = R + Deff inside
∂C A
∂r
Deff inside
∂C A
= kc C Ab − C As
∂r
(
)
= kc C A bulk
r=R
Matlab:
1) Guess C As ( C A surface)
2) Use boundary conditions to get corresponding
3) Solve ODE (ode15s)
4) Vary guess ( C As ) to make
∂C A
∂r
r=R
∂C A
= 0 at center
∂r
1st oder irrev.
η
Ω=
1+
η k1′′ Sa ρb
η=
3
φ12
(φ1 coth(φi ) − 1)
kc ac
φ1 = … k1′′
10.37 Chemical and Biological Reaction Engineering, Spring 2007
Prof. William H. Green
Lecture 21
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.
Downloaded on [DD Month YYYY].