Biomedical Engineering Reference
In-Depth Information
total surface of the particles
bed volume
a
c
¼
total surface of the particles
total volume of the particles
total volume of the particles
bed volume
¼
(E17-2.4)
2
1
4
pd
c
þ
pd
c
h
c
ð1
ε
Þ¼
2
d
c
þ 4
h
c
d
c
h
c
¼
ð1
ε
Þ
1
4
pd
c
h
c
Here
d
c
is the diameter of the cylindrical particle,
h
c
is the length of the cylindrical particle,
and
is the bed porosity.
Since mass transfer is limiting, the concentration of A on the catalyst surface is very small
as compared with the bulk concentration.
ε
C
AS
z
0
(E17-2.5)
Substituting
Eqns (E17-2.3) and (E17-2.5)
into
Eqn (E17-2.2)
, we obtain
d
C
A
U
d
z
þ k
c
a
c
C
A
¼ 0
(E17-2.6)
Integrating with the limit
C
A
¼
C
A0
at
z
¼
0, we obtain
U
z
C
A
C
A
0
¼ exp
k
c
a
c
¼ 0
(E17-2.7)
The conversion of A at the end of the reactor is given by
U
L
C
A
0
C
A
C
A
0
k
c
a
c
f
Ae
¼
¼ 1 exp
(E17-2.8)
Now we need to evaluate the mass transfer coefficient
k
c
. Correlations can be found in refer-
ences, for example, Perry's Chemical Engineers' Handbook. In this case, we can also use
Eqn (17.3)
.
The particle diameter may be computed via volume average, that is,
p
1
pd
c
h
c
3
3
2
d
c
h
c
3
¼ 3:663 10
3
mm
d
p
¼
¼
4
The Reynolds number
n
¼
3:663 10
3
10
d
p
rU
m
¼
d
p
U
Re ¼
¼ 81:407
4:5 10
4
The diffusivity needs to be corrected for temperature effects,
T
T
0
1:75
¼ 6:9 10
5
750
298
1:75
m
2
=
¼ 3:47 10
4
m
2
=
D
AB
¼ D
AB
;0
s
s
The Schmidt number
Search WWH ::
Custom Search