Environmental Engineering Reference
In-Depth Information
is the mass of pollutant per unit bed weight. The general Freundlich isotherm (see
Chapter 3) in the following form is found to best fit the data over a wide range of
concentrations for activated carbon:
[
1
/n
]
F
K
Freun
A
W
0
=
.
(6.149)
Hence
V
g
ρ
ads
K
1
/n
(
1
−
(
1
/n))
V
ads
=
Freun
[
A
]
,
(6.150)
F
where
V
g
=
ρ
g
A
c
is the superficial gas velocity.
Consider a differential volume of the bed
A
c
d
x
.A material balance on the pollutant
gives the following:
M
F
/
input by flow
=
output by flow
+
mass gained on the bed by transfer from gas to solid.
G
F
[
A
]=
G
F
(
[
A
]+
d
[
A
]
)
+
K
mt
A
C
(
[
A
]−[
A
]
eq
)
d
x
,
(6.151)
where [A]
eq
is the equilibrium value of air concentration that would correspond to the
actual adsorbed concentration
W
in the differential volume.
K
mt
is the overall mass
transfer coefficient (time
−
1
)
from gas to solid. Rearranging, we obtain
K
Freun
W
n
)
d
x
.
−
V
g
d
[
A
]=
K
mt
(
[
A
]−
(6.152)
[
]=[
]
F
at
x
=
Rearranging and integrating using the boundary conditions that
A
A
0
and
[
A
]=
0at
x
= δ
,
δ
V
g
K
mt
0
d
[
A
]
d
x
=−
K
Freun
W
n
)
.
(6.153)
(
[
A
]−
A
]
F
0
[
An overall mass balance over the differential volume gives [A]
G
F
=
A
c
W
ρ
ads
V
ads
.
n
[A]
1
−
n
F
Utilizing the expression for
v
ad
and rearranging, we obtain
K
Freun
W
n
=[
A
]
.
Hence,
V
g
K
mt
0
d
[
A
]
δ =−
F
.
(6.154)
1
/n
n
[
A
]−[
A
]
[
A
]
A
]
F
[
Note that as
K
mt
→∞
0 and the process becomes equilibrium controlled.
Utilizing the dimensionless variable
,
δ →
η =[
A
]
/
[
A
]
F
and
K
mt
δ
/V
g
=
St
, the
Stanton
number
, we can write
1
η
η − η
d
=
St
n
.
(6.155)
0
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