Environmental Engineering Reference
In-Depth Information
crystalline material. Instead, there are both crystalline and amorphous regions. These two
regions give rise to “dual mode” transport. The gas concentrated in the rubbery region
(
C
D
) is characterized by a Henry's Law type sorption while a Langmuir-type isotherm
describes gas concentration in the crystalline region (
C
H
). The total gas concentration is
written as the sum of the two contributions:
C
=
C
D
+
C
H
(9.3)
C
H
bP
1
=
k
D
P
+
bP
,
(9.4)
+
where
k
D
=
Henry's Law type coefficient
C
H
=
sorption capacity in crystalline region
b
=
constant
P
=
gas pressure.
The gas transport across the membrane is also the sum of the contributions through the
two regions
D
D
d
C
D
D
H
d
C
H
N
=−
d
x
−
d
x
.
(9.5)
The pure component permeability for a large feed pressure and a very small permeate
pressure is
k
D
D
D
1
FK
Q
=
+
,
(9.6)
1
+
bP
where
D
H
D
D
F
=
(9.7)
C
H
b
K
=−
k
D
.
(9.8)
For mixtures, the solute concentration and permeability are modified to account for the
fact that some fraction of the sorption capacity in the crystalline region is occupied by
each solute:
C
H
b
i
P
c
i
=
k
Di
P
+
(9.9)
j
=
1
b
j
P
n
1
+
.
F
i
K
i
Q
=
k
Di
D
Di
1
+
(9.10)
i
=
1
b
i
P
n
1
+
Search WWH ::
Custom Search