Environmental Engineering Reference
In-Depth Information
p
R
=
p
CO
2
,
R
+p
N
2
,
R
p
P
=
p
CO
2
,
P
+
p
N
2
,
P
ρ
(g)
N
2
,
R
ρ
CO
2
ρ
(g)
CO
2
,
R
ρ
(g)
ρ
N
2
CO
2
,
P
ρ
(g)
N
2
,
P
Figure 7.2.5
Mixture
Concentration profi les of a gas mixture across a membrane.
Note that
1. We can now write a mass balance for both CO
2
and N
2
,
but as we have a binary mixture only one is independent because total
mass is conserved:
θ
jx
=
jx
+
jx
F
CO ,
F
R
CO ,
R
P
CO ,
P
2
2
2
(
)
(
)
jx
=
j
1
− θ
x
+ θ
x
F
CO ,
F
F
CO ,
R
CO ,
P
2
2
2
If we know the permeability of our material and the thickness (
L
) of
our membrane, we can use the result of the previous section to relate the
fl ux per unit area through the membrane to the partial pressures of the
two components on both sides of the membrane:
′
P
(
)
CO
2
θ
jx
=
px
−
px
F
CO ,
P
R
CO ,
R
P
CO ,
P
L
2
2
2
′
P
(
)
N
θ
jx
=
2
px
−
px
FNP
,
RNR
,
PNP
,
2
L
2
2
These two equations, together with the mass balance equations, are
characterized by the known values of the feed
x
CO
2
,
F
, the fl ux of the feed
φ
F
, and the pressures on the permeate and retentate sides. We seek
expressions for the stage cut,
, the total area (
A
) and thickness (
L
) of our
membrane, as well as the compositions of the retentate and permeate
θ
Search WWH ::
Custom Search