Environmental Engineering Reference
In-Depth Information
We have seen that the design of a membrane follows from the mass
balance:
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
where
is the stage cut (
j
P
/
j
F
), and from the fact that all CO
2
and N
2
molecules have to pass the membrane:
θ
′
P
(
)
CO
θ
jx
=
2
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
2
2
where
P
i
is the permeance of component
i
,
p
R
is the pressure on the
retentate side, and
p
P
is the pressure on the permeate side.
These equations, together with the defi nition of the selectivity in
terms of the ideal selectivity, can be solved numerically.
Figure 7.3.2
gives the solution for the values in
Table 7.3.1
and a stage cut of 1%.
If we focus on the limit
0, the stage cut is so small that we can
assume that the composition and pressure of the retentate is equal to the
composition and pressure of the fl ue gas. This simplifi es our calculations
signifi cantly:
θ →
′
P
(
)
CO
θ
jx
=
2
px
−
px
,
F
CO ,
P
F
CO ,
F
P
CO ,
P
L
2
2
2
′
′
P
P
(
)
(
)
N
CO
θ
jx
=
2
px
−
px
=
2
px
−
px
,
F NP
,
F NF
,
P NP
,
F NF
,
P NP
,
∗
L
2
2
2
2
2
α
L
where
* is the ideal selectivity of our membrane. We can use this equa-
tion in the mass balance for CO
2
, to obtain:
α
(
)
(
)
(
)
′
PL
′
/
/
θ
j
p x
PL p x
/
fpx
CO
FF
CO ,
F
CO
F
CO ,
F
AF
CO ,
F
2
2
2
2
x
=
=
=
2
,
(
)
(
)
CO ,
P
fp
+
1
2
(
)
′
PL p
/
+
j
′
PL
/
/
θ
j
p
+
1
AP
CO
PP
CO
FP
2
2
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