Environmental Engineering Reference
In-Depth Information
Example 9.1
Problem:
Based on the dual-mode transport model, calculate the pure component and mixtures
permeability of CO 2 and CH 4 using a polysulfone membrane. The gas pressure is
10 atm for each component.
D D 10 8 cm 2
k D
C H cc(STP)
cc(STP)
cm 3
b (atm 1 )
F
s
cm 3
· atm
CO 2
0.664
4.40
17.90
0.326
0.105
CH 4
0.161
0.44
9.86
0.070
0.349
Solution:
Dual-mode model:
Pure-component calculation :
k D D D 1
C H b
k D
KF
=
Q
+
K
=
1
+
bP
17
(0
.
90(0
.
326)
.
105)
0
.
664
1
10 8 )
Q CO 2 =
0
.
664(4
.
40
×
+
1
+
0
.
326(10 atm)
cc(STP)
cm
10 8
Q CO 2 =
3
.
55
×
·
s
·
atm
(9
.
86)(0
.
070)(0
.
349)
0
.
161
10 8 )
1
Q CH 4 =
0
.
161(0
.
444
×
+
1
+
0
.
070(10 atm)
cc(STP)
cm
10 9
Q CH 4 =
1
.
34
×
·
s
·
atm
Q CO 2
α ideal =
Q CH 4 =
26
.
Mixture calculation :
k Di D Di 1
K i F i
Q i
=
+
1
+
b i P i +
b j P i
Note the two bP terms in the denominator - this takes into account
the competitive nature of the transport.
17
.
90(0
.
326)
(0
.
105)
0
.
664
1
10 8 )
Q CO 2 =
0
.
664(4
.
4
×
+
1
+
0
.
326(10)
+
0
.
07(10)
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