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Unformatted text preview: oretical value of permeability for CO2 based on the value for helium.
Analysis: For Knudsen flow, Eq. (1422) applies. Therefore,
PM CO = PM He
2 M CO2
M He 1/ 2 4.00
= 117, 000
44.01 1/ 2 = 35,300 barrer This is substantially lower than the experimental value. Therefore, check to see if Knudsen flow
is dominant by computing combined Knudsen and molecular diffusivities for He and CO2.
Helium:
1/ 2
1/ 2
T
298
−8
From Eq. (1421), DKHe = 4850d p
= 4850(40 × 10 )
= 0.0167 cm2 / s
M
4.0
For molecular diffusivity, use Eq. (336) with Table 3.1 at the highest pressure (8.16 atm),
0.00143(298)1.75
DHe,CO2 =
= 0.0722 cm2 / s
1/ 2
2
2
8.16
2.671/ 3 + 26.71/ 3
1 / 4.0 + (1 / 44.01) From a modification of Eq. (1418), the combined diffusivity is
1
DHe =
= 0.0136 cm2 / s
(1 / 0.0167) + (1 / 0.0722)
Carbon Dioxide:
1/ 2
1/ 2
T
298
−8
From Eq. (1421), DKCO = 4850d p
= 4850(40 × 10 )
= 0.00505 cm2 / s
2
M
44.01
1
The combined diffusivity is DHe =
= 0.00472 cm2 / s
(1 / 0.00505) + (1 / 0.0722)
For both helium and carbon dioxide, the combined diffusivities are within 20% of the Knudsen
values. One explanation for the larger value of the CO2 permeability is the possibility that CO2 is
partly adsorbed in the pores causing an increase in the permeability over that caused by Knudsen
diffusion alone. Exercise 14.9
Subject: Effect of partial condensation and surface diffusion on the permeability of components
of a gas mixture.
Given: Porous carbon membrane of not more than 5 microns thickness, with pores of 4 to 15
Angstroms in diameter. Feed gas mixture of hydrogen and the first four normal paraffins with
component mol% values given below in terms of partial pressures using Dalton's law.
Permeabilities of the components in the mixture are much different than for the pure
components. Pressure of 1.2 atm on feed side. Sweep gas on the permeate side such that the
partial pressures of the permeating components are negligible.
Assumptions: Mixture permeabilities are constant through the membrane.
Find: Permeate composition on a sweepgasfree basis.
Analysis: From Eq. (141),
PM
Fluxi = i ∆pi with
lM ∆pi = pifeed − pipermeate = pifeed − 0 Therefore, the flux is proportional to PMi pifeed and yipermeate = PMi pifeed
PMi pifeed The permeate composition in mole fractions is developed with the above equations: Component
H2
CH4
C2H6
C3H8
nC4H10 Total p, atm
in feed
0.492
0.242
0.114
0.113
0.239
1.200 PM , barrer
in mixture
1.2
1.3
7.7
25.4
112.3 PMp, barreratm
0.590
0.315
0.878
2.870
26.840
31.493 y in
permeate
0.019
0.010
0.028
0.091
0.852
1.000 Exercise 14.10
Subject: Effect of module flow pattern on the material balance and membrane area for the
separation of propylene and propane by gas permeation.
Given: Gas feed of 100 lbmol/h of 60 mol% propylene (C3=) and 40 mol% propane (C3) at
25oC and 300 psia. Polyvinyltrimethylsilane polymer membrane with a 0.1µm skin in spiralwound modules. From Table 14.9, PM for C3= is 9 barrer, and 2.8 barrer for C3. Pressure on the...
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 Spring '11
 Levicky
 The Land

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