Separation Process Principles- 2n - Seader &amp; Henley - Solutions Manual

# 14 49 where the y and x pertain to c3 yp x 1 1 r 1

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Unformatted text preview: oretical value of permeability for CO2 based on the value for helium. Analysis: For Knudsen flow, Eq. (14-22) 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. (14-21), DKHe = 4850d p = 4850(40 × 10 ) = 0.0167 cm2 / s M 4.0 For molecular diffusivity, use Eq. (3-36) 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. (14-18), 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. (14-21), 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 sweep-gas-free basis. Analysis: From Eq. (14-1), 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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