A mixture of carbon dioxide, methane, and nitrogen is fed to a perfectly mixed GP system with a natural rubber membrane. Membrane properties are given in Geankoplis data in Table 19-2. Membrane active layer thickness is \(1.0 \mu \mathrm{m}\). Feed pressure is \(17.0 \mathrm{bar}=\) retentate pressure and feed temperature is \(22^{\circ} \mathrm{C}\). Permeate pressure is \(1.1 \mathrm{bar}\). Feed is \(15.0 \mathrm{~mol} \%\) carbon dioxide, \(75.0 \mathrm{~mol} \%\) methane, and \(10.0 \mathrm{~mol} \%\) nitrogen. For \(\theta=\) 0.40 , find retentate mole fractions, permeate mole fractions, and membrane area (in \(\mathrm{m}^{2}\) ) needed for \(1.0 \mathrm{~m}^{3} / \mathrm{s}\) of feed gas at 17.0 bar and \(22^{\circ} \mathrm{C}\).

Suggestion: Set up on a spreadsheet or other computer solution method and converge \(\Sigma \mathrm{y}-\Sigma \mathrm{x}=0\) using Goal Seek or Solver to determine A.

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TABLE 19-2. Permeabilities of gases in Barrers in polymer membranes TC He H2 CO2 O2 CH4 N2 Ref Membrane Poly [1-(trimethylsilyl)-1-propyne] Poly (dimethylsiloxane) Poly (dimethylsiloxane) Poly (4-methyl pentene) Natural rubber Natural rubber 25 100 Natural rubber Silicone rubber Ethyl cellulose Ethyl cellulose Ethyl cellulose Poly (2.6-dimethyl phenylene oxide) Polystyrene Polystyrene Polystyrene Polycarbonate Butyl rubber Butyl rubber Acetyl cellulose Cellulose acetate Nylon 6 Nylon 66 PIM-1 (polymers of intrinsic porosity-ladder type) PIM-7 28,000 7730 - 4970 DR 25 230 - 3240 605 300 N 35 - - 4550 781 351 DR 93 32 - 8.0 N 25 23.7 90.8 99.6 17.7 6.12 N 25 - - 153.0 9.43 DR 25 31 49 131 24 30 8.1 G 25 300 550 2700 25 53.4- 113 35 500 800 250 G 15 - 3.0 N 5.0 12.4 3.4 DR 30 35.7 49.2 47.5 11.2 7.47 3.29 G 25 - - 75 15 4.43 N 20 16.7 - 10.0 2.01 - 0.32 N 35 - - 12.4 2.9 - 0.52 DR 30 40.8 56.0 23.3 7.47 2.72 2.55 G 25 19 - 8.0 1.4 - 0.30 N 25 8.42 5.2 1.30 0.33 N 35 - 5.18 - 0.324 DR 22 13.6- - 0.43 0.14 N 35 - - 4.75 0.82 0.15 DR 30 0.53- 0.16 0.038- N 25 1.0 - 0.17 0.034 0.008 G 1300 2300 370 12.5a 92.3b R ] 860 1100 190 62.1a 42.1b R