A crossflow membrane module is separating oxygen and nitrogen at \(25^{\circ} \mathrm{C}\). Feed rate \(\mathrm{F}_{\text {in }}=0.8270 \mathrm{~mol} / \mathrm{s}\). The membrane is \(1.1 \mu \mathrm{m}\) thick poly (4-methyl pentene). Feed is \(21 \mathrm{~mol} \%\) oxygen. Permeate pressure is 0.96 bar and retentate is at 3.7 bar. Cut is \(90 \%\). Assume an ideal gas. Data are in Table 19-2. Find Area, \(y_{p}, y_{r}\), and nitrogen product flow rate \(\mathrm{F}_{\mathrm{r}}\).

a. Find the solution for \(\mathrm{N}=1\), which is the perfectly mixed answer.

b. Find the solution for \(\mathrm{N}=1000\), which is the crossflow answer.

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) - 28,000 7730 - 4970 DR 25 230 - 3240 605 - 300 N 35 - - 4550 781 - 351 DR - 93 32 - 8.0 N Poly (4-methyl pentene) Natural rubber Natural rubber Natural rubber Silicone rubber Ethyl cellulose Polystyrene Polystyrene Polycarbonate Butyl rubber Butyl rubber Acetyl cellulose Cellulose acetate Nylon 6 Nylon 66 25 100 25 23.7 90.8 99.6 17.7 25 53.4- - 6.12 N 9.43 DR 25 - - 153.0 - - 25 31 49 131 24 30 8.1 G 25 300 550 2700 500 800 250 G 113 15 - 3.0 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 PIM-1 (polymers of intrinsic porosity-ladder type) PIM-7 1300 2300 370 860 1100 190 0.008 G 12.5 92.3b R 62.1 42.1b R