The natural gas company you work for wants to see the effect of a modern experimental membrane as compared to an older membrane for the removal of \(\mathrm{CO}_{2}\) from \(\mathrm{CH}_{4}\). Repeat Example 19-2, except use the PIM-1 membrane listed in Table 19-2. Use any solution method. For cut \(\theta=0.25\),

Example 19-2

a. Determine values of \(\mathrm{y}_{\mathrm{p}}\) and \(\mathrm{y}_{\text {out }}\).

b. If effective membrane thickness is \(\mathrm{t}_{\mathrm{ms}}=1.0 \mu \mathrm{m}=1.0 \times 10^{-6} \mathrm{~m}\), determine fluxes.

c. Determine membrane area for a feed gas flow rate of \(\mathrm{F}_{\mathrm{m}, \text { in }}=1.0 \mathrm{~mol} / \mathrm{s}\).

d. Compare answers with Example 19-2.

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Permeabilities of carbon dioxide and methane in a cellulose acetate membrane at 35.0C are Pco2 = 15.0 10-10 and PCH4 = 0.48 10-10 [cc(STP)cm]/[cm s cm Hg] (Chern et al., 1985). Separate a feed gas that is 50.0 mol% carbon dioxide and 50.0 mol% methane at 35.0C. (Many natural gas supplies contain CO2 in addition to CH4, so this is an important industrial separation problem.) Retentate pressure is pr = 20.0 atm, permeate pressure is pp = 1.1 atm, and tms = 1.0 m = 1.0 10-6 m. Use a completely mixed membrane module. a. Determine values of yp and yout for cut 0 = 0, 0.25, 0.5, 0.75, and 1.0 using analytical (e 0.25 only), spreadsheet (0 = 0.25 only), and graphical solutions. b. Determine CO2 and CH4 fluxes for 0 = 0.25. c. For 0 = 0.25, determine membrane area for a feed gas flow rate of Fm,in = 1.0 mol/s. Ideal gas molar density Pm = 1.0 mol/22.4 L STP. =