A mixture of 60 mol% propylene and 40 mol% propane at a flow rate of 100 lbmol/h and at 25°C and 300 psia is to be separated with a polyvinyltrimethylsilane polymer (see Table 14.10 for permeabilities). The membrane skin is 0.1 mm thick, and spiral-wound modules are used with a pressure of 15 psia on the permeate side. Calculate the material balance and membrane area in m² as a function of the cut (fraction of feed permeated) for: 

(a) Perfect-mixing flow pattern and 

(b) Crossflow pattern.

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Table 14.10 Predicted Values of Diffusivity and Solubility of Light Gases in a Glassy and a Rubbery Polymer Permeant Dx 10¹ m²/s Sx 10¹, gmol/m³-Pa Polyvinyltrimethylsilane (Glassy Polymer) 0.18 0.26 He Ne Ar Kr Xe Rn H₂ 0₂ CH4 C₂H6 C3H8 C4H10 C₂H4 C3H6 C₂H8 C₂H₂ C3H4 (m) C4H, (e) C3H₁ (a) C4H6 (b) 470 87 5.1 1.5 0.29 0.07 160 7.6 3.8 4.0 3.7 1.9 0.12 0.01 0.001 0.23 0.038 0.0052 0.58 0.17 0.053 0.15 0.03 1.95 6.22 20.6 69.6 0.54 1.58 0.84 13.6 1.28 3.93 30.2 98.1 347 17.8 77.6 293 16.8 138.1 318.5 186.5 226.1 PM, barrer 250 66 30 29 18 15 250 37 9 160 14 22 10 2.8 1.2 12 9 4.5 32 70 50 83 20