A CO2/CH4 gas mixture is to be separated using a hollow fiber membrane unit. The flowrate of gas to the unit is 2 x 105

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A CO2/CH4 gas mixture is to be separated using a hollow fiber
membrane unit.
The flowrate of gas to the unit is 2 x 105 cm3 (STP)/ sec with a
C02 mole fraction of 0.5. The
retentate has a composition of 0.2. The total membrane area
available in the unit is 5.15 x 107
cm2 and the membrane thickness is 1.5 x 10-3 cm. The stage cut
(Vout/Lin) is 0.5 and a vacuum is
applied to the permeate side (P2=0.)
a.) Derive the expression relating the local permeate composition
(y) to the local feed
composition (x) for this separation.
b.) What are the local permeate compositions at the inlet and
outlet?
c.) What is the upstream pressure that is required? Use arithmetic
averages of inlet and outlet
conditions.