Membrane Area for Gas Permeation: $(50$ points$)$

A mixture of $60$mol$\%$ propylene and $40$mol$\%$ propane at a flow rate of $100$kmo$\frac{l}{h}$ and at $25C$

and $400a$ is to be separated with a polyvinyltrimethylsilane polymer $($see Table $14\mathrm{.}9$ below

from Seader for permeabilities$).$ The membrane skin is $0\mathrm{.}1mm$ thick, and spiral$-$wound modules

are used with a pressure of $15a$ on the permeate side. Calculate the material balance and

membrane area in $m^2$ as a function of the cut $($fraction of feed permeated, $)$ for perfect$-$mixing

flow pattern. Plot the mole fraction of propylene in the permeate and the corresponding membrane

area required as a function of $.$

Table $14\mathrm{.}9$ Predicted Values of Diffusivity and Solubility of Light

Gases in a Glassy and a Rubbery Polymer