simplified model with the analytical solution, Calculate the membrane area A and the permeate flow rate Qp for the case

Homework 5

1. Use the simplified model with the analytical solution, the inlet mole fraction of the fast
permeating species in the feed (component 1) xf = 0.2 and the ratio of permeate
pressure and feed pressure Pp / Pf = 0.1 to:
1) Calculate the permeate and feed flow rate Qp/Qf (stage-cut) and the permeation
area factor  :

a)  = 0.1 for the permeate mole fractions Xp = 0.62, 0.56, and 0.50

b)  = 0.04 for the permeate mole fractions Xp = 0.76, 0.70, and 0.64

c)  = 0.02 for the permeate mole fractions Xp = 0.86, 0.80, and 0.77

(Hint: for a value of Xp , use Qr/Qf equation (Q/Qf equation for Q = Qr and X = Xr at
Z=L ) and two material balance equations to calculate Xr, Qr/Qf and Qp/Qf).
2) Make two plots, one for Xp and the other for Qp/Qf, as a function of  with
the above three value of  as the parameter.

3) Conclude from the above plots
4) Calculate the membrane area A and the permeate flow rate Qp for the case
(1)(c) above for a feed flow rate of 100,000 m3 (STP)/h, a feed pressure of 68
atm, a hydrogen permeability of 100 Barrers, and an effective membrane
thickness of 0.1 micron for the polyimide membrane module.
5) Plot Xp and Qp separately as a function of membrane area for (4) above.

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