i) Define a membrane in a process engineering context.

Two of the main desired attributes of membranes are high permeability and high selectivity. Define permeability and selectivity.

Explain why it is generally not possible to achieve both high permeability and high selectivity at the same time.

ii) Define a chromatography process and explain how the separation takes place.

Discuss briefly the separation mechanisms for the following two chromatographic processes:

i) Ion exchange chromatography

ii) Size exclusion chromatography

iii) Membranes are used extensively in air separation to produce oxygen and/or nitrogen. Consider a process which is to produce a product permeate stream qp of oxygen-enriched air in a single stage system. The process is to be carried out using a vacuum pump on the permeate side with an absolute total downstream pressure Pdown. The air flow rate qf is to be pumped into the membrane using a blower from an absolute total upstream pressure P_up.

A PDMS/tetraethoxysilicone hybrid membrane is considered for the separation. At 30 °C and a pressure difference of 0.08 MPa, the oxygen permeability coefficient and the ideal separation factor were found to be 370 Barrer and 3.45, respectively.

a) For the hybrid membrane, what is the maximum achievable permeate concentration of oxygen xp,O2?

b) Assume a membrane thickness of Δx = 1 μm. Find the permeability coefficient PO2 of oxygen through the membrane in m³ m^-2 h^r-1 atm^-1.

c) What is the flux of oxygen JO2 through the membrane in m³m^-2h^r-1 when the upstream pressure Pup is 1 atm and the pressure difference across the membrane is 0.08 MPa? (If you were not able to find the permeability coefficient PO₂ above, use a value of 1x10^-5m³ m^-2hr^-1atm^-1 but please note that this is not the value sought.)

d) The membrane unit is to consist of 4 identical membrane modules in parallel of 25 m² per module. What is the maximum achievable permeate flow rate of oxygen q_p,O₂ for the unit in m³hr^-1?

e) Would you expect to be able to achieve this permeate flow rate at all times and why/why not?