1. For a salt solution, reverse osmosis data are Cp=0.09%, Cw=6%, Cb=4%. Calculate polarisation modulus (Ans=1.5)
2. A UF membrane rejects solute completely. Limiting flux through it is 0.042 m3/m2.hr and the mass transfer coefficient on its surface = 5*10-6 m/s. What is the polarisation modulus? (Ans=10.03)
3. Find the is true rejection coefficient if bulk concentration on feed side = 2% mass, apparent rejection coefficient =0.975 in a UF module. Flux is given as 1.8*10-5 m3/m2.sec and mass transfer coefficient on the feed side is 4.4*10-5 m/s. (Ans=0.995)
4. In the study of gel polarisation of UF membrane the steady state solvent flux = 0.052 m3/m2.s. ∆P= 4 bar and Rm = 2.4*109 m-1. Compute the resistance offered by the gel layer?(µwater = 0.9 cp) (Ans=6.1*109 m-1)
5. In the ultrafiltration of a macromolecular solute a polycarbonate membrane is used. The temperature was 25°C. 96% solute rejection is achieved and the solution concentration was found to be 0.015 molar. Calculate effective pressure driving force if the feed side pressure is 4 bar and downstream pressure is 1.1 bar(absolute). The value of concentration polarisation modulus= 5.5 (Ans=2.543 bar,0.937 bar)
6. Calculate effective pressure driving force (i)at the beginning (ii) end of a batch ultrafiltration process in which a macromolecular solute is contained in a 0.02M feed solution. This is to be concentrated to 0.1M concentration at 25°C . The solute rejection is 95% and we can neglect concentration polarization. Assume that the upstream pressure as 3.5 atm(gauge) and downstream pressure = 1 atm. Also calculate fractional reduction in the solvent flux at the end the filtration process. (Ans=3.035 atm, 1.176 atm, 0.61)
7. In an ultrafiltration module with feed in cross flow, concentration of an enzyme is being carried out. The value of mass transfer coefficient at the membrane surface is found to be 3*10-5 cm/s. The Cb = 3% mass. Calculate the polarisation modulus and the enzyme concentration in the liquid at the membrane surface if the pure water flux is 0.41 m3/m2.hr. The solute rejection is 95% and the diffusivity of the enzyme is 8*10-7 cm2/s. With this information calculate the thickness of the mass transfer film. (Ans=14.02,4.2%mass, 0.0267 cm).
8. Some data on batch UF is given below(permeate flux as a function of permeate volume at constant ∆P).
Jw =(2.5*10-5) Vp-0.2 in m3/m2.s
Vp=permeate volume in m3.
If 1 m3 of milk is to be ultrafiltered to half the volume in 1 hr per batch, calculate the membrane area required. (Ans = 4 m2)
9. In order to concentrate a protein solution (Molecular Weight = 1213) by batch UF from 14 to 84 kg/m3 concentration, the feed volume = 3.028 m3 and batch time required is 2 hrs. Calculate membrane area. ∆P=3 bar, rejection coefficient= 0.97 and pure water flux= 0.468 m/s at this pressure. Effect of concentration polarisation can be neglected. (Ans=3.47 m2)
10. A cellulose membrane has pure water flux= (0.1/3600) m/s at ∆P= 100 bar. Calculate water and salt flux if a module is fitted with this membrane is used to desalinate 4% NaCl solution at operating Pressure difference = 90 bar. Salt rejection= 100% and osmotic pressure of 3% NaCl=17.62 bar. Polarisation modulus = 1 (Ans = 0.0665 m3/m2.hr, 0).