Special Topics on Membranes
Homework 8
1. 5 Points
Briefly describe the separation goals for microfiltration, ultrafiltration, nanofiltration, and
reverse osmosis.
2. 10 Points
A reverse osmosis membrane has a salt rejection of 95% for a feed solution of 5,000 ppm
NaCl at 25oC and a pressure difference of 15 bars across the membrane. The water permeability
coefficient (Lp) is 5 x 10-5 g/cm2-s-bar. Calculate the salt rejection at 30 bars. Assume that the
van’t Hoff equation applies.
3. 10 Points
A 5% solution of sucrose (Mw = 342.2) is concentrated using a tubular nanofiltration
membrane with an internal diameter of 6 mm. The membrane shows a complete rejection for
sucrose. The flux for this solution at 20oC is 48.9 liters/m2-h at a crossflow velocity of 4.5 m/s
and a pressure difference of 20 bars across the membrane. The osmotic pressure can be
described by: = 0.05 c1.1 , where is in bar, and c is in g/liter. The solution density is same as
water. Other data are: = 1.1 x 10-3 Pa-s and Dsucrose = 4.2 x 10-10 m2/s.
(1) Calculate the concentration polarization modulus.
(2) Estimate the flux at 10 bars, assuming that the concentration polarization modulus remains
the same.
(3) Is this assumption correct?
4. 10 Points
Microfiltration is frequently used for the recovery of a clear solution containing a soluble
product from fermentation broth. For a commercial-size MF module with an effective fiber
length of 40 inches containing 500 hollow fibers each with an outside diameter of 1.8 mm and a
membrane thickness of 0.4 mm, the time-dependent flux can be described by the equation:
jt = j0 t – 0.5 , where j0 = 150 liters/(m2-h). Calculate the time needed to recover 1,500 liters of a
clear solution from a 1,600-liter fermentation broth.
5. 10 Points
A polysulfone ultrafiltration membrane gave a pure water flux of 180 liters/(m2-h) under a
differential pressure of 3 atm. This membrane rejected 10 nm latex particles completely and was
then employed to concentrate a polymer suspension containing the latex particles at a differential
pressure of 6 atm, resulting in a water flux of 14 liters/(m2-h). Assume that the suspension had
the same viscosity as water.
(1) Could the membrane resistance be neglected? (Calculate the individual resistances for the
membrane and the latex cake layer above the membrane and compare them.)
(2) Assume that the specific cake resistance could be described by the following Carman-
Kozeny equation: rc= 180 (l - )2 / [ ( dp ) 2 3 ], where dp is the diameter of each latex particle,
and the porosity of the cake layer. Calculate the thickness of the cake layer for a porosity of
45%.
(3) Calculate the flux and the cake layer thickness (for the same porosity) when the pressure is
increased to 8 atm.
,
Homework 8
1. 5 Points
Briefly describe the separation goals for microfiltration, ultrafiltration, nanofiltration, and
reverse osmosis.
2. 10 Points
A reverse osmosis membrane has a salt rejection of 95% for a feed solution of 5,000 ppm
NaCl at 25oC and a pressure difference of 15 bars across the membrane. The water permeability
coefficient (Lp) is 5 x 10-5 g/cm2-s-bar. Calculate the salt rejection at 30 bars. Assume that the
van’t Hoff equation applies.
3. 10 Points
A 5% solution of sucrose (Mw = 342.2) is concentrated using a tubular nanofiltration
membrane with an internal diameter of 6 mm. The membrane shows a complete rejection for
sucrose. The flux for this solution at 20oC is 48.9 liters/m2-h at a crossflow velocity of 4.5 m/s
and a pressure difference of 20 bars across the membrane. The osmotic pressure can be
described by: = 0.05 c1.1 , where is in bar, and c is in g/liter. The solution density is same as
water. Other data are: = 1.1 x 10-3 Pa-s and Dsucrose = 4.2 x 10-10 m2/s.
(1) Calculate the concentration polarization modulus.
(2) Estimate the flux at 10 bars, assuming that the concentration polarization modulus remains
the same.
(3) Is this assumption correct?
4. 10 Points
Microfiltration is frequently used for the recovery of a clear solution containing a soluble
product from fermentation broth. For a commercial-size MF module with an effective fiber
length of 40 inches containing 500 hollow fibers each with an outside diameter of 1.8 mm and a
membrane thickness of 0.4 mm, the time-dependent flux can be described by the equation:
jt = j0 t – 0.5 , where j0 = 150 liters/(m2-h). Calculate the time needed to recover 1,500 liters of a
clear solution from a 1,600-liter fermentation broth.
5. 10 Points
A polysulfone ultrafiltration membrane gave a pure water flux of 180 liters/(m2-h) under a
differential pressure of 3 atm. This membrane rejected 10 nm latex particles completely and was
then employed to concentrate a polymer suspension containing the latex particles at a differential
pressure of 6 atm, resulting in a water flux of 14 liters/(m2-h). Assume that the suspension had
the same viscosity as water.
(1) Could the membrane resistance be neglected? (Calculate the individual resistances for the
membrane and the latex cake layer above the membrane and compare them.)
(2) Assume that the specific cake resistance could be described by the following Carman-
Kozeny equation: rc= 180 (l - )2 / [ ( dp ) 2 3 ], where dp is the diameter of each latex particle,
and the porosity of the cake layer. Calculate the thickness of the cake layer for a porosity of
45%.
(3) Calculate the flux and the cake layer thickness (for the same porosity) when the pressure is
increased to 8 atm.
,
