Page 380 - Water and wastewater engineering

REVERSE OSMOSIS AND NANOFILTRATION 9-19

15. Design a membrane array to achieve a given permeate recovery rate.
16. Determine the pH that can be achieved by stripping CO 2 .

9-7 PROBLEMS
9-1. Calculate the osmotic pressure for a seawater with a salinity of 35,000 mg/L. Assume
2 mole ions produced/mole of seawater, an osmotic coefficient of 0.85, a sea tem-
perature of 25 C, and a molecular weight of 58.5 g/mole.

9-2. Calculate the total osmotic pressure for a groundwater with a calcium bicarbonate
concentration of 720.0 mg/L and a magnesium bicarbonate concentration of 98.5
mg/L. Assume no other ions are present, 3 mole ions produced/mole of each com-
pound, an osmotic coefficient of 1.0, and a groundwater temperature of 5 C.
9-3. A high-pressure RO system is being evaluated for producing pure water from sea-
water. It is to be blended with sea water for a drinking water supply. Make an order
of magnitude estimate* of the required pressure differential ( P ) if the difference in
osmotic pressure must be 2,500 kPa. The mass transfer coefficient for water flux is
4
3
2
2
6.89 10 m /d · m · kPa and the required volumetric flux of water is 170 L/h · m .
9-4. A low pressure NF system is being evaluated for producing pure water from groundwa-
ter. It is to be blended with bypassed water for a softened drinking water supply. Make
an order of magnitude estimate* of the required pressure differential ( P ) if the differ-
ence in osmotic pressure must be 30 kPa. The mass transfer coefficient for water flux is
3
4
2
2
8.40 10 m /d · m · kPa and the required volumetric flux of water is 30 L/h · m .
2
9-5. Estimate the mass flux of solute (in kg/d · m ) for Problem 9-3 if the influent concen-
tration is 35,000 mg/L and the effluent concentration is to be 0.0 mg/L. Assume the
4
mass transfer coefficient for solute flux is 6.14 10 m/h.
2
9-6. Estimate the mass flux of solute (in kg/d · m ) for Problem 9-4 if the influent con-
centration is 818.5 mg/L and the effluent concentration is to be 0.0 mg/L. Assume the
4
mass transfer coefficient for solute flux is 6.14 10 m/h.
9-7. Each pressure vessel in a proposed design for the desalinization of seawater is rated
3
35% recovery at flow rates between 850 to 1,300 m /d. Design an array system that
3
will yield 2,000 m /d of pure water for a town of 5,000 people at a permeate recov-
ery of 50%.
9 -8. Each pressure vessel in a proposed design for the softening of groundwater is rated
3
45% recovery at a flow rates between 750 and 1,000 m /d. Design an array system
3
that will yield 4,000 m /d of pure water for a town of 6,666 people at a permeate
recovery of 80%.
9-9. Estimate the permeate recovery rate for a groundwater with the following characteristics:
Calcium 67.2 mg/L
Carbonate 0.72 mg/L

*Note that this is an “order of magnitude” estimate. As noted in the discussion, the performance of an NF/RO unit is computed
by numerical integration of differential elements along the membrane.