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CEE 350 - Korshin - Winter 2012 - Homework 9(1)

# CEE 350 - Korshin - Winter 2012 - Homework 9(1) - CEE 350...

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CEE 350 Homework Week 9 Solution Problem 1 (0.8 point) A single-pass membrane system is used to desalinate seawater containing 27,000 mg/L of sodium chloride. The concentration of sodium chloride in the permeate is 82 mg/L. The feed flow rate is 1·10 5 m 3 /day and the permeate flow rate is 7.5·10 4 m 3 /day. a. Calculate NaCl concentration in the retantate (brine) stream. b. Assuming that the density of water is defined mainly by sodium chloride, determine the dilution coefficient of the brine in the outfall to ensure that the density of the seawater/brine mixture is within 0.001% of that of seawater prior to its desalination. The dependence of water density vs. NaCl concentrations is given in the table below. Table HW9.1 Density of water containing varying concentrations of sodium chloride NaCl (mg/L) density (g/cm 3 ) 3449 0.9994 16427 1.0088 24751 1.0147 26442 1.0158 42056 1.0265 53943 1.0345 77460 1.0497 85071 1.0547 112595 1.0719 138996 1.0877 155417 1.0970 169650 1.1056 199497 1.1223 206423 1.1260 224880 1.1360 238101 1.1432 240072 1.1440 254493 1.1515 263823 1.1562 274693 1.1621 296519 1.1728 332356 1.1903 A. Concentration of chloride in the retantate stream can be calculated as ± ² L mg Q Q C Q C Q C p f p p f f brine / 754 , 107 10 · 5 . 7 10 · 1 82 10 · 5 . 7 000 , 27 10 · 1 4 5 4 5 ³ u ³ u ³ ³

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Parameter Value Unit Q f 1.00E+05 m 3 /day Q p 7.50E+04 m 3 /day C f 27000 mg/L C p 82 mg/L C brine 107754 mg/L B. The relationship between water density and concentration of chloride (in sodium chloride solutions) given in the above table can be fitted (see the figure below) using this quadratic equation: ± ² 99766 . 0 10 95976 . 6 10 55327 . 3 / 7 2 13 3 ´ ´ ³ ³ ³ Cl Cl C C cm g U Calculations using this equation shown that the density of permeate generated in these conditions is 1.068532 g/cm 3 . At the initial sodium chloride concentration, the density of water can be calculated using the above expression to be at 1.016195 g/cm 3 . The density of released mixture of retantate and native seawater must not however exceed the prescribed value, which is 1.016195·1.00001=1.016205 g/cm 3 . The concentration of sodium chloride that corresponds to this density can be done solving the quadratic equation relation the density and sodium chloride concentration: 99766 . 0 10 95976 . 6 10 55327 . 3 016205 . 1 7 2 13 ´ ´ ³ ³ ³ x x Solving this expression yields x=27,015 mg/L. This concentration is the target value (C t ) of chloride concentration in the released mixed brine. To determine the required dilution, we can use the following mass balance equation: 1 27015 arg ´ ´ Y C YC C brine feed et t In this equation, Y is the number of volumes of initial untreated seawater that need to be mixed with the released concentrate to achieve the prescribed density level. Rearranging the above expression, we can obtain the required dilution rate: 5377 27000 27015 27015 107754 arg arg ³ ³ ³ ³ feecd et t et t brine C C C C Y
y = -3.55327E-13x 2 + 6.95976E-07x + 9.97663E-01 R 2 = 9.99977E-01 0.9500 1.0000 1.0500 1.1000 1.1500 1.2000 0 50000 100000 150000 200000 250000 300000 350000 NaCl concentration (mg/L) Density (g/cm3) Figure HW9.1 Correlation between the concentration of NaCl and density of its solutions.

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