Multi-stage flash distillation is used to desalinate seawater so it is fit for h

Question

Multi-stage flash distillation is used to desalinate seawater so it is fit for human consumption. A flash distillation tank is composed of small chambers (called "stages"), each at a lower pressure than the previous stage. Salt water enters the first chamber, some fresh water flash evaporates, condenses, and is removed from the distillation tank. The remaining salt water moves to the next chamber, some fresh water flash evaporates, condenses, and is removed from the distillation tank. The remaining salt water moves to the next chamber, and the process repeats until very salty water is expelled as waste. Brine that is 35,000 ppm salt is desalinated through a 5-stage flash distillation process. The pressure in the stages is such that 11.5% by mass of the water entering the stage evaporates and leaves as fresh water. If the desalination plant wants to produce 1200.0 gallons of drinking water per day, how many gallons of brine must the plant take in per day? The density of fresh water is 1.000 g/cm3. The density of brine is 1.025 g/cm3.

2561 Gallons

1.What mass of waste brine is expelled in one day?

2. What is the ratio of the mass of fresh water produced to the mass of water in the incoming brine?

3. The larger this ratio is, the more fresh water is produced for the given incoming water. If additional stages are added, each removing 11.5% of the available incoming water, so that the above ratio gets above 0.5, what are the total number of stages in the multi-stage flash distillation tank? (respond with a whole number)

4. The energy requirement of this type of desalination plant is 26.5 kW·h/m3 of fresh water. How much energy does the plant require to produce 1200.0 gallons of fresh water?

Explanation / Answer

Let, 100 gallon initially entered in the plant. Then total volume of water wasted

= 100 * (88.5/100)5 = 54 gallon = 54% of brine

Freshwater produce in the process = 100 - 54 = 46%

Thus, to get 1200 gallon of fresh water the plant must take = ( 1200 * 100)/ 46 = 2609 gallon

1. Mass of waste brine = 2609-1200= 1409 gallon

2. Ratio of the mass of fresh water produced to the mass of water in the incoming brine= 1200/2609 = 46%

3. To get the above ratio above 0.5, the total number of stages in the multi-stage flash distillation tank,

     0.5= ((100-11.5)/100)n =0.885n

or, log 0.5 = n log 0.885

or, n = 5.67 = 6 (in whole no)

4. 1 gallon= 0.0037854 m3

     1200 gallon = 4.542 m3

      Energy required to produce 1200.0 gallons of fresh water

       = (4.542 * 26.5) = 120.36 kW/h

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