Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

The diagram below shows a desalination plant. The seawater at the inlet has an o

ID: 3278558 • Letter: T

Question

The diagram below shows a desalination plant. The seawater at the inlet has an osmotic pressure of 30 bar. According to the van't Hoff law, osmotic pressure is proportional to the concentration X of salt. The pump has an efficiency of 80% and operates at a pressure equivalent to twice the osmotic pressure of the concentrated seawater. I. Work out the specific energy consumption of the system in kWh/m^3 and the recovery ratio. II. To recover some energy, the valve is replaced by a turbine with efficiency of 75%. Work out the new specific energy consumption of the system. The density of the seawater and of the concentrated seawater may be taken as 1040 kg/m^3

Explanation / Answer

Work done by pump =P (delta)V

Pressure, P = 2 x osmotic pressure of concentrated water

Osmotic pressure of concentrated water = concentration x (30bar/ Xs)

= (0.038-0.0005) x (30/0.038)

= 29.6 bar

P = 59.2 bar

Volume of water entering pump in 1 sec = (1/1040) x 800 = 0.77 m3.

Work done by pump = 59.2 x 0.77 = 45.58 W

Work done in 1 hr per m3 of water = 213.1 kWh/m3.

Pump has 80% efficiency, i.e., work done/ energy consumed = 0.8

Energy consumed = 266.4 kWh/m3.

Recovery ratio = (800-500)/800 = 0.375 or 37.5 %

2.) Work done by water on turbine = 213.1 kWh/m3

75% of which is absorbed = 159.8 kWh/m3

So new energy consumed = 266.4 - 159.8 = 106.6 kWh/m3