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^3Explanation / 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