Evaporation of water for desalination

Let us consider the case of sea water desalination by evaporation. Suppose u tf kg/s is the flow rate of brine into an evaporator (evaporator 1), where kg/s of steam is supplied to evaporate water from brine. Let/o be the weight fraction of water in the feed stream (-0.965). Let the weight fraction of water left in the concentrated brine leaving this evaporator heff. Recognize that the amount of water vapor produced in this evaporator has considerable thermal energy in it. We can now condense this vapor in another evaporator (evaporator 2) fed with the concentrated brine 

Summing these relations containing weight fractions of water entering or leaving a given evaporator for n evaporators, we get 

This relation indicates that the total rate of water evaporation in this series of evaporators (total n in number) is n times that in any one evaporator (evaporator i, say), and that the total amount of water evaporated is n times the steam supplied to the first evaporator. Therefore the amount of energy supplied to evaporate 1 kg of water in 

The situation presented above would suggest that as we keep on increasing the value of n, the net heat required to evaporate 1kg of water will decrease as X/n. This is a simplistic picture. There are limits to the achievable value of n. We will consider now these aspects vis-k-vis the evaporation of water in sea water desalination. 

There are two basic limitations. First, if steam is supplied into evaporator 1 at 100 °C, the vapor space in the evaporator has to be maintained at a pressure less than 1 atm due to the boiling-point elevation of sea water. (Due to the presence of salts, the vapor pressure of sea water at a given temperature is lower than that of pure water therefore, at any pressure, the boiling point of sea water is higher than that of pure water by the amount of the boiling-point elevation.) Similarly, the brine in the second evaporator being more concentrated will require a somewhat lower vapor space pressure (than in evaporator 1), and so on till the last stage. 

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