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Desalination of Seawater by Thermal Distillation and Electrodialysis Technologies 533
liquid (L) and both have the same temperature. The pressure (P1) is the saturation vapor
pressure of the liquid of composition (XL) at its boiling point (TL).
During the operation, a saturated steam (S, kg/h) must be added to the evaporator
to provide heat to the feed solution. The steam has a temperature of Ts (K) and an enthalpy
of Hs. The condensed steam leaving the system (S, kg/h) has a temperature of Ts (K) and an
enthalpy of hs. The steam gives off its latent heat (l) as follows:
l ¼ Hs hs (2)
The latent heat of steam at the saturation temperature (Ts) can be obtained from the steam
tables. Since the system is operated at steady state, the rate of mass coming to the evaporator
is equal to that leaving the evaporator. Thus,
F ¼ L þ V (3)
The mass balance on the solute (solids) is
FðXFÞ ¼LðXLÞ (4)
In the heat balance, the total heat entering the system is equal to the total heat leaving the
system. Assuming no heat lost by radiation or concentration.
Heat in feed þ heat in steam ¼ heat in concentrated liquid þ heat in vapor
þ heat in condensed steam (5)
Substituting Eq. (2) into Eq. (6) yields
F hF þ S Hs ¼ L hL þ V Hv þ S hs (6)
F hF þ S l ¼ L hL þ V Hv: (7)
The heat q transferred to the evaporator can be determined by
q ¼ S ðHs hsÞ ¼S l: (8)
Example. A continuous evaporator is used for treatment of a salt solution that has a flow rate of 9,000
kg/h, 1% of salt, and a temperature of 37.8 C or 310.8 K. The concentrated liquid that leaves the
evaporator has 1.5% of salt. The vapor space of the evaporator is at 1 atm, whereas the steam supplied
is at 1.414 atm. The overall coefficient is 1,700 W/m 2 K. Determine the amounts of vapor and liquid
leaving the system, the amount of steam added, and the rate of heat transfer.
Solution. According to the given conditions, F = 9,000 kg/h, XF = 1%, XL = 1.5%. Thus,
F ¼ L þ V
9; 000 ¼ L þ V
F XF ¼ L XL
9; 000 0:01 ¼ L 0:015
On solving these equations, L = 6,000 kg/h and V = 3,000 kg/L.