Desalination of seawater can be accomplished in principle by many different processes. The same fundamental thermodynamic laws govern every such process. By means of a thermodynamic analysis for the so-called "differential process”, as it proceeds in series of infinitesimal steps with complete equilibrium being maintained at all times, the reversible, isothermal work for any steady state process regardless of mechanism may be found to be approximately —

Wmin = 2.98 kw-hr/1000 gallons or 2.83 kJ/kg

This figure (or a similar one depending on operating temperature and data chosen) is the one usually quoted as the minimum theoretical work. Practically, it is a very unrealistic figure, not only because it assumes complete reversibility of all operations, but also because it would involve pumping an infinite amount of feed water and the pumping work would then be infinite [2].

Distillation is a vaporization process driven by heat. Essentially, it is a heat pumping process driven by a heat engine. Here the work requirement depends not only on the quantity of heat to be pumped but also on the temperature difference over which it is pumped. When heat is used to vaporize water from a salt solution, the vapor evolved contains the full amount of heat of evaporation and the only net result is a slight degradation in temperature due to the Boiling Point Elevation (BPE) of a salt solution. This heat can all be reutilized merely by restoring it to its former temperature — i. e. by heat pumping. By using the first law of thermodynamics and the Carnot relationships, the minimum heat (Qk) necessary to drive an ideal distillation process over a given temperature range AK can be shown to be —

This parameter represents the amount of "effects” that the device is able to perform. "Effects” stand for the amount of kilograms of distillate obtained from a heat input equal to the latent heat of evaporation of 1 kilogram of seawater. A GOR of 1 thus means that there was no gained effect and the unit mass of distilled water corresponds with the amount of energy needed to evaporate that unit mass. Obviously, GOR above 1 indicates a system that is regenerating its heat for multiple effects. gOr serves as a factor by which distillation devices of different design may be compared with respect to their heat efficiencies.

We see therefore that in order to maximize the efficiency of a distillation process from a thermodynamic approach (and minimize irreversibilities) the whole process of heat insertion and removal should take place at just a fraction of a degree difference from each other (small AT). This however would require infinitely large surface areas and is thus impractical. Likewise, ideally, one would desire that the salinity of the incoming water remain constant and not increase as part of it is evaporated. This however, would require an infinite flow of water to be processed through the system and is also impractical. As

the thermal energy inserted into the system must be ultimately removed it would make sense to benefit from the removed heat in such a way that it could be reinserted into the system. Finally, in order to operate at a higher thermodynamic efficiency the temperature range of operation must also be large. Following is a basic diagram describing a process that incorporates these issues.

Figure 1- Parameters of a thermally optimized distiller

The described optimized enclosure operating over a large temperature range, with a small temperature drop, while regenerating its latent heat of condensation, will still have a limited ability to produce distillate. The amount of heat needed to "pre-heat" an amount of cold incoming seawater is considerably less than the latent heat released while the same equivalent amount of distillate condenses. Thus it is apparent that there is a practical limit to which a realistic regeneration device is able to reuse its heat. This is a function of the high and low temperature heat reservoirs, and the temperature drop necessary for heat transfer between the evaporator and condenser. Thus, the highest possible GOR any distillation device is able to feasibly operate at, may be expressed as

(3)11 MdT^T^.AT)-

Where Mr is the mass flow ratio between the cold incoming water (Ms) and the distillate (Md) and is defined using the first law of thermodynamics and humid air relationships.

____________________________________________ С pm *(Тк» ~ AT ~ Г„и )_______________________________________

I Cpa ■ {Thli — )- Сr ■ [g7to ■ (Тш )~ ПГрри ‘(Tpau )]+ hfgO^tJbq, 4J)

Ц 07 ha ~ .

Here Cpa and Cpw are the specific heats of the air and the water respectively and represents the specific humidity.

It is important to remember that this relationship represents the maximum efficiency attainable in a realistic regenerative distillation process and gives an indication as to how close a given device is operating with respect to the maximum possible. Thot and Tcoid are defined by the environment, and temperature drop — AT is defined by the size and quality
of the heat transfer surfaces. In effect therefore, one may “pre-define” the theoretical efficiency limitations of any given regenerative distillation device simply by defining these three factors. The upper and lower temperature limits are generally defined by the environment and AT depends on how much investment is made in the size and quality of the heat transfer surfaces. The goal of this research project has been to determine, by using CFD tools, how to promote the most effective natural convection so as to allow the device to approach this optimal efficiency at the given operating parameters.