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It depends on the definition of 'efficiency'.
If you mean "which technology gives the purest water after treatment?" , then the thermal processes like Multi Stage Flash or Multiple Effect Desalination are the most efficient.
If you mean "what is the cheapest way of desalinating water", it is highly dependant on the source of energy at your disposal.
For example, in countries were the price of Oil/Gas is cheap, like in Middle Eastern countries, the thermal processes will be cheaper.
If a country is low in oïl/gas ressources, it will be cheaper to use Reverse Osmosis techniques, as it will give a very pure water with a lower energy cost. Latest energy recovery systems make the process even more 'efficient'.
Moreover, some countries have tried to use thermal energy from the cooling systems of nuclear plants to desalinate water with an excellent cost/desalinated water ratio. It would give such 'efficiency' (the energy would normally be lost) it fits for irrigation purposes.
You can estimate the final cost of desalination with several technologies using this software : http://www.iaea.org/NuclearPower/Desalination
You can also read my technical note on desalination, if you can read and understand french idioma : http://www.agroparistech.fr/IMG/pdf/TATA-DUCRU_sr_final-2.pdf
In addition to that, we have to keep in mind that these technologies refer to large scale seawater desalination. For brakish water and small scale desalination, it is another question.
By comparing the three technologies:
RO Desalination Process:
1 1- Lower energy consumption compared to other desalination technologies.
2- 2- Less space requirements compared to other desalination technologies.
MED Desalination Process:
1- Low energy consumption compared to MSF technology.
2- Operates at low temperature (<70 C°) and at low concentration (<1.5) to avoid corrosion and scaling.
3- Highly reliable and simple to operate.
4- Can be adapted to any heat source such as “hot water, waste heat from power generation, solar heating…etc”.
5- Low maintenance cost.
MSF Desalination Process:
1- Low operating cost when waste heat is used for the distillation process.
2- The quality of feed water is not as important when compared with reverse osmosis technology.
3- Safe and reliable source of fresh water.
R.O.
MED