The theory of multi-effect distillation is that the vapors from the first evaporator condense in the second and their heat of condensation serve to boil the sea water in the second evaporator. In plainer terms, the second condenser acts as a condenser for the vapors of the first which in turn acts as a heater for the water in that evaporator. Each evaporator in the series is called an "effect".
It is obvious that the boiling temperatures and pressures cannot be the same in each evaporator. A reduced pressure in the vapor space of the first evaporator must be maintained to account for the difference in the boiling points of pure and salt water. Another requirement to maintain reasonable heat exchange between the pipes containing the condensing steam and those with the boiling sea water, the temperature of the sea water must be several degrees lower than that of the condensing steam. For example, if the heating steam entering the first effect is 100 degrees C at 1 atm, the boiling temperature in the first evaporator must be 95 degrees C and the pressure of the vapor must be 0.82 atm. At this pressure, the vapors entering the second condenser at 94.5 degrees C. To provide a reasonable temperature difference across the pipes, the desired boiling temperature of the second condenser would be 90 degrees C.
Pumps are necessary to deliver the fresh water at atmospheric pressure since the pressure in the system is less than atmospheric. They are also necessary to exhaust the steam space of the evaporators. A steam ejector coupled with a vacuum pump must also be employed to remove air and other noncondensing gases which would accumulate and eventually stop the boiling process.
The amount of fresh water produced per unit amount of heating steam increases almost proportionally with the number of stages. The problem is that increasing the number of effects causes a higher investment. So, as in many other industrial processes, an optimum number of effects must be determined depending on the needs of the plant.