Minimizing the total cost of multi effect evaporation systems for seawater desalination

A mathematical model developed recently by the authors is extended into a non linear mathematical programming problem to determine the nominal optimal sizing of equipment (heat transfer area) and optimal operation conditions that satisfy a fixed nominal production of fresh water at minimum total annual cost. Relative marginal values computed from the optimized results and a global sensitivity analysis are then used to rank the process parameters according to their influences on the total cost. Once the nominal design and operating conditions are determined, a new optimization problem is stated: Is it possible to increase (using the nominal optimal design) the water production over the nominal capacity of production? Thus, the new optimization problem consists of the maximization of the distillate production. Optimization results for both design problems are presented and discussed in detail. One of the obtained results reveals that the increase of the distillate production in 20% over the nominal capacity (200 kg/s), leads to increases in the total operating cost from 10.8 to 11.4 million US$/yr while the seawater flow rate and the steam temperature increase about 23 and 5%, respectively.