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Mathematical modeling of the multiple effect evaporation (MEE) desalination process has been carried out to determine the effects of the important design and operating variables on the parameters controlling the cost of producing fresh water. The model assumes the practical case of constant heat transfer areas for both the evaporators and feed preheaters in all effects. In addition, the model considered the impact of the vapor leak in the venting system, the variation in thermodynamic losses from one effect to another, the dependence of the physical properties of water on salinity and temperature, and the influence of noncondensable gases on the heat transfer coefficients in the evaporators and the feed preheaters. The modified fixed-point iterative procedure is used to solve the large number of highly nonlinear equations describing the MEE desalting system. The algorithm consists of 10 calculation blocks and 6 logical blocks. The algorithm is implemented using L-A-S computer aided language. Results show that the heat transfer coefficients increase with the boiling temperature. Also, the heat transfer coefficient in the evaporator is always higher than that in the feed preheater at the same boiling temperature. The plant thermal performance ratio is nearly independent of the top brine temperature and strongly related to the number of effects. The specific heat transfer area increases by raising the number of effects and reducing the top brine temperature. The effect of the top brine temperature on the specific heat transfer area is more pronounced with a larger number of effects. The required specific heat transfer areas at a top brine temperature of 100°C are 30.3% and 26% of that required at 60°C when the number of effects are 6 and 12, respectively. The specific flow rate of cooling water is nearly constant at different values of top brine temperature and tapers off at a high rate as the number of effects is increased. Two correlations are developed to relate the heat transfer coefficients in the preheater and the evaporator to the boiling temperature. Design correlations are also developed to describe variations in the plant thermal performance, the specific heat transfer area, and the specific flow rate of cooling water in terms of the top brine temperature and the number of effects.

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