Mathematical modeling and multivariable optimization of the multi-effect distillation coupled to a salt gradient solar pond

Abstract

The system of multi-effect distillation (MED) coupled to the salt gradient solar pond (SGSP) has been proposed as one of the solutions to the water shortage crisis. In this work, a developed model and a multivariable optimization were presented, which can be used to study the effect of heat exchanger areas within the system. For this purpose, the mass and energy equations of both SGSP and MED were solved simultaneously. The comparison between the model predictions and measured data demonstrated the validity of the proposed model. The results of this study indicate that the first effect should have the largest area within the system, and the optimal area of the heat exchangers increases progressively from the second to the fourth effect. Additionally, to present both general and quantitative results, several dimensionless ratios were introduced for the first time, representing the ratios of each heat exchanger’s area to that of the first effect heat exchanger. The optimal values of the dimensionless ratios for the SGSP heat exchanger, the condenser, and the second, third, and fourth effects of the MED system were found to be 0.89, 0.53, 0.6, 0.62, and 0.69, respectively. These optimal ratios can be utilized in future studies of the system under different conditions.