Optimal design of effluent-cooling systems using a mathematical programming model

This paper addresses the optimal design of cooling systems for reducing the temperatures of hot aqueous effluent streams to satisfy the discharge temperature regulation. A superstructure that involves all options of stream bypassing, splitting and mixing along with a cooling tower for effluent thermal treatment is proposed. The optimization of this superstructure is formulated as a Mixed Integer Non-Linear Programming (MINLP) problem whose objective is to minimize the total annual cost, which accounts for the capital cost of the cooling tower and the operating costs due to power consumption of the water pump and tower fan. A detailed model for the cooling tower based on the Merkel’s method is used. The solution to this problem provides simultaneously the optimal operating conditions and design parameters of the cooling tower as well as the optimal cooling system configuration. Three cases of study are used to show the application of the proposed approach.