Mathematical modeling and optimization in the design of a maturation pond

Abstract Many lagoon systems in Mexico, and generally in developing countries, do not meet the norm for water pouring into receptors bodies. It was applied mathematical modeling to optimize the design and cost of a maturation pond, considering the methodology adopted for Mexico by the National Water Commission, taking as variables the hydraulic retention time and the number of screens, then the results were compared with a traditional design of a maturation pond without screens. Both analyses fulfill the treated water quality standards for pouring into receptors bodies. The results show a reduction in the hydraulic retention time by 8.65 days, and a reduction by 48.16 percent in land requirement. About the cost, it was obtained a reduction of 42.24 percent in comparison whit the traditional method. A major advantage of the mathematical model is the obtaining of the optimal design, which would be very difficult to get with the traditional methodology because the process is iterative and uses more than one variable, also can be inferred that the use of screens increases the efficiency. The algorithm used was the interior point by Matlab's Fmincon function, which determines the optimal values to accomplish the water quality constraints and obtains the lowest possible cost for construction. It is included the sensitive analysis for the mathematical model. It is recommended to carry out the present research at real scale with the finality to check the results given by the optimization.