Design Optimization for Stabilization Ponds Using Non-Linear Programming

The article herein presents a mathematical optimization model to design lagoon systems containing two ponds: facultative and maturation. The objective function of the model was the cost. Four decision variables were considered: hydraulic retention time and number of screens in the facultative pond; in the maturation pond, also number of screens and retention time. Fecal coliform and organic matter were considered as restrictions. The resulting model was non-linear since the relations among the variables were not proportional. A pond system was designed using the traditional methodology adopted by the National Water Commission for Mexico. The mathematical model was then applied. A comparison of the results indicated a reduction in retention time of 14.16% and a decrease in cost of 12.04%. This finding is important given that the primary disadvantage of these systems is the need for land. In addition, a sensitivity analysis of the objective function and the restrictions is included. This analysis is sensitive to changes in the parameters. Both studies fully meet the quality standards stipulated by norms for treated water discharged into receptor bodies. Additional optimization studies that include different configurations are recommended.