Mathematical modeling and optimization of wastewater stabilization ponds using nonlinear programming

  • Hafiz Qasim Ali The University of Lahore, Department of Civil Engineering, Lahore Pakistan
  • Osman Üçüncü Karadeniz Technical University, Department of Civil Engineering, Trabzon Turkey


This research work proposes a mathematical optimization model for constructing two ponds (1. Facultative pond and 2. Maturation pond) provided in series. The model uses concrete volume as its objective minimization function. There were two decision variables; the first was the detention time (DT) and the second in the list was the number of provided baffle walls (NBW) in both ponds. The constraint parameters include fecal coliforms and biochemical oxygen demand (BOD5). The model was applied with the help of an Add-Ins of MS Office: Excel solver. The generalized reduced gradient algorithm was utilized in the solver (GRG). Before applying the mathematical optimization model, ponds were designed with the conventional method and then using optimized values of the variables. A comparison of the findings reveals that a 13.79 percent reduction in the DT, an 11.55 percent reduction in the area, and a 7.19 percent reduction in the volume of concrete occurred. The reduction values mentioned above are significant since these systems' fundamental drawback is the area's requirement. In addition, sensitivity analyses of the objective function and the removal of pollutants are also provided. The model described above is sensitive to variations in the parameters. Both analyses demonstrated that the effluent characteristics comply with the class-B irrigation standards in Turkey. It is advised to do more optimization studies for WSPs with the help of other algorithms and tools available in the literature for distinct wastewater treatment plants.

Jan 1, 2023
How to Cite
ALI, Hafiz Qasim; ÜÇÜNCÜ, Osman. Mathematical modeling and optimization of wastewater stabilization ponds using nonlinear programming. Mehran University Research Journal of Engineering and Technology, [S.l.], v. 42, n. 1, p. 198-206, jan. 2023. ISSN 2413-7219. Available at: <>. Date accessed: 06 feb. 2023. doi:
This is an open Access Article published by Mehran University of Engineering and Technolgy, Jamshoro under CCBY 4.0 International License