Parameter Estimation on Two-Dimensional Advection-Dispersion Model of Biological Oxygen Demand in Facultative Waste Water Stabilization Pond: Case Study at Sewon Wastewater Treatment Facility

Abstract

To build a precise mathematical model describing a natural phenomenon, parameter estimation is needed to achieve the best parameter value. In this paper, we have calculated the best parameter value for a two-dimensional advection-dispersion differential equation of the biological oxygen demand degradation process in a facultative wastewater stabilization pond. This research was conducted with case study data collected from Sewon, Bantul facultative wastewater treatment facility located in Yogyakarta, Indonesia. The method employed in this research is based on the least square value by minimizing the difference between the observed data and the simulated data via quadratic programming using the interior point algorithm. This method gave the best value for the parameters observed in the model i.e. dispersion constant and the flow rate velocity. From the results, we have achieved that the best value for dispersion constant is 0.25, the velocity of the flow rate in the x-direction is 0.1, and the velocity of the flow rate in the y-direction is 0.15 whereas the relative error of this parameter estimation was 11.5% that is acceptable.

Biochemical Oxygen Demand Modeling in Waste Stabilization Pond Model

“…Currently, Waste Stabilization Pond(WSP) is common method to treat waste water by natural based solution with biological treatment (Islami, et al , 2022) and also popular to employs in the urban, large communities to improve water quality (Sunarsih Sunarsih, 2018), wastewater treatment is very crucial process to reduce high concentration of pollutant contamination in water and conserve sustainable water and ecosystem Siwiec, et al , 2011), The WSP system includes an anaerobic, facultative and maturation ponds (Siharath, et al , 2024). Therefore, Biochemical Oxygen Demand (BOD) is a vital parameter to indicate the requirement of oxygen in water (Ogarekpe, et al , 2012), BOD is a measure of the dissolved oxygen consumed by microorganisms (Gitta Agnes, et al , 2017;Mekaoussi, et al , 2023;S Sunarsih, et al , 2020) during the oxidation of reduced substances in waters and wastes (Shekarabi, 2023;Siharath, Vilaychaleun, Thammathevo, Sonemanivong, Kannitha, Nhaovarath, et al , 2023), the use of mathematical models describing wastewater treatment is taken into consideration. the BOD concentrations were used in the first order kinetics parameters (Shekarabi, 2023) (ultimate BOD and BOD reaction rate constant) determination using various methods (Khusravi, et al , 2013;Mazumder & Bhaduri, 2020;Oke, et al , 2016;Siharath, Vilaychaleun, Thammathevo, Sonemanivong, Kannitha, Phommakone, et al , 2023).…”