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.