Use of stochastic differential equations in investigating the uncertainties related to the operation of the activated sludge wastewater treatment plant

Authors

1 Faculty Member of the Azarbaijan Shahid Madani University

2 Department of Water and Environmental Civil Engineering, Faculty of Civil Engineering, University of Tabriz, Iran.

3 tabriz univ

Abstract

Control and management of surface sewage and domestic sewage by sewage treatment plants, understanding the operation of the treatment plant is considered as a necessity of environmental engineering. In this research, a stochastic model using SDE instead of linear equations to simulate the activated sludge process and to consider the uncertainties in the calculations and to change the perspective of the mathematics of the problem to move from deterministic mathematics to non-deterministic mathematics. The performance of physical parameters in the field of sewage treatment plant has been discussed. This effort will lead to providing a comprehensive method for more productivity from the two perspectives of risk management in critical times and reducing economic costs and ease of monitoring the activated sludge part. Therefore, the linear equations of biological treatment became stochastic equations. Calculations with SDE and integral Ito solution by Euler-Maruyama method were performed for a period of 15 consecutive days during (2019-2020) for WWTP of Tabriz city. The optimal coefficients were extracted for two selected variables, Qeff and BODeff, whose observational data were collected from the secondary sedimentation outlet section of the wastewater treatment plant and compared with the calculated data. The results show the ability to solve numerically for the calculation variables as the final goal of the research, and the constant coefficients for Qeff and BODeff are respectively 0.0035, 0.0028, 0.005 and 0.7 with δt equal to 1-10-3, which aims to create a specific trend of δt in the most optimal state was calculated.

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