Mathematical Model of Oxygen Regime Analysis in a Bioreactor

Abstract

Purpose. Today, aeration tanks are widely used to treat industrial and municipal wastewater. Assessing the efficiency of water treatment in aeration tanks under different operating conditions is an important task. To solve this problem, it is necessary to have mathematical models that allow to quickly obtain data on the effect of treatment in aeration tanks. The main objective of this work is to develop a numerical box model to determine the efficiency of wastewater treatment in an aeration tank. Methodology. For mathematical modeling of the biological wastewater treatment process in a bioreactor, zero-dimensional material balance equations are used, which are written in relation to the concentration of substrate, activated sludge, and dissolved oxygen in wastewater. The Monod model is used to calculate the substrate oxidation process. The Euler method is used to integrate the modeling equations. A simplified model of biological water treatment in a bioreactor is considered, which makes it possible to obtain an analytical solution to the problem. The obtained analytical expression makes it possible to quickly determine the change in the concentration of dissolved oxygen in wastewater depending on the change in the concentration of activated sludge in the bioreactor. The constructed numerical model makes it possible to determine the dynamics of changes in the concentration of contaminants, activated sludge and oxygen in wastewater during their stay in the bioreactor. Findings. A tool for theoretical evaluation of the efficiency of biological wastewater treatment in an aeration tank is proposed. A numerical model has been built that allows determining the concentration of dissolved oxygen, substrate and activated sludge at the outlet of the aeration tank. Originality. An effective numerical model has been developed that allows to quickly calculate the dynamics of wastewater treatment in a bioreactor and, based on this information, to evaluate the efficiency of the reactor. Practical value. The constructed mathematical model can be useful in the reconstruction of biological wastewater treatment facilities, as well as at the design stage of bioreactors to take into account their operation under different operating conditions. A computer program has been developed that implements the constructed numerical model. The results of a computer experiment are presented.