Mathematical models for water treatment problems

Purpose. Assessing the efficiency of water treatment in different structures is a problem of big importance. To solve this a problem, it is necessary to have mathematical models that allow to quickly obtain data on the cleaning effect in different structures. The aim of the work is to develop numerical models to determine the efficiency of water treatment in an aeration tanks, settlers and mixers. Methodology. For mathematical modeling of the process of water treatment in a bioreactor, balance equations were used. These equations allow to determine concentrations of substrate, activated sludge and dissolved oxygen in s structure. The Monod model is used to calculate the substrate oxidation process. To study effectiveness of water treatment process in vertical settler Euler’s equation were used with convective-diffusive equation. To simulate reagent mixing in mixer equation of potential and convective-diffusive equation were used. To solve governing equations finite- difference schemes of splitting were used. Findings. A tool for theoretical assessment mass transfer processes in aeration tank, vertical settler, mixer was developed. Originality. Effective numerical models to simulate water treatment in bioreactor, vertical settler, mixer were developed. Fundamental equations of Fluid Dynamics and Mass Transfer were used to build the models. Proposed models can be used in practice at the stage of «sketch designing». The models take into account the main physical parameters which influence the process of Mass Transfer and are quick computing. Practical value. The constructed mathematical model can be useful during the reconstruction and designing structures for water treatment. Computer programs have been developed to carry out numerical experiment. The results of a computer experiment are presented.