MATHEMATICAL MODELING IN WATER TREATMENT PROBLEMS

Abstract

Problem statement. Analysis of the treatment facilities efficiency in sewerage at the stage of their design is great importance. Also, at the stage of structures’ reconstruction or their operation adjustment under different load conditions, it is necessary to know the efficiency of water treatment in different areas of treatment facilities. Such information makes it possible to rationally operate facilities. For solving problems of this class, the most effective tool is the use of the numerical modeling method. The work considers development of numerical models set for solving problems of this class. Methodology. Two fundamental models are used to solve the velocity field determination of the wastewater flow in the sewage treatment plant. The first is a model of the vortex-free motion for an incompressible fluid. The second model is the Navier-Stokes equations written in Helmholtz variables. The mass transfer equation is used to determine impurity concentration fields in sewage treatment plants, which takes into account flow velocity, diffusion and the presence of impurity emission sources. Material balance equations for the substrate and activated sludge are used to calculate the process of biological wastewater treatment. Finite-difference schemes are used to build numerical models that allow calculating the hydrodynamics of the flow and the distribution of the impurity concentration in the facility. The Euler method is used for the numerical solution of the material balance equations. Results. Numerical models were built, which were used to develop a complex of computer programs. These computer programs allow real-time analysis of the water treatment efficiency in the facility. Scientific novelty. Numerical models have been developed that allow investigating the process of water treatment in facilities of the «settler» type and in aeration tanks, that is, for a significant class of treatment facilities used in practice. Practical value. The calculation time of the velocity field and the impurity concentration field in a water treatment plant with a complex geometric shape is few seconds. This allows usinge the developed numerical models for serial calculations in project organizations in daily work.