3D MODELING OF BIOLOGICAL WASTEWATER TREATMENT IN AERATION TANK

Dep. «Hydraulics and Water Supply», Dnipro National University of Railway Transport named after Academician V. Lazaryan, Lazaryana St., 2, Dnipro, Ukraine, 49010, tel. +38 (056) 273 15 09, e-mail water.supply.treatment@gmail.com, ORCID 0000-0002-1531-7882 Dep. «Hydraulics and Water Supply», Dnipro National University of Railway Transport named after Academician V. Lazaryan, Lazaryana St., 2, Dnipro, Ukraine, 49010, tel. +38 (056) 273 15 09, e-mail water.supply.treatment@gmail.com, ORCID 0000-0002-1230-8040 Dep. «Hydraulics and Water Supply», Dnipro National University of Railway Transport named after Academician V. Lazaryan, Lazaryana St., 2, Dnipro, Ukraine, 49010, tel. +38 (056) 273 15 09, e-mail water.supply.treatment@gmail.com, ORCID 0000-0001-9257-763X Dep. «Economics and Management», Dnipro National University of Railway Transport named after Academician V. Lazaryan, Lazaryana St., 2, Dnipro, Ukraine, 49010, tel. +38 (096) 469 60 09, e-mail v.a.zadoya@gmail.com, ORCID 0000-0001-9408-4978 Dep. «Hydraulics and Water Supply», Dnipro National University of Railway Transport named after Academician V. Lazaryan, Lazaryana St., 2, Dnipro, Ukraine, 49010, tel. +38 (056) 273 15 09, e-mail water.supply.treatment@gmail.com, ORCID 0000-0003-3057-9204 Dep. «Power Engineering», Ukrainian State University of Chemical Technology, Haharina Av., 8, Dnipro, Ukraine, 49000, tel. +38 (056) 753 56 38, e-mail zinaidaya25@gmail.com, ORCID 0000-0002-9893-3479


Introduction
To determine the efficiency of biological wastewater treatment at the design stage of aeration tanks, it is necessary to use special mathematical models [3,4,6]. Nowadays, balance, empirical and analytical models are most often used to solve this problem [1][2][3][4][5][7][8][9][10][11][12][13][14][15][16][17]. But in some cases, these models cannot provide a reliable result, because they do not take into account primarily the geometric shape of the reactor and the process of hydrodynamics, as well as a number of other parameters. In this regard, the problem of the development of mathematical models that allow theoretical investigation of the process of biological wastewater treatment in aeration tanks, taking into account the most important factors is relevant [1,2,[6][7][8][9][10].

Purpose
The work is aimed to develop a threedimensional CFD-model of the process of biological wastewater treatment in aeration tanks. The model must perform real-time calculation. In addition, the model should be acceptable for implementation on low-and medium-power computers.

Methodology
To model the biological wastewater treatment in the aeration tank the following equations are used: Determining these parameters experimentally is a rather difficult task.
For practical use of equations of model (1) -(4) it is necessary to calculate the non-uniform flow velocity field in the reactor, i.e. to determine the parameters ( , , ) u x y z , ( , , ) v x y z , ( , , ) w x y z , under the action of these parameters there is a convective transfer of substrate and activated sludge in the bioreactor. To calculate the non-uniform flow velocity field in the bioreactor, we use the 3D equation for the velocity potential: ,, The boundary conditions for modeling equations are as follows: on the surfaces of the building, solid walls, CFD model. The method of solving the mass transfer equations from system (1) -(2) will be considered using the example only for the substrate transfer equation. The equation for the transfer of activated sludge has a similar form. The threedimensional equation for the substrate transfer from the system (1) is split into a system of onedimensional equations as follows: Equations from system (7) describe the process of substrate transfer in the directions of the x, y, z axes.
Then, we split equation (14) as follows: The calculated dependencies (Richardson's method) for determining the unknown value P based on equation (15) have the form: The calculated dependencies for determining the unknown value P based on equation (16) have the form: The calculated dependencies for determining the unknown value of Р based on equation (17) have the form: The calculation according to these dependencies ends when the condition is met: where εsmall number; niteration number. At the next stage we determine the flow velocity: FORTRAN was used to encode the difference equations. The BIO-3К code has been created. To use it, one needs to specify the following input data: concentration of the substrate entering the bioreactor and its change over time; concentration and consumption of activated sludge entering the bioreactor and its change over time; dimensions of the bioreactor, its geometric BIO-3K code includes the following subroutines: SLE3velocity potential calculation in the bioreactor; SLE3velocity field calculation in the bioreactor; SLМ33calculation of the substrate concentration field in the bioreactor and its change over time; SLМ33calculation of the concentration field of activated sludge in the bioreactor and its change over time; SLМ33calculation of changes in the concentration of substrate and activated sludge in the bioreactor according to the dependencies of the Monod model; SLEM5print of the modeling results.
Result of this code is the concentration fields of the substrate and activated sludge in the bioreactor and the change of these fields over time.

Findings
The following are the results of solving the problem of evaluating the efficiency of a biological reactor for wastewater treatment based on the de- . We study the process of substrate destruction in the reactor over time according to the Monod model and taking into account mass transfer.
It should be noted that the calculation of spatial flow in multiconnected domains is one of the most complex problems of hydrodynamics.
Evaluation of the bioreactor performance is determined by the substrate concentration at the reactor outlet. Fig. 1-6 show the distribution of substrate concentration in the bioreactor for all scenarios, where each number indicates the concentration as a percentage of the maximum concentration in the calculation area (the time shown in the figures is dimensionless). The number 99 corresponds to the maximum value of the concentration in percent. These values are printed in the INTEGER format, i.e. only the integer value of the real number is printed. For example, if at some point in the reactor the concentration is 61.95 %, then the number 61 is printed. Since the three-dimensional problem is being solved, the concentration is shown in different sections of the bioreactor, the time is dimensionless. The figures show that inside the reactor there is a significantly uneven distribution of the substrate concentration, i.e. the process of biological treatment is uneven. The use of plates changes the concentration distribution in the structure, which affects the performance of the reactor.
To analyze the performance of the reactor Table 1 shows the substrate concentration at the outlet for the time t = 0.40. Analysis of data from table 1 shows that the use of plates makes it possible to increase the performance of the biological reactor. That is, we have the opportunity to control the process of wastewater treatment in the bioreactor.

Originality and practical value
A three-dimensional CFD model has been developed to model the process of biological wastewater treatment in an aeration tank. The potential motion model was used to calculate the flow velocity field in the aeration tank. The process of substrate and activated sludge transfer was determined based on the mass transfer equation. The Monod model was used to calculate the biological treatment process.
The constructed model can be used at the stage of sketch design of structures for wastewater treatment.

Conclusions
The article considers an efficient CFD model that allows you to quickly calculate the process of biological wastewater treatment in the aeration tank, in particular in the presence of additional plates in the middle of the reactor. To solve the problem, the fundamental equations of continuum dynamics are used.
In the future, it is planned to develop a threedimensional CFD model based on the Navier-Stokes equations.