COMPUTER SIMULATION OF BIOLOGICAL WASTEWATER TREATMENT PROCESSES IN AEROTANKS WITH PLATES

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. «Fluid Dynamics, Energy and Mass Transfer», Oles Honchar Dnipro National University, Haharina Av., 72, Dnipro, Ukraine, 49000, tel. +38 (056) 374 98 22, e-mail water.supply.treatment@gmail.com, ORCID 0000-0003-2399-3124 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 gidro_eko@ukr.net, ORCID 0000-0003-3057-9204 Dep. «Physics», Ukrainian State University of Chemical Technology, Haharina Av., 8, Dnipro, Ukraine, 49005, tel. +38 (056) 753 56 38, e-mail physics@udhtu.edu.ua, ORCID 0000-0002-9893-3479


Introduction
Biological treatment is one of the most effective methods of wastewater treatment [3,4,6]. Efficiency determination of this treatment at the stage of design or reconstruction of bioreactors, in which this method of wastewater treatment is carried out, requires the use of special mathematical models and calculation methods. Moreover, these theoretical calculation methods are the main toolkit, since a physical experiment in the field of biological treatment always requires a long time and expensive equipment. To date, a significant number of mathematical models have been developed that allow, with different approximation degrees, determining the bioreactor efficiency. But the existing mathematical models (empirical, balance, analytical) [1][2][3][4][5][7][8][9][10][11][12][13][14][15][16][17] do not take into account a number of important parameters affecting the efficiency of bioreactors (their geometric shapes and design features, movement hydrodynamics activated sludge and substrate in them, the presence of additional elements, various modes of operation), or require significant time when implemented on computers (CFD-models). Therefore, the development of mathematical models for assessing the efficiency of biological reactors, which allow taking into account these important factors and quickly determining the values of the parameters necessary for the designer, is an important scientific task.

Purpose
This work provides for the development of a numerical model to assess the efficiency of wastewater treatment in aerotanks. The task is to create a multifactorial computer model that makes it possible to quickly calculate the process of biological wastewater treatment, taking into account the geometric shape of the bioreactor.

Methodology
When building a model, we will take into account the following factors: geometric shapes of aerotank; the process of changing the substrate concentration in aerotanks over time; the process of changing the of activated sludge concentration in aerotanks over time; the presence of additional elements in aerotanks.
The material balance equations for the substrate and activated sludge in the reactor based on the Monod model has the following form: where d Kactivated sludge measurement coefficient; ttime; Xaveraged concentration of activated sludge in the bioreactor ; Saveraged concentration of substrate in the bioreactor; diffusion coefficient; Yparameter in the Monod model; , uvcomponents of the water flow velocity in the bioreactor in the direction of the x, y axes, respectively;   , xy    components of the diffusion coefficients at the considered plane point in the x, y direction. The averaged concentration of activated sludge and substrate over the width of the bioreactor is determined as follows: Equations (1) and (2) describe the change in the concentration of activated sludge and substrate over time in the aeration tank due to movement 6 and diffusion. Equations (3) -(5) describe the process of substrate consumption by activated sludge.
The limiting conditions for modeling equations are as follows: 1) at the inlet, the boundary condition is: where , in in SXknown concentrations of substrate and sludge, respectively; 2) boundary conditions at the exit from the bioreactor:  concentrations in the last computational cell; ( , ) S i j ( , ) X i jconcentrations in the previous computation cell; 3) on rigid surface: where nunit normal to the surface. The initial conditions are as follows: at t=0 X=X0, S=S0.
To solve the hydrodynamics problemdetermining the components field of the flow velocity vector in the aerotanka model of potential motion was used [8,29]: where Рvelocity potential.
Knowing the potential field, the values of the components of the flow velocity vector in the bioreactor are determined by the formulas [8,9,14]: Let us consider the difference in dependencies, with the help of which the numerical integration of the modeling equations is carried out. Thus, to calculate the substrate concentration in the bioreactor, an alternating-triangular two-step splitting scheme is used [2]. At the first stage of splitting, the calculated dependence has the form: At the second step of splitting, the calculated dependence is as follows: For the second equation, the difference schemes have the form: calculated dependence at the first step: calculated dependence at the second step: To construct a local one-dimensional scheme for solving equation (6) where tfictitious time. Further, we divide equation (11) as follows: Equation (12) describes the change in the value of Р in the direction of the X axis, and equation (13) describes the change in the Y direction.
The calculated dependencies (Richardson's method) for determining the unknown value of Р based on equation (12) Accordingly, the calculated dependencies (Richardson's method) for determining the unknown value of Р based on equation (13) Since we solve the evolutionary equation, the calculation by dependencies (14)-(15) ends when the following condition is met: where εsmall number; niteration number.
We calculate the flow velocity as follows: For numerical integration of equations (3)-(4), the Euler method is used.
The algorithm for solving this problem includes two main stages.
At the first stage, the following steps are performed: 1) the velocity potential field P (x, y) in the aerotank is calculated; 2) the flow velocity field u (x, y), v in the aerotank is determined.
The second stage (calculation at the time step dt) contains the following steps: 1) the change in the concentration of activated sludge in the aerotank due to flow movement and diffusion is calculated; 2) the change in the concentration of the substrate in the aerotank due to the flow movement and diffusion is calculated; 3) the change in the concentration of activated sludge and substrate in each difference cell based on the Monod model is calculated; 4) the calculation is repeated at a new time step, starting from item 1.
Based on the constructed numerical model, the BIO-2K computer program was developed. Programming is carried out in the FORTRAN algorithmic language.

Findings
Let us present the results of solving the problem of assessing the efficiency of the aeration tank using the developed CFD model. The following scenarios were considered: scenario no. 1: the aerotank works without additional elements inside the structure; scenario no. 2: aerotank has one plate inside the structure; scenario no. 3: aerotank has two plates inside the structure; scenario no. 4: aerotank works as a reservoir for the substrate destruction, but there is no entry and exit of the substrate and activated sludge. That is, in this scenario, the aerotank is a tank filled with activated sludge and substrate, and the process of changing their concentration was studied using the Monod model.
Calculations were performed with the following initial data: Sin = 360 mg/lthe concentration of the substrate (Biological oxygen demand (complete), which enters the structure;  As can be seen from the above figures, the field of substrate concentration inside the reactor can be divided into two zones. The first zone corresponds to the concentration range from 99 to 10% and occupies approximately the first half of the reactor. The second zone corresponds to the substrate concentration in the range of 10-3% (output from the reactor). The border between the zones looks like a «slanting» line. The second zone even has a «sparse» view. A significant concentration of the substrate in the first zone is caused by its constant ingress into the structure through the inlet. Fig. 5 shows the field of activated sludge concentration in the structure (each number is the activated sludge concentration in percent of the maximum concentration value at a given time, for this time -Xmax = 620.76 mg/l). This concentration gradually decreases from the inlet (where the active sludge enters the reactor) to the outlet.
Thus, Table 1 shows the average value of the substrate concentration at the outlet from the reactor for the time t =1.5 for each scenario.
As you can see from Table 1, the plates in the strcture affect the efficiency of water purification in the bioreactor. The most active process of water purification takes place if there is no movement in   It is also important to compare the dynamics of the water purification rate in the reactor if there is no movement (scenario no. 4) and when there is movement (scenario no. 1). Biological reactors in scenarios no. 1 and no. 4 have the same geometry, so this comparison is logical. Data analysis of Table 2 shows that approximately from the moment of time t = 0.96, the deceleration of the water purification process starts in the reactor, where the movement takes place, (scenario no. 1). By the time moment t = 1.5, the substrate concentration at the outlet from the reactor, where there is movement, is significantly different from the concentration for the reactor, where there is no movement.
Note that the time for calculating each scenario was 5 s.

Originality and practical value
A new numerical 2D model is proposed to assess the operation efficiency of the aerotank. A feature of the model is the ability to assess the operation of the aerotank, taking into account its geometric shape and location of additional plates in the structure. The simulated equations reflect the fundamental law of continuum mechanicsthe law of mass conservation.
The developed numerical model makes it possible to determine the concentration field of the substrate and activated sludge in the bioreactor. The model can be useful when performing calculations in the case of designing biological treatment facilities or when reconstructing existing bioreactors.

Conclusions
In the article, a new numerical model has been developed that allows one to determine the aerotank operation efficiency, taking into account its geometric shape. The results of computational experiments show that the use of additional elements in the aerotank improves the efficiency of water purification.
In the future, this scientific direction should be developed in the field of development of numerical models for evaluating the aerotank operation efficiency based on the Navier-Stokes equation.