# State Analysis of the Water Quality in Rivers in Consideration of Diffusion Phenomenon
## 3 Results and Discussion
The effect of velocity when diffusion is included and omitted at different velocities is shown in Figure 11. Excluding diffusion after the introduction of a pollutant, the pollutant concentration is higher than when diffusion is allowed for, which results in a faster decomposition of BOD. Considerations to date have focused on the introduction of pollutants into the river without prolonged perseverance. Another consideration concerns the prolonged stamian of the introduced contaminant for a fixed time, over a given length. This phenomenon can be represented by a grid (Figure 12), which illustrates the persistence of a pollutant at a certain time along a given length, depending on the parameters adopted. Figure 11: BOD distribution at different velocities in the same moments of time including diffusion \((D>0)\) and excluding diffusion \((D=0)\). Figure 10: BOD distribution excluding diffusion, no self-cleaning process for \(V=0.001\). The figure above illustrates the range over which pollution is maintained. The blue dots indicate the tenacity of the pollution over a given length at relevant moments in time, while the white dots are the beginning of the spread of the pollution. The simulation results are shown in Figure 13, and Table 5 summarises the values used. It is evident that the initial pollution introduced into the water persists over a long period of time at an appropriate length (cf. Figure 7(a),b). In the initial moments of time at a given length, the BOD concentration is high, after which it spreads accordingly over the given area. Depending on the speed of the river, the distribution of pollutants in the river at the same moments of time, along the same length, is different: see Figure 14. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Value** & **Figure 13a** & **Figure 13b** & **Figure 15a** & **Figure 15b** \\ \hline \(BOD\left[\text{mg}/\text{L}\right]\) & 10 & 10 & 10 & 10 \\ \(A\) & 0 & 0 & 0.2 & 0.2 \\ \(D\left[\text{m}^{2}/\text{h}\right]\) & 3600 \(\times\) 5 \(\times\) 10\({}^{-9}\) & 3600 \(\times\) 5 \(\times\) 10\({}^{-9}\) & 3600 \(\times\) 5 \(\times\) 10\({}^{-9}\) & 3600 \(\times\) 5 \(\times\) 10\({}^{-9}\) \\ \(V\left[\text{m}/\text{h}\right]\) & 0.001 & 0.005 & 0.001 & 0.01 \\ \(dz\left[\text{m}\right]\) & 0.001 & 0.001 & 0.001 & 0.001 \\ \(dt\left[\text{h}\right]\) & 0.0014 & 0.0014 & 0.0014 & 0.0014 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The initial values adopted in the simulation studies for the cases shown in Figures 13 and 15. Figure 12: Grid representing the distribution of pollution excitations over length and time. Figure 13: BOD distribution including diffusion for \(V=0.001\) (**a**) \(V=0.005\) (**b**). The above considerations concerned the distribution of BOD taking into account the phenomenon of diffusion and disregarding the self-cleaning process of the river. The effect of the self-cleaning process of the river, at different velocities, is shown in Figure 15, and Table 5 summarises the values used for the study. It can be seen that the self-cleaning of the river influences the BOD distribution, resulting in a shorter occurrence of high concentrations of pollutants in a given section of the river. Figure 14: BOD distribution, including diffusion \((D>0)\), at different velocities in the same time moments. Figure 15: BOD distribution including diffusion for \(V=0.001\) (**a**) \(V=0.01\) (**b**) including the self-cleaning process. Figure 16 illustrates the changes in BOD concentration as a function of speed, taking into account the self-cleaning processes. Comparing Figures 14 and 16, the influence of the river's self-cleaning, on the distribution of pollutants in the section under consideration, can be clearly seen. At the same moments in time, respectively, at the same water mass flow rates, the BOD concentration values are different. The self-cleaning of the river accelerates the breakdown of pollutants, so that the river returns to a clean state more quickly.