# ABACO: A New Model of Microalgae-Bacteria Consortia for Biological Treatment of Wastewaters
## 3 Results
### Validation  
The validation data used to verify the values of the characteristic parameters obtained during the calibration process were obtained in a separate vessel reactor, operated in parallel with the one used for calibration. These data collect the experimental measurements from 14 days, represented in Figure 6. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Symbol** & **Parameter** & **Value** & **Unit** \\ \hline \(\mu_{\text{alg,max}}\) & Microalgae maximum growth rate & 1.591 & day\({}^{-1}\) \\ \hline \(\mu_{\text{het,max}}\) & Heterotrophic bacteria maximum growth rate & 1.235 & day\({}^{-1}\) \\ \hline \(\mu_{\text{init,max}}\) & Nitrifying bacteria maximum growth rate & 0.730 & day\({}^{-1}\) \\ \hline \(\mu_{\text{min,alg}}\) & Microalgae endogenous respiration minimum rate & 0.01 & day\({}^{-1}\) \\ \hline \(\mu_{\text{max,alg}}\) & Microalgae endogenous respiration maximum rate & 0.276 & day\({}^{-1}\) \\ \hline \(\text{Y}_{\text{con}}\left[\frac{\text{NH}_{4}}{\text{Ag}_{6}}\right]\) & Ammonium consumption rate from microalgae & 0.369 & \(\text{g}_{\text{NH}_{4}}\text{g}_{\text{alg}}^{-1}\) \\ \hline \(\text{Y}_{\text{con}}\left[\frac{\text{NO}_{4}}{\text{Ag}_{6}}\right]\) & Nitrate consumption rate from microalgae & 0.214 & \(\text{g}_{\text{NO}_{3}}\text{g}_{\text{alg}}^{-1}\) \\ \hline \(\text{Y}_{\text{con}}\left[\frac{\text{PO}_{4}}{\text{Ag}_{6}}\right]\) & Phosphate consumption rate from microalgae & 0.008 & \(\text{g}_{\text{PO}_{4}}\text{g}_{\text{alg}}^{-1}\) \\ \hline \(\text{Y}_{\text{gen}}\left[\frac{\text{BSOM}}{\text{Ag}_{6}}\right]\) & BSOM generation rate from microalgae & 0.148 & \(\text{g}_{\text{BSOM}}\text{g}_{\text{alg}}^{-1}\) \\ \hline \(\text{Y}_{\text{con}}\left[\frac{\text{NH}_{4}}{\text{het}}\right]\) & Ammonium consumption rate from heterotrophic bacteria & 0.299 & \(\text{g}_{\text{NH}_{4}}\text{g}_{\text{het}}^{-1}\) \\ \hline \(\text{Y}_{\text{con}}\left[\frac{\text{PO}_{4}}{\text{het}}\right]\) & Phosphate consumption rate from heterotrophic bacteria & 0.017 & \(\text{g}_{\text{PO}_{4}}\text{g}_{\text{het}}^{-1}\) \\ \hline \(\text{Y}_{\text{gen}}\left[\frac{\text{BSOM}}{\text{het}}\right]\) & BSOM generation rate from heterotrophic bacteria & 0.153 & \(\text{g}_{\text{BSOM}}\text{g}_{\text{het}}^{-1}\) \\ \hline \(\text{Y}_{\text{con}}\left[\frac{\text{BSOM}}{\text{het}}\right]\) & BSOM consumption rate from heterotrophic bacteria & 0.478 & \(\text{g}_{\text{BSOM}}\text{g}_{\text{het}}^{-1}\) \\ \hline \(\text{Y}_{\text{con}}\left[\frac{\text{NH}_{4}}{\text{nit}}\right]\) & Ammonium consumption rate from nitrifying bacteria & 3.224 & \(\text{g}_{\text{NH}_{4}}\text{g}_{\text{nit}}^{-1}\) \\ \hline \(\text{Y}_{\text{gen}}\left[\frac{\text{NO}_{4}}{\text{nit}}\right]\) & Nitrate generation rate from nitrifying bacteria & 0.355 & \(\text{g}_{\text{NO}_{3}}\text{g}_{\text{nit}}^{-1}\) \\ \hline \(\text{Y}_{\text{con}}\left[\frac{\text{PO}_{4}}{\text{nit}}\right]\) & Phosphate consumption rate from nitrifying bacteria & 0.182 & \(\text{g}_{\text{PO}_{4}}\text{g}_{\text{nit}}^{-1}\) \\ \hline \(\text{Y}_{\text{gen}}\left[\frac{\text{BSOM}}{\text{nit}}\right]\) & BSOM generation rate from nitrifying bacteria & 0.149 & \(\text{g}_{\text{BSOM}}\text{g}_{\text{nit}}^{-1}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Calibration parameters for the ABACO model. For the validation process, calibration using genetic algorithms has been used to determine the initial percentages of microorganisms in the reactor. In this way, it is possible to estimate the starting points for the concentration of microalgae and bacteria. In this case, the initial percentages obtained were 85% for microalgae, 12.6% for heterotrophic bacteria, and 2.4% for nitrifying bacteria, very similar to the percentages obtained during the calibration test.