## 3 Results and Discussion
### Kinetic Analysis of Methane Production
The kinetic parameters fitted to the selected models for the control test (MC), nanoparticle test (MN), and ozone pre-treated nanoparticle test (MNO) are presented in Table 4.  
Figure 4: Cumulative volume of methane over time of the Biochemical Methane Potential test (**A**) and yield of methane production (**B**). Control (MC), nanoparticles (MN) and nanoparticles together with ozone pre-treatment (MNO). Figure 5 displays the experimental methane data points alongside the simulation data. The two kinetic models applied describe the methane production kinetics with R\({}^{2}\) values above 0.99 in all cases, except for the MC experiment in the modified Gompertz model, where R\({}^{2}\) was 0.70. Therefore, both models are applicable for all experiments except the MC. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **Parameter** & **MC** & **MN** & **MNO** \\ \hline \multirow{6}{*}{Modified Gompertz} & P (mL) & 293.0600 & 277.8353 & 402.4725 \\  & Difference (\%) & 4.8740 & 7.7165 & 1.2018 \\  & Rm (mL/h) & 1.2500 & 1.9060 & 1.9691 \\  & \(\measuredangle\)(h) & 168.0000 & 247.6787 & 69.9502 \\  & R\({}^{2}\) & 0.7000 & 0.9897 & 0.9977 \\  & RMSE & 30.48190 & 12.1915 & 7.3175 \\ \hline \multirow{6}{*}{Cone} & P (mL) & 291.7044 & 276.3757 & 411.5291 \\  & Difference (\%) & 5.4830 & 8.2551 & 2.3411 \\ \cline{1-1}  & K\({}_{\text{hyd}}\) (1/h) & 0.0031 & 0.0031 & 0.0058 \\ \cline{1-1}  & n & 8.6779 & 8.7669 & 3.2656 \\ \cline{1-1}  & R\({}^{2}\) & 0.9910 & 0.9918 & 0.9962 \\ \cline{1-1}  & RMSE & 11.9357 & 10.8882 & 9.15775 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Kinetic analysis for methane to control (MC), nanoparticles (MN) and nanoparticles together with ozone pre-treatment (MNO). Figure 5: Experimental methane data and simulation data from the modified Gompertz and Cone models: control (**A**), nanoparticles (**B**) and nanoparticles together with ozone pre-treatment (**C**). Regarding the difference between estimated and actual methane production (difference), the MN experiment showed a larger difference of more than 7% in both models. The RMSE values for both models were relatively low (Table 4), especially when considering the size or magnitude of the variable being predicted. This indicates that both models provide accurate predictions of the experimental data. However, the fit of the Gompertz model to the control test (MC) showed high RMSE. Both the estimated methane production (P) and the maximum methane production rate (R\({}_{\text{m}}\)) obtained from the Gompertz model and the hydrolysis rate constant (Khyd) obtained from the Cone model confirm that the use of iron nanoparticles alone does not affect methane production, whereas ozone treatment does, with MNO showing higher values for these parameters. The nanoparticle experiment produced a methane curve similar to that of the C experiment. As noted above, nanoparticles appear to have no effect on methane production, as they show a lag time of 10 days. In contrast, ozone reduces the lag phase to 3 days, as shown by the steeper slope in the early days (Figure 5). This has been confirmed by other studies, which show that similar doses of ozone used in this study on sludge also resulted in a reduction in the initial lag phase [18].