## 3 Results and Discussion
### Kinetic Analysis of Methane Production  
Figure 4A shows the cumulative methane production during the BMP test, which was carried out over a period of 28 days. As can be seen in this figure, all the substrates tested showed a similar methane production trend characterized by rapid production in the early days, followed by a gradual decrease until stabilization, consistent with previously reported findings [19]. The MNO test showed the highest methane production results, with 397 mL accumulated, representing a 29% increase in methane volume when compared to the control sample. Similar results have been reported in other studies [8]. These studies used ozonated pre-treated biosolids from the municipal wastewater treatment plant. At a dose of 0.1 gO\({}_{3}\)/gTS (higher than the dose used in this study, which was 0.018 gO\({}_{3}\)/gTS), these biosolids produced 25% more methane than raw sludge in BMP tests. Ozone treatment prior to the anaerobic co-digestion of sewage sludge and wine vinasse leads to a significant increase in methane production. This difference in the methane yield attributed to ozone pre-treatment is statistically significant according to the Wilcoxon test, with a \(p\)-value of 1.90 \(\times\) 10\({}^{-5}\) and an effect size (r) of 0.533 (large). This finding is consistent with previous studies reported in the literature [21], which confirmed that ozone pre-treatment during AD of sludge increases methane production. In contrast, ozone pre-treatment during the AD of wine vinasse does not lead to a significant increase in methane production. This negligible effect can be attributed to the role of ozone in reducing the content of biodegradable organic matter in the vinasse, thereby reducing both COD and DOC, as supported in the literature [38]. Figure 4: _Cont._  
However, with the dosage of iron nanoparticles encapsulated in carbon used in this work, an increase in methane production was not observed for the anaerobic co-digestion of sewage sludge and wine vinasse. There were no significant differences detected according to the Wilcoxon test, with a \(p\) value of 0.45 and an effect size (r) of 0.107 (small). This finding contradicts what has been approved by the supplier for other substrates. Other studies using Fe\({}^{0}\) affirm the biogas production rate [39] using higher doses. For example, a 58.99% increase in methane yield from swine manure was achieved using a dose of 10 mg Fe\({}^{0}\)/g VS, as reported by [PERSON] et al. [40]. Figure 4B shows the CH\({}_{4}\) yield data of each test expressed in terms of added VS. It should be noted that the MNO showed the highest yield again, i.e., 195 mL CH\({}_{4}\)/gSV added, while that for C was 160 mL CH\({}_{4}\)/g SV. In the literature, it has been demonstrated that for mixed sludge (primary and secondary sludge) from a domestic wastewater treatment plant ozonized at 0.05 g O\({}_{3}\)/g COD, a positive effect of the pre-treatment was observed [18]. This dosage is close to that used in this study, which was 0.018 gO\({}_{3}\)/TS\({}_{0}\) = 0.045 gO\({}_{3}\)/g TCOD. However, in the study reported in the literature [18], higher levels of performance were observed with sludge alone, at 6.8 mL CH\({}_{4}\)/g COD-d compared to 1.1 mL CH\({}_{4}\)/g COD-d obtained in this study. This is because the substrate originates from a prior acidogenic process where organic matter degradation and hydrogen and carbon dioxide production have already occurred [31]. The variations in methane yields obtained in other BMP tests reported in the literature using similar substrates may be attributed to various factors, including variations in operating conditions, experimental parameters, or substrate loading. As a result, the yield results may not be directly comparable to each other. The modified Gompertz and Cone models were fitted to the experimental data of the cumulative volume of methane over time with the aim of predicting the methane production rate during the BMP experiment.