*3.3. Biomethane Production Kinetics*

The mean kinetic parameters evaluated by the model for control (D + FW) were *<sup>k</sup>* = 0.240 d<sup>−</sup>1, *EBMPe* = 351.4 mlCH4 × gVS−<sup>1</sup> and *<sup>r</sup>* = 84.43 mlCH4 × (gVS × d)−<sup>1</sup> (Table 5). All determined kinetics had a high determination coefficient (R > 0.99) (Table 5), which suggests that the used model fits the experimental data well. In general, the first-order model is used for quickly and abruptly stopping degradation substrates [57]. Furthermore, there was no need to use more sophisticated models like the modified Gompertz equation (good fitting when a lag phase is present), the mondo model (good fitting when gas production slowly declining at the end of the process), or two first-order equations (good fitting when two separate degradation profiles occur) [57] since here no such situation took place and biodegradation of over 75% was obtained in 21 days (Table 4).



The biochar addition changed the values of kinetic parameters slightly, but these changes were not statistically significant (*p* < 0.05). The highest constant production rate of biomethane was observed for 300/60/15 (*k* = 0.246 d−1), while the lowest for 400/60/15 (*k* = 0.229 d<sup>−</sup>1). Overall, 400/60/15 addition resulted in the worst kinetics, and the *EBMPe* and *<sup>r</sup>* were 334.22 mlCH4 × gVS−<sup>1</sup> and 76.36 mlCH4 × (gVS × d)<sup>−</sup>1, respectively. On the other hand, the best kinetics were obtained for 300/60/0 and 400/60/0 (Table 5). These results are a little confusing since the experiment showed that the highest methane production was for 400/60/0 and HTC280; nevertheless, this is probably due to a simplification of the model, which was not able to consider the increase in CH4 production after 17 days visible for HTC280 (Figure 3).

Overall, the results of methane production kinetics were determined accurately. The maximum methane potential and process kinetics are highly dependent on substrate, inoculum, equipment, and process conditions such as TS and pH. Deepanraj et al. [58] analyzed the kinetic of biogas production from kitchen waste at different TS concentrations (5–15%) and pH (5–9). The results of Deepanraj et al. [58] showed that first-order model kinetics (Gompertz model name by author) fit well to experimental data and had a determination coefficient >0.994. Moreover, results showed that the highest biogas production was obtained for TS = 7.5% and pH of 7 [58]. Is worth noting that these values are close to the ones used in this study (TS varied from 6.53 to 6.59%, and pH varied from 7.62 to 7.91). This suggests that those are important parameters for food waste anaerobic digesting and should be always considered when a BMP test of FW is prepared. There are pieces of evidence in the literature for which biochar addition can improve anaerobic digestion of food waste e.g., by improving process stability, decreasing lag phase, increasing methane yield, etc. Some theories described a process, how biochar enhances AD. Nevertheless, the abundance of food waste and used equipment/procedures lead to different AD enhancement results among studies—bearing in mind that biochar production consumes energy, and biochar transport to biogas plants costs as well. Different low-temperature biochars that potentially could be made using residual heat from biogas combined heat and power unit (CHP) (300–400 ◦C) were tested. It must be noted that biochars were made from a substrate used in a biogas plant and added to reactors at only one low dose (0.05 gBC × gTSsubstrate<sup>−</sup>1, or 0.65 gBC × <sup>L</sup>−1). The application of different BC doses might influence biomethane production more significantly. It should be further investigated.
