## 3 Results and Discussion
### Methane Production and Its Kinetics
[44], in the co-digestion of wastewater with ice-cream production residues mixed at a ratio of 9:1, the methane production was established at the level of 396 mL CH\({}_{4}\)/g VS; in turn, in the control, with mono-digestion of wastewater, it was only 91 mL CH\({}_{4}\)/g VS. This indicates the significant potential of using such wastes as a co-substrate in the AD process. Other studies show that supplementation of FOG improved biogas production by nearly 30% [32]. However, its implementation on a technical scale might be challenging mainly due to several operational problems, including digester foaming, blockade of pipes and gas collectors, process inhibition by LCFAs, and sludge flotation [45,46]. Therefore, its application should be particularly controlled and preceded by laboratory-scale tests. A similar effect to those obtained in these studies was also achieved by [PERSON] et al. [19]. Therein, to avoid d-limonene inhibition, crude glycerol was proposed as an additional substrate to orange peel. The biochemical methane potential (BMP) of mixed wastes was established at the level of 501.3 mL/g VS, while for OW it was only 160.5 mL/g VS. Another example of successful co-digestion with orange by-products was found in the author's previous studies--in this case, supplementation with brewer's spent grain, resulting in a methane production of 395 mL CH\({}_{4}\)/g VS, compared to MSS mono-digestion, which showed an increase of 12% [47]. Another strategy enabling the d-limonene inhibition to be overcome was its adsorption as well as microbial immobilization by biochar. BMP, depending on the biochar type and adopted doses, varied from 163.9 to 186.8 mL/g VS, while for citrus peel, it was only 165.9 mL/g VS [13]. In other studies, such as the one by [PERSON] et al. [12], it was demonstrated that the extraction of d-limonene from OW using hexane can significantly influence biogas production. The highest biogas yield was achieved with an orange waste and hexane ratio (\(w\)/\(v\)) of 12:1 at a temperature of 20 \({}^{\circ}\)C for 10 min, resulting in more than a threefold increase in methane production, from 61 to 217 mL/g VS. Kinetic evaluation is an indispensable tool that allows the biogas production rate to be predicted. It allows for an efficient operation of digesters, as well as prediction of how the system will respond to various indicators, e.g., co-substrate introduction. Such an evaluation involves the analysis of potential maximum methane production, its production rates, and the lag phase [48,49]. Thus far, several models have been developed to simulate AD as well as to indicate the rate of methane production. However, in particular in the case of mono-digestion of complex organic substrates or co-digestion systems, the models should include more parameters that take into account the variable rate of decomposition during the AD process [49]. The results obtained in terms of methane production in both models correspond to the experimental data. This fact confirms the possibility of using both models, e.g., hyperbolic and logistic growth, to predict methane production from multi-component mixtures [50]. Importantly, the experimental results are higher than those obtained in both models, which also proves the accuracy of the selected operating parameters. As can be seen in Table 3, a major improvement was achieved in S3 supplied by IPW. In this case, as compared to MSS mono-digestion, enhancements of 17 and 19% for the LGM and HM were observed. It is worth mentioning that in the three-component series, a significant improvement in Rm was achieved as compared to both S1 and S2. In the case of lag phase, the introduction of IPW resulted in its shortening. However, major changes were noticed in IPW and MSS co-digestion (S3). Therein, the lag phase was reduced by 65% in comparison to the control series (S1). This effect was achieved by other researchers, and it resulted from the introduction of readily biodegradable substrates.