## 3 Results and Discussion
### Methane Production and Its Kinetics  
The results in terms of biogas and methane production are presented in Figure 2 and Table 3. With regard to biogas production, the introduction of co-substrates did not lead to significant changes in biogas production compared to MSS mono-digestion. However, the key factor in assessing the efficiency of co-digestion of selected wastes is methane production. As compared to the control series (S1), significant improvements in the methane yield of S3 and S4 were achieved in the presence of IPW, reaching 16 and 14%, respectively. In turn, in MSS and OW co-digestion, a minor deterioration of this parameter was observed. The decrease in methane production occurred despite the improved COD/TN ratio in feedstock. For this reason, this fact might indicate the phenomenon of d-limonene inhibition present in OW (Table 1). Previous studies confirmed that this essential oil has a toxic effect on methanogens, which are responsible for producing methane in the final stages of the anaerobic digestion process [39; 40]. D-limonene, being a hydrophobic compound, might disrupt microbial cell membranes and interfere with cellular functions [41]. High concentrations of limonene can inhibit methanogenic activity, leading to a decrease in biogas production. Another adverse effect of this essential oil is related to hydrolytic and acidogenic bacteria inhibition, which are microbes responsible for the initial breakdown of organic materials into simpler compounds, e.g., fatty acids and alcohols. This inhibition can lead to slower degradation of organic waste and reduced methane production. Moreover, d-limonene might lead to an accumulation of VFAs that might finally result in process instability [42]. Importantly, the introduction of IPW to OW and MSS overcame the difficulties related to the presence of OW. In this case, a major improvement in the COD/TN ratio also occurred. The balanced feedstock composition resulted in an improvement in methane production. IPW is waste rich in lipids that might be easily converted into methane by specific microbial communities, enhancing biogas yield. Moreover, the introduction of fat-rich wastes might improve the degradation of organic matter, leading to higher methane production and improved system performance. A previous study indicated that such wastes contain long-chain fatty acids (LCFAs), which are readily degraded by specific hydrolytic and acidogenic bacteria. These bacteria can work in concert with other microorganisms in sewage sludge to \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Description** & **Parameter** & **Unit** & **S1** & **S2** & **S3** & **S4** \\ \hline \multirow{2}{*}{\begin{tabular}{c} Experimental \\ data \\ \end{tabular} } & Biogas yield & mL/g VS & 563.8 & 558.2 & 595.5 & 590.5 \\  & Methane & mL/g VS & 351.3 & 344.3 & 407.6 & 401.6 \\  & yield & CH\({}_{4}\) & \% & 62.3 & 61.68 & 68.45 & 68.01 \\ \hline \multirow{2}{*}{\
\begin{tabular}{c} LGM \\ \end{tabular} } & M\({}_{\text{p}}\) & mL/g VS & 329.9 & 323.3 & 384.8 & 379.1 \\  & R\({}_{\text{m}}\) & mL/g VS d & 62.6 & 61.4 & 62.2 & 64.3 \\  & \(\lambda\) & - & 0.33 & 0.33 & 0.11 & 0.23 \\  & R\({}^{2}\) & - & 0.9889 & 0.98733 & 0.98576 & 0.9879 \\ \hline \multirow{2}{*}{
\begin{tabular}{c} HM \\ \end{tabular} } & M\({}_{\text{p}}\) & mL/g VS & 337.2 & 330.6 & 400.2 & 394.1 \\  & k & 1/d & 0.273 & 0.274 & 0.243 & 0.246 \\  & R\({}^{2}\) & - & 0.98729 & 0.98729 & 0.99086 & 0.98936 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results of kinetics evaluation in corresponding experimental series. Figure 2: Cumulative biogas (**a**) and methane (**b**) production in corresponding experimental series (average values and standard deviation are given). break down a broader range of organic matter, improving the overall degradation process. In particular, the moderate lipid levels might be easily converted into methane through the acetoclastic pathway without VFA accumulation [43]. In a study conducted by [PERSON] et al.