## 3 Results and Discussion
### Energy Balance of Anaerobic Digestion and Ultrasonic Pretreatment  
In general, UP enhances the yield of methane. On the other hand, the sonication process consumes additional energy; thus, an energy balance should be performed to assess the cost-effectiveness of this process. Taking into account the technological parameters of the AD process, the amount of CH\({}_{4}\) obtained, and its energy value of 9.17 Wh/L, the highest gross energy outputs (E\({}_{\rm{Gout}}\)) generated from the methane production were obtained in V4 and V5, and, respectively, were 4.89 \(\pm\) 0.17 Wh/g VS and 5.14 \(\pm\) 0.15 Wh/g VS, while in V1 without UP, this was only 3.02 \(\pm\) 0.18 Wh/g VS (Table 6, Figure 4). The contribution of the specific energy input (E\({}_{\rm{s}}\)) was proportional to the duration of the disintegration and ranged from 0.23 Wh/g VS to 1.32 Wh/g VS (Table 6). Considering the energy expenditures, the highest net energy  
Figure 3: Correlation analysis: (**a**) concentrations of organic compounds in the dissolved phase depending on sonication time; and (**b**) biogas and methane production yield depending on sonication time. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Variant** & **Parameter** & **Unit** & **Value** \\ \hline \multirow{3}{*}{V1} & Biogas & cm\({}^{3}\)/g VS & 506 \(\pm\) 38 \\  & Methane & \% & 65.5 \(\pm\) 3.0 \\  & & cm\({}^{3}\)/g VS & 329 \(\pm\) 20 \\ \hline \multirow{3}{*}{V2} & Biogas & cm\({}^{3}\)/g VS & 577 \(\pm\) 42 \\  & Methane & \% & 66.2 \(\pm\) 1.6 \\  & & cm\({}^{3}\)/g VS & 382 \(\pm\) 29 \\ \hline \multirow{3}{*}{V3} & Biogas & cm\({}^{3}\)/g VS & 697 \(\pm\) 37 \\  & Methane & \% & 68.7 \(\pm\) 2.1 \\  & Methane & cm\({}^{3}\)/g VS & 479 \(\pm\) 22 \\ \hline \multirow{3}{*}{V4} & Biogas & cm\({}^{3}\)/g VS & 782 \(\pm\) 40 \\  & Methane & \% & 68.2 \(\pm\) 1.4 \\  & Methane & cm\({}^{3}\)/g VS & 534 \(\pm\) 16 \\ \hline \multirow{3}{*}{V5} & Biogas & cm\({}^{3}\)/g VS & 808 \(\pm\) 41 \\  & Methane & \% & 69.4 \(\pm\) 3.2 \\ \cline{1-1}  & Methane & cm\({}^{3}\)/g VS & 561 \(\pm\) 17 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Effects of ultrasonic pretreatment on biogas and methane production depending on experimental variant. output (E\({}_{\text{Nout}}\)) was achieved in V4 and it was 4.21 \(\pm\) 0.17 Wh/g VS. In the remaining variants, the E\({}_{\text{Nout}}\) was significantly lower and ranged from 3.02 \(\pm\) 0.18 Wh/g VS in V1 to 3.93 \(\pm\) 0.20 Wh/g VS in V3 (Table 6, Figure 4). The net energy gain (E\({}_{\text{net}}\)) is shown in Figure 4. The highest E\({}_{\text{net}}\) was recorded in V4 and it was 1.19 \(\pm\) 0.18 Wh/g VS (Table 6, Figure 4). There was a strong positive correlation between the duration of the UP and the gross energy output (R\({}^{2}\) = 0.9671), as well as the net energy output (R\({}^{2}\) = 0.6.759), (Figure 4). Biomass solubilization efficiency mostly depends on specific energy input (E\({}_{\text{s}}\)), and the threshold of Es used for UP usually reported in literature is between 1000 and 16,000 kJ/kg TS [73; 74; 75]. The ultrasonication time also affects the results of the methane generation, however, a long sonication exposure period could result in the release of free radicals, lipids oxidation, and an accumulation of generated heat, which is not favorable in the enhancement of AD [76]. It should be also noted that a higher E\({}_{\text{s}}\) and longer sonication consume more energy. In this study, the longest sonication time of 200 s and highest E\({}_{\text{s}}\) of 1.32 Wh/g VS provided the highest solubilization of organic matter and methane production. Taking into account the energy consumption, the highest net energy output and net energy gain were achieved with a sonication time of 150 s and an E\({}_{\text{s}}\) of 0.69 Wh/g VS. [PERSON] et al. [71] found that an increase in the methane production yield after the UP of biomass (the energy obtained was 2.17 kJ/g VS) compensated the energy needed for the sonication (1.03 Wh/g VS). [PERSON] et al.