## 2 Materials and Methods
### Laboratory Equipment  
The process of initial fragmentation and homogenization of the H-LSPW was carried out using a laboratory knife mill PULVERISETTE 11 (Fritsch GmbH, Idar-Oberstein, Germany). The H-LSPW feedstock to the mill was 1.0 dm\({}^{3}\). The fragmentation process was carried out using a four-bladed titanium knife operating at a rotational speed of 10,000 rpm for 90 seconds. The CTP and UTP were carried out in the IS-1K reactor (InterSonic, Olsztyn, Poland), in which the H-LSPW was heated using electric heaters or ultrasonic waves, depending on the experimental stage. Then, 1.0 dm\({}^{3}\) of pre-homogenized and disintegrated H-LSPW was introduced into the IS-1K reactor chamber. In S1 and S2, the substrate was heated using a set of electrical heaters with a power of 500 W, whereas in S3 and S4, the substrate was treated with ultrasounds having the frequency of 35 kHz and power of 400 W. The IS-1K reactor was thermally insulated with 10 cm\({}^{3}\) thick polystyrene to prevent heat loss. In all experimental stages, energy consumption for heating was monitored by means of an Orno OR-WAT-435 watt meter (Elmak Ltd., Rzeszow, Poland). In S1 and S3, the H-LSPW temperature was kept within the range of 70 \({}^{\circ}\)C to 73 \({}^{\circ}\)C, whereas in S2 and S4 it was kept within the range of 90 \({}^{\circ}\)C to 93 \({}^{\circ}\)C. Electrical heaters or ultrasound heads were started and stopped automatically when the temperature limits had been reached. The control system was integrated with a Pt100 temperature sensor (Jumo Ltd., Wroclaw, Poland) monitoring the temperature in the H-LSPW.  
The AD analyses were conducted with the use of kits for the OxiTop(r)-IDS AN 6 Anaerobic Degradation Measuring System (WTW, Cologne, Germany). The system registers biogas partial pressure changes in a measuring chamber. In each experimental variant,  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Indicator** & **Unit** & **Value** \\ \hline Biological oxygen demand (BOD\({}_{\text{S}}\)) & [mgO\({}_{\text{2}}\)/dm\({}^{3}\)] & 59,260 \(\pm\) 3030 \\ Total organic carbon (TOC) & [mg/dm\({}^{3}\)] & 28,640 \(\pm\) 1470 \\ COD:N ratio & - & 10.72 \(\pm\) 1.52 \\ BOD\({}_{\text{S}}\):N ratio & - & 8.71 \(\pm\) 1.13 \\ TOC:N ratio & - & 4.22 \(\pm\) 0.76 \\ pH & - & 6.78 \(\pm\) 0.05 \\ \hline \hline \end{tabular}
\end{table}
Table 1: _Cont._  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Indicator** & **Unit** & **Value** \\ \hline TS & [\%] & 5.7 \(\pm\) 1.1 \\ VS & [\% TS] & 76.9 \(\pm\) 2.0 \\ MS & [\% TS] & 23.1 \(\pm\) 1.9 \\ TN & [mg/gTS] & 71.3 \(\pm\) 9.6 \\ TP & [mg/gTS] & 11.7 \(\pm\) 1.3 \\ TC & [mg/gTS] & 882 \(\pm\) 104.7 \\ TOC & [mg/gTS] & 690.8 \(\pm\) 58.3 \\ C:N ratio & - & 12.4 \(\pm\) 0.9 \\ pH & - & 7.07 \(\pm\) 0.12 \\ Protein & [\% DM] & 44.6 \(\pm\) 3.3 \\ Lipids & [\% DM] & 14.1 \(\pm\) 1.5 \\ Saccharides & [\% DM] & 3.7 \(\pm\) 0.9 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Characteristics of anaerobic sludge biomass.  
500 cm\({}^{3}\) of anaerobic sludge were fed to digesters followed by the assumed doses of H-LSPW (V1--1.0 gCOD \(\approx\) 14 cm\({}^{3}\), V2--2.0 gCOD \(\approx\) 24 cm\({}^{3}\), and V3--3.0 gCOD \(\approx\) 48 cm\({}^{3}\)). Measurements were performed at a temperature of 42 \(\pm\) 1 \({}^{\circ}\)C. AD was continued for 20 days, with pressure changes registered in the digester every 6 h. To ensure anaerobic conditions, the digester was purged with nitrogen for 5 min with the efficiency of 100 dm\({}^{3}\)/min.