# Effect of Bioaugmentation on Biogas Yields and Kinetics in Anaerobic Digestion of Sewage Sludge
## 3 Results and Discussion
### Kinetics  
In the quasi-flow system, the reactor was fed once a day with the portion of substrate or substrates and the same volume of digested medium was removed from the reactor. For this reason, the production of biogas between each feeding related to a temporal interval of 0-24 h. Accordingly, \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Parameter** & **Unit** & **R1 (Control)** & **R2** & **R3** & **R4 (Control)** & **R5** \\ \hline Daily biogas production & dm\({}^{3}\) d\({}^{-1}\) & 23.23 \(\pm\) 3.7\({}^{\text{b}}\) & 24.26 \(\pm\) 3.8 & 24.53 \(\pm\) 3.8 & 19.59 \(\pm\) 2.2 & 19.86 \(\pm\) 2.1 \\ Biogas yield & m\({}^{3}\) kg\({}^{-1}\) VS added & 0.38 \(\pm\) 0.07 & 0.40 \(\pm\) 0.07 & 0.40 \(\pm\) 0.07 & 0.38 \(\pm\) 0.05 & 0.37 \(\pm\) 0.05 \\  & m\({}^{3}\) kg\({}^{-1}\) TS added & 0.29 \(\pm\) 0.05 & 0.31 \(\pm\)0.05 & 0.31 \(\pm\)0.05 & 0.29 \(\pm\)0.04 & 0.29 \(\pm\)0.04 \\  & m\({}^{3}\) kg\({}^{-1}\) VS removed & 0.83 \(\pm\) 0.20 & 0.86 \(\pm\) 0.21 & 0.84 \(\pm\) 0.21 & 0.82 \(\pm\) 0.22 & 0.83 \(\pm\) 0.22 \\  & m\({}^{3}\) kg\({}^{-1}\) TS removed & 0.75 \(\pm\) 0.18 & 0.78 \(\pm\) 0.21 & 0.77 \(\pm\) 0.19 & 0.79 \(\pm\)0.27 & 0.78 \(\pm\) 0.29 \\  & m\({}^{3}\) kg\({}^{-1}\) COD removed & 0.52 \(\pm\) 0.09 & 0.53 \(\pm\) 0.11 & 0.53 \(\pm\)0.11 & 0.55 \(\pm\) 0.09 & 0.55 \(\pm\) 0.13 \\ Methane content & \% & 56.25 \(\pm\) 1.93 & 56.56 \(\pm\) 1.58 & 56.16 \(\pm\) 2.06 & 55.22 \(\pm\) 1.98 & 55.57 \(\pm\) 2.50 \\ \hline \hline \end{tabular} a—the average value, b—in normal conditions.  
\end{table} 
Table 2: Biogas production and corresponding yields as well as methane content for bioaugmented and non-bioaugmented reactors. the reaction rate constant was expressed in hours, distinct from the typical units used for batch experiments (d\({}^{-1}\)). The average volume of biogas produced day by day (calculated for the exemplary 30 measurement days) is shown in Figure 4.  
For a mathematical description of the changes in the biogas volume (V) produced in time (t), the most appropriate was the equation of first-order reaction [33] as V = V\({}_{\text{max}}\) (1 - exp(-k\(\cdot\)t)). This was confirmed by the determination coefficients (R\({}^{2}\)). The experimental data allowed to determine the reaction rate constant (k) and the maximum gas volume (V\({}_{\text{max}}\)), which theoretically can be derived from the feed portion feeding the reactor once a day. The results indicate that the biogas production rate constants for sewage sludge were comparable and equaled 0.066 h\({}^{-1}\) and 0.069 h\({}^{-1}\) for R1 and R4, respectively. In the bioaugumented reactors, the k values were 0.071 h\({}^{-1}\), 0.081 h\({}^{-1}\), and 0.087 h\({}^{-1}\) in R2, R3, and R5, respectively. It was probably caused  
Figure 4: Biogas production in time (the average values from 30 measurement days and standard deviations are given), the values of kinetic constants and coefficients of determination for specified reactors: (**a**) R1, (**b**) R2, (**c**) R3, (**d**) R4, (**e**) R5, and (**f**) k constant as a function of Arkea/SS volumetric ratio. by the enhanced microorganisms' activity in the bioaugmented systems. This was confirmed by the increased biogas production rate constant k. The k value increased with the increasing the dose of bioaugmenting mixture, according to the equation \(y=0.5247\chi^{2}-0.0045\chi+0.0675\) (Figure 4f). In each phase, the differences between the maximum biogas production from the reactor feed (V\({}_{\text{max}}\)) and the actual value of biogas production obtained after the period of 24 h (V\({}_{t}\)) were determined (Figure 4). The difference \(\text{V}_{\text{max}}-\text{V}_{\text{f}}\) corresponds to the value of biogas potential in the digest and varied from 3.13 to 7.09 dm\({}^{3}\) in the reactors. The best results were obtained in the bioaugmented reactors, with increasing doses of bioaugmenting mixture in the feedstock. In such cases, the untapped biogas potential decreased and amounted to 16.5% (R2), 12.0% (R3), and 10.6% (R5).