## 3 Results and Discussion
### Kinetic Evaluation and Analysis  
It is necessary to obtain a suitable model for the design and optimisation of a continuous process for biomethane production from SBL. To do this, two models were used to assess the accumulated BMP of the silages. Experimental BMP were fitted to the models, and kinetic parameters were estimated using Excel software. The measured data and the predicted curves from the models are shown in Figure 3. The two models provide a reasonably good fit to the measured data, as seen from the high values of coefficient of determination, R\({}^{2}\) (Table 4). However, the dual pool kinetic model (DPKM) fitted the measured BMP better than the modified Gompertz model and therefore was more appropriate in describing the BMP of the substrates, probably because, unlike the modified Gompertz model, the DPKM was derived on the assumption that complex substrates such as sugar beet leaves used for AD contain both fast and slow degradable components [53]. Other  
Figure 2: Cumulative biomethane potential of silages (error bars indicate standard deviation). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Silage** & \begin{tabular}{c} **\% of BMP** \\ **Increase** \\ \end{tabular} & \
\begin{tabular}{c} **Name of** \\ **Additive** \\ \end{tabular} &
\begin{tabular}{c} **Duration of** \\ **Ensiling (Days)** \\ \end{tabular} & **References** \\ \hline Switch grass & 13.08 & _L. brevis_ & 30 & [7] \\ Maize & Negligible & _L. plantarum_ & 90 & [34] \\ Grass & 10.34 & homo LAB & 110 & [50] \\ Sorghum & 13.64 & Biochar & 90 & [39] \\ Grass & 20 & L. buchneri & 90 & [51] \\ Sugarcane trash & 71.1 & Mol + LAB & 70 & [52] \\ Sugar beet leaves & 45 & (see M\&M) & 370 & This study \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Effect of different biological additives on the BMP of different silages. parameters that were used to determine a better fit of a model to the experimental data are shown in Table 4. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{**Silages**} \\ \cline{2-5}
**Equation Parameters** & **Control** & **A50:1** & **B150:1** & **C500:1** \\ \hline \multicolumn{5}{c}{Dual Pool Kinetic Model} \\ G\({}_{0}\) (mL/gVS) & 351.044 & 531.083 & 457.115 & 454.658 \\ \(\alpha\) & 0.580 & 0.851 & 0.748 & 0.681 \\ k\({}_{1}\)(/day) & 0.244 & 0.359 & 0.326 & 0.319 \\ k\({}_{2}\)(/day) & 0.013 & 0.049 & 0.021 & 0.032 \\ R\({}^{2}\) & 0.9889 & 0.9832 & 0.9821 & 0.9874 \\ RMSE & 13.545 & 4.385 & 4.242 & 6.713 \\ BIC & 159.098 & 96.102 & 94.248 & 119.953 \\ AIC & 153.936 & 90.773 & 88.919 & 114.624 \\ T\({}_{\text{eff}}\) & 8 & 14 & 14 & 14 \\ \hline \multicolumn{5}{c}{Modified Gompertz Model} \\ G\({}_{0}\) (mL/gVS) & 343.564 & 484.466 & 413.286 & 403.674 \\ R\({}_{\text{max}}\) (mL/gVS) & 74.286 & 83.273 & 79.005 & 68.277 \\ \(\lambda\)(days) & 0.235 & 0.00 & 0.00 & 0.00 \\ R\({}^{2}\) & 0.9629 & 0.9702 & 0.9633 & 0.9652 \\ RMSE & 14.332 & 33.956 & 30.304 & 29.376 \\ BIC & 159.264 & 207.401 & 201.028 & 199.286 \\ AIC & 155.102 & 203.404 & 197.032 & 195.289 \\ T\({}_{\text{eff}}\) & 6 & 7 & 7 & 7 \\ \hline \hline \end{tabular} \({}_{0}\), ultimate methane yield (mL/gVS); \(\alpha\), fraction of fast degrading material; k\({}_{1}\), first-order degradation constant of fast degrading component (1/day); k\({}_{2}\), first-order degradation constant of slow-degrading component (1/day); R\({}_{\text{max}}\), maximum rate of methane production (mL/gVS. days); \(\lambda\), lag phase (days); T\({}_{\text{eff}}\), the effective biomethane production time; R\({}^{2}\), coefficient of determination; RMSE, root mean square error; BIC, Bayesian information criterion; AIC, Akaike information criterion; CTL, control; A50:1: mixture of 1 g of additive and 50 g of sugar beet leaves; Bi50: mixture of 1 g of additive and 150 g of sugar beet leaves; C500:1: mixture of 1 g of additive and 500 g of sugar beet leaves.  
\end{table} 
Table 4: Kinetic data and criteria for selection of best fit model.