## 3 Results and Discussion
### Kinetic Evaluation and Analysis
Figure 3: Experimental data and model simulation of cumulative biomethane potential of the silages using the dual pool kinetic model (**a**) and the modified Gompertz model (**b**). An indication of a more appropriate model to describe a process is the lower values of RMSE, BIC, and AIC [54]. The dual pool kinetic model (DPKM) was seen to exhibit a better BMP fit for the experimental data than the modified Gompertz model. The deviations between the cumulative experimental and predicted BMP from the DPKM for CTL, A50:1, B150:1, and C500:1 silages were 1.2%, 0.04%, 0.08%, and 1.5%, respectively. From the modified Gompertz model, the deviations for CTL, A50:1, B150:1, and C500:1 silages were 3.3%, 6.1%, 6.2%, and 6.6%, respectively. From the DPKM, the values of hydrolytic constant of fast degradable components, k\({}_{1}\), were at least nine times higher than the hydrolytic constants of slow degradable components, k\({}_{2}\), in all silages, an indication that components of SBL degrade at different rates. The hydrolytic constants (k\({}_{1}\) and k\({}_{2}\)) of the silages with additives were significantly higher in compared to the values of the CTL silage, an indication of increased enzymatic hydrolysis. The fraction of degradable components, \(\alpha\), were significantly higher (\(p<0.05\)) in the silages with additives, an indication that the additive may have enhanced the biodegradation of structural carbohydrate [37]. Values of \(\alpha\) and R\({}_{\text{max}}\) were in the order of A50:1 \(>\) B150:1 \(>\) C500:1 \(>\) CTL. Figure 3 also shows the presence of a logarithmic phase (1-10 days), as well as the absence of a lag phase, except for the CTL silage, wherein the lag phase was seen to be about 0.24 days. In AD processes, a short lag phase, which is an indication of higher activity and tolerance for the system in the reactor [55], is usually preferred. Using the values of the lag phase (\(\lambda\)), maximum rate of biomethane production (R\({}_{\text{max}}\)) and accumulated methane yield from the modified Gompertz model, the maximum time, t\({}_{\text{max}}\), at which the maximum methane rate was obtained, was calculated to be 2.09, 2.14, 1.93, and 2.00 days for CTL, A50:1, B150:1, and C500:1 silages, respectively. These values are true only for the CTL silage, as seen in Figure 1, confirming that the Gompertz model does not provide a better fit of the experimental data. However, the values provide an approximation of the time within which the maximum rate of biomethane production can be achieved. An important parameter that can also be deduced from the curves is the effective methane production time, T\({}_{\text{eff}}\). This is the time it will take for 90% of the cumulative biomethane to be produced. The measured T\({}_{\text{eff}}\) for the substrates without additive was 8 days, and 14 days for the silages with additive. T\({}_{\text{eff}}\) from the DPKM were closer to the measured values than T\({}_{\text{eff}}\) from the modified Gompertz model. In both models, silages with additive had a higher T\({}_{\text{eff}}\) than the silage without additive (Table 4). [PERSON] et al. [56] has reported that a higher T\({}_{\text{eff}}\) is associated with substrates that have a shorter lag phase and a higher BMP.