## 3 Results and Discussions
### Anaerobic Digestion Experiments
From Table 4, it can be seen that the exponential model best describes the kinetics of cumulative biomethane production during the degradation of WHDS only, Mix-1, Mix-4 and SY only substrates. This is because the exponential model presents the lowest RMSE of 2.747, 2.017, 10.03 and 5.967 for predicting the cumulative biomethane yield from the degradation of substrates of WHDS only, Mix-1, Mix-4 and SY only, respectively. The cone model is seen to be sufficient in describing the cumulative biomethane potential from the degradation of Mix-2 and Mix-3 substrates. This is because the cone model presents the lowest RMSE of 3.568 and 5.417 for predicting cumulative biomethane yield from the degradation of Mix-2 and Mix-3, respectively. The sufficiency of the exponential model and the cone model in WHDS only, Mix-1, Mix-2, Mix-3, Mix-4 and SY only is indicative of the dominance of the rate biomass hydrolysis or solubilization in dictating the kinetics of biomethane generation. The graphical illustration of the model fitted for the different biomethane yields is shown in Figure 4:3 The modified gompertz model was the least reliable biomethane kinetic model for all substrate mixtures considered, since the predicted cumulative biomethane production did not follow a sigmoid growth curve pattern as shown in Figure 8, with rapid biomethane generation recorded in the first day of degradation. The observed trend was largely due to the absence of a sufficiently long 'lag' phase, which characterizes typical sigmoid patterns, during the degradation of substrate mixtures. Additionally, the results suggest that the synergizing effects observed in Mix-3 and Mix-1 as illustrated by the high CPI value (>1) may have led to an enhanced substrate solubilization rate, thus promoting rapid bioavailability of degradable organic matter. This is because the increase in the CPI determined for Mix-3 (CPI = 1.33) and Mix-1 (CPI = 1.72) mirrored the increase in the substrate solubilization rate constants (constants \(k\) in Equations (3) and (4)) calculated to be 0.417 d\({}^{-1}\) and 0.448 d\({}^{-1}\) for Mix-3 and Mix-1 substrate mixtures, respectively. Moreover, further investigation of the substrate solubilization rates (constants \(k\) in Equations (3) and (4)) showed that for Mix-4, the low solubilization rate highlighted by the lower value of constant \(k\) of 0.207 d\({}^{-1}\) did not necessarily result in poor biomethane yields as illustrated by its highest cumulative biomethane yield (264.13 mL/gVS\({}_{\rm added}\)). Additionally, the substrate Mix-4 presented the highest synergizing effect as illustrated by the highest CPI value of 1.78. This observation is consistent with previous studies that showed that the biomethane yield was not solely dependent on the solubilization rate, since high (low) solubilization rates did not always lead to high (low) biomethane yields [43]. While the solubilization (hydrolysis) rate enhanced the AD process and was therefore important, it did not constitute the only factor governing biomethane productivity. In addition to the solubilization rate, the importance of other factors, such as pH, microbial nutrient availability and the microbial population present, were also reinforced when the biomethane kinetic parameters describing biomethane yield from Mix-2 was assessed. It was observed that, although the ACD Mix-2 substrate exhibited the highest rate of substrate solubilization of 0.532 d\({}^{-1}\) (constants \(k\) in Equations (3) and (4)), this high solubilization rate did not translate to the highest CPI (1.67) or the highest biomethane yield (179 mL/gVS\({}_{\rm added}\)).