## 3 Result and Discussion
### Simulation Results  
Using a single disintegration constant assumes all particulates disintegrate equally. K\({}_{\rm dis}\) values in this mode of simulation are usually estimated based on the fast degrading fractions and this leads to an overestimation of methane production. In mode 1 simulation of the RF sample, methane production peaked very early in the digestion process (4-5 d) and continued to decline for the rest of the digestion, which differs significantly from the pattern of methane production observed in the experimental results. This phenomenon is visible in Figure 7a. Classifying particulates into fast degrading and slow degrading fractions seemed to rectify the overestimation of methane production (mode 2). Accounting for slow degrading particulates led to similar patterns in the timing of peak methane production. When the two modes of simulations are compared, it is apparent that the contribution of slow degrading particulates to the methane production became more and more significant at the later stages of digestion. Application of both modes of simulations on CF samples did not lead to significantly different results. Unlike RF, CF samples contain relatively small quantities of solid particulates, which are the main causes of reduced disintegration rate. Even if K\({}_{\rm dis}\), K\({}_{\rm dis1}\) and K\({}_{\rm dis2}\) values for CF and RF are the same, the relative proportion of fast and slow degrading fractions are different. RF contains far more slow disintegrating particulates than CF. As a result, it is expected that simulations of CF in mode 1 (where all particulates are assumed to be degraded at K\({}_{\rm dis}\) of 0.17 d\({}^{-1}\)) and mode 2 (where 85% of particulates are assumed to be degraded at K\({}_{\rm dis1}\) of 0.17 d\({}^{-1}\)) lead to similar patterns of methane production. Both modes of simulations suggested peak methane productions slightly earlier than observed. Comparing both modes of simulations for CF samples (Figure 7b) it is noticeable that mode 1 simulation seemed a better fit for CF samples than mode 2, suggesting that classification of particulates into fast and slow degrading fractions may be better suited for particle-rich substrates than particle \"free\" substrates. The patterns of degradation of particulates were compared using data from mode 1 and mode 2 simulation results (Figure 8). In both RF and CF mode 1 simulations, Xc followed a \"logarithmic\" decline throughout the course of the digestion process. In RF mode 2 simulation, slow degrading particulates decline in a similar fashion as the one observed by Xc in mode 1 simulations, however fast degrading particulates increased first (until 8-10 days) followed by a gradual decline. The increase in the fast degrading particulates is partly attributed to decaying microorganisms being added into Xc1. Particle size and presence of recalcitrant substances contribute heavily to the slow degradation of solid particulates. After disintegration, the rest of the anaerobic digestion process continues the same way whether the disintegrated particulate originated from slow or fast disintegrating fractions. As a result of this, the slowly disintegrated particulates are continuously being added into a rapidly disintegrated fraction that contributes to the increase in Xc1 at the beginning of the digestion. Mode 2 simulation of the CF sample did not show increasing Xc1 mainly due to the absence of enough slowly disintegrating particulates continuously added to it. In addition, the contribution from microbial decay was minimal. \begin{table}
\begin{tabular}{c c} \hline \hline
**Sample** & **K\({}_{\rm h}\) (d\({}^{-1}\))** \\ \hline RF & 0.088 \\ RF-CEL & 0.154 \\ CF & 0.094 \\ CF-CEL & 0.120 \\ BLANK & 0.062 \\ BLANK-CEL & 0.148 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Hydrolysis rate constant values estimated using Equation (2). Figure 8: Comparison of particulate degradation in samples: RF (**a**) and CF (**b**).