## 2 Materials and Methods
### Anaerobic Digestion Model No. 1 (ADM1) Simulation  
Aquasim software was used to implement the ADM1 model to simulate the batch reactors (Table 4). Two modes of disintegration kinetics were used. In the first mode, first-order disintegration kinetics was used, and all complex particulates were assumed to be equally degradable (single disintegration constant, K\({}_{\text{dis}}\) used). In the second mode, the complex particulates were classified into fast degrading and slow degrading fractions, where two separate disintegration constants, K\({}_{\text{dis1}}\) for fast degrading and K\({}_{\text{dis2}}\) for slow degrading fractions, were used (Figure 4). Classification of particulates into fast degrading and slow degrading was carried out as follows: \begin{table}
\begin{tabular}{l c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & **RF** & **RF** & **CF** & **CF** \\ \cline{2-5}  & **K\({}_{\text{dis}}\)** & **K\({}_{\text{dis1}}\) and K\({}_{\text{dis2}}\)** & **K\({}_{\text{dis}}\)** & **K\({}_{\text{dis1}}\) and K\({}_{\text{dis2}}\)** \\ \hline Disintegration constant (d\({}^{-1}\)) & 0.17 & 0.17, 0.075 & 0.17 & 0.17, 0.075 \\ Amino acid degrading organisms (kg \(\text{COD/m}^{3}\)) & 1.70 & 1.70 & 1.70 & 1.70 \\ Acetate degrading organisms (kg \(\text{COD/m}^{3}\)) & 2.23 & 2.23 & 2.23 & 2.23 \\ Butyrate/valerate degrading & 0.69 & 0.69 & 0.69 & 0.69 \\ organisms (kg COD/m\({}^{3}\)) & 1.85 & 1.85 & 1.85 & 1.85 \\ Fatty acid degrading organisms (kg \(\text{COD/m}^{3}\)) & 1.05 & 1.05 & 1.05 & 1.05 \\ Propionate degrading organisms (kg \(\text{COD/m}^{3}\)) & 0.29 & 0.29 & 0.29 & 0.29 \\ Sugar degrading organisms (kg \(\text{COD/m}^{3}\)) & 1.68 & 1.68 & 1.68 & 1.68 \\ Soluble amino acids (kg COD/m\({}^{3}\)) & 0.2 & 0.2 & 0.2 & 0.2 \\ Soluble fatty acids (kg COD/m\({}^{3}\)) & 0.25 & 0.25 & 0.25 & 0.25 \\ Soluble acetates (kg COD/m\({}^{3}\)) & 0.66 & 0.66 & 0.66 & 0.66 \\ Soluble butyrate (kg COD/m\({}^{3}\)) & 0.15 & 0.15 & 0.15 & 0.15 \\ Soluble propionate (kg COD/m\({}^{3}\)) & 0.05 & 0.05 & 0.05 & 0.05 \\ Soluble valerates (kg COD/m\({}^{3}\)) & 0.08 & 0.08 & 0.08 & 0.08 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Selected simulation parameters and values used to implement ADM1 in Aquasim. Figure 4: ADM1 simulation scheme for mode 1 and mode 2 simulations. a. Calculate particulate COD (Xc)  
\[\text{Particulate COD}=\text{COD}_{\text{total}}-\text{COD}_{\text{soluble}} \tag{11}\]  
\[\text{COD}_{\text{total}}=\text{Total g COD in reactor/V reactor}=\text{Sample COD}_{\text{total}}\times\text{V}_{\text{sample}}\text{/V}_{\text{ reactor}} \tag{12}\]  
For simplification of the simulation, soluble COD was assumed to equal to COD of volatile fatty acids (COD\({}_{\text{VFA}}\)) and some minor constituents as seen in Table 4, according to Equation (13). \[\text{COD}_{\text{soluble}}=\text{COD}_{\text{VFA}}+\text{(COD}_{\text{ soluble amino acids}}+\text{COD}_{\text{soluble fatty acids}}+\text{COD}_{\text{soluble inerts}}+\text{COD}_{\text{soluble sugars}}) \tag{13}\]  
b. Classify particulate COD into fast (Xc1) and slow (Xc2) degrading fractions:  
Classification of Xc into Xc1 and Xc2 was carried out separately for RF and CF. The ratio of total dissolved solids to total solids was used as a basis to estimate the fast degrading fraction (Xc1) from which Xc2 was estimated (Xc2 = 1 - Xc1). Since RF contains a relatively large fraction of solid particulates, it was estimated that 85% of the COD comes from slowly degrading fragments and the rest from fast degrading fragments. In the case of CF, most of the solid particulates are removed due to centrifugation making COD from solid particles constitute a small part of the total COD. We estimated that 15% of COD comes from slow degrading and 85% comes from fast degrading particulates.