## 3 Results and Discussion
### Model Validation  
The performances of the gLOG and gGOM model with experimental datasets were compared based on the AIC values as shown in Figure 5. The bar represents the relative quality of the models  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Substrate**} & **Dig. Temp** & \multirow{2}{*}{**Model**} & **S (L kg\({}^{-1}\) VS)** & \multicolumn{2}{c}{\(R_{m}\) (L kg\({}^{-1}\) VS)**} & \multirow{2}{*}{\(\lambda\) **(d)**} & \multicolumn{2}{c}{**SMY estimated (L**} & \multicolumn{2}{c}{**Goodness of fit**} \\  & \({}^{\circ}\)C & & & & \(d^{-1}\)) & & **kg\({}^{-1}\) VS** & **R\({}^{2}\)** & **MAE** \\ \hline \multirow{6}{*}{Husk} & 37 & gLOG & 155.5 & 17.29 & 3.5 & 154.5 & 0.993 & 4.86 \\  & gCOM & 159.9 & 15.03 & 3.6 & 159.5 & 1.000 & 1.86 \\  & gLOG & 152.0 & 9.86 & 4.2 & 150.7 & 0.994 & 4.05 \\  & gCOM & 154.3 & 9.07 & 4.3 & 151.8 & 0.997 & 4.82 \\  & gLOG & 147.5 & 9.44 & 5.1 & 139.6 & 0.959 & 7.60 \\  & gCOM & 147.1 & 7.00 & 5.2 & 133.5 & 0.986 & 10.02 \\  & gLOG & 244.7 & 21.67 & 3.8 & 244.1 & 0.998 & 3.29 \\  & gCOM & 249.7 & 20.67 & 4.2 & 248.5 & 0.992 & 6.72 \\  & gLOG & 235.6 & 11.93 & 5.2 & 231.4 & 0.995 & 4.31 \\  & gCOM & 256.7 & 10.70 & 4.1 & 238.2 & 0.997 & 4.06 \\  & gLOG & 223.9 & 4.32 & 7.0 & 197.0 & 0.987 & 6.48 \\  & gCOM & 265.7 & 3.92 & 3.9 & 197.1 & 0.991 & 6.08 \\  & gLOG & 289.6 & 23.16 & 3.6 & 289.5 & 0.989 & 9.30 \\  & gCOM & 297.8 & 24.90 & 1.3 & 293.7 & 0.998 & 4.06 \\  & gLOG & 281.9 & 13.92 & 5.0 & 277.7 & 0.991 & 7.34 \\  & gCOM & 304.8 & 15.96 & 2.0 & 294.4 & 0.960 & 14.99 \\  & gLOG & 272.0 & 5.30 & 6.8 & 242.6 & 0.980 & 12.15 \\  & gCOM & 313.8 & 6.00 & 2.9 & 267.2 & 0.981 & 12.27 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Specific methane yield (SMY) of coffee husks, pulp and mucilage at different fermentation temperatures as estimated by the generalized modified Logistic model (gLOG) and generalized modified Gompertz model (gGOM) together with ultimate methane yield (S), maximum daily methane yield (\(R_{m}\)) and lag time (\(\lambda\)).  
Figure 4: Residual specific methane yield (SMYR) of husks, pulp and mucilage in the course of batch assay residence time (t) at different fermentation temperatures as compared to the prediction by generalized modified Logistic model (gLOG) and generalized modified Gompertz model (gGOM) vs residence time (t).  
for the methane yield dataset of each substrate regardless of fermentation temperature. The gGOM model showed lower AIC for all substrates, particularly for mucilage. Therefore, the gGOM model is better than the gLOG model to fit the experimental data set of methane yields from husks, pulp and mucilage.  
Projections of the daily methane yield from husks, pulp and mucilage were made by the gGOM model, considering fermentation temperatures in a range from 21 \({}^{\circ}\)C to 37 \({}^{\circ}\)C (Figure 6). Thus, the maximum daily methane yields for all substrates occur at the earliest at the highest temperature of the fermentations. Moreover, the projections indicated that higher fermentation temperatures favor a quick recovery of methane in shorter hydraulic retention periods. However, digestion at lower temperatures required an extended hydraulic retention time to recover the methane formation potential of substrates, particularly from pulp and mucilage.  
Figure 5: Comparison of the generalized modified Logistic model (gLOG) and generalized modified Gompertz (gGOM) model on fitting experimental datasets with the Akaike information criterion (AIC) for husks, pulp and mucilage.  
Figure 6: Daily specific methane yield (SMYd) projections by the generalized modified Gompertz model (gGOM) for husk, pulp and mucilage at fermentation temperatures 21 \({}^{\circ}\)C–37 \({}^{\circ}\)C vs. residence time (t).