## 3 Results and Discussion  
### Model Fitting for Different Fermentation Temperatures  
Figure 1 shows the measured methane yield from husks, pulp and mucilage at fermentation temperatures of 21 \({}^{\circ}\)C, 30 \({}^{\circ}\)C and 37 \({}^{\circ}\)C as data points in the course of the anaerobic batch assay. The methane recovery was faster in all batch assays at 37 \({}^{\circ}\)C compared to digestions at 30 \({}^{\circ}\)C and 21 \({}^{\circ}\)C. The specific methane yield (SMY) of substrates at the end of the batch assay was nearly equal for digestions at 30 \({}^{\circ}\)C and 37 \({}^{\circ}\)C. However, digestion at 21\({}^{\circ}\)C showed a slower methane recovery and a lower SMY at the end of the batch assay, even after a residence time of 60 days. The distance of the SMY curves clearly shows that higher fermentation temperatures favor quicker methane recovery. About 90% of the methane potential of pulp was recovered in two, three and seven weeks of the batch assay while digested at 37 \({}^{\circ}\)C, 30 \({}^{\circ}\)C and 21 \({}^{\circ}\)C, respectively. [PERSON], et al. [40] reported similar results from batch assay of banana stalk digested at 37 \({}^{\circ}\)C. The LOG and GOM models were fitted to experimental data points. Both models fit very well to the experimental data. Table 2 shows the model parameters estimated by non-linear optimization and the goodness of fit. Both models estimated three parameters: the ultimate methane yield (S), maximum daily methane yield (\(R_{m}\)) and lag time (\(\lambda\)). The LOG and GOM models basically have the same physical parameters, but in different mathematical arrangements. The MAE from the GOM model was less than in the LOG model regardless of substrate type. Furthermore, the MAE showed an increasing trend while fermentation temperatures decreased. This suggests that both models perform very well at an optimal digestion temperature of 37 \({}^{\circ}\)C. The GOM model fits very well for experimental data from husks, pulp and mucilage at all operating temperatures. Samples operated at 30 \({}^{\circ}\)C exhibited a lower methane production rate (\(R_{m}\)) and higher lag time (\(\lambda\)) than samples evaluated at the other operating temperatures. The pulp exhibited longer lag phases at the beginning of the digestion period. The highest methane yield was predicted from mucilage followed by pulp and husk. The LOG model predicted the maximum methane production rate (\(R_{m}\)) and lag time (\(\lambda\)) higher than that of the GOM model. However, the SMY of digesters operated at 37 \({}^{\circ}\)C was underestimatedby the LOG model. There was a slight difference in the correlation coefficients (R\({}^{2}\)) between the experimental dataset and the SMY predicted by the models. Both the LOG and GOM models show an inherent short-coming for the starting condition of fermentation: both models estimate a non-zero methane yield at t = 0. This fact could be attributed to the original purpose of the models, which were designed to describe bacterial growth rather than the bacterial product (methane in our case) [31; 41]. [PERSON], [PERSON] and [PERSON] [38] also reported non-zero methane yield from the LOG and GOM model at t = 0, and explained that the situation has no physical meaning. Figure 1: Measured specific methane yield (SMY) of coffee husks, pulp and mucilage in the course of batch residence time (t) at different fermentation temperatures and curves fitted with the modified Gompertz model (GOM) and modified Logistic model (LOG); error bars show standard deviation, \(n=6\). \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Substrate**} & \multirow{2}{*}{**Dig. Temp (\(\mathrm{\SIUnitSymbolCels}\))**} & \multicolumn{2}{c}{**SMV, measured**} & \multirow{2}{*}{**Model**} & \multirow{2}{*}{**S \(\mathbf{\Omega}\). kg\({}^{-1}\) VS**} & \multirow{2}{*}{**\(\mathbf{R_{m}}\).