# Biomethane Potential of Sludges from a Brackish Water Fish Hatchery
## 3 Results and Discussions
### Kinetic Analysis  
In general, the Gompertz model demonstrated better correlations between the measured and the predicted values of CH\({}_{4}\) yields, when inoculum was used. In fact, R\({}^{2}\) resulted from 0.9934 to 0.9946 for IS50 and IS03, respectively, with an intermediate R\({}^{2}\) value for IS30 (Figure 4). The first-order model, instead, simulated better than Gompertz equation the S100 behavior, with R\({}^{2}\) value of 0.9634, higher than the value of 0.9238 calculated for Gompertz equation. The hydrolysis constant \(k\) applied to get these results was in the range 0.11-0.15 1/day, with the lowest value for S100 and the highest for IS50 (Table 2).  
Figure 3: BMP values calculated from the different tested inoculum/substrate ratios (means and standard errors are indicated by numbers and bars, all significant differences \(p<0.01\)).  
As no other recent study related to AD kinetics of aquaculture effluents was found in literature, studies on other effluents can be taken as a reference for a fruitful comparison. The hydrolysis constant k calculated by our data set was lower than that reported by [PERSON] and colleagues [23], which found \(k\) values between 0.36 and 0.55 1/day when treating cheese whey. Instead, the calculated \(k\) from AD of fish sludges seems to be more similar to that reported for AD of livestock manures, namely \(k\) = 0.13 1/day [36] and \(k\) = 0.05-0.12 1/day [37], to give some examples.  
\begin{table}
\begin{tabular}{c c c c} \hline
**I/S Ratio** & **K (I/Day)** & \(\lambda\) **(Day)** & **R\({}_{\text{max}}\) (NmL/g VS Day)** \\ \hline
50 (IS50) & 0.15 & 14.0 & 63.1 \\ \hline
30 (IS30) & 0.13 & 13.5 & 40.3 \\ \hline
3 (IS03) & 0.11 & 5.5 & 16.0 \\ \hline
0 (S100) & 0.11 & 7.6 & 15.4 \\ \hline \end{tabular}
\end{table}
Table 2: Determination of the hydrolysis rate constant (\(k\)), lag phase duration (\(\lambda\)) and maximum methane production rate (R\({}_{\text{max}}\)) from the first-order kinetic model and the modified Gompertz model.  
Figure 4: Linear regressions obtained between the tested models (Gompertz equation and first-order model) and the experimental methane production tests. The coefficients of determination R\({}^{2}\) are indicated for each regression function.  
The lag phase duration (\(\lambda\)) calculated with Gompertz model resulted to be from 5.5 to 14.0 days, which can be considered quite a long duration, indicating a slow adaptation of the anaerobic biomass to the substrate and a slow hydrolysis kinetics. However, with the highest content of substrate with respect to inoculum (IS03), the lowest lag phase duration was found (\(\lambda\) = 5.5 days), showing the highest degree of correlation (R\({}^{2}\) = 0.9946). Indeed, this inoculum to substrate ratio was the best performing test in terms of AD process rate, also in agreement with the trends reported in Figures 1 and 2. In particular, the present results were very similar to those reported by [PERSON] and colleagues [24], which indicated a lag phase duration from 4.76 to 5.88 days for the mesophilic digestion of beer lees and biochar in an AMPTS system. As observed in this last study, performing AD in thermophilic conditions, rather than actual mesophilic range, could further shorten the lag phase duration [24].  
Finally, the maximum daily specific methane yield (Rmax, NmL CH\({}_{4}\)/g VS day, Table 2) resulted to be higher for IS50 and gradually lower for the others I/S ratios, with the lowest values obtained on IS03 and S100 (16.0 and 15.4 NmL CH\({}_{4}\)/g VS day, respectively).