## 3 Results and Discussion
### Kinetic Modelling
#### 3.4.2 Transference Function Model (TFM)  
The TFM parameters obtained for single _P. oceanica_ biomass and the different mixtures tested in this study are shown in Table 5. The appropriateness of the proposed model for describing methane production time is supported by the low standard deviations and elevated determination coefficient values obtained from the experimental results. Figure 3 shows as an example the variation of the experimental data of methane production with time for the mixture P.o.:Cas. and the theoretical curve obtained with the TFM. The determined lag times were nearly negligible across all instances, owing to the rapid consumption of readily available biodegradable components in the various mixtures examined during the anaerobic co-digestion processes investigated [49]. The minimal lag time values additionally suggest prompt microbial acclimatization to the digestion conditions and effective methanation of organic substances [37]. Therefore, the absence of a lag phase (Figure 3) suggests that the microbiota thrived in an environment conducive to degradation [47]. This adaptation to the substrate is reflected in the coherence of the negligible or minimal values of \(\lambda\). As can be seen in Table 5, the highest values of the maximum methane production rate (\(R_{max}\)) were found for the co-AD of the mixtures of _P. oceanica_ with peptone, casein, and synthetic casein compared to the anaerobic mono-digestion of the sole _P. oceanica_. Specifically, the highest \(R_{max}\) value was found for the co-AD of the mixture P.o.-Pep. (183 \(\pm\) 5 mL CH\({}_{4}\) (g VS\(\cdot\)d)\({}^{-1}\)), which was 10.9 times higher than the lowest value, which was found for the digestion of the single _P. oceanica_ biomass tested (16.8 \(\pm\) 0.9 mL CH\({}_{4}\) (g VS\(\cdot\)d)\({}^{-1}\)). All co-ADs between the _P. oceanica_ and the nitrogen-rich substrates have higher maximum methane production rates compared to mono-digestion of the single _P. oceanica_ sample, except the non-simulated P.o.:Ur. This fact indicates that the co-AD of these samples has a positive effect on the anaerobic degradation rate. The worst co-substrate was the microalgae _R. subcapitata_ as it showed a negative effect on both the methane production rate and yield. This fact may be attributable to the low bioavailability of nitrogen in the case of this microalgae, which is located within the cell wall hindering the hydrolysis step of the anaerobic process [50]. A \(R_{max}\) value of 40.5 mL CH\({}_{4}\) (g VS\(\cdot\)d)\({}^{-1}\), some higher than that obtained in the present research for single _P. oceanica_, was reported by [PERSON] et al. [46] in BMP tests of fresh seagrass \begin{table}
\begin{tabular}{c c c c c c} \hline
**Substrate** & **B\({}_{\text{max}}\) (NL CH\({}_{4}\) kg\({}^{-1}\) VS)** & \(R_{max}\) (NL CH\({}_{4}\)(kg VS\(\cdot\)d)\({}^{-1}\))** & **\(\lambda\) (d)** & **R\({}^{2}\)** & **S.E.E.** & **Error (\%)** \\ \hline _P.o._ & 82 \(\pm\) 1 & 16.8 \(\pm\) 0.9 & 0.14 \(\pm\) 0.01 & 0.9942 & 3.214 & 3.8 \\ \hline _P.o.:_**Pep.** & 387 \(\pm\) 2 & 183 \(\pm\) 5 & 0.03 \(\pm\) 0.01 & 0.9987 & 6.673 & 0.5 \\ \hline _P.o.:_**Cas.** & 414 \(\pm\) 6 & 117 \(\pm\) 7 & 4.5-10\({}^{-10}\) & 0.9935 & 6.489 & 0.8 \\ \hline _P.o.:_**Syn.Cas.** & 376 \(\pm\) 2 & 140 \(\pm\) 3 & 0.05 \(\pm\) 0.01 & 0.9989 & 6.171 & 0.1 \\ \hline _P.o.:_**R.s.** & 184 \(\pm\) 4 & 54 \(\pm\) 4 & 1.2-10\({}^{-9}\) & 0.9880 & 9.770 & 5.0 \\ \hline \end{tabular}
\end{table} 
Table 5: Values of the parameters obtained from the transference function model for the different substrates studied. Values are given as means \(\pm\) standard deviations. Zostera marina_. However, this value increased up to 65.7 mL CH\({}_{4}\) (g VS-d)\({}^{-1}\) when the seagrass was previously stored in a well-ventilated and open plastic tank for 15 days. Likewise, in the current study [46], the \(R_{max}\) values increased up to 131.5 and 150.4 mL CH\({}_{4}\) (g VS-d)\({}^{-1}\) when the fresh _Z. marina_ and the stored _Z.