## 3 Results and Discussion
### Kinetic Modelling
#### 3.4.1 First-Order Kinetic Model  
A summary of the kinetic parameters obtained from Equation (A1) for the anaerobic digestion of single _P. oceanica_ and co-AD of _P. oceanica_ and nitrogen-rich substrates is shown in Table 4. The experimental results align well with the proposed model, as evidenced by the low standard deviations and high determination coefficient values obtained for all the assayed tests. Figure 3 shows, as an example, the variation of the experimental values of methane production with time for the mixture P.o.:Pep. and the theoretical curve obtained with the first-order model. The highest specific rate constant obtained in the present research was found for the mixture P.o.:Pep. (0.46 \(\pm\) 0.01 d\({}^{-1}\)), which was 130% higher than that obtained for a single _P. oceanica_ (0.20 \(\pm\) 0.01 d\({}^{-1}\)). The low value observed in the case of individual _P. oceanica_ can be attributed to the elevated lignin content (35% VS) and the presence of high salinity residues in the marine plant. Consequently, the viability of _P. oceanica_ as a feedstock for anaerobic digestion may be primarily influenced by two characteristics: its elevated lignin content and the existence of saline residues. This lignin content was very similar as observed for _Pine pinaster_ or _Date palm_ leaves [4]. The anaerobic digestibility of _P. oceanica_ could be improved by using pre-treatments or considering co-digestion with other substrates, given its notable lignin content. Additionally, concerning the existence of saline residues, previous authors emphasized that elevated salinity and the concentration of specific ions may hinder the activity of anaerobic microorganisms crucial for the digestion process, ultimately resulting in decreased efficiency [4]. As can be observed in Table 4, the first-order kinetic constant, \(k\), obtained for the other co-AD tested was also higher than the value obtained for the sole _P. oceanica_, with values 40%, 80%, and 45% higher for the mixtures P.o. :Cas., P.o. :Syn.Cas., and P.o. :R.s., respectively. A lower value of the first-order kinetic constant (0.10 d\({}^{-1}\)) was reported by [PERSON] et al. [46] in the batch anaerobic digestion of fresh seagrass biomass, while the kinetic constant increased up to values in the range of 0.15-0.19 d\({}^{-1}\) when the seagrass was previously stored in well-ventilated open tanks. On the other hand, a \(k\) value of 0.24 d\({}^{-1}\) was achieved when the seagrass was co-digested with chicken manure [46], this value being very similar to that obtained in the present research when the _P. oceanica_ was co-digested with the microalgae _R. subcapitata_ (0.29 d\({}^{-1}\)) or with casein (0.28 d\({}^{-1}\)). A recent study investigated the utilization of biomass from three frequently employed macrophytes in constructed wastewater treatment wetlands--_Water Hyacinth_ sp., _Typha_ sp., and _Cyperus_ sp.--as a substrate for methane production [47]. The assessment of biochemical methane potential for these three biomasses was carried out in batch mode at 37 \({}^{\circ}\)C. Additionally, a kinetic analysis of AD was performed for these substrates, using the first-order model. _Hyacinth_ sp. showed the highest degradation rate, with \(k\) values between 0.35 and 0.53 d\({}^{-1}\) (for tests at ISR ratios between 1 and 4), which was expected due to its lower level of lignin when compared to _Typha_ sp. and _Cyperus_ sp. : 7.5%, 12%, and 17%, respectively [47]. This highest degradation rate contributed to the lowest total digestion time. The lowest value of \(k\) was observed in _Cyperus_ sp. AD at an ISR of 4, 0.07, and 0.09 d\({}^{-1}\), while \(k\) values of between 0.109 and 0.186 d\({}^{-1}\) were achieved for _Typha_ sp. biomass. The