## 3 Results and Discussion
### Evolution of Chemical Parameters  
The dry algal biomass had a TS, VS, total carbon (TC), and total nitrogen (TN) content of 96.43 wt%, 90.39 wt%, 514.98 mg/g TS, and 113.95 mg/g TS, respectively. To assess AcoD stability, the pH, VFAs, NH\({}_{4}\)+-N, and SCOD of the system were also characterized as responses to mixing ratios of FW and MA. Variation in pH indicates solubilization or  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Models**} & \multirow{2}{*}{**Parameters**} & \multirow{2}{*}{**Units**} & \multicolumn{6}{c}{**Treatments (FW/MA Ratio)**} \\ \cline{3-8}  & & & **0:1** & **1:3** & **1:1** & **3:1** & **1:0** \\ \hline \multicolumn{8}{c}{P-experimental} & mL/g VS & 302.69 & 562.08 & 636.13 & 738.62 & 864.24 \\ \hline \multirow{3}{*}{\begin{tabular}{c} First-order \\ model \\ \end{tabular} } & \(P_{0}\)-potential yield & mL/g VS & 292.30 & 540.29 & 613.09 & 703.59 & 832.09 \\  & \(k\) & 1/d & 0.25 & 0.30 & 0.30 & 0.25 & 0.22 \\  & R\({}^{2}\) & & 0.98 & 0.97 & 0.98 & 0.96 & 0.96 \\ \hline \multirow{3}{*}{\begin{tabular}{c} Modified \\ Gompertz \\ model \\ \end{tabular} } & \(P_{0}\)-potential yield & mL/g VS & 286.63 & 531.31 & 603.99 & 688.08 & 811.92 \\  & \(R_{m}\) & mL/(g Vs d) & 48.72 & 109.22 & 123.81 & 121.68 & 122.55 \\  & \(\lambda\) & d & 0 & 0 & 0 & 0 & 0 \\  & R\({}^{2}\) & & 0.96 & 0.93 & 0.95 & 0.91 & 0.91 \\ \hline \multirow{3}{*}{\
\begin{tabular}{c} Logistic model \\ \end{tabular} } & \(P_{0}\)-potential yield & mL/g VS & 284.78 & 528.75 & 601.29 & 683.78 & 806.42 \\  & \(R_{m}\) & mL/(g VS d) & 47.07 & 104.90 & 118.37 & 117.66 & 117.41 \\  & \(\lambda\) & d & 0 & 0 & 0 & 0 & 0 \\  & R\({}^{2}\) & & 0.94 & 0.91 & 0.93 & 0.89 & 0.88 \\ \hline \multirow{3}{*}{
\begin{tabular}{c} Cone model \\ \end{tabular} } & \(P_{0}\)-potential yield & mL/g VS & 306.06 & 595.36 & 657.19 & 817.59 & 964.00 \\  & \(k\) & 1/d & 0.36 & 0.44 & 0.45 & 0.33 & 0.29 \\  & \(n\) & & 1.41 & 1.01 & 1.16 & 0.90 & 0.93 \\  & R\({}^{2}\) & & 0.99 & 0.99 & 0.99 & 0.99 & 0.99 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Estimated kinetic parameters of first-order model, modified Gompertz model, logistic model, and Cone model used for co-digestion of FW and MA at various mixing ratios.  
Figure 2: (**a**) Relationships between the experimental final biogas yield (P-experimental), the predicted biogas potential yield (\(P_{0}\)), the decomposition rate (\(k\)), and the FW/MA ratio. (**b**) Relationships between the experimental final biogas yield (P-experimental), the predicted biogas potential yield (\(P_{0}\)), the maximum biogas production rate (\(R_{m}\)), and the FW/MA ratio.  
decomposition of organic matter, whereas the variation in VFA concentrations indicates the hydrolytic-acidogenic stage [19].  
As shown in Figure 3, VFA accumulation was apparent during the initial period as the VFA production rate was higher than the consumption rate; simultaneously, the pH value changed rapidly from 7.3 \(\pm\) 0.1 to 6.4 \(\pm\) 0.2 due to increased VFA accumulation. VFAs serve as intermediate products of AcoD; subsequently, they are consumed by acetophilic methanogenic bacteria and isotype acetogenic bacteria or are utilized in combination with substrates, resulting in a gradual decrease in total VFA concentrations during which the digestion system remains in good condition. It can be seen that co-digestion played a key role in alleviating the inhibition of VFA throughout the process. A pH rise was seen from the second to the third day before stabilizing. It has been reported that an appropriate pH range of 6.8 to 7.2 is required for efficient biogas production [43]. The co-digestion of FW and MA has been proven to adjust and buffer the pH, especially at mixing ratios of 1:1 and 1:3; these recovered and remained at pH 7.2 \(\pm\) 0.1, the same as the initial pH values.