## 4 Conclusions  
In this study, the matrix of the experimental runs was determined using the central composite design (CCD) of the response surface methodology (RSM). This supported the data screening, designing, optimization, model testing, and validation of the results obtained and the determination of the multifunctional impact of the input variables. Thus, the modelled experimental data provided reasonable prediction performance of a bio-stimulated AD process with nanoparticle and biochar additives. The synergistic effect of additives resulted in over 70% degradability of the wastewater. RSM results revealed that the methanogenesis phase and stability of the wastewater biodegradation moved toward a neutral pH. At constant temperature (37 \({}^{\circ}\)C) and HRT (28 days), the optimized load of nanoparticles (0.46 g) and biochar (0.66 mgVS/L) resulted in a biogas production of 19.26 mL/day, a pH of 7.07, and a COD removal of 75.17%. This established the trade-off between biogas productivity, biodegradability, and the stability of an AD process operation. Moreover, this result requires the consideration of the use of nanoparticles as a bio-stimulant to build up the process for commercialization in the future.  
The following are available online at [[https://www.mdpi.com/article/10.3390/app122312037/s1](https://www.mdpi.com/article/10.3390/app122312037/s1)]([https://www.mdpi.com/article/10.3390/app122312037/s1](https://www.mdpi.com/article/10.3390/app122312037/s1)), Table S1: Central composite design optimized conditions.  
Figure 5: Ramp plot of the optimization result of methane production and COD reduction.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Number**} & \multirow{2}{*}{\begin{tabular}{c} **Nanoparticle** \\ **Load (g)** \\ \end{tabular} } & \multicolumn{2}{c}{\
\begin{tabular}{c} **Biochar** \\ **Loading** \\ **(mgVS/L)** \\ \end{tabular} } & \multirow{2}{*}{**pH**} & \multicolumn{2}{c}{
\begin{tabular}{c} **Biogas** \\ **(mL/day)** \\ \end{tabular} } & \multirow{2}{*}{**COD Removal**} & \multirow{2}{*}{**Desirability**} \\ \cline{1-1} \cline{5-6}  & & & & & & \\ \hline
1 & 0.46 & 0.66 & 7.07 & 19.26 & 75.17 & 1 \\
2 & 0.4 & 1.5 & 7.04 & 11.83 & 69.5 & 1 \\
3 & 0.6 & 1 & 7.17 & 23.51 & 69.63 & 1 \\
4 & 0.4 & 1 & 7.01 & 23.89 & 70.93 & 1 \\
5 & 0.4 & 0.5 & 7.06 & 11.4 & 78.4 & 1 \\
6 & 0.2 & 1 & 6.87 & 18.41 & 68.37 & 1 \\
7 & 0.6 & 1.5 & 7.23 & 9.06 & 68.7 & 1 \\
8 & 0.2 & 1.5 & 7.21 & 8.72 & 66.46 & 1 \\
9 & 0.6 & 0.5 & 6.99 & 13.42 & 76.62 & 1 \\
10 & 0.26 & 0.5 & 6.9 & 6.5 & 77.26 & 1 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Selected optimized conditions.  
**Author Contributions:** Conceptualisation E.K.T. and J.A.A.; writing--original draft G.A.-D. and J.A.A.; writing-reviewing and editing E.K.T., E.K.A. and S.R.; supervision S.R. and M.C.; Administration E.K.T. All authors have read and agreed to the published version of the manuscript with no conflict of interest.  
**Funding:** This research received no external funding.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Not applicable.  
**Acknowledgments:** The authors would like to thank the Green Engineering Research Group, under the Department of Chemical Engineering Department of the Durban University of Technology, South Africa, for their support.  
**Conflicts of Interest:** The authors state that they have no recognized competing financial or personal interests that might have influenced the work presented in this publication.