## 3 Results and Discussion
### Optimisation of Cathode Potential  
The total methane production in the 34 days of continuous flow operation was about 541 mL (22.1 mmol) with an average methane percentage of about 85% (432 mL or 17.7 mmol). It has been previously reported that when the applied cathode potentials are more negative than \(-0.75\) V vs. SHE electrochemical CO\({}_{2}\) reduction reactions result in simultaneous production of acetic acid (electrochemical) and methane rather than methane alone [5]. Therefore, to identify the optimal cathode potential for methane production, we begin the experiment at \(-0.80\) V and reduce it step by step to \(-0.55\) V.  
The methane production rates (MPR; Figure 2) in these experiments ranged from 0.94 to 6.10 mmol/L(reactor)-day. The lower production rates during first two days of the experiment could be due to the use of autoclaved feed and the total dependence on biocathode for methane production. \begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Result** \\ \hline Biogas production & 550 mL (22.5 mmol) \\ Methane & 500 mL (20.5 mmol) \\ Carbon dioxide & 34 mL (1.4 mmol) \\ COD Consumption & 1644.3 mg (52\%) \\ Voltage & \(-0.8\) V vs. SHE \\ Methane Concentration & 90.9\% \\ Mass Balance Efficiency & 80.5\% \\ Electrochemical Methane Yield & 467.8\% \\ \hline \end{tabular}
\end{table} 
Table 1: Results of 1-week biomethane production experiment. However, the MPRs increase and stabilize around 1.5 to 3 mmol/L(reactor)-day over the next few days, suggesting biofilm acclimatization to the experimental conditions. The production rates increased as the cathode potentials were changed from \(-0.80\) to \(-0.65\) V and decreased thereafter. High MPRs of about 5.75 to 6.10 mmol/L(reactor)-day occurred when the cathode potential was maintained at \(-0.65\) V, which was double the production rate obtained in Section 3.2. MPRs were also low when the cathode potentials were more negative than \(-0.65\) V which could be due to CO\({}_{2}\) conversion to acetic acid rather than methane [4]. The electrochemical reduction of CO\({}_{2}\) to acetic acid contributes to the increase in COD concentration of the effluent and thereby results in a low COD to methane conversion rate. The methane concentration in biogas was found to be around 83-87% during the first 23 days of operation that correspond to cathode potentials of \(-0.8\) to \(-0.65\) V. High concentrations of methane (90-93%) were obtained when the applied potential was \(-0.60\) V. Therefore, the optimum cathode potential for electrochemical CO\({}_{2}\) reduction to methane with relatively high MPRs was found to be between \(-0.70\) V and \(-0.60\) V.  
This is also reflected in the EMY plot (Figure 3) where the yield gradually increased from 45% to 110% when the potentials were changed from \(-0.80\) V to \(-0.55\) V. The slight dips in the EMY plot correspond to the changes in applied cathode potentials. However, the EMY recovers and surpasses its previous value at every cathode potential. Unlike EMY, the current generated increased gradually from the applied potentials of \(-0.80\) V to \(-0.65\) V and decreased abruptly at a potential of \(-0.60\). The current remained constant and never recovered even after 9 days of potentiostatic operation at \(-0.55\) V.  
It can also be observed that at cathode potentials of \(-0.60\), and \(-0.55\) V, the EMY is consistently maintained above 100% even with decreasing current from 6.43 mA to 5.40 mA, respectively (Figure 3). This can be attributed to favourable heterotrophic methane production. In other words, cathode potentials more positive than \(-0.65\) V limit the electrochemical activity of CO\({}_{2}\) reduction to either acetic acid or methane, and cathode potentials more negative than \(-0.65\) V support simultaneous electrochemical acetic acid and methane production. An optimised cathode potential or voltage provides an opportunity to decrease the input cost of the electrochemical technology.