## 3 Results and Discussion
### Simulation of Continuous Mode MFC
#### 3.3.2 Effect of External Resistor  
The next simulation was implemented for changing electrical currents by varying \(R_{ext}\) at the operating conditions of \(S_{in}\) and \(D\) listed in Table 4. The relationship between \(R_{ext}\) and current \(I\) was depicted in the inset of Figure 7A. These results were useful for determining a suitable range of the external resistor for better substrate removal, power generation or overall energy recovery. As shown in Figure 7A and Table 4, all cases resulted in a maximum power generation (\(P_{ext,\ max}\)) of 0.106 mW at \(R_{ext}\) of 352 \(\Omega\), except for the case of the lowest substrate loading (\(S_{in}\) = 100 mg L\({}^{-1}\) and \(D\) = 0.1), which had a highest power of 0.091 mW at \(R_{ext}\) of 1007 \(\Omega\). For the lowest substrate loading, a further decrease of \(R_{ext}\) distributed more organic substrate utilization for heat generation and would finally lead to a system failure without electrical generation due to substrate limitation for biomass growth. On the contrary, all the MFCs with enough substrate generated the same external powers at given \(R_{ext}\). Figure 7B plotted the results of MFC cell efficiency (\(\eta_{cell}\), defined in Equation (28)), which showed that MFC cell efficiency decreased with the increasing circuit current (or the decreasing external resistor) because of the increased heat loss through the cell (Equation (24)). Again, the curve of the lowest substrate loading differed from the others and was interrupted at \(R_{ext}\) less than 928 \(\Omega\) due to insufficient substrate available for biomass growth.  
Figure 7C,D showed the overall energy efficiencies for the influent substrate concentrations of 100 and 2400 mg L\({}^{-1}\), respectively. For the lower substrate cases, the maximum overall energy efficiencies (\(\eta_{overall,\ max}\)) were between 0.105 and 0.322, and were achieved at different external resistors depending on dilution rates (928 \(\Omega\) at D = 0.1 d\({}^{-1}\); 405 \(\Omega\) at D = 1 d\({}^{-1}\); and 1017 \(\Omega\) at D = 2 d\({}^{-1}\)). For the higher substrate cases, the maximum overall energy efficiencies were between 0.0011 and 0.0167, and were achieved at \(R_{ext}\) = 352 \(\Omega\) at which the \(P_{ext,\ max}\) values were concurrently obtained. Therefore, the lower substrate concentration reactor had one or two orders of magnitude of higher overall efficiency than that of the higher substrate concentration. This substantial difference was a result of more proliferated biomass growth at higher substrate concentrations and the biomass in turn consumed more substrate. Please also note that the internal resistance \(R_{in}\) estimated by polarization curves was 471 \(\Omega\), and was independent of these operating parameters. The steady state substrate concentration (\(S\)) and substrate removal were almost staying unchanging at different electrical current (Figure 7E,F), but depended on the influent substrate concentration and dilution rate, as discussed earlier. Removal efficiencies greater  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \(S_{in}\) & \(D\) & **Steady State S** & \(S\) _Removal_ & \(P_{ext,\ max}\) & \(\eta_{overall,\ max}\) & \(R_{in}\)a  & \(R_{ext,\ p}\)b  & \(R_{ext,\ q}\)c  \\ \hline mg/L & d\({}^{-1}\) & mg/L & \% & mW & \(\Omega\) & \(\Omega\) & \(\Omega\) \\ \hline  & 0.1 & 0–5.26 & \(>\)94.7 & 0.091 & 0.322 & & 1007 & 928 \\
100 & 1 & 57.6–73.5 & 26.5–42.4 & 0.106 & 0.105 & & 352 & 405 \\  & 2 & 79–100 & \(<\)21.0 & 0.106 & 0.156 & & 352 & 1017 \\ \hline  & 0.1 & 5.17–5.26 & 100 & 0.106 & 0.0167 & & 352 & 352 \\
2400 & 1 & 73.9 & 96.9 & 0.106 & 0.0017 & & 352 & 352 \\  & 2 & 531 & 77.9 & 0.106 & 0.0011 & & 352 & 352 \\ \hline \end{tabular}
\end{table}
Table 4: Simulated MFC performance: substrate removal, power generation and overall energy efficiency.  
than 94.7% or about 100% were achieved at \(S_{in}\) = 100 mg L\({}^{-1}\) and \(D\) = 0.1 d\({}^{-1}\), and \(S_{in}\) = 2400 mg L\({}^{-1}\) and \(D\) = 0.1 d\({}^{-1}\), respectively.