## 3 Results and Discussion
### Simulation of Batch Mode MFC
#### 3.2.2 Effect of External Resistor  
From the comparisons of external voltage and overall energy efficiency, it could be seen that under this experimental condition, a 100 mg L\({}^{-1}\) of initial substrate worked best among the four tested substrate concentrations. The next step of this study simulated the impact of the external resistor on the batch mode MFC voltage and power generation as well as overall energy efficiency. In MFC study, the internal resistance (\(R_{in}\)) is used for indicating the overall resistance of a reactor, which is a useful index because varying an external resistor to the value of internal resistance generates the maximum external power density [21]. Depending on the reactor design and operation, the values of \(R_{in}\) might differ but usually was within a range of several hundreds of Ohms, which was also in accordance with the observations (332 \(\Omega\) in the experimental study; and 471 \(\Omega\) in the simulation study) in MFC reactors in this study. In order to see the effect of external resistors on MFC energy and power generation, a range of resistor covering the values of internal resistance was chosen for simulation, i.e., 10, 300, 1000, and 2200 \(\Omega\).  
The simulation results were presented in Figure 5. The smaller the value of the external resistor was, the more rapidly the substrate was consumed (Figure 5A), which was also observed in two-chamber MFC reactors for organic matter removal [22; 23]. The main reason was that the increased heat generation, which depicted the part of energy loss through overpotentials (Equation (24)), consumed the substrate at a higher rate as a result of the increased current with the smaller external resistor [24]. When the resistor reduced to 10 \(\Omega\), a major part of the substrate was lost via heat, so that there was not enough substrate to fully support the suspended (Figure 5B) and attached microbial growth. Therefore, the 10-\(\Omega\) resistor caused an apparently impaired power generation performance due to the failure of the microbial growth. On the other hand, the small resistor was beneficial for organic substrate removal because of its higher substrate utilization rate, being more appropriate for treating high strength wastewater, such as swine wastewater [25]. A greater external resistor yielded  
Figure 4: Simulated polarization curves at different moments of inoculation. Attached bacteria concentration reached a plateau value after about 2 d, and the polarization curves did not change much thereafter.  
a higher external voltage (Figure 5C), and took a longer substrate consumption time. Simulation of external power generation (Figure 5D) confirmed that 300 \(\Omega\), which was the closest among the three to the internal resistance observed in this study, generated the largest power. A similar trend was also observed in a previous experimental study [23]. However, this value of resistor sustained a shorter reaction time by 2 to 3 d compared to that of 1000 and 2200 \(\Omega\). Overall, the 1000 \(\Omega\) resistor harvested the most energy from substrate, achieving overall energy efficiency of 20.7% (Table 3). Energy efficiency between 15% and 20% achieved in experimental studies was considered the best cases [26; 27], while a value of around 5% was more frequently observed for general cases [27; 28].