## 3 Results and Discussion
### Simulation of Batch Mode MFC  
#### 3.2.1 Effect of Initial Substrate Concentration  
Simulation of the proposed model was performed through Matlab on a personal computer to illustrate the processes of substrate utilization, biomass concentration evolution, and voltage generation across an external resistor. Since most MFC studies in literature were carried out in batch mode, this simulation assumed the medium dilution rate D = 0 with initial substrate (HAc) concentrations of 10, 100, 1000, and 2400 mg L\({}^{-1}\), consecutively. The simulation results are shown in Figure 3. Initial substrate concentrations of 1000 and 2400 mg L\({}^{-1}\) did not show obvious decrease in the first 4 d (Figure 3A), but substrate was consumed dramatically after this period. MFCs started with the lower substrate concentrations behaved differently from the higher strength cases, as a continuous and gradual decrease was observed. The substrate in the case of 100 mg L\({}^{-1}\) lasted the longest, i.e., 9 d, which almost doubled that in the higher strength cases. These results indicated that it was not always that more concentrated substrate \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Estimated Parameters** & **Description** & **Value** & **Units** \\ \hline \(\alpha_{\text{A}}\) & Charge transfer coefficient, anode & 0.318 & Dimensionless \\ \(\alpha_{\text{C}}\) & Charge transfer coefficient, cathode & 0.694 & Dimensionless \\ j\({}_{\text{oA}}\) & Exchange current density, anode & 62.5 & mA/m\({}^{2}\) \\ j\({}_{\text{oAU}}\) & Unit exchange current, anode & 0.189 & mA/mg \\ j\({}_{\text{oC}}\) & Exchange current density, cathode & 0.975 & mA/m\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Estimated electrochemical parameters for MFC in this study. Figure 2: Electrochemical parameters estimation and validation; (**A**) the electrode potential during polarization experiment; (**B**,**C**) model validation for experimental data from another identical microbial fuel cell (MFC) reactor (**B** for \(U_{ext}\), and **C** for \(P_{ext}\)); and (**D**) comparison of the simulated and experimental \(U_{ext}\) during inoculation stage. could sustain the longest reaction period, and a moderate substrate concentration should be chosen for keeping MFC from starvation. Trends of substrate utilization were generally the work of suspended bacteria, which could accumulate to a high level and subsequently, consumed substrate at a high rate that rapidly reduced substrate concentration (Figure 3B). For example, in the initial substrate concentrations of 100 and 2400 mg L\({}^{-1}\), the peak suspended biomass concentrations were 2.5 and 117 mg L\({}^{-1}\), respectively. The latter was 47 times higher than the former, which consumed substrate at a higher rate due to two reasons: the higher level of biomass concentration and the enhanced specific substrate utilization rate indicated by the Monod equation (Equations (15) and (16)). The attached biomass concentrations (Figure 3C) accumulated to their plateau values (0.033 mg cm\({}^{-2}\)) for all initial substrate concentrations (in 2 d for 1000 and 2400 mg L\({}^{-1}\), and in 4 d for 100 mg L\({}^{-1}\)), except for the one with 10 mg L\({}^{-1}\) substrate, indicating that there might exist a lower limit for substrate concentration. Thus, a substrate concentration lower than 10 mg L\({}^{-1}\) should be avoided during inoculation stage. The higher the initial substrate concentration, the longer the attached biomass would sustain: both lasted more than 25 d for 1000 and 2400 mg L\({}^{-1}\), but only 23 d for 100 mg L\({}^{-1}\) before the biomass disappeared. The electricity generation (Figure 3D) was simulated in a form of external voltage (\(U_{ext}\)) for the initial substrate concentrations of 100 and 2400 mg L\({}^{-1}\), because both of them fully developed the attached biomass, and were also the typical levels for the low and high substrate concentrations, respectively.