The model proposed in this study was based on the assumption that the biomass attached to the anode served as biocatalysts for microbial fuel cell (MFC) exoelectrogenesis, and this catalytic effect was quantified by the exchange current density of anode. By modifying the Freter model and combining it with the Butler–Volmer equation, this model could adequately describe the processes of electricity generation, substrate utilization, and the suspended and attached biomass concentrations, at both batch and continuous operating modes. MFC performance is affected by the operating variables such as initial substrate concentration, external resistor, influent substrate concentration, and dilution rate, and these variables were revealed to have complex interactions by data simulation. The external power generation and energy efficiency were considered as indices for MFC performance. The simulated results explained that an intermediate initial substrate concentration (about 100 mg/L under this reactor configuration) needed to be chosen to achieve maximum overall energy efficiency from substrate in the batch mode. An external resistor with the value approximately that of the internal resistance, boosted the power generation, and a resistor with several times of that of the internal resistance achieved better overall energy efficiency. At continuous mode, dilution rate significantly impacted the steady-state substrate concentration level (thus substrate removal efficiency and rate), and attached biomass could be fully developed when the influent substrate concentration was equal to or higher than 100 mg/L at any dilution rate of the tested range. Overall, this relatively simple model provided a convenient way for evaluating and optimizing the performance of MFC reactors by regulating operating parameters.
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