Abstract
Several recent studies demonstrated significant charge storage in electrochemical biofilms. Aiming to evaluate the impact of charge storage on microbial fuel cell (MFC) performance, this work presents a combined bioelectrochemical–electrical (CBE) model of an MFC. In addition to charge storage, the CBE model is able to describe fast (ms) and slow (days) nonlinear dynamics of MFCs by merging mass and electron balances with equations describing an equivalent electrical circuit. Parameter estimation was performed using results of MFC operation with intermittent (pulse-width modulated) connection of the external resistance. The model was used to compare different methods of selecting external resistance during MFC operation under varying operating conditions. Owing to the relatively simple structure and fast numerical solution of the model, its application for both reactor design and real-time model-based process control applications are envisioned.
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National Research Council of Canada publication number NRC-EME055740.
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Appendix: On-line parameter estimation procedure
Appendix: On-line parameter estimation procedure
The voltage dynamics at the capacitor (V c) of the equivalent circuit shown in Fig. 1 can be described by the following first order differential equation:
By applying Kirchhoff’s law and solving Eq. (28), the analytical solution of MFC output voltage (V cell) is obtained in the following form:
where U c,initial and U c,final are the initial and final voltage values shown in Fig. 8.
First, R 1 estimation is obtained during MFC operation at a high frequency (e.g. 100 Hz) from the following equation:
where U high and U low are the high and low output voltage levels measured in the experiment (Fig. 8).
Subsequently, E oc estimation is obtained by operating the MFC at a low frequency (e.g. 1.0 Hz) and low duty cycle. It is assumed that U oc is equal to the voltage at the end of the open circuit part of the cycle:
Finally, R 2 and C estimations are obtained using voltage measurements at a low operating frequency. It is assumed that V cell reaches a steady-state value at the end of the closed circuit part of each cycle. In Fig. 8 this value is denoted as U final.
The value of R 2 is estimated as:
The value of C is calculated as
where \(\tau\) is the time constant shown in Fig. 8.
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Recio-Garrido, D., Perrier, M. & Tartakovsky, B. Combined bioelectrochemical–electrical model of a microbial fuel cell. Bioprocess Biosyst Eng 39, 267–276 (2016). https://doi.org/10.1007/s00449-015-1510-8
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DOI: https://doi.org/10.1007/s00449-015-1510-8