### Abstract

Microbial electrolysis cells (MECs) are a promising new technology for producing hydrogen cheaply, efficiently, and sustainably. In these devices, electroactive bacteria oxidize a biodegradable substrate and produce current in an external circuit. The current creates a potential difference between anode and cathode that enables reduction of protons to form hydrogen. Methanogenic archaea reduce the efficiency of the system by competing for the available substrate and producing methane. To better understand these devices, we present a differential-algebraic equation (DAE) model of an MEC with an algebraic relationship for current. We then perform sensitivity and bifurcation analysis for the DAE system. The model can be applied either to batch-cycle MECs, in which the quantity of interest is the maximum current density, or to continuous-flow MECs, in which the quantity of interest is the current density at the stable equilibria. We conduct differential-algebraic sensitivity analysis after fitting simulations to current density data for a batch-cycle MEC. The sensitivity analysis suggests which parameters have the greatest influence on the current density at particular times during the experiment. In particular, growth and substrate consumption parameters for electroactive bacteria have a strong effect prior to the peak current density. We also examine stable equlibria in a continuous-flow MEC. We characterize the minimum dilution rate required for a stable equilibrium with nonzero current and we demonstrate transcritical bifurcations in the dilution rate parameter that exchange stability between several curves of equilibria. Specifically, increasing the dilution rate transitions the system through three regimes where the stable equilibrium exhibits (i) competitive exclusion by methanogens, (ii) coexistence, or (iii) competitive exclusion by electroactive bacteria. Positive long-term current and hydrogen production are feasible only in the final two regimes. These results suggest how to modify system parameters to increase peak current density in a batch-cycle MEC or to increase the current density at equilibrium in a continuous-flow MEC.

Original language | English (US) |
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Pages (from-to) | 709-728 |

Number of pages | 20 |

Journal | SIAM Journal on Applied Dynamical Systems |

Volume | 18 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 2019 |

### All Science Journal Classification (ASJC) codes

- Analysis
- Modeling and Simulation

### Keywords

- Bifurcation
- DAE
- Differential-algebraic equation
- MEC
- Microbial electrolysis cell
- Sensitivity analysis

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## Cite this

*SIAM Journal on Applied Dynamical Systems*,

*18*(2), 709-728. https://doi.org/10.1137/18M1172223