Bioenergetic Modeling of the Relationship Between Voltage and Electroactive Microbial Biomass Yield for Bioelectrochemical Carbon Dioxide Reduction to Methane

Abstract

Optimal product synthesis in bioelectrochemical systems (BESs) requires a comprehensive understanding of the relationship between external voltage and microbial yield. While most studies assume constant growth yields or rely on empirical estimates, this study presents a novel thermodynamic model, linking anodic oxidation and cathodic carbon dioxide ((Formula presented.)) reduction to methane ((Formula presented.)) by growing microbial biofilm. Through integrating theoretical Gibbs free energy calculations, the model predicts electron and proton transfers for autotrophic methanogen and anode-respiring bacteria (ARB) growth, accounting for varying applied voltages and substrate concentrations. The findings identify an optimal applied cathodic potential of −0.3 V vs. the standard hydrogen electrode (SHE) for maximizing (Formula presented.) production under standard conditions (pH 7, 25 °C, 1 atm) regardless of ohmic losses. The model bridges the stoichiometry of anodic and cathodic biofilms, addressing research gaps in simulating anodic and cathodic biofilm growth simultaneously. Additionally, sensitivity analyses reveal that lower substrate concentrations require more negative voltages than standard condition to stimulate microbial growth. The model was validated using experimental data, demonstrating reasonable predictions of biomass growth and (Formula presented.) yield under different operating voltages in a multi substrate system. The results show that higher voltage inputs increase biomass yield while reducing (Formula presented.) output due to non-optimal voltage. This validated model provides a tool for optimizing BES performance to enhance (Formula presented.) recovery and biofilm stability. These insights contribute to finding optimum voltage for the highest (Formula presented.) production for energy efficient (Formula presented.) reduction for scaling up BES technology.