Determination of biological kinetics: a model for acetic acid production in a lab-scale CSTR reactor

Optimizing continuous stirred tank bioreactors for gas fermentation requires predictive models that integrate microbial kinetics with process dynamics. Thermoanaerobacter kivui is a promising thermophilic acetogen for converting CO₂ and H₂ into acetic acid, yet no kinetic framework exists for this microorganism. In this work, we introduce the first 0D macroscopic model describing T. kivui under CO₂/H₂ fermentation, derived directly from experimental data. The model combines biological kinetics for cell growth and acetic and formic acid production with gas-liquid mass transfer, while considering key operational parameters such as pressure, inlet gas composition, gas flow rate, and impeller speed. Validation against literature data confirms its ability to reproduce major experimental trends, including the increase in acetic acid productivity with pressure up to 10 bar and the dependence on H₂:CO₂ ratio. The model identifies optimal conditions for maximizing acetic acid productivity. According to model predictions, peak productivity occurs at 10 bar pressure, a gas flow rate of 0.63 vvm, and an inlet gas mixture with an H₂:CO₂ ratio of approximately 3:1. Under these predicted conditions, the model estimates that ∼ 70% of CO₂ and 50% of H₂ are converted into products. Experimental validation, performed at lower pressures due to equipment safety constraints, shows that these predictions are in close agreement with experimental results and support the model's reliability. This framework offers a robust and computationally efficient tool for evaluating operating scenarios, enabling process optimization, guiding scale-up and intensification, and advancing the use of thermophilic acetogens in sustainable CO₂ valorization.