Fermentation bioreactor with stochastic consumption rate

We present a mathematical model to describe the operation of a bioreactor designed to reduce the substrate concentration in an aqueous solution via microbial activity. The system works in cycles: once the substrate concentration reaches a pre-established minimum level, the bioreactor empties and is reloaded with a new solution that restores the initial concentration. The study evaluates the system's operational viability, analyzing the length of the intervals between consecutive filling and emptying cycles. To achieve this, we establish mathematical bounds —defined by the model's parameters— guaranteeing the finiteness of these waiting times. In addition, we propose minimal conditions for the microbial consumption rate of the substrate, including stochastic perturbations to the metabolic process.