Modeling heterogeneity in large‐scale bioreactors using the method of moments with a truncated normal distribution

ABSTRACT Large‐scale bioreactors in industrial bioprocesses pose challenges due to extracellular concentration gradients and intracellular heterogeneity. This study introduces a novel approach integrating the method of moments with truncated normal distributions (MM‐TND) to model intracellular heterogeneity while maintaining computational feasibility compared to continuum simulations. The MM‐TND framework reconstructs intracellular state distributions while respecting physical constraints, which previous methods could not ensure. Validation against experimental data confirms that MM‐TND effectively captures microbial population dynamics, particularly in large‐scale systems where convection and metabolic adaptation timescales are comparable. The results underscore the importance of intracellular heterogeneity in bioprocess modeling and highlight computational advantages of the MM‐TND approach. This approach offers valuable insights into microbial behavior under industrially relevant conditions.