Coupling Metabolic and Hydrodynamic Compartmental Models for Bioreactor Simulations

Abstract

Large-scale bioreactors are widely employed across bioprocessing industries for the production of chemicals, pharmaceuticals, and biofuels. The increasing demand for specialized pharmaceuticals has motivated industries to optimize bioreactor operations. However, the complexity of multiphase interactions and the emergence of concentration gradients and intracellular heterogeneity in bioreactors pose significant challenges in accurately predicting and optimizing the performance of bioreactors. Simulations of numerical models have become invaluable for understanding these systems; however, the high computational cost of detailed models—particularly those involving multiphysics—limits their practicality. The computational cost of these models precludes them from being used for real-time applications or for extensive design optimizations.

To address this challenge, this thesis proposes computationally efficient methods to solve coupled metabolic and hydrodynamic compartmental models that describe key process dynamics.

The compartmental model (CM) approach is based on steady-state multiphase computational fluid dynamic simulations and is designed to accurately represent hydrodynamic properties such as turbulent dissipation energy, oxygen mass transfer, and flow topology. Conventional compartmentalization methods were found to introduce nonphysical ``short-cutting'' effects, leading to inaccuracies in mixing time predictions. To mitigate this, a refined compartmentalization approach was developed to better capture hydrodynamic mixing patterns. Then, a metabolic model was integrated with the compartmental model to explore the metabolic and hydrodynamic interactions.

In terms of the metabolic behavior, two key scenarios were considered: i) the intracellular concentrations were assumed to reach instantaneous equilibrium with their extracellular environments at all times and ii) the intracellular concentrations were not in equilibrium with their extracellular environments.

For the first case, where intracellular and extracellular equilibration was assumed, a binary search tree metabolic model (BSTMM) was developed from a dynamic flux balance analysis model and coupled with a CM describing the extracellular environment. This method significantly reduces computational complexity by substituting traditional linear optimization solvers with an online point-location approach. The coupled BSTMM-CM successfully captured diauxic growth dynamics and demonstrated substantial computational efficiency, enabling long-term bioprocess simulations on standard desktop hardware. However, kinetic parameters for metabolic models calibrated in small-scale bioreactors could not be directly applied to large-scale systems without recalibration. This finding suggested that intracellular heterogeneity may play a crucial role in metabolic regulation and must therefore be explicitly accounted for.

To address this, the second case considered a finite-rate adaptation mechanism governing equilibration between the extracellular and intracellular environments. A method of moments approach, assuming a truncated normal distribution, was implemented to reconstruct the number density function efficiently. This approach demonstrated that intracellular heterogeneity is most pronounced when the characteristic timescales of microbial adaptation and extracellular advection are comparable. The application of this approach to E. coli fermentation data reported in the literature resulted in improved fitting as compared to a model that ignores intracellular heterogeneity. Furthermore, the impact of population heterogeneity on metabolic regulation was evaluated, revealing distinct variations in growth rate and substrate uptake across different regions of the bioreactor.

To further improve computational efficiency of the coupled PBM-CM, an adaptive population compartmental scheme is proposed, which dynamically adjusts the compartmentalization over the course of a simulation to balance accuracy and computational cost. This approach was found to be particularly effective for large-scale bioreactor simulations, especially when advection rates exceed microbial adaptation rates, leading to substantial reductions in simulation time with minimal loss of predictive accuracy.

This research significantly advances the modeling of large-scale bioreactors by integrating hydrodynamic and metabolic models into a computationally efficient framework. The developed methods provide more in-depth insights into the influence of concentration gradients and intracellular heterogeneity on microbial behavior, ultimately improving the predictive accuracy and scalability of bioprocess simulations.