Modeling large‐scale bioreactors with diffusion equations. Part II: Characterizing substrate, oxygen, temperature, carbon dioxide, and pH profiles

Abstract

Large‐scale fermentation processes involve complex dynamic interactions between mixing, reaction, mass transfer, and the suspended biomass. Empirical correlations or case‐specific computational simulations are usually used to predict and estimate the performance of large‐scale bioreactors based on data acquired at bench scale. In this two‐part‐study, one‐dimensional axial diffusion equations were studied as a general and predictive model of large‐scale bioreactors. This second part focused on typical fed‐batch operations where substrate gradients are known to occur, and characterized the profiles of substrate, pH, oxygen, carbon dioxide, and temperature. The physically grounded steady‐state axial diffusion equations with first‐ and zeroth‐order kinetics yielded analytical solutions to the relevant variables. The results were compared with large‐scale Escherichia coli and Saccharomyces cerevisiae experiments and simulations from the literature, and good agreement was found in substrate profiles. The analytical profiles obtained for dissolved oxygen, temperature, pH, and were also consistent with the available data. Distribution functions for the substrate were defined, and efficiency factors for biomass growth and oxygen uptake rate were derived. In conclusion, this study demonstrated that axial diffusion equations can be used to model the effects of mixing and reaction on the relevant variables of typical large‐scale fed‐batch fermentations.

Digital Twin for Continuous Production of Virus-like Particles toward Autonomous Operation

“…The change in the carbon dioxide concentration in the bioreactor is calculated in the same way as for the oxygen concentration. It is known from the literature that the volumetric mass transfer coefficient for CO 2 is approximately 11% lower than that for oxygen normald c normalC O 2 normald t = 0.89 · k L a · ( c normalC O 2 * − c C normalO 2 ) + r normalO 2 c C normalO 2 * = p C normalO 2 H m i x …”

“…It is known from the literature that the volumetric mass transfer coefficient for CO 2 is approximately 11% lower than that for oxygen. 118 The change in pH due to the formation of CO 2 and the addition of base is calculated using the Henderson− Hasselbalch equation 119…”

Modeling large‐scale bioreactors with diffusion equations. Part I: Predicting axial dispersion coefficient and mixing times

“…The literature correlations that were used in calculating the dispersion coefficient and thus the mixing times are compiled in Table 3 along with their uncertainties. The following dispersion coefficient calculation method is used also in Part II of this study for characterization of substrate, temperature, dissolved oxygen, and pH profiles in large-scale bioreactors (Losoi et al, 2023).…”

“…The model's theoretical predictions were also studied and compared to the collected literature data, and various mixing time measurement techniques were interpreted and unified in the context of the diffusion equation. In Part II of this study (Losoi et al, 2023), the focus is on 1D steady-state diffusion equations with first-and zeroth-order kinetics, which were developed to predict and characterize the potentially heterogeneous profiles of substrate, pH, oxygen, and temperature in large-scale stirred bioreactors.…”