Bioreactor scale-up is complicated by dynamic interactions between mixing, reaction, mass transfer, and biological phenomena, the effects of which are usually predicted with simple correlations or case-specific simulations. This two-part study investigated whether axial diffusion equations could be used to calculate mixing times and to model and characterize large-scale stirred bioreactors in a general and predictive manner without fitting the diffusivity parameter. In this first part, a resistances-in-series model analogous to basic heat transfer theory was developed to estimate the diffusivity such that only available hydrodynamic numbers and literature data were needed in calculations. For model validation, over 800 previously published experimentally determined mixing times were predicted with the transient axial diffusion equation. The collected data covered reactor sizes up to 160 m 3, single- and multi-impeller configurations, aerated and non-aerated operation in turbulent and transition flow regimes, and various mixing time quantification methods. The model performed excellently for typical multi-impeller configurations as long as flooding conditions were avoided. Mixing times for single-impeller and few non-standard bioreactors were not predicted equally well. The transient diffusion equation together with the developed transfer resistance analogy proved to be a convenient and predictive model of mixing in typical large-scale bioreactors.

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 CO 2 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.