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

Abstract

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 dispersion coefficient. In this first part, a resistances‐in‐series model analogous to basic heat transfer theory was developed to estimate the dispersion coefficient 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 m3, single‐ and multi‐impeller configurations with diverse impeller types, 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 nonstandard 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.

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

“…A general feel for the time-scale ratio and mixing limitations can be given by taking the longest t 95 (95% mixing time with probe and feed as wide apart as possible) as the measure of mixing rate according to eq. ( 5) in Part I of this study (Losoi et al, 2023),   S K = = 0.05 g L S −1 as the mean substrate concentration and Monod constant, both quite likely values in fed-batch operations (Bylund et al, 2000(Bylund et al, , 1998Castan & Enfors, 2002;Larsson et al, 1996;Xu, Jahic, Blomsten, et al, 1999), and q = 1 g g h S −1 −1 as the biomass-specific maximal uptake rate. Under these conditions Equation ( 6) is simplified to…”

“…The aim of this two-part study was to comprehensively model largescale stirred bioreactors using 1D diffusion equations. Part I of this study (Losoi et al, 2023) presented a computation formula for the model's parameter, the axial dispersion coefficient, and validated it against a large set of previously published experimental data. This second part employed the model to characterize substrate, pH, oxygen, CO 2 , and temperature profiles in typical fed-batch contexts.…”

“…First, it should be noted that the model was not optimized to any of the experimental or numerical references, but the dispersion coefficients were calculated directly from operating conditions using the methodology developed in Part I of this study (Losoi et al, 2023), and the kinetic parameters and mean concentrations were obtained or calculated from the referenced works. The model involved two main assumptions on the kinetics: (1) The substrate consumption was considered to be linear or first-order with respect to substrate concentration.…”

“…As for the hydrodynamic assumptions, the use of turbulent dispersion for the liquid phase was treated and validated in Part I of this study (Losoi et al, 2023). Plug-flow assumption for the gas phase was necessary here to obtain an estimate of CO 2 profiles.…”

“…Table 1 lists relevant variables and quantities regarding the experiments. The axial dispersion coefficients and mixing times were calculated from operating conditions as in Part I of this study (Losoi et al, 2023). Bylund et al (1998) reported ranges of stirrer and gas flow rates, and here the midpoint of these ranges was used as the operating condition.…”