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\begin{document}

\title{Modeling large-scale bioreactors with diffusion equations. Part II:
Characterizing substrate, oxygen, temperature, pH, and CO
\textsubscript{2} profiles}



\author[1]{Pauli Losoi}%
\author[1]{Jukka Konttinen}%
\author[1]{Ville Santala}%
\affil[1]{Tampereen yliopisto - Hervannan kampus}%


\vspace{-1em}



  
  \date{June 15, 2024}


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\begin{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 \emph{Escherichia
coli} and \emph{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.%
\end{abstract}%



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