Get access

A new dynamic model for highly efficient mass transfer in aerated bioreactors and consequences for kLa identification

Authors

  • Stefan Müller,

    Corresponding author
    1. Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenberger Straße 69, 4040 Linz, Austria; telephone: +43-1-51581-6553; fax: +43-1-51581-6550
    • Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenberger Straße 69, 4040 Linz, Austria; telephone: +43-1-51581-6553; fax: +43-1-51581-6550
    Search for more papers by this author
  • Douglas B. Murray,

    1. Institute for Advanced Biosciences, Keio University, Tsuruoka, Japan
    Search for more papers by this author
  • Rainer Machne

    1. Institute for Theoretical Chemistry, University of Vienna, Vienna, Austria
    Search for more papers by this author

Abstract

Gas–liquid mass transfer is often rate-limiting in laboratory and industrial cultures of aerobic or autotrophic organisms. The volumetric mass transfer coefficient kLa is a crucial characteristic for comparing, optimizing, and upscaling mass transfer efficiency of bioreactors. Reliable dynamic models and resulting methods for parameter identification are needed for quantitative modeling of microbial growth dynamics. We describe a laboratory-scale stirred tank reactor (STR) with a highly efficient aeration system (kLa ≈ 570 h−1). The reactor can sustain yeast culture with high cell density and high oxygen uptake rate, leading to a significant drop in gas concentration from inflow to outflow (by 21%). Standard models fail to predict the observed mass transfer dynamics and to identify kLa correctly. In order to capture the concentration gradient in the gas phase, we refine a standard ordinary differential equation (ODE) model and obtain a system of partial integro-differential equations (PIDE), for which we derive an approximate analytical solution. Specific reactor configurations, in particular a relatively short bubble residence time, allow a quasi steady-state approximation of the PIDE system by a simpler ODE model which still accounts for the concentration gradient. Moreover, we perform an appropriate scaling of all variables and parameters. In particular, we introduce the dimensionless overall efficiency κ, which is more informative than kLa since it combines the effects of gas inflow, exchange, and solution. Current standard models of mass transfer in laboratory-scale aerated STRs neglect the gradient in the gas concentration, which arises from highly efficient bubbling systems and high cellular exchange rates. The resulting error in the identification of κ (and hence kLa) increases dramatically with increasing mass transfer efficiency. Notably, the error differs between cell-free and culture-based methods of parameter identification, potentially confounding the determination of the “biological enhancement” of mass transfer. Our new model provides an improved theoretical framework that can be readily applied to aerated bioreactors in research and biotechnology. Biotechnol. Bioeng. 2012; 109: 2997–3006. © 2012 Wiley Periodicals, Inc.

Ancillary