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

Abstract

Gas-liquid mass transfer is often rate-limiting in laboratory and industrial cultures of aerobic or autotrophic organisms. The volumetric mass transfer coefficient k(L) a 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 (k(L) a ≈ 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 k(L) a 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 k(L) a 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 k(L) a) 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.