Modelling and advanced understanding of unsteady-state gas transfer in shaking bioreactors

In shaken bioreactors equipped with a sterile closure (e.g. a cotton plug), a realistic understanding and estimation of gas transfer is advantageous to avoid oxygen limitation or carbon dioxide inhibition of a microbial culture. Therefore, in the present study, an unsteady-state gas-transfer model for shake flasks was developed and experimentally investigated for a wide range of gas-transfer resistances (k(plug)). The introduced approach is based on the model of Henzler and co-workers [Henzler and Schedel (1991) Bioprocess Eng. 7, 123131; Mrotzek, Anderlei, Henzler and Buchs (2001) Biochem. Eng. J. 7, 107-112], which describe the spatially resolved gas partial pressures inside the sterile closure, affecting the local gas diffusion coefficients and convective Stefan flow. For further easy processing the resulting total mass-transfer resistance (k(plug)) is described as a function of the mass flow through the sterile plug (OTR(plug)) by an empirical equation. This equation is introduced into a simulation model which calculates the gas partial pressures in the head space of the flask. Additionally, the gas-transfer rates through the sterile closure and gas/liquid interface inside the flask is provided. Simulations indicate that neglecting the oxygen in the head space volume of the flask under initial conditions (simple steady-state assumption) may lead to an underestimation of the oxygen transfer into the liquid phase. The extension of error depends on the conditions. A good agreement between the introduced unsteady-state model and experimental results for the sulfite oxidation as a chemical model system confirmed the validity and usefulness of the proposed unsteady-state approach.