Modelling of bubble breakage and coalescence in stirred and sparged bioreactor using the Euler-Lagrange approach

Abstract

Gas-liquid systems are commonly used in industry to carry out biochemical reactions. Such process must be carried out to ensure sufficient mass transfer while there is no damage to the living cells/microorganisms. This is given mainly by the bubble size distribution (BSD) and process parameters such as the impeller speed and gas sparging rate. The correct prediction of BSD is crucial to choosing the optimal process parameters and meeting the requirements of a given culture. This work aimed to use computational fluid dynamics (CFD) to predict the breakage and coalescence of individual bubbles and therefore to predict the whole BSD under broad range of process parameters. The gas-liquid system of the stirred and sparged bioreactor was modelled utilizing the Euler-Lagrange (EL) approach. The continuous phase was modelled as a 3D time-dependent problem using the Reynolds-averaged Navier-Stokes (RANS) method with a realizable k-ε model for the description of turbulence. The motion of discrete Lagrangian bubbles was tracked by Newton's equation of motion. Both the breakage and coalescence of individual bubbles were implemented. For bubble coalescence, the model developed by Prince and Blanch and further modified by Sommerfeld and Sungkorn for use in the Lagrangian approach to bubbles was used. For breakup, a model developed by Martínez-Bazán was used. There, the effect of daughter distribution function (DDF) on the resulting gas dispersion was studied. Experiments and simulations were performed in the Minifors stirred and sparged bioreactor with a working volume of 3.5 L. The impeller speeds ranged from 200 to 500 rpm (corresponding to Reynolds number in the range from 10,889 to 27,222), while the gas feed rate was constant and reached a value of 1.2 L min–1. To validate the whole CFD model, we compared the BSDs obtained from the simulations against experimentally determined BSDs. There, for all cases, the simulations matched the experimental data relatively well. Subsequently, a general characterization of the system studied was performed in terms of the volumetric mass transfer coefficient (kLa) and the maximum hydrodynamic stress (τVS) to which the cell could be exposed. Also in this case, under all tested conditions, we achieved satisfactory agreement with experiments.