Modelling of a Batch Whey Cultivation of Kluyveromyces marxianus var. lactis MC 5 with Investigation of Mass Transfer Processes in the Bioreactor

Abstract

This study presents a mathematical model of a batch fermentation of lactose oxidation from a natural substratum in a cultivation by the strain Kluyweromyces marxianus var. lactis MC 5. In the model of the process, the mass transfer in the bioreactor for oxygen concentration in the gas phase (GP) and in the liquid phase (LP) is based on the dispersion model of the GP. In addition, perfect mixing in LP is included. Nine models were investigated for specific growth rate and specific oxygen consumptions rate: Monod, Mink, Tessier, Aiba, Andrews, Haldane, Luong, Edward and Han-Levenspiel. In regard to the parameter estimation, the worst observed error was used for all experiments as an objective function. This approach is a special case of multi objective parameter estimation problems allowing the parameter estimation problem to become a min-max problem. The results obtained (values of criteria, relative error and statistics λ) for the specific growth rate showed that the best fit to experimental data is achieved when applying the Mink model. In a combination a Mink, and Monod, Mink, Luong, Haldane, and Han-Levenspiel are used for specific oxygen consumptions rate. Based on the investigation, it was discovered that the best fit belonged to the models of Mink and Haldane, Mink and Luong and Mink and Han-Levenspiel. Therefore, these particular models are used for modeling the batch processes