Towards a single empirical correlation to predict kLa across scales and processes

Mathematical models are increasingly used in fermentation. A major limitation is that the parameters they include are often strain and scale dependent, meaning that they have to be determined every time a new process is introduced. One of these parameters in aerobic fermentations is the volumetric mass transfer coefficient (k_La).

Oxygen transfer was studied in order to establish a single equation to predict k_La. Operation data from a wide range of processes were extracted from the Novozymes pilot and production scale databases. On-line viscosity was measured for all processes (56 batches). Off-line rheological measurements were performed for the pilot scale processes (26 batches); and the apparent viscosity was evaluated with 5 different calculations of the average shear rate. The experimental k_La value was determined with the direct method; however, eight variations of its calculation were considered. Several simple correlations were fitted to the measured k_La data. For the on-line viscosity set, 18 correlations were fitted to the data, while 5 equations were tested for the off-line viscosity data set. The standard empirical equation was found to be best for predicting k_La in all processes at pilot scale using off-line viscosity measurements, and using the equation from Henzler and Kauling (1985) to evaluate the shear rate. In addition, a parameter set of the standard empirical equation was found that can predict oxygen transfer in low viscosity processes at all scales using on-line viscosity measurements. However, no single correlation for all processes and all scales could be established.