A virtual sensor was designed based on the alginate production by Azotobacter vinelandii with the objective to estimate the effective shear rate generated by Rushton turbines in a lab stirred fermenter. This virtual sensor is able to simulate the growth rate of bacterium. One of the components of this sensor is the volumetric oxygen transfer coefficient (kLa) which was determined experimentally by the method of gas elimination with nitrogen (only at the beginning of the culture). The experimental value of kLa matched with a correlation proposed by García-Ochoa and Gómez which is used for non-Newtonian fluids. The main components of such correlation are the superficial velocity (Vs), power consumption (P/V)-determined experimentally by a dynamometer bearing- and effective viscosity (eff). The values of the effective viscosity of the broth cultures of A. vinelandii depends on the correlation used to estimate the shear rate (), flow index behavior (n) and consistency index (K). The correlations evaluated in order to estimate the shear rate were: Metzner and Otto, Bowen, Calderbank and Moo-Young, Witchterle and colleagues. Kelly and Gigas, Vogel and Kroner, and Sánchez-Pérez et al. These correlations affected the oxygen transfer rate (OTR) predicted for the cultures, therefore, the oxygen was considered as a limiting substrate. In this context, the main component of our virtual sensor is the Monod equation; the sensor was able to simulate the growth of A. vinelandii for cultures performed at 140, 180, 200 and 340 rpm and the kinetics were simulated at by means of the software SSBP. In all batch simulations, the Witchterle et al.-Vogel and Kroner correlations simulated better the growth of bacterium; however, the perfect simulations were not obtained due to the accumulation of an intracellular metabolite known as poly--hydroxybutyrate (PHB), under anaerobic conditions. The virtual sensor demonstrated that the shear rate values are at less two or three order of magnitude higher than the other correlations tested. Finally, the quality of the alginates at 340 rpm was better with 1.08 x 106 g/gmol of mean molecular weight.
Key words: Alginate, Azotobacter vinelandii, consistency index, flow behavior index, oxygen transfer rate, shear rate, virtual sensor, volumetric oxygen transfer coefficient.