Dynamic Modeling of the Impact of Temperature Changes on CO2 Production during Milk Fermentation in Batch Bioreactors

Abstract

Knowledge of the mathematical models of the fermentation processes is indispensable for their simulation and optimization and for the design and synthesis of the applicable control systems. The paper focuses on determining a dynamic mathematical model of the milk fermentation process taking place in a batch bioreactor. Models in the literature describe milk fermentation in batch bioreactors as an autonomous system. They do not enable the analysis of the effect of temperature changes on the metabolism during fermentation. In the presented extensive multidisciplinary study, we have developed a new mathematical model that considers the impact of temperature changes on the dynamics of the CO2 produced during fermentation in the batch bioreactor. Based on laboratory tests and theoretical analysis, the appropriate structure of the temperature-considered dynamic model was first determined. Next, the model parameters of the fermentation process in the laboratory bioreactor were identified by means of particle swarm optimization. Finally, the experiments with the laboratory batch bioreactor were compared with the simulations to verify the derived mathematical model. The developed model proved to be very suitable for simulations, and, above all, it enables the design and synthesis of a control system for batch bioreactors.

Practical Approaches to the Control of Milk Fermentation with Kefir Grains

“…For the considered laboratory experimental system, the parameters of the mathematical model were obtained from the measured trajectories of the microorganisms, substrate, and product by the particle swarm optimization. The integral absolute error between measured and simulated trajectories represented the applied performance index [20]. The mathematical model parameters, which were obtained from the experiments of the laboratory kefir production and the subsequent optimization, are shown in Table 1.…”

“…The enhanced mathematical model, which considers the influence of the bioreactor's temperature changes on the dynamics of the fermentation process, is described by a system of four differential Eqs. ( 4)-( 7) [20]:…”

“…Function μ mϑ (t) denotes the impact of temperature on the maximum microorganisms' growth rate (h À1 ), and function P iϑ (t) denotes the impact of temperature on the product inhibition constant (g/L). Both functions are identified in such a way that they enable good fitting of the mathematical model's responses to the measured trajectories [20]. Different analytical expressions were tested.…”

“…The use of the heating system for control of the fermentation process in batch bioreactors was presented in Refs. [18][19][20][21][22], and use of the stirrer system in Refs. [18,23].…”