Modeling of growth and sporulation of Bacillus thuringiensis in an intermittent fed batch culture with total cell retention

An extended dynamical model for growth and sporulation of Bacillus thuringiensis subsp. kurstaki in an intermittent fed-batch culture with total cell retention is proposed. This model differs from reported models, by including dynamics for natural death of cells and substrate consumption for cell maintenance. The proposed model uses sigmoid functions to describe these kinetic parameters. Equations for time evolution of substrate, vegetative, sporulated and total cell concentration were taken from previous works. Model parameters were determined from batch experimental data obtained in pilot plant. Parameter identification was developed in two stages: (1) coarse identification using a multivariable optimization with constraints algorithm, (2) fine identification by heuristic fit of model parameters looking for a minimal model error. The proposed model estimates adequate time evolution of the process variables with a mean error of 2.6% on substrate concentration and 6.7% on biomass concentration.