Mathematical Modeling of Macroscale Phenomena: Oxygen Transfer for Solid-state Fermentation in Static Tray Bioreactor

Abstract

Aims: To develop a mathematical model for prediction of variation in oxygen concentration inside the bed of tray type bioreactor for solid state fermentation and comparison of oxygen profile of unsteady state and pseudo steady state approximation. Place and Duration of Study: All the simulations were performed at the Applied and Industrial Microbiology laboratory, Indian Institute of Technology, Madras, from October 2013 to September 2014. Methodology: Models for various reaction kinetics (zero order, first order and Monod’s kinetics) were derived from the general model. Ordinary differential equations (Pseudo steady state approximation) and partial differential equations (unsteady state assumption) were solved by numerical techniques – Finite difference method (FDM) and Runge-kutta method. Simulation runs were carried out for various parameters such as bed height gas phase oxygen concentration, saturation constant, and porosity of the bed. Results: Oxygen profiles of unsteady state and pseudo steady state assumption were compared and results show lower oxygen concentration in case of unsteady state assumption. Concentration of oxygen was low for the organism following first order when compared to zero order and Monod kinetics. Results of simulation runs revealed that the oxygen concentration decreases as the bed height increases irrespective of the kinetics of the reaction. And it increases with increasing gas phase oxygen concentration, saturation constant and porosity. Conclusion: Mathematical model with unsteady state assumption was reported and it can be employed in calculating the design and operational parameters for solid state fermentors to yield optimal productivity.