Dynamic mathematical modeling of heat and mass transfer incorporating with the local nutrient and biomass limitation of growth in a packed-bed solid-state bioreactor.

This research develops on our previous semi-mechanistic model that describes the dynamic physical and biochemical processes taking place in a packed-bed bioreactor to analyze the relationship of nutrient limitation, biomass accumulation, metabolic heat generation, and mathematical description of packed-bed porous media. The experimental and simulation data proved that glucose concentration gradients in the biofilm could be neglected due to small biofilm thickness and high diffusivity of glucose in the biofilm. The prediction results also showed that an increase in the initial substrate concentration leads to a rise in the temperature gradient in the bed. The model proposes that if the diameter of substrate particle is too large (r > 0.1 cm), the growth rate will decrease significantly due to the high biomass accumulation in the biofilm, and temperature gradients decrease in the column. This can be used as a strategy to control the overheating problem in the bed.