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Cell growth and death rates as factors in the long‐term performance, modeling, and design of immobilized cell reactors

The viable fraction of immobilized cells in a bioreactor may be critical in predicting long‐term or steady‐state reactor performance. The assumption of near 100% viable cells in a bioreactor may not be valid for portions of immobilized cell reactors (ICRs) characterized by conditions resulting in appreciable death rates. A mathematical model of an adsorbed cell type ICR is presented in which a steady‐state viable cell fraction is predicted, based on the assumptions of no cell accumulation in the reactor and a random loss of cells from the reactor. Data on cell death rates, cell growth rates, and productivity rates as functions of temperature, substrate, and ethanol concentration for the lactose utilizing yeast K. fragillis were incorporated into this model. The steady‐state reactor viable cell fraction as predicted by this model is a strong function of both temperature and ethanol concentration. For example, a stable 20% viable fraction of the immobilized cells is predicted in ICR locations experiencing continuous conditions of either 30 g/L ethanol at 40°C, or 95 g/L ethanol at 25°C. Steady‐state ICR “plug flow” concentration profiles and column productivities are predicted at three operating temperatures, 20, 30, and 40°C using two different models for ethanol inhibition of productivity. These profiles suggest that the reactor operating temperature should be low if higher outlet ethanol concentrations are desired. Three reactor design strategies are presented to maximize the viable cell fraction and improve long‐term ethanol productivity in ICR's: (1) reducing outlet ethanol concentrations, (2) rotating segments of an ICR between high and low ethanol environments, and (3) simultaneous removal of the ethanol produced from the reactor as it is formed.