Optimal biocatalyst loading in a fixed bed

The optimal distribution of biocatalyst in a fixed bed operating at steady state was determined to minimize the length of the bed for a fixed conversion of 95%. The distribution in terms of the biocatalyst loading on an inert support depends upon the axial distance from the bed entrance (continuous solution) as well as a set of dimensionless parameters that reflect the bed geometry, the bulk flow, reaction kinetics and diffusional characteristics. A mathematical model of the system with the following features was used to obtain the results: (1) convective mass transfer and dispersion in the bulk phase; (2) mass transfer from the bulk phase to the surface of the catalyst particle; and (3) simultaneous diffusion and chemical reaction in the catalyst particle with Michaelis-Menton kinetics and a reliable diffusion model (Zhao and DeLancey in Biotechnol Bioeng 64:434-441, 1999, 2000). The solution to the mathematical model was obtained with Mathematica utilizing the Runge Kutta 4-5 method. The dimensionless length resulting from the continuous solution was compared with the optimal length restricted to a uniform or constant cell loading across the entire bed. The maximum difference in the dimensionless length between the continuous and uniform solutions was determined to be 6.5%. The model was applied to published conversion data for the continuous production of ethanol that included cell loading (Taylor et al. in Biotechnol Prog 15:740-751, 2002). The data indicated a minimum production cost at a catalyst loading within 10% of the optimum predicted by the mathematical model. The production rate versus cell loading in most cases displayed a sufficiently broad optimum that the same (non-optimal) rate could be obtained at a significantly smaller loading such as a rate at 80% loading being equal to the rate at 20% loading. These results are particularly important because of the renewed interest in ethanol production (Novozymes and BBI International, Fuel ethanol: a technological evolution, 2004).