The effect of dispersion on optimum residence times of chemical reactor systems using perturbation expansion techniques

This work is a mathematical study of the effect of dispersion on the optimum residence times of several chemical reactor systems. The models considered are (1) the axial dispersed plug flow tubular reactor, (2) the ideal tubular reactor and the perfectly mixed tank reactor connected in parallel, and (3) the ideal tubular reactor with a small zone of perfect mixing. Attention is confined to the range of very small and very large dispersion. This allows us to use the technique of perturbation expansions to obtain asymptotic solutions which are excellent approximations in these limiting cases. The results of this work show the suitability of the technique. The consecutive reaction system A to B to C, where B is the desired intermediate product, is used exclusively. The optimum residence time is then defined as that which maximizes the yield of B from each isothermal reactor model. The axial dispersed plug flow reactor model proves to be well suited for modeling more complex reactor systems in the range of small dispersion. Finally, an interesting maximum effect in the optimum residence time for the axial dispersed tubular reactor is discussed and compared to the results of another study