Impact of dispersion and reaction kinetics on performance of biological reactors—solution by “s” series

Abstract

Abstract A differential equation representing Monod-type substrate utilization in dispersed plug flow mediums is solved by convergent series techniques. The system has two particular solutions each inherently related with the analytical expression of ideal plug flow reactors for Monod-type substrate removal and with those of dispersed plug flow reactors for substrates undergoing first order degradation. The particular solutions satisfy the differential equation with a high precision. The fraction of the effluent substrate concentration, calculated by imposing Wehner and Wilhelm-type boundary conditions on the particular solutions, is independent from influent substrate concentration and it is solely a function of the Peclet number characterizing longitudinal dispersion, and the reaction rate Kθ. Results are illustrated in tabular and graphical forms. Application to practice is illustrated by design examples. The findings in this paper may be useful for engineers in design considerations based upon Monod-type substrate removal.