Simple Solutions for Steady‐State Biofilm Reactors

Simple, analytical models for use in preliminary calculations are developed to approximate the steady‐state concentration and biofilm thickness in a biofilm reactor. The models consider the case in which a single substrate limits growth. These models assume that flux of substrate to the biofilm has a first‐order dependence on the bulk substrate concentration. This assumption restricts the use of the models to low initial substrate concentrations. One of the models assumes plug flow, and the other incorporates longitudinal dispersion of substrate. The models allow the substrate concentration to approach the minimum rate‐limiting concentration and the biofilm thickness to approach zero as predicted by the steady‐state theory. Predictions of these models are compared to those of a steady‐state numerical model developed by Rittmann. For an example taken from the literature, the solution of the model with longitudinal dispersion is in good agreement with the numerical solution.