Analytical effectiveness calculations concerning the degradation of an inhibitive substrate by a steady-state biofilm

A reaction engineering model for the degradation of an inhibitory substrate by a steady-state biofilm is presented. The model describes both the metabolic rate controlling behavior of this substrate in the biofilm and the effect of diffusion limitation caused by an arbitrary substrate on the active biofilm thickness. An analytical expression for the biocatalyst effectiveness factor is presented on the basis of Pirt kinetics for cell maintenance, first order substrate inhibition kinetics, and zero order substrate consumption kinetics. The proposed expression for the biocatalyst effectiveness factor is much more convenient to incorporate into a macroreactor model than the numerical alternatives. Simple criteria are presented to check the applicability of the model in case of true Monod kinetics. The analytical solution is expected to be particularly applicable to processes where a low soluble organic substrate controls the biomass growth, a situation which is often met in wastewater purification processes of industrial importance. The degradation of phenol by Pseudomonas sp. is treated as an example.