Analytical effectiveness calculations concerning the formation of an inhibitive fermentation product associated with growth of biomass films immobilized in or around carriers

A reaction engineering model is presented for the bioproduction of chemicals associated with the growth of immobilized biomass in or around carriers. The model describes multiple‐substrate diffusion limitations and first‐order growth inhibition by one of the products. Analytical solutions are presented for intra‐biofilm substrate and product concentrations, active biofilm thickness, biocatalyst effectiveness factor and degree of catalyst utilization. Simple criteria for optimal catalyst design are derived. Where applicable, the presented explicit analytical solutions for the biocatalyst effectiveness factor are much more convenient to incorporate into a macro‐reactor model than the numerical alternatives.