EFFECTIVENESS FACTOR FOR SPHERICAL BIOFILM CATALYSTS

Immobilization is a method of avoiding wash-out of biocatalyst from a reactor system. For the modelling of these biocatalysts slab, cylinder, sphere and biofilm geometries are frequently used. A biofilm particle consists of an inert core which is used as a carrier for a layer that contains the enzymes or micro-organisms. This paper deals with the modelling and effectiveness factor calculations for such a biofilm particle and a general model for an immobilized, non-growing biocatalyst is presented. The model includes internal and external mass transfer resistance, the partitioning effect and inhibition or reversible reaction kinetics. Due to the non-linear reaction rate equations of the Michaelis Menten type, numerical techniques must be used for the solution of the combined diffusion reaction equation and calculation of the effectiveness factor. In this work we have used two different methods, orthogonal collocation and a method based on Runge-Kutta integration. Comparable use of CPU-time was found for these methods, but numerical stability and accuracy favour the Runge-Kutta method. In the case of Michaelis Menten kinetics (irreversible and without inhibition effects), an analytical expression for an approximate solution is presented. This method, which has an acceptable accuracy, takes far less CPU-time than the fore-mentioned numerical techniques. © 1990 Springer-Verlag.