The dispersed flow model for a biological reactor as applied to the activated sludge process

A theoretical analysis of a dispersed flow biological reactor is presented in which Monod growth kinetics are used to describe the substrate utilization rate and the bacterial growth rate. Different bacterial and substrate dispersion coefficients are taken into account. Approximate perturbation solutions are established for two limiting situations, when the inverse Peclet number ϵ is very small and when it is very large. In the former case the perturbation analysis is singular. These perturbation solutions are compared with the solutions of the numerically integrated equations over a range of parameters corresponding to actual activated sludge systems. The application to the activated sludge system is discussed. On presente une analyse theorique d'un reacteur biologique a debit disperse et dans lequel on emploie la cinetique de croissance de Monod pour decrire le taux d'utilisation du substrat et celui de la croissance bacterienne. On considere differents coefficients de dispersion des bacteries et du substrat. On a etabli des solutions approximatives des perturbations dans le cas de deux situations limitatives, a savoir lorsque le nombre inverse de Peclet(ϵ) est tres petit et lorsqu'il est tres considerable; dans le premier cas, l'analyse des perturbationes est singuliere. On compare les solutions des perturbations avec celles d'equations integrees numeriquement, et ce, pour une echelle de parametres qui correspond a des systemes reels de boue activee. On discute l'application des resultats au systeme de boue activee.