A vertical cylindrical packed-bed plug-flow reactor employed for a substance degradation is modeled. The question of its best performance is mathematically formulated, and the existence of the corresponding optimal flow axial velocity is proven. A way to compute this optimal velocity is exhibited as well. Results are obtained under a rather general hypothesis on the reaction velocity : it may be applied to first- and second-order reactions, Michelis-Menten reactions, and others. An application to lactose hydrolysis on a beta-galactosidase-immobilized chitosan bed is presented.