A multi-stage industrial agitator system adapted to the mixing of a mixture whose viscosity varies during the process has been characterized by using CFD. In the entire study the mixture is supposed to have a Newtonian behavior even though it is rarely the case. It is shown that the well-adapted propeller is able to efficiently blend high viscous media provided the Reynolds number is not too low. A scale-up study of the agitated system has also been carried out by respecting the classical scale-up rules such as the geometrical similarity and the conservation of the power per volume in the particular case of viscous media. Using an Eulerian approach, the hydrodynamics of three different scales with geometrical similarity have been numerically characterized by the energy curve (power number versus Reynolds number) and by the Metzner and Otto constant in which both are required for scale-up procedure. Experimental power measurements have been carried out at the smaller scale so that simulations have been partially validated. New hydrodynamic criteria have also been introduced in order to quantify the flows in the case of a multi-stage stirrer running at low Reynolds number. It has been shown how this hydrodynamic differs dramatically from one scale to another when scale-up at constant energy per volume is applied. From the CFD results, recommendations about the widely used scale-up rules have been suggested and modifications of stirring geometry have been proposed in order to reduce the flow pattern variations during scale-up.