A common Enhanced Oil Recovery method consists in injecting a polymer solution in the oil reservoir, thus reducing the hydrodynamics instabilities and increasing the sweep efficiency. Such polymer solutions have a non-Newtonian behaviour, which is often described by a power-law model. Tomographic characterizations also offer new ways of understanding the topological complexity of the resulting flow fields. We look at two different types of porous medium: a beads pack, mildly disordered, and a typical rock. The pore space geometrical features are analysed using statistical tools. Common aspects and differences between these two media are emphasized in terms of homogeneity, disorder, tortuosity. Direct numerical simulations of the non-linear Stokes equations are obtained using a finite volume method. To quantify the pore-scale distribution, the probability density functions of the velocity field are calculated. The results in terms of back-flow, preferential channels, and velocity distribution can be explained by the fundamental geometrical differences between the two media. The non-linear Stokes equations are up-scaled using a volume averaging methodology. This procedure leads to a closure problem that is solved by numerical methods. Non-Newtonian permeabilities can then be computed from the closure variables and compared to direct numerical simulations.