  Many natural or industrial fluids exhibit non-linear behavior. Non-Newtonian
fluids can therefore be found in different applications related to porous or
fractured media such as mud flows, oil recovery, hydraulic fracturing or foam
injection clean-up. This work focuses on the understanding of the flow of these
fluids in large scale heterogeneous porous media, and particularly in the
coupling between flow heterogeneity and rheology. This work consider fluids
that exhibit a change in behavior, where the viscosity changes above a certain
velocity threshold. This change of viscosity affects drastically the
inhomogeneity of velocity field. In this paper, we analyse some general
mathematical properties for non-linear rheologies at the microscopic and
macroscopic scale. Most non-linear rheologies imply the existance of two
asymptotic limit, at low and high flow rate. The velocity field of both limits
are obtained by solving a power-law rheology in the medium, which is analysed
using a perturbation expansion. As an example, we will consider fluids which
are Newtonian for low shear-rate but becomes shear-thinning or shear-thickening
at higher shear rate. Three macroscopic flowing regimes are then observed. It
will be shown that the limits at low and high flow-rate are governed by the
properties of power-law fluids. The transition between these two regimes is the
analysed. The range depends on the heterogeneity permeability field but also on
the rheological parameters. The statistical properties of the flow field
displays interesting statistical and geometrical properties such as multi-scale
(fractal), similarly to other critical systems (percolation, avalanches, etc.)
