  In this paper we study the filtration laws for the polymeric flow in a porous
medium. We use the quasi-Newtonian models with share dependent viscosity
obeying the power-law and the Carreau's law. Using the method of homogenization
the coupled micro-macro homogenized law, governing the quasi-newtonian flow in
a periodic model of a porous medium, was found. We decouple that law separating
the micro from the macro scale. We write the macroscopic filtration law in the
form of non-linear
  Darcy's law and we prove that the obtained law is well posed. We give the
analytical as well as the numerical study of our model.
