Non-Newtonian Fluids in Porous Media
The current implementation of non-Newtonian flow in a porous medium is based on the idea of an apparent shear rate. This apparent shear rate is the shear rate that results in the same pressure drop for a non-Newtonian fluid flowing through a porous medium as if the same fluid would flow in free flow. A general formulation of the apparent shear rate is
with the correction factor α which accounts for the structure of the porous material, the velocity magnitude | u |, and the permeability κ and porosity εp of the porous medium. There is no unified theory on the value of α; it has to be either determined experimentally or computed from pore scale models.
Then, the apparent viscosity of a power law fluid can be written as
with the fluid consistency coefficient m, a reference shear rate and the flow behavior or power law index n. Darcy’s Law can then be written as