Extension of Darcy-Forchheimer law to shear thinning fluids by CFD pore-scale simulations

Flow of non-Newtonian fluids through porous media at high Reynolds numbers is often encountered in chemical, pharmaceutical and food as well as petroleum and groundwater engineering and in many other industrial applications. In all abovementioned applications, it is of paramount importance to correctly predict the pressure drop resulting from non-Newtonian fluid flow through the porous medium. The Darcy law is used to describe steady-state flow of Newtonian fluids through porous media at low Reynolds numbers. For higher Reynolds numbers non linearities between pressure drop and flow rate arise, the and the Darcy-Forchheimer law can be applied. For non-Newtonian fluids, the usual formulation of Darcy law can be applied in the low flow regime, provided that all non-Newtonian effects are lumped together into a proper viscosity parameter. Similarly, at higher Reynolds numbers the Forchheimer law could be applied under the same hypotheses. In this work, an extended formulation of the Darcy-Forchheimer law for shear-thinning fluids is proposed and validated against results of micro-scale flow simulations. Flow simulations were performed on four different 2D porous domains for Newtonian and non-Newtonian fluids (Cross, Ellis and Carreau models). The micro-scale flow simulation results are analyzed in terms of “macroscale” pressure drop between inlet and outlet of the model domain as a function of flow rate. The validity of the extended Darcy-Forchheimer law is shown for the three shear-thinning models.