DERIVATION OF THE DARCY-SCALE FILTRATION EQUATION FOR POWER-LAW FLUIDS WITH THE VOLUME AVERAGING METHOD

The large-scale continuum models for transport of power-law fluids in porous media are derived from the pore-scale control equations using the volume averaging method. The averaging procedure leads to an equation of motion and a continuity equation expressed in terms of the volume-averaged pressure and velocity. The closure problem for the powerlaw fluid flow is assumed to be analogous to the Newtonian fluid flow. Then a tensorial form of Darcy-scale filtration equation is obtained and the power-law relation between the averaged velocity and the gradient of the averaged pressure are confirmed. Different from Newtonian fluids, the apparent permeability significantly depends upon the filtration velocity direction for higher-dimensional flow (d 2). Numerical test also validates this conclusion.