An Analytical Pore-Scale, Shear Stress Model for Purely Viscous Non-Newtonian Fluids Traversing Porous Media

摘要

An analytical model for incompressible, generalized Newtonian fluids traversing granular porous media is proposed. This model is based on the volume averaging of the governing equations. Interstitial quantities are obtained through means of a pore-scale model. For flow through porous media in the Darcy regime, the fluid-solid interaction term is written in terms of the interstitial wall shear stress which is a function of the average interstitial channel velocities. The wall shear stress is obtained by assuming fully developed flow in the interstitial channels. Approximations are made in order to obtain explicit expressions for the wall shear stress. The final analytical expressions obtained for predicting the flow through porous media can easily be implemented numerically and allow for a wide variety of practical implementations.