A Unified Method for the Mobility Prediction of an Inelastic Non-Newtonian Fluid Through Complex Porous Media

In this work, we propose a novel method to quantify flows of inelastic non-Newtonian fluids in porous media based on the energy dissipation rate. Unlike the permeability of a Newtonian fluid with Darcy’s law, the permeability of a non-Newtonian fluid shows complicated behaviors due to non-separable effects of the geometry and rheology. We suggest a simple energy dissipation-based flow characterization method to resolve this problem, employing the concepts of effective viscosity and effective shear rate. These effective quantities can be defined with two flow numbers (the energy dissipation rate coefficient and the effective shear rate coefficient) independent of fluid rheology. New expressions for the permeability of Newtonian and mobility of non-Newtonian fluids were derived for model porous media in this approach. We show that the mobility (a ratio of permeability to viscosity) of a non-Newtonian fluid for a given porous media can be factored into the permeability of Newtonian fluid and the effective viscosity, exactly the same as in case of a Newtonian fluid. The proposed quantification method was validated through example problems of flows using numerical simulations (1) in two-dimensional (2D) transverse fibrous porous media (quadratic and hexagonal), (2) flows in three-dimensional (3D) regularly packed beds with spheres (faced-centered cubic and body-centered cubic), and (3) finally randomly distributed unidirectional fibers in 2D. The suggested method can quantitatively assess tortuous path in porous electrode for electrolyte transport and in the secondary oil recovery, offering the potential to optimize performance and efficiency in these applications.