Flow of viscoelastic fluids through porous media

TLDR

Local volume averaging of the continuity and momentum equations over a porous medium is examined. The study proposes a correlation and extrapolation method for experimental data on a single viscoelastic fluid in geometrically similar porous structures. For steady, inertia‑free flow, a resistance transformation converts the local average velocity into the force per unit volume on pore walls, and the resistance coefficient’s dependence on fluid model is derived via the Buckingham‑Pi theorem for Ellis, power‑law, Newtonian, and Noll simple fluids. The resistance transformation is shown to be invertible, symmetric, and positive‑definite, and the resistance coefficient’s functional form for various fluid models is established.

Abstract

Abstract Local volume averaging of the equations of continuity and of motion over a porous medium is discussed. For steady state flow such that inertial effects can be neglected, a resistance transformation is introduced which in part transforms the local average velocity vector into the local force per unit volume which the fluid exerts on the pore walls. It is suggested that for a randomly deposited, although perhaps layered, porous structure this resistance transformation is invertible, symmetric, and positive‐definite. Finally, for an isotropic porous structure (the proper values of the resistance transformation are all equal and are termed the resistance coefficient) and an incompressible fluid, the functional dependence of the resistance coefficient is discussed with the Buckingham‐Pi theorem used for an Ellis model fluid, a power model fluid, a Newtonian fluid, and a Noll simple fluid. Based on the discussion of the Noll simple fluid, a suggestion is made for the correlation and extrapolation of experimental data for a single viscoelastic fluid in a set of geometrically similar porous structures.