Flow of Viscoelastic Fluids through Porous Media

Abstract

In the laminar flow of purely viscous non-Newtonian fluids through porous media, the effects of shear thinning on pressure drop are well understood and can be readily accounted for with appropriate modification of the Blake-Kozeny equation. For viscoelastic fluids at large deformation rates, a gross increase in pressure drop over and above the prediction from the purely viscous theory has been observed. This deviation was observed for two sets of viscoelastic fluids: aqueous polymer solutions (shear thinning elastic) and corn syrup-Separan mixtures (elastic but constant viscosity).

A modified Rabinowitsch equation employing two geometric parameters, originally proposed by Kozicki et al. (1967), is used in conjunction with the Carreau viscosity equation to describe the anomalous flow resistance observed for the flow of aqueous polymer solutions through a packed bed. For fluids which are highly shear thinning and elastic, a prediction based solely on the zero shear viscosity represents the upper bound of the viscous contributions. The difference in pressure drop between the experiment and the upper bound prediction can be attributed to the elastic effect.

The Deborah number, an elastic parameter based on Maxwellian relaxation time, does not uniquely correlate the observed excess flow resistance for the highly elastic but nearly constant viscosity fluids (Boger fluids). An alternative correlation is proposed using a modified Deborah number based on the zero shear viscosity.