Upscaling Hydrodynamic Dispersion in non-Newtonian Fluid Flow through Porous Media

Hydrodynamic dispersion in flow through porous media is an essential phenomenon in many geosystems. While dispersion in flow of Newtonian fluids is relatively well-understood, many subsurface applications, such as groundwater remediation, use the flooding system with non-Newtonian fluids, such as polymer oxidants. Despite its significance, however, very limited studies have been carried out focusing on hydrodynamic dispersion in flow of non-Newtonian fluids. The present study addresses a fundamental question regarding how solute transport in flow of non-Newtonian fluids in porous media differs from the Newtonian limit. We report on the results of an extensive pore-scale study of upscaling of advection-diffusion in flow of a non-Newtonian, shear-thinning fluid through disordered and spatially-correlated porous media, using an advanced GPU-based pore-scale simulator, in order to delineate effects of the fluid's rheology, dynamics of fluid flow, and pore-scale spatial correlations on hydrodynamic dispersion. The simulations indicate a surprising non-monotonic relation between the injection rate (or injection velocity) and the dispersivity. While dispersivity in Newtonian fluid flow in porous media is constant in the flow regime that we study, we find, however, that the dispersivity in flow of non-Newtonian fluids is shear-dependent. This highlights the gap in the existing theories of transport through porous materials for non-Newtonian fluids, which can lead to erroneous estimates of dispersion coefficients in porous materials, when the fluid's rheology cannot be represented by Newtonian mechanics.