Hydrodynamic Porosity: A New Perspective on Flow through Porous Media, Part I

Pore-scale flow velocity is an essential parameter in determining transport through porous media, but it is often miscalculated. Researchers use a static porosity value to relate volumetric or superficial velocities to pore-scale flow velocities. We know this modeling assumption to be an oversimplification. The variable fraction of porosity conducive to flow, what we define as hydrodynamic porosity, ${\theta }_{mobile}$, exhibits a quantifiable dependence on the Reynolds number (i.e., pore-scale flow velocity) in the Laminar flow regime. This fact remains largely unacknowledged in the literature. In this work, we quantify the dependence of ${\theta }_{mobile}$ on the Reynolds number via numerical flow simulation at the pore scale for rectangular pores of various aspect ratios, i.e., for highly idealized dead-end pore spaces. We demonstrate that, for the chosen cavity geometries, ${\theta }_{mobile}$ decreases by as much as 42% over the Laminar flow regime. Moreover, ${\theta }_{mobile}$ exhibits an exponential dependence on the Reynolds number, Re = $R$. The fit quality is effectively perfect, with a coefficient of determination (R²) of approximately 1 for each set of simulation data. Finally, we show that this exponential dependence can be easily fitted for pore-scale flow velocity through use of only a few Picard iterations, even with an initial guess that is 10 orders of magnitude off. Not only is this relationship a more accurate definition of pore-scale flow velocity, but it is also a necessary modeling improvement that can be easily implemented. In the companion paper (Part 2), we build upon the findings reported here and demonstrate their applicability to media with other pore geometries: rectangular and non-rectangular cavities (circular and triangular).