05 Oct 2023
 | 05 Oct 2023
Status: this preprint is currently under review for the journal HESS.

Hydrodynamic Porosity: A Paradigm Shift in Flow and Contaminant Transport Through Porous Media, Part I

August H. Young and Zbigniew J. Kabala

Abstract. 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, θmobile, exhibits a quantifiable dependence on 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 θmobile on Reynolds number via numerical flow simulation at the pore scale. We demonstrate that, for a medium with the chosen cavity geometries, θmobile decreases by as much as 42 % over the Laminar flow regime. Moreover, θmobile exhibits an exponential dependence on Reynolds number. 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 solved 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.

August H. Young and Zbigniew J. Kabala

Status: open (until 08 Dec 2023)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on hess-2023-208', Jesús Carrera, 13 Nov 2023 reply

August H. Young and Zbigniew J. Kabala

Data sets

Simulation Data August Young, Zbigniew Kabała

Model code and software

Wolfram Language Code August Young, Zbigniew Kabała

August H. Young and Zbigniew J. Kabala


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Short summary
Contaminant transport in the subsurface is driven by the pore-scale velocity of local and induced flows. But often, this parameter is miscalculated – standard practice is to assume that the volume of pore space conducive to through-flow is constant. By simulating flow at the pore scale, we show that not only is this volume of the pore space variable, but its dependence on local flow conditions can be quantified. Thus, we present the concept of hydrodynamic porosity.