the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Hydrodynamic Porosity: A Paradigm Shift in Flow and Contaminant Transport Through Porous Media, Part I
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.
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Interactive discussion
Status: closed
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RC1: 'Comment on hess-2023-208', Jesús Carrera, 13 Nov 2023
This review is identical to that of hess-2023-209
The papers contain some interesting results, but also confusing and irrelevant disgressions. See detailed comments in the attached document,
- AC1: 'Reply on RC1', August Young, 08 Feb 2024
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RC2: 'Comment on hess-2023-208', Anonymous Referee #2, 05 Dec 2023
The paper is very well written with an extended (but not exhaustive) state of the art on the concept of porosity.
It addresses the notion of porosity through the variable fraction of porosity conducive flow. Based on numerical simulation, the authors provide an empirical exponential function that relates this fraction of porosity (or pore-space partitioning coefficient) to the Reynolds number. Finally, the authors show how to introduce this concept of porosity in a porous media flow model.
The studied pore geometry is oversimplified (channel + rectangular cavity, see fig. 6) and the parameters of the empirical function are fitted for each geometry.Â
The second paper is an extension of the previous one to different type of cavities (triangle, circular, periodic squares). Again, the pore geometry is oversimplified and the results cannot be extended to realistic porous network. As for the first paper, the main missing elements are the 3D geometry of the pores, the change in the pore diameter and the effects of interconnections.
Both papers are technically very sound but they could be partly improved by studying the relationship between the fitted parameters and the characteristics of the geometry for example.
Therefore, these results are of limited interest for a publication in HESS, which promotes research in Earth Systems. However, I leave the final decision to the editor concerning the suitability of both papers for HESS. If yes, I recommend major revision by merging both papers in one manuscript.
Citation: https://doi.org/10.5194/hess-2023-208-RC2 - AC2: 'Reply on RC2', August Young, 08 Feb 2024
Interactive discussion
Status: closed
-
RC1: 'Comment on hess-2023-208', Jesús Carrera, 13 Nov 2023
This review is identical to that of hess-2023-209
The papers contain some interesting results, but also confusing and irrelevant disgressions. See detailed comments in the attached document,
- AC1: 'Reply on RC1', August Young, 08 Feb 2024
-
RC2: 'Comment on hess-2023-208', Anonymous Referee #2, 05 Dec 2023
The paper is very well written with an extended (but not exhaustive) state of the art on the concept of porosity.
It addresses the notion of porosity through the variable fraction of porosity conducive flow. Based on numerical simulation, the authors provide an empirical exponential function that relates this fraction of porosity (or pore-space partitioning coefficient) to the Reynolds number. Finally, the authors show how to introduce this concept of porosity in a porous media flow model.
The studied pore geometry is oversimplified (channel + rectangular cavity, see fig. 6) and the parameters of the empirical function are fitted for each geometry.Â
The second paper is an extension of the previous one to different type of cavities (triangle, circular, periodic squares). Again, the pore geometry is oversimplified and the results cannot be extended to realistic porous network. As for the first paper, the main missing elements are the 3D geometry of the pores, the change in the pore diameter and the effects of interconnections.
Both papers are technically very sound but they could be partly improved by studying the relationship between the fitted parameters and the characteristics of the geometry for example.
Therefore, these results are of limited interest for a publication in HESS, which promotes research in Earth Systems. However, I leave the final decision to the editor concerning the suitability of both papers for HESS. If yes, I recommend major revision by merging both papers in one manuscript.
Citation: https://doi.org/10.5194/hess-2023-208-RC2 - AC2: 'Reply on RC2', August Young, 08 Feb 2024
Data sets
Simulation Data August Young, Zbigniew Kabała https://doi.org/10.17605/OSF.IO/JPMRV
Model code and software
Wolfram Language Code August Young, Zbigniew Kabała https://doi.org/10.17605/OSF.IO/8EZM3
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