Quinn’s Law of Fluid Dynamics, Supplement #4 Taking the Mystery out of Permeability Measurements in Porous Media

Hubert Michael Quinn

doi:doi:10.11648/j.fm.20220801.11

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Quinn’s Law of Fluid Dynamics, Supplement #4 Taking the Mystery out of Permeability Measurements in Porous Media

Hubert Michael Quinn

Published in Fluid Mechanics (Volume 8, Issue 1)

Received: 18 February 2022 Accepted: 15 March 2022 Published: 29 March 2022

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Abstract

The published literature on porous media is filled with erroneous and contradicting assertions relating to measurements of permeability. In this paper, we present a new and novel approach to remedy this situation, by demonstrating a standard methodology using a new fluid flow model. This model is different from any model currently in use and provides a unique analytical solution for the input variables underlying packed beds containing porous media of discrete particles, be they porous or nonporous in nature. The model is based upon the fundamental principles of the physics involved in fluid flow through packed beds which includes, amongst other things, a unique normalization coefficient which acts as an exchange rate between viscous and kinetic contributions, on the one hand, and certification, via a built-in methodology, on the other hand, that the Laws of Continuity are always adhered to. In addition, the model is thorough with respect to both wall effect and fluid path tortuosity, which means that a new Law of Fluid Flow in closed conduits is identified as a straight-line relationship between viscous normalized pressure drop, on one side of the equality sign, and normalized fluid flow, on the other side of the equality sign. The model is based upon the discovery of a new vector entity, n_p, the number of particles of a given diameter, say d_p, present in a packed conduit and, therefore, applies seamlessly to both packed and empty conduits which, in turn, enables its validation over 10 orders of magnitude of the modified Reynolds number. This vector has never been identified heretofore and is valid for all particle porosities which include fully porous particles, i.e., particles of free space and, hence, empty conduits are considered as packed conduits with particles of free space. The vector n_p specifies, simultaneously, the matched set of a given value for the particle diameter d_p and the external porosity, ε₀, in any packed conduit under study, much the same as a velocity vector specifies, simultaneously, the matched set of a given value for the speed and direction of a projectile or moving object. The model is explained herein and applied to a number of experimental studies, demonstrating a standardized methodology which guarantees an exact correlation between measured and calculated values in the permeability relationship, when reporting on actual experiments in closed conduits.

Published in	Fluid Mechanics (Volume 8, Issue 1)
DOI	10.11648/j.fm.20220801.11
Page(s)	1-15
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Permeability, Pressure Drop, Viscous, Kinetic, Friction Factor

References

[1]	Quinn, H. M. Quinn’s Law of Fluid Dynamics Pressure-driven Fluid Flow Through Closed Conduits, Fluid Mechanics. Vol. 5, No. 2, 2019, pp. 39-71. doi: 10.11648/j.fm.20190502.12.
[2]	Ergun, S. and Orning, A. A., Fluid Flow through Randomly Packed Columns and Fluidized Beds, Ind. Eng. Chem. vol. 41, pp. 1179, 1949.
[3]	Farkas, T., G. Zhong, G. Guiochon, Validity of Darcy’s Law at Low Flow Rates in Liquid Chromatography Journal of Chromatography A, 849, (1999) 35-43.
[4]	Quinn, H. M., A Reconciliation of Packed Column Permeability Data: Deconvoluting the Ergun Papers Journal of Materials Volume 2014 (2014), Article ID 548482, 24 pages http://dx.doi.org/10.1155/2014/548482.
[5]	Quinn, H. M., Quinn’s Law of Fluid Dynamics: Supplement #1 Nikuradze’s Inflection Profile Revisited. Fluid Mechanics. Vol. 6, No. 1, 2020, pp. 1-14. doi: 10.11648/j.fm.20200601.11.
[6]	Quinn, H. M., Quinn’s Law of Fluid Dynamics: Supplement #2 Reinventing the Ergun Equation. Fluid Mechanics. Vol. 6, No. 1, 2020, pp. 15-29. doi: 10.11648/j.fm.20200601.12.
[7]	Nikuradze J., NASA TT F-10, 359, Laws of Turbulent Flow in Smooth Pipes. Translated from “Gesetzmassigkeiten der turbulenten Stromung in glatten Rohren” VDI (Verein Deutsher Ingenieure)-Forschungsheft 356.
[8]	Mckeon, B. J. C. J. Swanson, M. V. Zagarola, R. J. Donnelly and A. J. Smits. Friction factors for smooth pipe flow; J. Fluid Mech. (2004), vol. 511, pp. 41-44. Cambridge University Press; DO1; 10.1017/S0022112004009796.
[9]	Mckeon, B. J., M. V. Zagarola, and A. J. Smits. A new friction factor relationship for fully developed pipe flow; J. Fluid Mech. (2005), vol. 238, pp. 429-443. Cambridge University Press; DO1; 10.1017/S0022112005005501.
[10]	Buchwald T., Gregor Schmandra, Lieven Schützenmeister, Tony Fraszczak, Thomas Mütze, Urs Peuker Gaseous flow through coarse granular beds: The role of specific surface area; Powder Technology 366 (2020) 821-831.
[11]	Nikuradze J., NACA TM 1292, Laws of Flow in Rough Pipes, July/August 1933. Translation of “Stromungsgesetze in rauhen Rohren.” VDI-Forschungsheft 361. Beilage zu “Forschung auf dem Gebiete des Ingenieurwesens” Ausgabe B Band 4, July/August 1933.
[12]	Forchheimer, P.: Wasserbewegung durch boden. Zeit. Ver. Deutsch. Ing 45, 1781–1788 (1901).
[13]	Quinn Hubert Michael. Quinn’s Law of Fluid Dynamics: Supplement #3 A Unique Solution to the Navier-Stokes Equation for Fluid Flow in Closed Conduits. Fluid Mechanics. Volume 6, Issue 2, December 2020, pp. 30-50. doi: 10.11648/j.fm.20200602.11.
[14]	Van Lopik Jan H. Roy Snoeijers Teun C. G. W. van Dooren Amir Raoof Ruud J. Schotting; Transp Porous Med (2017) 120: 37–66 DOI 10.1007/s11242-017-0903-3.
[15]	Van Lopik Jan H. Roy, L. Zazai • N. Hartog, R. J. Schotting, Nonlinear Flow Behavior in Packed Beds of Natural and Variably Graded Granular Materials Transport in Porous Media (2019) 131: 957–983 https://doi.org/10.1007/s11242-019-01373-0
[16]	U. D. Neue J. Mazzeo, M. Kele, R. S. Plumb; Analytical Chemistry, December 2005, 460-467.
[17]	Cabooter D., J. Billen, H. Terryn, F. Lynen, P. Sandra, G. Desmet; Journal of Chromatography A, 1178 (2008) 108–117.

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APA Style

Hubert Michael Quinn. (2022). Quinn’s Law of Fluid Dynamics, Supplement #4 Taking the Mystery out of Permeability Measurements in Porous Media. Fluid Mechanics, 8(1), 1-15. https://doi.org/10.11648/j.fm.20220801.11

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ACS Style

Hubert Michael Quinn. Quinn’s Law of Fluid Dynamics, Supplement #4 Taking the Mystery out of Permeability Measurements in Porous Media. Fluid Mech. 2022, 8(1), 1-15. doi: 10.11648/j.fm.20220801.11

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AMA Style

Hubert Michael Quinn. Quinn’s Law of Fluid Dynamics, Supplement #4 Taking the Mystery out of Permeability Measurements in Porous Media. Fluid Mech. 2022;8(1):1-15. doi: 10.11648/j.fm.20220801.11

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@article{10.11648/j.fm.20220801.11,
  author = {Hubert Michael Quinn},
  title = {Quinn’s Law of Fluid Dynamics, Supplement #4 Taking the Mystery out of Permeability Measurements in Porous Media},
  journal = {Fluid Mechanics},
  volume = {8},
  number = {1},
  pages = {1-15},
  doi = {10.11648/j.fm.20220801.11},
  url = {https://doi.org/10.11648/j.fm.20220801.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.fm.20220801.11},
  abstract = {The published literature on porous media is filled with erroneous and contradicting assertions relating to measurements of permeability. In this paper, we present a new and novel approach to remedy this situation, by demonstrating a standard methodology using a new fluid flow model. This model is different from any model currently in use and provides a unique analytical solution for the input variables underlying packed beds containing porous media of discrete particles, be they porous or nonporous in nature. The model is based upon the fundamental principles of the physics involved in fluid flow through packed beds which includes, amongst other things, a unique normalization coefficient which acts as an exchange rate between viscous and kinetic contributions, on the one hand, and certification, via a built-in methodology, on the other hand, that the Laws of Continuity are always adhered to. In addition, the model is thorough with respect to both wall effect and fluid path tortuosity, which means that a new Law of Fluid Flow in closed conduits is identified as a straight-line relationship between viscous normalized pressure drop, on one side of the equality sign, and normalized fluid flow, on the other side of the equality sign. The model is based upon the discovery of a new vector entity, np, the number of particles of a given diameter, say dp, present in a packed conduit and, therefore, applies seamlessly to both packed and empty conduits which, in turn, enables its validation over 10 orders of magnitude of the modified Reynolds number. This vector has never been identified heretofore and is valid for all particle porosities which include fully porous particles, i.e., particles of free space and, hence, empty conduits are considered as packed conduits with particles of free space. The vector np specifies, simultaneously, the matched set of a given value for the particle diameter dp and the external porosity, ε0, in any packed conduit under study, much the same as a velocity vector specifies, simultaneously, the matched set of a given value for the speed and direction of a projectile or moving object. The model is explained herein and applied to a number of experimental studies, demonstrating a standardized methodology which guarantees an exact correlation between measured and calculated values in the permeability relationship, when reporting on actual experiments in closed conduits.},
 year = {2022}
}

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TY  - JOUR
T1  - Quinn’s Law of Fluid Dynamics, Supplement #4 Taking the Mystery out of Permeability Measurements in Porous Media
AU  - Hubert Michael Quinn
Y1  - 2022/03/29
PY  - 2022
N1  - https://doi.org/10.11648/j.fm.20220801.11
DO  - 10.11648/j.fm.20220801.11
T2  - Fluid Mechanics
JF  - Fluid Mechanics
JO  - Fluid Mechanics
SP  - 1
EP  - 15
PB  - Science Publishing Group
SN  - 2575-1816
UR  - https://doi.org/10.11648/j.fm.20220801.11
AB  - The published literature on porous media is filled with erroneous and contradicting assertions relating to measurements of permeability. In this paper, we present a new and novel approach to remedy this situation, by demonstrating a standard methodology using a new fluid flow model. This model is different from any model currently in use and provides a unique analytical solution for the input variables underlying packed beds containing porous media of discrete particles, be they porous or nonporous in nature. The model is based upon the fundamental principles of the physics involved in fluid flow through packed beds which includes, amongst other things, a unique normalization coefficient which acts as an exchange rate between viscous and kinetic contributions, on the one hand, and certification, via a built-in methodology, on the other hand, that the Laws of Continuity are always adhered to. In addition, the model is thorough with respect to both wall effect and fluid path tortuosity, which means that a new Law of Fluid Flow in closed conduits is identified as a straight-line relationship between viscous normalized pressure drop, on one side of the equality sign, and normalized fluid flow, on the other side of the equality sign. The model is based upon the discovery of a new vector entity, np, the number of particles of a given diameter, say dp, present in a packed conduit and, therefore, applies seamlessly to both packed and empty conduits which, in turn, enables its validation over 10 orders of magnitude of the modified Reynolds number. This vector has never been identified heretofore and is valid for all particle porosities which include fully porous particles, i.e., particles of free space and, hence, empty conduits are considered as packed conduits with particles of free space. The vector np specifies, simultaneously, the matched set of a given value for the particle diameter dp and the external porosity, ε0, in any packed conduit under study, much the same as a velocity vector specifies, simultaneously, the matched set of a given value for the speed and direction of a projectile or moving object. The model is explained herein and applied to a number of experimental studies, demonstrating a standardized methodology which guarantees an exact correlation between measured and calculated values in the permeability relationship, when reporting on actual experiments in closed conduits.
VL  - 8
IS  - 1
ER  -

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Author Information

Hubert Michael Quinn

Department of Research and Development, The Wrangler Group LLC, Brighton, USA

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Hubert Michael Quinn. (2022). Quinn’s Law of Fluid Dynamics, Supplement #4 Taking the Mystery out of Permeability Measurements in Porous Media. Fluid Mechanics, 8(1), 1-15. https://doi.org/10.11648/j.fm.20220801.11

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ACS Style

Hubert Michael Quinn. Quinn’s Law of Fluid Dynamics, Supplement #4 Taking the Mystery out of Permeability Measurements in Porous Media. Fluid Mech. 2022, 8(1), 1-15. doi: 10.11648/j.fm.20220801.11

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AMA Style

Hubert Michael Quinn. Quinn’s Law of Fluid Dynamics, Supplement #4 Taking the Mystery out of Permeability Measurements in Porous Media. Fluid Mech. 2022;8(1):1-15. doi: 10.11648/j.fm.20220801.11

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@article{10.11648/j.fm.20220801.11,
  author = {Hubert Michael Quinn},
  title = {Quinn’s Law of Fluid Dynamics, Supplement #4 Taking the Mystery out of Permeability Measurements in Porous Media},
  journal = {Fluid Mechanics},
  volume = {8},
  number = {1},
  pages = {1-15},
  doi = {10.11648/j.fm.20220801.11},
  url = {https://doi.org/10.11648/j.fm.20220801.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.fm.20220801.11},
  abstract = {The published literature on porous media is filled with erroneous and contradicting assertions relating to measurements of permeability. In this paper, we present a new and novel approach to remedy this situation, by demonstrating a standard methodology using a new fluid flow model. This model is different from any model currently in use and provides a unique analytical solution for the input variables underlying packed beds containing porous media of discrete particles, be they porous or nonporous in nature. The model is based upon the fundamental principles of the physics involved in fluid flow through packed beds which includes, amongst other things, a unique normalization coefficient which acts as an exchange rate between viscous and kinetic contributions, on the one hand, and certification, via a built-in methodology, on the other hand, that the Laws of Continuity are always adhered to. In addition, the model is thorough with respect to both wall effect and fluid path tortuosity, which means that a new Law of Fluid Flow in closed conduits is identified as a straight-line relationship between viscous normalized pressure drop, on one side of the equality sign, and normalized fluid flow, on the other side of the equality sign. The model is based upon the discovery of a new vector entity, np, the number of particles of a given diameter, say dp, present in a packed conduit and, therefore, applies seamlessly to both packed and empty conduits which, in turn, enables its validation over 10 orders of magnitude of the modified Reynolds number. This vector has never been identified heretofore and is valid for all particle porosities which include fully porous particles, i.e., particles of free space and, hence, empty conduits are considered as packed conduits with particles of free space. The vector np specifies, simultaneously, the matched set of a given value for the particle diameter dp and the external porosity, ε0, in any packed conduit under study, much the same as a velocity vector specifies, simultaneously, the matched set of a given value for the speed and direction of a projectile or moving object. The model is explained herein and applied to a number of experimental studies, demonstrating a standardized methodology which guarantees an exact correlation between measured and calculated values in the permeability relationship, when reporting on actual experiments in closed conduits.},
 year = {2022}
}

Copy | Download

TY  - JOUR
T1  - Quinn’s Law of Fluid Dynamics, Supplement #4 Taking the Mystery out of Permeability Measurements in Porous Media
AU  - Hubert Michael Quinn
Y1  - 2022/03/29
PY  - 2022
N1  - https://doi.org/10.11648/j.fm.20220801.11
DO  - 10.11648/j.fm.20220801.11
T2  - Fluid Mechanics
JF  - Fluid Mechanics
JO  - Fluid Mechanics
SP  - 1
EP  - 15
PB  - Science Publishing Group
SN  - 2575-1816
UR  - https://doi.org/10.11648/j.fm.20220801.11
AB  - The published literature on porous media is filled with erroneous and contradicting assertions relating to measurements of permeability. In this paper, we present a new and novel approach to remedy this situation, by demonstrating a standard methodology using a new fluid flow model. This model is different from any model currently in use and provides a unique analytical solution for the input variables underlying packed beds containing porous media of discrete particles, be they porous or nonporous in nature. The model is based upon the fundamental principles of the physics involved in fluid flow through packed beds which includes, amongst other things, a unique normalization coefficient which acts as an exchange rate between viscous and kinetic contributions, on the one hand, and certification, via a built-in methodology, on the other hand, that the Laws of Continuity are always adhered to. In addition, the model is thorough with respect to both wall effect and fluid path tortuosity, which means that a new Law of Fluid Flow in closed conduits is identified as a straight-line relationship between viscous normalized pressure drop, on one side of the equality sign, and normalized fluid flow, on the other side of the equality sign. The model is based upon the discovery of a new vector entity, np, the number of particles of a given diameter, say dp, present in a packed conduit and, therefore, applies seamlessly to both packed and empty conduits which, in turn, enables its validation over 10 orders of magnitude of the modified Reynolds number. This vector has never been identified heretofore and is valid for all particle porosities which include fully porous particles, i.e., particles of free space and, hence, empty conduits are considered as packed conduits with particles of free space. The vector np specifies, simultaneously, the matched set of a given value for the particle diameter dp and the external porosity, ε0, in any packed conduit under study, much the same as a velocity vector specifies, simultaneously, the matched set of a given value for the speed and direction of a projectile or moving object. The model is explained herein and applied to a number of experimental studies, demonstrating a standardized methodology which guarantees an exact correlation between measured and calculated values in the permeability relationship, when reporting on actual experiments in closed conduits.
VL  - 8
IS  - 1
ER  -

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