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

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.

Permeability, Pressure Drop, Viscous, Kinetic, Friction Factor

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

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

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

Copyright © 2022 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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