Quinn’s Law of Fluid Dynamics: Supplement #2 Reinventing the Ergun Equation

Hubert Michael Quinn

doi:10.11648/j.fm.20200601.12

Abstract

This paper is directed at the important contribution to fluid dynamics made by Sebri Ergun. In his three papers published in 1949, 1951 and 1952, using various gases as his percolating fluid, Ergun used his empirical permeability results of packing conduits with fractured coke (irregularly shaped particles), in combination with some theoretical concepts, to generate an equation which captured the viscous and kinetic contributions to packed conduit permeability in two separate terms in that equation, resulting in his now famous “Ergun Equation”. In addition, he identified a discrete “constant” for each of the terms which we label herein the “viscous” and “kinetic” constants, respectively. We demonstrate herein, however, that the values assigned by Ergun to both his constants are not certifiable and, thus, are problematic in predicting the permeability of packed conduits. Moreover, since the publication of his 1952 paper, in which he disclosed the values of 150 and 1.75 for the viscous and kinetic constants, respectively, many scholarly works have been published which claim to validate these values. As a result, these values have become erroneously embedded in conventional folklore concerning fluid flow in closed conduits and have enjoyed widespread acceptance as being a legitimate feature of fluid dynamics dogma. With the advent recently of Quinn’s Law, a novel approach to the understanding of fluid flow in closed conduits, we are able to articulate in a manner not heretofore possible, the significance of this discrepancy in Ergun’s values of the constants, which we demonstrate is far too important to ignore.

Highlights

We begin by defining the problem in light of the recent publication of Quinn’s Law which, for the first time, provides a comprehensive analytical road map for the comparison of packed conduit permeability both in the laminar and turbulent regions of the fluid flow regime
This is a critical feature of Quinn’s Law, since the Ergun equation is supposed to be accurate over the entire range of the fluid flow regime, because one can use the permeability of an empty conduit as an independent reference point against which one can titrate the permeability results for packed conduits across the entire spectrum of the fluid flow regime
In this paper we have demonstrated that the recent publication of Quinn’s Law has enabled us to clearly demonstrate the shortcomings of the Ergun equation in a manner which is both comprehensive and easy to understand

Summary

Introduction

We begin by defining the problem in light of the recent publication of Quinn’s Law which, for the first time, provides a comprehensive analytical road map for the comparison of packed conduit permeability both in the laminar and turbulent regions of the fluid flow regime. We will establish the magnitude of the problem posed by the erroneous values of the constants in Ergun’s equation, by showing a comparison between the dictates of Quinn’s Law for a typical packed conduit in routine use today for HPLC (High Pressure Liquid Chromatography) analyses [1], and the Ergun equation, both in the laminar (linear) and turbulent (non-linear) regions of the fluid flow regime [2,3,4].

Results

Discussion

Conclusion