A Reconciliation of Packed Column Permeability Data: Column Permeability as a Function of Particle Porosity

In his textbook teaching of packed bed permeability, Georges Guiochon uses mobile phase velocity as the fluid velocity term in his elaboration of the Darcy permeability equation. Although this velocity frame makes a lot of sense from a thermodynamic point of view, it is valid only with respect to permeability at a single theoretical boundary condition. In his more recent writings, however, Guiochon has departed from his long-standing mode of discussing permeability in terms of the Darcy equation and has embraced the well-known Kozeny-Blake equation. In this paper, his teaching pertaining to the constant in the Kozeny-Blake equation is examined and, as a result, a new correlation coefficient is identified and defined herein based on the velocity frame used in his teaching. This coefficient correlates pressure drop and fluid velocity as a function of particle porosity. We show that in their experimental protocols, Guiochon et al. have not adhered to a strict material balance of permeability which creates a mismatch of particle porosity and leads to erroneous conclusions regarding the value of the permeability coefficient in the Kozeny-Blake equation. By correcting the experimental data to properly reflect particle porosity we reconcile the experimental results of Guiochon and Giddings, resulting in a permeability reference chart which is presented here for the first time. This reference chart demonstrates that Guiochon’s experimental data, when properly normalized for particle porosity and other related discrepancies, corroborates the value of 267 for the constant in the Kozeny-Blake equation which was derived by Giddings in 1965. 1. Introduction The value of the constant of proportionality between pressure gradient and fluid flow velocity in a column packed with granular material and how it relates to column porosity have been controversial topics for some time [1]. This is especially true in the field of chromatography because columns packed with porous particles have, at least for the last 50 years, been the main vehicle by which chromatographic separations have been carried out, and, thus, this feature has added a new dimension to the controversy. The complication arises, in part, because of the difficulty of differentiating between the free space between the particles and the free space within the particles in columns packed with porous particles; a problem that does not exist in the case of columns filled with nonporous particles. More recently, because current chromatographic analytical and purification applications are being driven by the need for