Dimensional Analysis of Liquid Flow through Packed Columns

In 1952, Sabri Ergun published an article reconciling all the data pertaining to flow through packed columns at that time.  The equation presented in that paper has since become known as the Ergun equation.  It has been used with varying degrees of success since its publication.  The Ergun equation has various problems.  First, it uses a Reynolds number based on particle diameter, not fluid conduit diameter.  Thus, the Reynolds number used in the Ergun equation does not describe fluid flow.  Second, the Ergun equation was developed for spheres.  However, myriad odd-shaped packing exists; thus, the Ergun equation must be modified when using non-spherical packing.  That modification is generally encapsulated in a dimensionless “sphericity factor” … a cheat factor, in other words.  Third, the Ergun equation violates geometric similarity, thus it cannot be used for scaling up or scaling down.

            In this paper, we address these problems via Dimensional Analysis.  We use Dimensional Analysis to formulate a new method for characterizing liquid flow through packed columns; i.e., for characterizing filtration.  We also propose a new method for characterizing the packing material.  Since our results obey the laws of similarity, our analysis can be used for up scaling and down scaling filtration units.