A simple method for determining sphere packed bed radial porosity

A new and simple method is established to examine the radial porosity profile of mono-sized spheres in packed bed cylinders based on the sphere center coordinates. The method is derived from geometrical and analytical techniques and uses arc lengths to calculate the radial porosity profile at any given axial position, a given interval axial position, or the total axial position, thus evaluating the local, interval, or axially averaged radial porosity profile, respectively. The new method and analytical functions are simple and straightforward and provide an accurate representation of the radial porosity profile given the sphere center coordinates. The simple method is used to calculate the radial porosity profile for the fixed packing of identical spheres in cylindrical containers with D/d ≥ 1.0. The evaluated results for the radial porosity profile are benchmarked with existing analytical equations and available experimental and numerical data, respectively, for mono-sized spheres in cylindrical containers. A concise FORTRAN program for the new arc length-based technique is presented for this simple method for calculating radial porosity profiles.