Isotropy of sphere packings in a cylindrical confinement

The underlying structure in apparently "randomly-packed" packed beds is a subject of topical interest, particularly in the context of deep processing, such as deep hydrodesulfurization. Packed beds typically exhibit "packing defects"; for instance, surface abnormalities such as a slope, a bump (convex surface), a hollow (concave surface), or even donut-shaped rings on the top surface of a packed bed. While these defects are observed at the top free surface of the packed bed, there are concerns that this may continue to propagate down the height, and in turn, cause local flow variations and differential wetting, which affect reactor performance, catalyst life, and formation of local hot spots. These defects come because of different protocols that are followed for packing particles, which are mainly developed out of empiricism since the physics of granular flow in confinements (such as a vertical cylindrical reactor vessel) is as yet not well understood. Earlier work on the structure of packed beds relates only to the spatial distribution of voidage, and not on how the particles are arranged with respect to each other in the reactor. This work is an attempt in that direction. We present first the use of Sequential Ballistic Deposition (SBD) algorithm to model the packing process itself, i.e., how the method of packing (modeled in this work through some simple protocols) yields a certain structure of the bed. Second, we show the use of Voronoi tessellation and the use of two of the Minkowski tensors (the Volume Moment Tensor and the Surface Orientation Tensor) to characterize the packed bed structure. Further analysis is presented which shows that we are able to fingerprint the packed bed formed through different packing methods, hence creating a link between the two.