Fractal dependence of the packed bed porosity on the particles size distribution

Packed beds formed by granular materials are the heart of many engineering and scientific applications. For a better understanding of transport processes occurring in such porous mediums, first the structural characteristics of packed beds should be known. The discrete element method (DEM) has been used widely as a powerful and reliable tool to study packed beds formed by granular materials. In all DEM-based models, the number of particles is a limiting factor as the computational time increases with the number of particles. To overcome this issue, it is common to neglect small particles in the bed. However, due to missed small particles, the porosity of the packed bed is underestimated. This has an impact on the fluid flow and consequently the heat and mass transfer in the bed. In the present work, a relation between the diameter of the smallest particle in a packed bed and the porosity of the bed is formed by performing a series of well-defined DEM simulations. This relation gives the possibility to consider the effect of small particles on the porosity of the bed without considering them in the computational domain. The results showed that the bed porosity decreases with decreasing the size of the smallest particle. Moreover, it was shown that the relation between the core porosity of the bed and the smallest particle size in the bed can be described by a fractal law.