A Semi-empirical Correlation for Pressure Drop in Packed Beds of Spherical Particles

The effect of a confining wall on the pressure drop of fluid flow through packed beds of spherical particles with small bed-to-particle diameter ratios was investigated to develop an improved pressure drop correlation. The dependency of pressure loss on both wall friction and increased porosity near the wall was accounted for by using a theoretical approach. A semi-empirical model was created based upon the capillary-orifice model, which included a wall correction factor for the inertial pressure loss. In this model, packed beds were treated as a bundle of capillary tubes whose orifice diameter in the core region was different from that of the wall region. Using this model, a new pressure drop correlation was obtained, based on the Ergun equation and applicable for a wide range of Reynolds numbers (10⁻²–10³). The proposed correlation was compared with previous correlations, as well as with experimental data. This correlation showed close agreement with the experimental data for both low- and high-Reynolds number regimes and for a wide range of bed-to-particle diameter ratios. The ratio of the pressure drop in finite packing to that in homogeneous packing was then calculated. This ratio clearly shows how the wall effect depends on the Reynolds number and the bed-to-particle diameter ratio.