Void Fraction as a Function of Depth and Pressure Drops of Packed Beds of Porous Media Formed by Granular Materials

A mathematical equation that describes the void fraction as a function of location, bulk density at the surface, bulk density at the location of interest in the bed, maximum bulk density, bin geometry, friction properties of the grain, and the ratio of lateral to vertical pressures of the grain in a deep packed bed of bulk solids was developed. Variation in the void fraction caused variation in the pressure drop per unit of bed depth. Since bulk density and void fraction are functionally related to each other, the void fraction was expressed as a mathematical function of bed depth, and the model was verified using fundamentals of mathematics. In order to develop the model, Ergun's equation was used and integrated over the bed depth, substituting a void fraction that varied with the bed depth. Model results were compared to Shedd's data. Agreement between Shedd's data and this model was good to a bed depth of 10 m. For bed depths greater than 10 m, results from this model gave much greater pressure drop values than were given by Shedd. The model showed that pressure drop per unit of bed depth increases exponentially with the bed depth.