Estimation of the radial distribution of axial velocities in fixed beds of spherical packing

Abstract

The vessel wall of densely packed beds exert a strong influence on particle distribution that generates a radial porosity profile and, in turn, a radial profile of axial velocity. A direct consequence is the appearance of an uneven flow distribution on the bed cross-section and radial variations of transport properties. A widespread alternative for estimating such a velocity profile is to solve the so-called extended Brinkman equation, using an available radial porosity profile. To this end, it is employed a local version of an expression quantifying the drag force on the packing (usually the Ergun equation) and an effective viscosity to account for the radial transport of axial momentum. It is shown that the existing expressions to evaluate the effective viscosity are only suitable for a restricted range of Reynolds numbers. Supported on the expressions from averaging the microscopic conservation equations, it is reassessed the local evaluation of the drag force and the estimation of the effective viscosity. The use of the extended Brinkman equation with such changes allows a satisfactory description of the radial velocity profile for mono-sized spherical packing, as arisen from the comparison with available experimental results and with an important number of results from pore-scale simulation.