Analysis of particle porosity distribution in fixed beds using the discrete element method J. Theuerkauf a, ⁎ , P. Witt b , D. Schwesig c a Dow Chemical Company, Solids Processing, 2301 N. Brazosort Blvd. Freeport Texas, USA b Dow Chemical Company, Reaction Engineering, Midland, Michigan, USA c University Duisburg-Essen, Institute for Physics, Theoretical Physics, Germany Received 1 November 2004; received in revised form 19 October 2005; accepted 20 March 2006 Available online 13 June 2006 Abstract This report discusses the use of the discrete element method (DEM) to the porosity distribution of spherical particles in narrow pipes as a function of the pipe-to-particle diameter ratio. It was found that the packing structure depends mainly on the pipe-to-particle ratio and the particle friction. The numerical results with respect to the radial porosity distribution are in agreement with experimental data from the literature. Radial porosity distributions were calculated using algorithms developed by Mueller. The packing structure of the particles shows channeling for small pipe to particle diameter ratios. The simulated height averaged porosity distribution agrees with models from the literature. Moreover, DEM provides the possibility to include particle properties which reflect on the porosity distribution. © 2006 Elsevier B.V. All rights reserved. Keywords: Discrete element method; Fixed bed; Porosity distribution 1. Introduction Packed bed porosity has been actively studied for many decades [1,2]. Some of this work has focused on developing correlations to predict overall void fraction for use in global prediction of pressure drop, such as the Ergun equation [3]. These correlations assume that a relationship between tube diameter and some effective particle diameter, D/d, controls the packing structure within the bed. These correlations give a general trend for void fraction as a function of D/d, but due to the stochastic nature of the packing process, accurate and reliable predictions are elusive. Of particular interest is D/d ratios greater than approximately 3. This ratio is typical of wall cooled, packed bed reactors. Recently studies have focused on predicting or measuring local bed porosity [4–16]. Hosseini-Ashrafi and Tüzün [7] list several experimental techniques to measure porosity distributions. The local changes in porosity can lead to large variations in predicted velocity profile and therefore non-uniform head loss along the packed bed [14]. The accurate prediction of local porosity is also important for predicting heat transfer in packed beds, which is critical for stability analysis [18,19] and reactor control. In addition to the experimental investigations, mathematical algorithms used to simulate a packing were provided [14]. These algorithms usually do not consider the particle and pipe properties. These limitations are overcome using the discrete element method (DEM), which considers particles and pipe properties. Thus, the simulations mimic the real system behavior more closely. Based on the packing structure gener- ated in the simulation a height averaged porosity distribution can be analyzed indicating zones where bypass is probable. Recently several authors have investigated the packing structure of spheres using DEM. One such study used a 2D analysis to investigate how circles settle under the force of gravity [10]. Other studies used a 3D analysis to investigate how spheres pack dynamically [9] and considered the effect of capillary forces [24]. These studies demonstrate that the DEM techniques originally developed by Cundall and Stack [20] for geophysics can be used to simulate the filling of pipes with a narrow pipe- Powder Technology 165 (2006) 92 – 99 www.elsevier.com/locate/powtec ⁎ Corresponding author. E-mail address: Jtheuerkauf@dow.com (J. Theuerkauf). 0032-5910/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2006.03.022