Analysis of fluid permeation through a particle-packed layer using an electric resistance network as an analogy Yoshiyuki Endo a, ⁎, Caroline L.Y. Ngan b , Asep B.D. Nandiyanto c , Ferry Iskandar c , Kikuo Okuyama c a Sumitomo Chemical Co., Process and Production Technology Center, 3-1-98 Kasugade-naka, Konohana-ku, Osaka 554-8558, Japan b Department of Civil Engineering, Faculty of Applied Science, University of British Columbia, 2329 West Mall Vancouver, BC, Canada V6T 1Z4 c Department of Chemical Engineering, Graduate School of Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashi Hiroshima 739-8527, Japan abstract article info Article history: Received 18 December 2007 Received in revised form 5 July 2008 Accepted 11 August 2008 Available online 14 September 2008 Keywords: Fluid permeation Powder bed Particle bed structure Electric resistance network analogy Electrical circuit Packing density Fluid permeation resistance through a particle-packed bed with a non-uniform structure was investigated both theoretically and experimentally to confirm the relationship between pressure drop and air flow rate. Multiple-block construction consisting of various types of powders in the particle bed was used in this experiment. With the goal of design and operation simplification, a model bed was used to simulate an actual powder bed with a non-uniform structure due to local variation in particle size, particle shape and packing density. An electrical network circuit analogy was used to express the theoretical model bed where fluid flows in a zigzag manner among particles in the bed. The results showed good agreement between the theoretical model and experimental data. The results also verified that the fluid flow was irregular in all directions when using the non-uniform structure. In addition, the present study demonstrated that the concept of “tortuosity” should be considered due to the irregular flow path in the bed. Thus, the results of the present study suggest that the electric resistance network analogy might be useful in solving the problem of fluid permeation in actual particle layers with non-uniform structures. © 2008 Elsevier B.V. All rights reserved. 1. Introduction Fluid permeation through porous media and particle-packed beds is an important phenomenon in the design and operation of filtration devices [1]. A large number of articles that explain the phenomena, especially as it occurs in the Stokes regime, have been published. In this regime, the pressure drop across a particle-packed layer, or porous medium, is proportional to the fluid velocity through the bed. This relationship is known as Darcy's law [2] and is described by the Kozeny–Carman equation [3,4]. The complexity of the phenomenon of fluid permeation has encouraged several researchers to develop and verify simple models that can explain fluid permeation [5]. Most models, including the Kozeny–Carman equation, are derived based on channel theory. In this theory, the voids in a particle bed are assumed to consist of a bundle of tiny channels (tubes) that allow for fluid flow. Another commonly used model is the drag model [6–9], where the pressure drop across a particle bed is assumed to have resulted from the drag force acting on all particles in the bed. The effects of several factors, such as particle size distribution, particle shape and bed porosity, on fluid permeation in particle beds have been described using both of these common models [9]. Although the application of these models appears feasible under several assumptions, non-uniform structures have not been considered. In other words, even though local variations in particle size, particle shape, and bed porosity existed within the bed, these parameters were assumed to be uniform. For this reason, modeling of actual beds using the current models remains problematic. Bear approached the problem of modeling actual beds from a different point of view, explaining fluid permeation using an electrical circuit analogy [10]. In this analogy, the pressure drop of the particle layer is estimated using equations that relate voltage to current and resistors. According to Ohm's law, the current passing through an electric circuit between two points is proportional to the voltage and inversely proportional to the resistance. Thus, applying Ohm's law to fluid permeation, the flow rate through a particle-packed bed that has permeation resistance is proportional to the pressure drop. Although this simple electric circuit analogy is easily understood and explained, its application to fluid permeation through particle- packed layers in actual particle bed models has not been rigorously investigated. Application of the electric circuit analogy presents several limitations related to the inhomogeneity of actual packed beds. In addition, application of the analogy requires consideration of differences in particle size and distribution [11], material type and properties [12], particle bed porosity [1], packing structure [13], and combinations of these factors [6–9]. For this reason, the electric circuit analogy must be simplified for application to actual packed beds. The purpose of the present study was to verify the electric cir- cuit analogy in a sequence of experiments. The initial experiment Powder Technology 191 (2009) 39–46 ⁎ Corresponding author. Tel.: +816 6466 5153; fax: +81 6 6466 5473. E-mail address: endouy@sc.sumitomo-chem.co.jp (Y. Endo). 0032-5910/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2008.08.026 Contents lists available at ScienceDirect Powder Technology journal homepage: www.elsevier.com/locate/powtec