A revisit of pressure drop-flow rate correlations for packed beds of spheres Esra Erdim a,1 , Ömer Akgiray b, ⁎, İbrahim Demir a a Istanbul Technical University, Faculty of Civil Engineering, Department of Environmental Engineering, Istanbul, Turkey b Marmara University, Faculty of Engineering, Department of Environmental Engineering, Istanbul, Turkey abstract article info Article history: Received 13 January 2015 Received in revised form 1 June 2015 Accepted 4 June 2015 Available online 14 June 2015 Keywords: Head loss Packed bed Porous media Pressure drop A large number of correlations can be found in the literature for the calculation of pressure drop caused by fluid flow through packed beds. New correlations continue to be proposed and there appears to be no general agree- ment regarding which correlation is the most accurate. In this work, experiments have been carried out with water using glass spheres of nine different sizes, varying from 1.18 mm to 9.99 mm. For each size, experiments were repeated with at least two different porosities. A total of 38 correlations from the literature have been eval- uated and a uniform notation was established to facilitate the comparison of the correlations. While the Ergun equation remains the most widely-used correlation, the data collected in this work shows that it should not be used above Re m ≈ 500. A simple new equation (f V = 160 + 2.81Re m 0.904 ) is proposed to represent the data collect- ed in this work. The new equation yields the smallest mean error among all the correlations considered here. While a substantial amount of the data collected in this work involved D/d P ratios less than 10, the correlations that fit the current data best do not have any wall effect correction terms. © 2015 Elsevier B.V. All rights reserved. 1. Introduction Flow of fluids through packed beds of solid particles occurs in a variety of important applications in several engineering fields. A quanti- ty of primary interest is the pressure drop (or the head loss) generated as a result of fluid flow through the porous medium. The equation pub- lished by Ergun [1] about sixty years ago remains the most popular and the most widely-quoted pressure drop–flow rate relation for fluid flow through packed beds. For incompressible flow through a bed of spherical particles of identical size, the Ergun equation can be written as follows: -ΔP L ¼ 150μ 1-ε ð Þ ε 3 2 V d 2 p þ 1:75ρ 1-ε ð Þ ε 3 V 2 d p ð1Þ where -ΔP = piezometric pressure drop in the bed, L = depth of the bed, V = velocity based on the empty cross-section of the bed, ε = porosity of the bed, d P = particle diameter, and ρ = fluid density, μ = fluid viscosity. It may be noted that -ΔP = ρgh, where h = head loss in the bed. In addition to a number of historically significant equations that pre- date it, many additional equations have been proposed since the publi- cation of the Ergun equation and new correlations continue to be developed and published. Each new correlation is claimed to be more accurate than, or in some other way superior to the previously proposed correlations. However, there aren't many independent comparisons of these correlations. The few studies evaluating and comparing various correlations ignore most of the correlations in the literature and focus only on a few correlations. The purposes of this work can be outlined as follows: (1) Review all the widely-used and/or well-known correla- tions that exist in the relevant literature. (2) Present all the mentioned correlations using a uniform notation so that their application and com- parison with each other are facilitated. (3) Test and compare the accura- cy and the applicability of the correlations. Some recently proposed correlations have also been included in this evaluation. In what follows, the definitions of various quantities of interest and the notation used in this work are first described. Correlations consid- ered in this work are then rewritten using the described notation instead of the notation used by their original authors. Expressing corre- lations from different sources using a uniform notation will facilitate the comparison of the mentioned correlations and the observation of differ- ences as well as similarities between the different equations. Powder Technology 283 (2015) 488–504 Abbreviations: -ΔP, piezometric pressure drop -(P 2 - P 1 ); A, a characteristic area for the bed; A x , the cross-sectional area of the empty bed; D, column diameter; d P , particle diam- eter; ε, porosity of the bed; ε b , bulk zone porosity; f, friction factor; f k , friction factor ( f k =3f); f V , friction factor (f v ¼ f k Re 1-ε ); f P , modified particle friction factor f p ¼ f v 1-ε ð Þ 2 ε 3 Re   ; F k , kinetic force exerted by the fluid on the solids; h, head loss in the bed; K, a characteristic kinetic en- ergy per unit volume; L, depth of the bed; V, velocity based on the empty cross-section of the bed; V b , bulk zone velocity; ρ, fluid density; μ, fluid viscosity; Re, Reynolds number ( ρdpV μ ); Re m , modified Re number ( Re 1-ε ); Re 1 , modified Re number ( Re 61-ε ð Þ ); T, tortuosity. ⁎ Corresponding author. Tel.: +90 216 348 02 92/261; fax: +90 216 348 02 93. E-mail address: omer.akgiray@marmara.edu.tr (Ö. Akgiray). 1 Present address: Marmara University, Faculty of Engineering, Department of Environmental Engineering, Istanbul, Turkey. http://dx.doi.org/10.1016/j.powtec.2015.06.017 0032-5910/© 2015 Elsevier B.V. All rights reserved. Contents lists available at ScienceDirect Powder Technology journal homepage: www.elsevier.com/locate/powtec