chemical engineering research and design 86 ( 2 0 0 8 ) 508–516 available at www.sciencedirect.com journal homepage: www.elsevier.com/locate/cherd A statistical approach of heat transfer coefficient analysis in the slurry bubble column Ali Fazeli a , Shohreh Fatemi a,* , Ensieh Ganji b , Hamid Reza Khakdaman b a School of Chemical Engineering, Faculty of Engineering, University of Tehran, P.O. Box 11365/4563, Tehran, Iran b Gas Division, Research Institute of Petroleum Industry (RIPI), Tehran, Iran article info Article history: Received 3 June 2007 Accepted 26 January 2008 Keywords: Slurry bubble column reactors Convection heat transfer coefficient Full factorial Design of experiments abstract Heat transfer plays an important role in slurry bubble column reactors (SBCRs). Design of heat transfer equipments for SBCRs is a limiting step in sizing and scale up of them. In order to study the convection heat transfer coefficient (CHTC) in industrial SBCRs, a proper col- umn was designed and manufactured in pilot scale with a special convection heat transfer coefficient measurement probe (CHTC MP). In this study, influence of effective parameters such as solid fraction, superficial gas velocity, radial and vertical position of the column was investigated on CHTC. The design of experiments was performed using a full factorial method including 3 1 × 2 2 × 9 1 = 108 experiments, to determine the main effects, binary and ternary interactions of variables. Study of the curvature functionality of CHTC versus gas velocity and effect of flow regime transition from homogeneous to heterogeneous flow was the other goal of this work. A statistical model including the main variables and their sig- nificant binary and ternary interactions was explained for CHTC with a good fitness with experimental data. Interactions of four effective parameters including solid fraction, super- ficial gas velocity, radial and vertical position of the column was studied for the first time in the SBCRs. A dimensionless correlation for local Stanton number was developed as a func- tion of Pr, Re, Fr, non-dimensional radial position and non-dimensional distance from the sparger. Considering local positions in the correlation is a novel work and this correlation has good agreement with experimental data. © 2008 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. 1. Introduction Effective heat transfer and good temperature stability in the SBCRs specially working at the heterogeneous regimes are the important benefits of SBCRs, however deep knowledge of heat transfer coefficient in these reactors is required to achieve to effective heat transfer and good temperature stability, which guides to optimal and economical design of the industrial SBRCs. There are comprehensive reviews of bubble column reac- tors (Deckwer, 1992; Kantarci et al., 2005). Kolbel et al. reported that adding sand particles to the water in average diameter of 0.2 mm enhances CHTC, however adding Kieselguhr particles Abbreviations: AARD, average absolute relative deviation; ANOVA, analysis of variance; CHTC, convection heat trans- fer coefficient; CHTC MP, convection heat transfer coefficient measurement probe; DC, direct current; DOE, design of experiment; FTS, Fischer-Tropsch synthesis; SBCRs, slurry bubble column reactors. ∗ Corresponding author. Tel: +98 21 61112229; fax: +98 21 66957784. E-mail address: shfatemi@ut.ac.ir (S. Fatemi). to water causes reduction of CHTC in slurry bubble columns (Kolbel et al., 1958, 1960). Deckwer et al. (1980) found that adding alumina particles with average diameter of 5 m to melting paraffin increases CHTC at superficial gas velocities lower than 0.04 m/s. Although some researchers reported that increasing slurry concentration enhanced CHTC (Kolbel et al., 1960; Deckwer et al., 1980), Li and Prakash (1997) obtained opposite trends. One of the aims of this research was a detail study to achieve the correct trends of CHTC in the case of Fischer- Tropsch synthesis in SBCRs. SiO 2 powder in average size of 50 m was used for the slurry content of the column because of its similarity to the FTS catalysts based on SiO 2 . 0263-8762/$ – see front matter © 2008 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.cherd.2008.01.009