Particuology 11 (2013) 288–293 Contents lists available at SciVerse ScienceDirect Particuology j o ur nal hom epag e: www.elsevier.com/locate/partic Using S-statistic for investigating the effect of temperature on hydrodynamics of gas–solid fluidization Mohammad Reza Tamadondar a , Reza Zarghami a , Hedayat Azizpour a , Navid Mostoufi a,∗ , Jamal Chaouki b , Ramin Radmanesh b a Multiphase Systems Research Lab., Oil and Gas Processing Centre of Excellence, School of Chemical Engineering, College of Engineering, University of Tehran, P.O. Box 11155/4563, Tehran, Iran b Department of Chemical Engineering, École Polytechnique de Montréal, P.O. Box 6079, Station Centre-Ville, Montréal, Québec, H3C 3A7, Canada a r t i c l e i n f o Article history: Received 29 February 2012 Accepted 11 May 2012 Keywords: S-statistic Effect of temperature Particle trajectory Fluidized bed a b s t r a c t The influence of temperature on fluidization was investigated by a statistical chaotic attractor comparison test known as S-statistic. After calibration of the variables used in this method, the S-test was applied to the radioactive particle tracking (RPT) data obtained from a lab-scale fluidized bed. Experiments were performed with sand as fluidized particles and in temperatures from ambient up to 600 ◦ C with super- ficial gas velocities of 0.29, 0.38 and 0.52 m/s. Considering the behavior of bubbles and comparing with frequency domain analysis, it was concluded that S-statistic is a reliable method for characterization of fluidization process behavior at different temperatures. © 2012 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved. 1. Introduction Many chemical processes, such as coal gasification and combus- tion, are carried out in high temperature gas–solid fluidized beds. Although temperature directly affects mass transfer and reaction rates in the bed, most investigations on fluidized bed hydrody- namics are limited to ambient temperatures. Lack of accurate knowledge of high temperature hydrodynamics can be attributed to difficulties associated with measuring techniques. Cui, Sauriol, and Chaouki (2003) studied the effect of temperature on local two-phase flow structure. Rapagna, Foscolo, and Gibilaro (1994) investigated the quality of fluidization of three powders in a gas–solid fluidized bed. The influence of temperature on minimum fluidization velocity was investigated by Subramani, Balaiyya, and Miranda (2007). In spite of the above mentioned studies, there is still need for fundamental studies at high temperatures using robust and reli- able measurement techniques. Effect of temperature on solid phase mixing and phase dynamics of FCC powder was studied by Cui et al. (2003) and Cui and Chaouki (2004) using optical fiber probe to measure instantaneous particle concentration in the fluidized bed. X-ray technique, which provides a moving image of the inter- nal flow patterns of fluids and solids inside a vessel, was used by Lettieri, Yates, and Newton (2000) for investigating fluidization ∗ Corresponding author. E-mail address: mostoufi@ut.ac.ir (N. Mostoufi). behavior at elevated temperatures. Doucet, Bertrand, and Chaouki (2008) showed radioactive particle tracking (RPT) technique as an accurate, non-intrusive method for monitoring the motion of solid particles in fluidized bed. Recently many investigators (Bai, Bi, & Grace, 1997; Zarghami, 2009) showed that fluidized beds exhibit chaotic behavior. The embedding theorem has been utilized to reconstruct attractors which describe the fluidization process. Diks, van Zwet, Takens, and De Goede (1996) combined this reconstruction with a statisti- cal test to determine the statistical changes between two different time series. van Ommen, Coppens, van den Bleek and Schouten (2000) presented an enhanced monitoring method based on the statistical test developed by Diks et al. (1996) and comparison of attractors for monitoring small changes in the bed and detec- ting agglomeration in early stages. Also, Shiea, Sotudeh-Gharebagh, Azizpour, Mostoufi, and Zarghami (in press) applied this attractor comparison to vibration signals of a fluidized bed for predicting the onset of the turbulent regime. In the present work, the RPT technique was used for characterization of the hydrodynamics of gas–solid fluidized bed due to its excellent performance under severe conditions at high temperatures. Comparing reconstructed attractors in state space was used to obtain more information on the effect of temperature on fluidization hydrodynamics. 2. Theory The S-statistic test provides a criterion for the comparison of reconstructed delay vectors coming up from a stationary state 1674-2001/$ – see front matter © 2012 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.partic.2012.05.007