Ind. Eng. zyxwvuts Chem. Res. 1995,34, zyxwvu 2971-2980 2971 zyxwvutsrqp Experimental Characterization of the Solid Phase Chaotic Dynamics in Three-phase Fluidization Miryan Cassanello,l Fa’iqal Larachi, Marie-NoGlle Marie, Christophe Guy, and Jamal Chaouki” Department zyxwvutsrqp of Chemical Engineering, Ecole Polytechnique de Montreal, P.O. Box 6079, Station “Centre-Ville”, Montreal, Quebec, Canada, H3C 3A7 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA An experimental study of the solid phase dynamics in a three-phase fluidized bed reactor using heavy and light particles is carried out. A radioactive particle tracking technique is employed to obtain extended time series of the tracer path. The tracer has the same properties as the rest of the particles in the bed. A rescaled range analysis is applied to time series of the fluctuating velocities to investigate the features of solid phase turbulence. It is found that turbulence is anisotropic. In the axial direction, the correlations between the fluctuating velocities are persistent in time, indicating a superdispersive axial dispersion of the solids. Hence a constant axial dispersion coefficient, which is traditionally used in these reactors to represent the solid phase turbulence, only constitutes a lumped parameter hardly extrapolable to different operating conditions, different systems, and different geometries. The tracer path is also analyzed according to the theory of deterministic chaos. It is found that the solids motion is chaotic. An increase in the gas flow rate increases the values of the parameters that quantify the chaotic behavior of the solids motion. This analysis is found to constitute a promising tool to determine flow regime transitions. Introduction Gas-liquid-solid fluidized bed reactors are exten- sively used in the chemical, petrochemical, and bio- chemical industries. Development of accurate math- ematical models for such reactors is still a challenge partially due to the complex and hardly understood dynamics of the fluidized particles. The solids motion is a resultant of interactions among the particles, with the fluid phases and the reactor walls, and is still poorly characterized (Wild and Poncin, 1993; Fan, 1989). Only a few works have studied the solids mixing of uniform particles in three-phase fluidized beds or sparged reac- tors (Bickel and Thomas, 1982; Euzen and Fortin, 1987; Khare et al., 1989; Fan et al., 1992; Tzeng et al., 1993). The last works have given a qualitative description of instantaneous solids patterns within wakes and vortices from video recording in a two-dimensional reactor. From them it became apparent that the solids dynamics is complex. Therefore, it is very important to achieve further fundamental insights in the solids motion in order to formulate precise hypotheses on their behavior for simulation or scale-up of three-phase fluidized bed reactors. The solids motion is generally ensured by convection and dispersion. The dispersive characteristics of the particles motion can be determined from the analysis of their high-frequency fluctuations. In turbulent flow, such fluctuations are usually correlated and lead to “superdispersive” mechanisms, where the mean square fluctuating displacements scale with time as ta, a zyxwv > 1. It has been shown (Wang and Lung, 1990) that certain dispersive mechanisms, in which the fluctuations are not Markovian, can be modeled by considering that the particles follow a fractional Brownian motion (FBM)as defined by Mandelbrot and Van Ness (1968). In a FBM, * Author to whom correspondence should be addressed. E-mail: zyxwvutsrq jchaouki@mailsrv.polymtl.ca. ’ Present address: PINMATE, Departamento de Industrias, FCEyN, Universidad de Buenos Aires, 1428 Ciudad Univer- sitaria, Buenos Aires, Argentina. 0888-5885/95/2634-2971$09.0Q/O the fluctuating particles steps are correlated even for very long time. The magnitude of this correlation can be quantified by a rescaled range (RIS) statistical analysis. This analysis was first proposed by Hurst (1951) and modified and applied to FBM by Mandelbrot and Wallis (1969a). A mean convective pattern of solids motion in three- phase fluidized bed reactors was evidenced by a radio- active particle tracking (RPT) technique and character- ized by an Eulerian velocity map (Larachi et al., 1993). Notwithstanding, the qualitative information obtained by Tzeng et al. (1993)and some very high instantaneous velocities found with RPT indicate a solids dynamics much more complex than what is reflected in the mean patterns. As was suggested by Stringer (1989)and only recently shown by Daw et al. (1990, 1991, 19921, Schouten and van den Bleek (1992), and van den Bleek and Schouten (1993a,b), the hydrodynamics of a gas-solid fluidized bed is chaotic. This was put into evidence from the analysis of pressure fluctuations and local voidage time series. Moreover, it was suggested that to account for the chaotic hydrodynamics would be of relevant impor- tance in modeling and scale-up of gas fluidized beds (van den Bleek and Schouten, 1993a,b). The chaotic behavior may arise from the particles motion, and consequently it may also be a feature of the solids motion in three- phase fluidization. A chaotic dynamics can be experimentally diagnosed by analyzing time series of a characteristic variable. The tools employed constitute the theory of deterministic chaos. This theory is a very fast growing field that proved to be applicable in many disciplines. Introduc- tory references (Stewart, 1989; Ruelle, 1991) and com- prehensive treatments specially written for engineers and applied scientists (Hilborn, 1994; Ott, 1993; Moon, 1992) are now available. The purpose of this work is to experimentally study the qualitative characteristics of solids dispersion and convection in three-phase fluidized beds. Extended time series of positions of a solid tracer freely moving within zyxwvutsr 0 1995 American Chemical Society