Pergamon (hcmw, ti hnqlm'~'rola 5octal. Vol 52. Nos 21 22. pp 3931 3939. 1997 , 1997 l!lseuer Science Lid All rights reserved Printed m Great Britain PII: S0009-2509(97)00236-4 t~9 2~o997 sr.0o - ot~ Trajectory length and residence-time distributions of the solids in three-phase fluidized beds Karim Kiared,* Faigal Larachi,*"Christophe Guy*'* and Jamal Chaouki* * Biopro Research Center, Department of Chemical Engineering, Ecole Polytechniqt,e, P.O. Box 6079, Station "Centre-Ville", Montreal, Qc, Canada H3C 3A7 : Department of Chemical Engineering, Laval University, Quebec, Qc, Canada G I K 7P4 [Accepted 1 July 19971 Abstract--The novel concept of trajectory length distribution (TLD), recently introduced by Villermaux (1996, Chem. En,qn,q Sci. 51, 1939) for characterizing the macromixing of fluid elements in flow systems, is used to describe solids mixing in the fully developed zone (FDZ) of three-phase fluidized beds. Tests with monodispersed and binary mixtures of solids of different sizes and densities were performed in the dispersed and the coalesced bubble flow regimes. The Lagrangian trajectories of single traced particle were measured non-invasively via radioactive particle tracking (RPT}. A macromixing index was derived from the experimental TLDs for describing solids mixing in both upward and downward sections of the FDZ. Residence-time distributions (RTDs} of the solid particles, moving upwards in the column core section and downwards in the sidewall section of the FDZ, were generated from the RPT-measured trajectories. Based on the observed physical features of the solids flow, these RTDs were modeled using a two-zone one-dimensional cross-flow multistage stirred reactors (CFMSR} model. Part of the CFMSR input parameters were obtained taking advantage of the exhaustive three-dimensional trajectories measured from RPT. Thc model is shown to compare well with thc experimental RTDs in both ascending and descending sections, c 1997 Elsevier Science l,td Kevwords: Fluidized beds: three phase: RTD: TLD: particle tracking. txrRom;CTIOg Three-phase fluidized beds are employed extensively in various industrial applications such as coal lique- faction, hydrotreating of petroleum resids, turbulent contacting absorption for flue gas desulfurization and particulate removal, waste-stream treatment, fermen- tation, etc. In spite of their industrial importance and because of the extreme entanglement between phases, proper design of gas-liquid-solid fluidized-bed reac- tors continues to be a matter of know-how and still relies upon intuition and rules of thumb. The phe- nomenology of three-phase fluidization is complex: it is an outcome of microscopic and macroscopic phe- nomena such as jetting, bubbling, wake discharge, gulf streaming, evanescent vortices, particle collisions and drift, etc. Though myriad of studies were devoted to gas-liquid solid fluidization, among the three phases the solids dynamics was the less comprehensively +Corresponding author. Fax.: I 514 3404159. E-mail: cguy@mailsr', .polymtl.ca. studied and the less well understood, especially when mixed particle systems differing in shape, size and density are involved. Recent attempts aimed at refin- ing the characterization of the solids behavior in gas-liquid solid fluidized beds are now being re- ported, in which use is made of advanced noninvasive measuring techniques such as particle image velocimetry ((7hen et al.. 1994: Reese and Fan, 1997) and radioactive particle tracking (Larachi et al., 1996, 1997). The axial dispersion model (ADM) has been pro- posed for the interpretation of solids dynamics and mixing in three-phase fluidized beds (Bickle and Thomas, 1982; Euzen and Fortin, 1987). The solids phase was assumed to be in plug flow with axial dispersion superimposed. Recent experimental evid- ence portrayed a far more complex solids flow struc- ture, thus, shedding doubts on the appropriateness of single-parameter models such as ADM to describe the solids motion and mixing (Cassanello et al., 1995: l.arachi et ul., 1996). Bv means of laser sheeting and particle image veloeimetry, Chen et al. (1994) set up, for the vortical spiral flow regime in dilute lluidized 3931