Solid Trajectories and Cycle Times in Spouted Beds Marı ´a J. San Jose ´ ,* Martin Olazar, Miguel A. Izquierdo, Sonia Alvarez, and Javier Bilbao Departamento de Ingenierı ´a Quı ´mica, Universidad del Paı ´s Vasco, Apartado 644, 48080 Bilbao, Spain A study has been made of the effect of both the geometric factors of the contactor (base angle and gas inlet diameter) and the experimental conditions (stagnant bed height, particle diameter, and gas velocity) on the trajectories of the particles in the three zones (spout, annulus, and interface) of spouted beds. The trajectories have been determined from the experimental results of the vertical component of the particle velocity measured by means of an optical fiber probe. Cycle time distributions have been calculated from the trajectories, and they have been compared with the experimental results obtained by monitoring colored particles using video-imaging treatment. Original correlations have been proposed for calculating the average cycle time from the geometric factors and experimental conditions. 1. Introduction Spouted beds are the focus of renewed attention for physical and chemical operations that require handling of solids for which fluidized beds have problems because of their great size, irregular texture, or sticky nature, as is the case of combustion of vegetable biomass or bituminous coal, 1,2 pyrolysis of vegetable biomass, 3,4 pyrolysis of waste plastics, 5,6 and catalytic polymeriza- tions. 7,8 The good performance for conventional applica- tions (drying, granulation, and coating) and for those of a more recent nature is due to the cyclic movement of particles and to the versatility in the properties related to solid circulation (such as the time required by a particle to complete a cycle and the fractions of this time spent in the spout and the annular zones). The aim to reach in the design of spouted beds for their application in operations or processes is the establish- ment of the optimum trajectories by acting on the experimental conditions (geometric factors of the con- tactor-particle system and gas velocity). Consequently, knowledge of particle circulation and of the effect of the process conditions on it is of great relevance in the application of spouted beds. Several authors have experimentally studied the trajectories of the solid, 9-12 and others have proposed theoretical models for predicting these trajectories in the annular zone. 12-15 From the results obtained in the studies on cycle times, the importance of experimental conditions is noteworthy. Thus, the contactor base angle, 9,16 particle diameter, 17,18 stagnant bed height, and gas inlet 19 all influence the cycle time. Roy et al. 20 determined that the average cycle time is independent of the bed level. In this paper, particle trajectories have been deter- mined by means of the results obtained in a previous paper in which longitudinal and radial profiles of the vertical and horizontal components of the particle velocity were determined in the three zones of the spouted bed: annulus, spout, and fountain. 21 This previous study was extended to a wide range of geo- metric factors of the contactor (base angle and gas inlet diameter) and of experimental conditions (stagnant bed height, particle diameter, and gas velocity). From the trajectories, cycle time distributions have been calcu- lated, and they have been compared with the experi- mental results obtained in this paper for different values of geometric factors and experimental conditions. The main contribution of this paper is the extension of the study of solid trajectories to the three zones (spout, annulus, and fountain) of the spouted bed, whereas previous studies correspond to the trajectories in the annulus. 12-15 2. Experimental Section Five contactors of poly(methyl methacrylate) have been used, which have the following dimensions (geom- etry defined in Figure 1): column diameter D c , 0.152 m; base diameter D i , 0.063 m (except for γ b ) 180°, where D i ) D o ); height of the conical section H c , 0.168, 0.108, 0.078, 0.026, and 0 m; angle of the contactor base γ b , 30, 45, 60, 120, and 180°; gas inlet diameter D o , 0.03, 0.04, and 0.05 m; stagnant bed height H o , between 0.05 and 0.35 m. The solids studied are glass spheres (density ) 2420 kg m -3 ) of particle diameters 2, 3, 4, and 5 mm. Three air velocities have been used: 1.02u ms , 1.2u ms and 1.3u ms . The minimum spouting velocity, u ms , has been calculated using the equation of Mathur and Gishler. 22 In a previous paper, the validity of this equation for the calculation of u ms for solids of different density and shape factors has been proven in a wide range of experimental conditions (base angle, air inlet diameter, stagnant bed height, particle size, and air velocity at the inlet). The average relative error of the equation of Mathur and Gishler for predicting the values corre- sponding to glass spheres is 4%. 23 The values of the velocity vector in the spout, annulus, and fountain have been determined from the experi- mental results of the vertical component of the particle velocity obtained by means of an optical fiber probe. These values and the technique used have been de- scribed in detail in a previous paper. 21 The distribution of cycle times has been measured by monitoring a colored particle using an image treatment system that is composed of a camera, a video recorder, a monitor, and the computer support needed for treat- ment of the data obtained. The camera used is a Hitachi * To whom correspondence should be addressed. Tel.: 34- 94-6015362. Fax: 34-94-6013500. E-mail: iqpsaalm@lg.ehu.es. 3433 Ind. Eng. Chem. Res. 2004, 43, 3433-3438 10.1021/ie030668x CCC: $27.50 © 2004 American Chemical Society Published on Web 05/26/2004