1. Introduction. ) exceeded the terminal velocity (U t

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1 Excerpt from the Proceedins of the COMOL Conference 010 India Cluster Diameter Determination of Gas-solid Dispersed Particles in a Fluidized Bed Reactor *Mitali Das Department of Biotechnoloy, PEIT Banalore *Correspondin author: PEIT, Department of Biotechnoloy, 100ft rin road Banashankari III tae, Karnataka,Banalore , India, mitali_das_iit@yahoo.com, Abstract: Clusterin is a common hydrodynamic characteristic observed amon suspended as-solid particles in a fast fluidized bed (FFB) reime of a circulatin fluidized bed (CFB) system. These suspended particles are unstable in nature and the cluster size is solely dependent on density of the particles. In this paper clusterin behavior has been studied with Geldart roup B particles like coal and iron ore in a circulatin fluidized bed of diameter m and heiht 5.6 m. Clusterin phenomena has been investiated by considerin the effects of acceleration and friction into homoeneous assolid cluster suspension model. The cluster size when calculated from the homoeneous cluster suspension model seems to match the measured data when the particle concentration in the suspension lies mostly in the dilute phase. It has been found that the acceleration effect has some effect on the cluster diameter; however, the solid friction does not have any sinificant role. The result of the present study ives a thorouh understandin of the FFB. The complex relation between the continuous and disperse phase onto the suspended particles can be modeled usin computational fluid dynamics (CFD) module which describes the hydrodynamics i.e., momentum, heat and mass transfer and the reaction module which describes the homoeneous as phase reactions. These modules ive rise to a multi-scale model for a particular clusterin process which can be solved usin COMOL Multiphysics and MATLAB software. Keywords: Fast fluidized bed, circulatin fluidized bed, cluster diameter, hydrodynamics, Geldart particles, computational fluid dynamics (CFD). 1. Introduction Fast-fluidized bed (FFB) has wide rane of applications in petrochemical, mineral and metallurical industries. This particular reime of fluidized bed has athered importance where hih solid throuhputs, transfer rates and thermal uniformity within a reactor are desired. The common hydrodynamic features of a fast fluidized bed in a circulatin fluidization system are usually lare as--solid slip velocity, clusterin behavior of as--solid suspension and solid down flow over the wall. Earlier it was believed that in a vertical fluidparticle system, once the superficial fluid velocity (U 0 ) exceeded the terminal velocity (U t ) of the individual particles, the particles would be carried out of the system. Later, it has been shown that some entrainment do occur at a relatively dense suspension (volumetric solids concentration of the order of ) with the aid of a cyclone at the top of the system that would capture the solids escapin from the top and return them to the lower part of the system. The phenomenon of lare slip velocity in a FFB has been attributed by Rhodes and Geldart due to the radial nonuniformity in the flowin as-solid systems which lead to the core-annulus flow model whereas others analyzed the same with the concept of cluster formation. Accordin to this second roup of thouht the vertical flow of a homoeneous as-solid suspension are unstable in nature. It has also been indicated that the rowth distance of disturbances decreases with increasin suspension density. Therefore, clusterin seems to be a characteristic of the suspension in a CFB system. Assumin the clusters of uniform shape (spherical), size, voidae and velocity Yerushalmi et al. tried to calculate the averae dra coefficient of the same. Pritchett et al. tried to fit a model for the clusterin suspension usin numerical simulation. Yerushalmi et al. stated that the lare slip velocities were due to the solid areation in the fast bed. Accordin to them, most particles do not remain sinle but tend to ather in clusters, strands or packets which have effective free fall velocities reater than those of individual particles. When the clusters are sufficiently lare to be sustained by the risin as, they will disinterate and rain back into the

2 system, thereby resultin in hih deree of solid back mixin in the fast bed. Later, Yerushalmi et al proposed a simplified homoeneous model for the computation of the cluster diameter with the assumption that the bed was a uniformly dispersed suspension of spherical clusters of diameter, Dc. They computed the cluster diameter, Dc usin the experimental data for air-fcc catalyst and air-dicalite 000 systems and plotted it aainst the solid volumetric concentration (1 ε). In the present investiation, an attempt has been made to modify Yerushalmi s model with wide-rane data enerated in an FFB on dra coefficient and also takin into consideration the effect of acceleration into the force balance equation.. Literature review and use of COMOL Multiphysics Various attempts have been made to study the behavior of lean as solid suspensions in terms of clusterin tendency of the particles. A cluster model was developed with the assumption that the cluster was like an impermeable particle with cluster porosity of 0.5. With the help of the model, he explained different hydrodynamic phenomena such as chokin, elutriation rate constant and pressure drop radient for dilute phase transport. Li and Kwauk analyzed the phenomena of enery transport and reime transition based on the method of enery minimization in multiscale modelin of twophase flow, which consisted of areated fluid cavities (as bubbles) and of areated solid particles (clusters). Li et al. studied the clustersize distribution and motion behavior in a FFB by optical fiber probes and a computer data acquisition system. The results revealed that thouh the local time-averaed cluster lenths remain almost constant radially both in the upper dilute and lower dense reion of the cluster lenth. Noymer and Glicksman observed the motion of clusters of particles at the wall of a CFB by usin a thermal-imain technique for flow visualization. Xu and Kato have tried to establish a simple correlation for calculatin the equivalent diameter of clusters in as--solid flow. They reported that the hydrodynamic equivalent cluster diameter is close to that of the crosssectional size, but much less than the vertical cluster heiht experimentally measured. Harris et al. developed correlations to predict the cluster characteristics in lare-scale units. Mostoufi and Chaouki analyzed the existence of clusters in dense fluidized bed by the time-position data of a tracer. Nova et al studied the particle clusterin phenomena usin a novel as--solid optic probe equipped with raded refractive index lens. Wan et al acquired the imae sequences of the formation, movement and decomposition of the lass beads cluster on a cold CFB. Thus various models and techniques which have been proposed to study cluster-related and allied phenomena so far can probably be done usin the finite element proram, Comsol Multiphysics. Moreover, the problem can best be handled numerically, say for a cluster movin in an infinite medium, the dimension of the domain should be lare enouh to take care of its boundary conditions or so. 3. Clusterin nature of as-solid suspension in fast fluidized bed It has been observed that FFB consists of uniformly dispersed suspension of spherical particles. The effective voidae ε or the volumetric concentration of clusters (1 ε ) has been related to the actual voidae, ε by the followin relation. (1- ε) = (1- ε ) (1- ε mf ) (1) Nelectin the acceleration and frictional effects, one can equate the pressure drop with ravity and the resulted balance is presented in Eqn (). P = (1 ε )ρ P (1 ε mf ) L... () Writin the pressure drop owin to the dra exerted by the as upon the clusters, 1 N U P= U C f ( ) D A ρ ε t ε 4 (3) Notin that, N D 3 / 6 = (1 ε ) A L, s ds c c one can equate the two Eqs (1) and () and simplify to et D c 3 ρ[( U / ε ) U s ] Cdsε = 4 ρ (1 ε ) P mf t n (4) where N is the number of clusters in a bed section of thickness L and A t is the crosssectional area of the bed. U is the mean solid

3 velocity of the clusters. C ds is the familiar dra coefficient for a spherical particle movin at uniform relative velocity. In this case, it is the dra coefficient for a sinle cluster and functions of Reynolds number based upon cluster diameter and slip velocity, i.e. C ds = C ' ds ρ D U U ε µ C s where µ is the viscosity of the as..(5) The function f (ε ) has been introduced to take into account the hindered settlin effects resultin from the proximity of particles clusters. The effective voidae has been chosen based on Richardson-Zaki equation, viz. f ( ε ) n ε = (6) where n is the Richardson-Zaki index and is a function of the Reynolds number based upon the terminal settlin velocity, U t, cl of the cluster. Thus, n = 4.65; Re t, c < Re ; 0. < Ret < Re -0.1 t,c ; 1.0 < Ret,c < ; Ret,c > 500.(7) where Ret,c = ρ DC Ut,cl/µ Equation (4) can be used for computin the cluster diameter, DC, provided the as velocity, solid rate and fluidized-bed density [or (1 ε)] are known. The solids, while bein transported upward by the as, form areates of clusters and these clusters et dispersed into the as. The resultin pressure drop occurs due to the interaction between these clusters and as on one hand and their interaction with the wall on the other hand. On the basis of the measured pressure drop data and calculated voidaes, the cluster diameter has been computed usin Eqn (4) and plotted in Fi. 1 for coal and iron particles. Fiure shows an identical plot for iron ore, FCC catalyst and alumina based on the data reported by Kwauk et al. It is enerally found that up to a value of (1 ε) equal to 0.1, the cluster diameter predicted by all the workers [present author, Kwauk et al] aree fairly well. Beyond the value of (1 ε) iven by 0.1, the computed cluster diameter from Kwauk s data are found to be appreciably hiher. Cluster Diameter,cm Fiure1: Effect of solid concentration on (1-ε) cluster diameter (D c ) for different size of particles. Cluster Diameter,cm coal Iron Ore olid Concentration FCC Catalyst Iron Conc. Alumina olid Concentration Fiure : Effect of solid concentration on (1-ε) cluster diameter (D c ) for different size of particles {Li Kwauk data, mean line drawn}. 4. Modification of Yerushalmi s Theory: 4.1 Effect of acceleration and friction At the lower end of the riser, the acceleratin effect contributes to as much as 9-40% of the total pressure drop, while in the top dilute zone the frictional losses due to solid may be about 5% of the total pressure drop. Accordinly, an attempt has been made to modify Eq.4 for cluster diameter by includin the effects of acceleration and friction. The total pressure drop alon a lenth ( L) of the riser due to ravity, friction and acceleration is

4 4 P = ρp 1 ε) L + D t ( τ + τ ) L + ρ (1 ε) U ( F P P The wall as shear stress, τ F is iven by τ F = (1/) f ρ U. (8).(9) where f is evaluated from Colebrook equation for smooth pipe: f = 16 / N Re ; for N Re < 500 or, 1 f (10) Where N Re is the Reynolds number based on pipe diameter, N Re = D t U ρ / µ The wall shear stress, τ P can be expressed as τ P = (1/) f s (1-ε) ρ P and f = a = 4lo b (11) U U (1) U (13) Here, tromber s relationship is used for which a=0.003 and b= NRe 10 f ubstitutin the values of τ F and τ P from Eqs. (9) and (1) respectively and usin Eqs.() and (8), one ets after rearranement: Horio et al. reported cluster diameter with 1.5 times cluster lenth pierced by the probe from the analysis of the raw sinals of reflected liht intensity from the optical fiber probe. The cluster size was found to be small (5-40 mm when the bed solid concentration ranes from 0.05 to 0.). The cluster size was almost constant in the core irrespective of the heiht, while it was lare (more than 10mm) and rew in size as it moved downwards in the annulus. As already stated, the cluster diameter was recalculated by incorporatin the effects of solid friction with wall and acceleration of the particles at the bottom of the riser. It is observed that while the acceleratin force has some effect on the cluster diameter, the solid friction factor does not have.(3.4) any sinificant role. Binary and multicomponent solid mixtures flowin in a vertical pipe, the solid wall friction effect is smaller in comparison with that for the flow of sinle-sized particles. These may be due to collisions between the particles of different sizes that accelerate the heavier particle but decelerate the lihter one. On the basis of the assumption that the clusterphase particle fraction (ε P, cl ) is of the order of 0., the cluster diameters have been recalculated for the present data and those reported in the literature. Fiure 3 ives such a plot, which shows that the recalculated cluster diameter is 1 order hiher than the earlier case (when the cluster-phase voidae was assumed to be ε mf ). The cluster diameter calculated from homoeneous cluster suspension model appears to tally with the measured data when the particle concentration in the suspension lies between 0.01 and 0.10, i.e. the as--solid suspension remains in the dilute phase. 3 ρ(1 ε)( U / ε U) Cdsε DC = 4 4 ρp(1 ε)(1 εmf ) + F P P D t n ( τ + τ ) + [ ρ (1 ε)(1 ε ) U / L] mf.(14) 4. Comparison of calculated cluster diameter based on homoeneous suspension model with the measured data of Horio

5 Fiure 3: Recalculated cluster diameter with ε p,cl = Conclusions In the present investiation, the cluster behavior of fast fluidization have been studied thorouhly by usin Geldart s roup A as well as roup B type of particles in a typical N type CFB system. The homoeneous model proposed by Yerushalmi et al to predict the cluster diameter has been modified by includin the effects of acceleration and frictional forces. It is observed that the acceleration has some effect on the cluster diameter. However, it is interestin to note that the solid friction does not have any sinificant effect on cluster diameter. The cluster diameter calculated from homoeneous cluster suspension model appears to tally with the measured data when the particle concentration in the suspension lies below 0.0, i.e. the as--solid suspension remains in the dilute phase. 6. References 1. Rhodes, M.J., and Geldart, D., Model for the CFB, Powder Technoloy, 53, (1987).. Yerushalmi, J., Turner, D.H., quires, A.M.,The fast-fluidized bed, Industrial Enineerin Chemistry and Process Desin Development, 15,47-53(1976). 3. Pritchett J.W., Blake T.R., Gar.K, AIChE ymp. er., 74, 134(1978). 4. Li, H., Xia, Y., Tun, Y., Kwauk, M., Microvisualization of clusters in a fast-fluidized bed, Powder Technoloy, 66, 31-35(1991a). 5. Noymer, P.D., Glicksman, L. R., Near-wall hydrodynamics in a scale-model circulatin fluidized bed, International Journal of Heat and Mass transfer, (1999). 6. Xu, G., Kato, K., Hydrodynamic equivalent diameter for clusters in heteroeneous as-solid flow, Chemical Enineerin cience, 54, (1999). 7. Harris, B. J., Davidson, J. F., Xue, Y., Axial and radial variations of flow in circulatin fluidized bed risers, CFB Technoloy IV, (1994). 8. Mostoufi, N., Chaouki, J., Flow structure of solids in as-solid fluidized beds, Chemical Enineerin cience, 59, (004). 9. Nova,., Krol,., Lasa, Huo de., Particle velocity and particle clusterin in down-flow reactors, Powder Technoloy, 148, (004). 10. Wan, Q.H., Gao, Q., hi, H.X., Wu, X.C., Luo, Z.Y., Cen, K.F., Formation, structure and motion of clusters in circulatin fluidized bed, Journal of Zhejian University (Enineerin cience), 40,1, (006). 11. Horio, M., Morishita, K., Tachibana, O., Murata, N., olid distribution and movement in CFBs, CFB Technoloy, II, (1988). 7. Nomenclature P pressure drop, k/m acceleration due to ravity, m/s. L heiht of the column, m. N number of clusters per unit volume A t cross-sectional area of the riser column, m. U 0 superficial fluid velocity, m/s. U as velocity, m/s. Us solid velocity, m/s. Ut terminal settlin velocity of individual particles, m/s. Gs solid circulation rate, k/m s. C ds dra coefficient. Dc cluster diameter, m. Dt tube diameter, m. n Richardson-Zaki index. Ret,c cluster Reynolds number.

6 Ret Reynolds number at terminal settlin. Ut,cl terminal settlin velocity of clusters, m/s. f as friction factor fs solid friction factor NRe Reynolds number based on pipe diameter. Greek Letters ε voidae. ε averae voidae. εmf minimum fluidization velocity. εp,cl cluster-phase particle fraction. ρp solid density, k/m 3. ρ as density, k/m 3. µ as viscosity, k/m s. τ F shear stress due to as, k/m. τ P shear stress due to solid, k/m.