Packing and fluidization properties of binary mixtures of spherical particles

Powder Technology,

66 (1991) 259-264

Packing and fluidization particles

259

properties

of binary

mixtures

of spherical

B. Formisani Diparttmento

dl Chrmrca,

Sezione Ingegnen’a

Chlmrca,

Umversltci della Calabna,

87030 Arcavacata

di Rende,

Cosenza

(Italy)

(Received April 30, 1990. in revised form July 23, 1990)

Abstract

Literature equations for calculating the minimum fluidization velocity of binary sohd mixtures have been reviewed, and their capability to give a realistic interpretation of the fluidization behaviour of such systems discussed. For well-mixed beds of two solids of equal denstty, measured values of u,r can be successfully correlated by means of a classical equation such as Carman-Kozeny’s, if their packing properties are correctly accounted for and a proper average particle diameter is assumed. On this basis, the lowering effect of the addition of a small amount of fines on the minimum fluidization velocity of a bed of coarser particles can be explained.

Introduction

Although most of the literature dealing with fluidtzation of powders has been developed from the study of monodisperse beds of particles, practical apphcations of fluidlzation technology are often concerned with mtxtures of solids differing at least in size, whenever a wide granulometric distribution of particles IS present, if not also in density and shape, as in the case of processes which use more than one particulate species. Both in fixed and fluidized bed applications, however, important properties of a multicomponent bed can hardly be related to those of individual solids; for this purpose, a study of binary mixtures of spheres can give an important insight into more complex systems behaviour. It is in fact believed that a satisfactory model of the fluidization pattern of such systems would greatly facilitate understanding of the behaviour of multicomponent mixtures. This study is therefore concerned with the fluidization process of mixtures of two solid components of the same density, and aims at comparing experimental results wtth theoretical predictions based on the extension to such mixtures of relationships commonly uttlized in the description of the fluidization behaviour of monodisperse beds.

0032-5910/91/$3 50

Theory Definition binary

of the mmimum

jluldtzatlon

veloctty

of a

mature

When an inittally well-mixed bed of two parttculate solids of the same density but of different sizes is fluidized by progressively increasmg the gas flow rate through it, and then defluidized by gradually reducing it again to zero, a plot of the bed pressure drop versus superficial gas velocity similar to that of Fig. 1 is generally obtained. At increasing gas velocities, unless the Reynolds number in the bed is high, the pressure drop increases along a straight line which provides the measure of uM; gradually, a value of velocity IS reached at which the smaller particles (the ‘fluidized’ component), having a u,r lower than the bigger ones (the ‘packed’ component), begin to form a segregated layer at the top of the bed, thus promoting a local decrease in pressure drop values. A further rise m gas velocity leads to the progressive growth of the segregated layer, accompanied with a wavelike trend of the pressure drop curve, which finally attains, at the full fluidization velocity uFF, a constant value corresponding to the full fluidization regime. By progressively decreasing gas velocity, segregation gives rise to a different pressure drop pattern. Starting from UFF, most of the bigger component sinks, forming a fixed layer at the bottom, upon which the smaller

0 Elsevier Sequoia/Printed

m The Netherlands

260

0

by adopting a ‘mixture diameter’ definition such as to give the same total surface area per unit weight of the binary system:

n

=

150

E

1

w,

WP

&PF

dpp,

=-++

ig 2

Analogously, (l), that is,

100

Ar =ARe,:

o

50

0

decreasmg

5

0

u

u

,

particles remain fluldized; accordingly, pressure drop decreases linearly until a marked change of slope, occurring at a velocity near to the u,rvalue of the smaller component, indicates that the segregated bed IS now all packed. Figure 1 also shows how, for a segregated bed, a us can be defined, by extrapolating the steepest slope of the defluidlzation curve; although used by some authors, this parameter, however, identifies only an apparent minimum fluidization point. Calculatron of the mimmum fluidization velocity of a bmary mixture: previous work

The attempts to relate the minimum fluidization velocity of a binary mixture of particles of different sizes and/or densities to the properties of its mdividual solid components have generally been based on the extension of equations originally developed for predicting the umf of a monodisperse bed. Among these, the correlation proposed by Wen and Yu [l] + 1 650Remf

1

WF

WP

6

PF

Pp

form of eqn.

(4)

+ 1242Re,,

(2)

and found that the smallest deviation between experlmental and calculated values of umf was obtained

(5)

based on u,,data obtained at decreasing gasvelocltles both for well-mixed (uh.() and segregated (us) binary beds. More recently, Noda et al. [4] pointed out that defining the minimum fluidization velocity of a segregated binary mixture as the us-value of Fig. 1 IS misleading and of no practical use, because the packed component is not yet fluidized at that velocity. Instead, they assumed uFF to be the proper minimum fluldizatlon veloaty, remarking that variations between values obtained at increasing and decreasmg fluidization velocities are very small, as in the case for the uM-values obtained for homogeneous beds. For both mixed and segregated beds, they apphed eqn. (4) together with eqns. (2) and (3), obtammg for parameter A a correlation given by -0 A=36.2

196

2:

(

(6)

1 B, respectively

and for parameter

0 296

B=I397

he ( dF PP1

for completely

(7a)

mixed beds, and

(1)

which eliminates the difficulty of determining the shape factor and voidage in the calculation of u,f, has often been a favourite starting-point. Goossens et al. [2] applied eqn. (1) to homogeneous beds of binary mixtures of dissimilar materials, whose minimum fluidization velocities uhl were determined at increasing gas velocities. For this purpose, they assumed the ‘mixture density’ to be -_=-+-

+ BRemf

Ar = 31Re,:

cm/s

Fig. 1. Bed pressure drop ZIS superficial gas velocity. Dcfimtlon of uM, us and urF (mutture: GB483-GB240).

Ar = 24SRe,:

starting from the general

and with fi and 2 defined as in eqns. (2) and (3), Thonglimp et al. [3] proposed the following correlation: 15

10

(3)

-1 B=6443

86

flziE

( dF

PP

)

C’b)

for partially segregated beds. The possibility of predicting the u,f of binary solid mixtures by applying Ergun’s equation to them was examined by Chiba et al. [5]; in particular, in the laminar flow region, they characterized a completely mixed bed of two particulate species by assummg for it the volume average density of eqn. (2) and a volume to number mean particle diameter defined as ci = (fNFdF3 +fNpdp3)“3

(8)

261

With the further assumption of constant voidage over the whole range of composition, they found unsattsfactory agreement between theoretical predictions and experiments. Despite all efforts so far made to give a theoretical description of the dependence of the minimum fluidization velocity of a binary bed on the basic characteristics of its solid components, the fully empirical correlation of Cheung et al. [6] I-. \ (l-=P UM _= -UP

UF

(1 UF

originally proposed for well-mixed mixtures of equal density having a mean size ratio dp/dFc3, is still considered perhaps the most suitable equation for its calculation. Though requiring the values of u,f of both single components, its simple form proved successful m correlating a great deal of data, even when applied sequentially to mrxtures of more than two components.

Experimental

apparatus

and procedure

Experiments were performed m a Perspex fluidization column of 0.101 m ID, equipped with a porous plate distributor. Compressed air was used as fluidizing gas, and its flow rate was metered by a set of rotameters. Bed heights were read on four external graduated rules which equally quartered the column circumference, and from them void fractions were calculated. Pressure drops across the bed were measured by an electronic transducer, connected to a pressure tap 1 mm above the distributor and to the freeboard. A series of pressure taps at different levels on the column wall allowed verification of the linearity of the static pressure profile across the bed, as a check of uniform mixing of the solids in the bed, whenever required. In each experiment, a batch of 1.2 kg of glass ballotmi (GB), such as to give a bed aspect ratio H/D about 1, was used, varying the amount of either component to achieve desired compositions of the bmary mtxture. Single solid components were obtained by sieving, and their mean diameters and granulometric distributions were determined by a Sympatec Helos particles size laser analyser. Such data, together with their minimum fluidization properties, are reported in Table 1. Before each experiment the particle mixture was vigorously fluidized for a few minutes to obtain a well-mixed bed. Then the gas flow was rapidly reduced below the fluidization threshold, and the uniformity of packing composition verified by a check of the linearity of the pressure profile along the fixed bed.

Successively, the gas flow rate was brought down to zero and the four values of the bed height read and averaged. The correspondmg voidage was assumed as the Emf of the mixture. The total bed pressure drop was then measured both at increasing and decreasing gas velocity.

Results Experimental results were obtained from binary mtxtures with dp/dF ratios ranging from 1.40 to 2.79. For each of them, fluidization experiments were performed with fines volume fractions xr of 0.20, 0.40,0.60 and 0.80, at which voidage l,rwas measured. The relevant data, all referring to completely mixed beds, are reported in Table 2. Figure 2 shows three of the four trends of emf versus xF, with a smooth curve drawn through the voidage data. In spite of some scatter, they always exhibit a minimum; although they start from different end points, the curves show how increasing the coarse/ fines size ratio increases the change in emmt,and reduces the value of+ at which the minimum occurs, in accordance with the behaviour reported by Yu and Standish [7]. Pressure drop plots at varymg composition, obtained from the binary mixture flutdization tests of this study, were generally similar to that shown in Fig. 1; only for GB335-GB240 mixture, having a d,/ dF ratio equal to 1.40, was no segregation tendency observed, and fluidization and defluidization curves were practically coincident. For each mixture tested, minimum fluidization velocities at increasing gas flow rate are plotted in terms of uM versus xF in Figs. 3, 4, 5 and 6. Results are compared with predictions obtained by the Carman-Kozeny equation [8] 180 3

sv

U, 9

=(ps-Pf)g(l-E,f)

(10)

in which __=-+-

1

XF

XP

a’ S”

dF

4

(11)

and usmg the experimental values of l,,,r, both for the binary particle system and for its single components. A comparison is also made with predictions of eqn. (9) by Cheung et al. [6]. The ability of both equations to provide reliable estimates of uM is evident. It should be emphasized, however, that eqn. (9) benefits from being fitted to the data at xF=O and xr= 1, through the use of the umf of both components as an input parameter. The whole set of experimental values of uM, at any xF, is then

262 TABLE

1. Experimental

GB483 GB335 GB240 GB173 GB153 “Glass ballotmi

properties

d,x 10"

d,

(m)

(m)

uld, (-)

483 335 240 173 153

497 344 246 177 158

0.43 0 45 0 47 0.49 0.56

0.424 0.442 0.438 0.432 0.432

L&fx lo2 (m/s)

R&r (-)

21 2 10 6 5.9 3.2 2.4

6.8 2.4 0.94 0.37 0.24

of binary mixtures

tested

l,r

d,& (-)

(-) xF=

2.01 2 79 1.40 2.19

GB483-GB240 GB483-GB173 GB335-GB240 GB335-GB153

x 10”

(GB), p.=2 530 kg/m3

TABLE 2. Packing properties Mixture

of mixture components”

0.20

0.40

0.60

0.80

0.402 0 388 0.431 0.402

0.405 0.372 0.428 0.405

0.405 0 383 0.421 0.409

0.420 0 405 0.421 0.427

0

02

04

06

08

1

XF

Fig. 3. MYcture mmlmum fluidization velocity vs. fines volume fraction for GB483-GB240 mixture. -, This study, eqns. (10) and (11); ---, Cheung et al [6], eqn. (9).

0

02

04

06

08

1

XF

Fig. 2. Voidage

at mimmum fluidlzation

vs. fines volume

fraction. collected and plotted in Fig. 7 versus those calculated by eqns. (10) and (11). The agreement is very good, with practically all data falling within a 15% approximation.

Discussion

Predicting the minimum fluidization velocity of mixtures of two particulate solids has so far been based on the extension to them of well-established relatlonships developed for the case of monodisperse beds of particles. To this purpose, variables such as particle mean diameter and density, which greatly influence values of u,~, are generally re-expressed

in some average form, such as eqns. (2) and (3), to account for the binary nature of the system. In a similar way, the dependence of bed voidage on parameters characterizing the mixture should be carefully analysed, as the sensitivity to voldage of the minimum fluidization velocity of a monosrzed bed 1s very high. Nevertheless, most correlations so far proposed for calculating the u,~ of binary mixtures are implicitly based on the assumption of constant voidage with varymg component sizes and composition. This is the case for all the correlations which, like those due to Goossens et al. [2], Thonglimp et al. [3] and Noda et al. [4] previously reviewed, are derived from the original Wen and Yu equation [ 11; in their general form, expressed by eqn. (4), any dependence of u,,,~ on E,~ is concealed, as this is incorporated in the numerlcal value of the parameters. On the contrary, as shown in Fig. 2 and confirmed also by authors such as Yu and Standish [7], the packing characteristics of a two-component bed seem

263 25

I

I

I

I

< E ” E 20 1

15

10

0

02

04

06

06

1

XF

Frg. 6 Mrxture mmimum fluidrzation velocity ratro VS. fines volume fractton for GB335-GB153 mtxture -, This study, eqns. (10) and (ll), ---, Cheung et al [6], eqn. (9).

5

0 0

02

04

06

08

1

XF

Frg. 4. Mrxture

minimum

flurdization

velocity

US. fines Thus study, Cheung et al. [6], eqn. (9).

volume fraction for GB483-GB173 mtxture. -, eqns. (10) and (ll),

---,

‘“I 0

GB463

- GBl73

20 expenmental

0

I

I

I

02

04

06

I

I

06

1

Frg. 7. Comparison values of Us.

behveen

experrmental

U,

, cm/s

and calculated

XF

Fig. 5. Mixture mimmum fluidrzatron velocrty vs. fines volume fractron for GB335-GB240 mixture. -, This study, eqns. (10) and (ll), ---, Cheung et al. [6], eqn. (9).

to be greatly mfluenced by the dp/dFratio and mixture composition, and any equatton aiming at realistic description of fluidization of a binary particulate system should take these dependences into account. On this basis, because it gives a physical repreof gas-solid interaction, the Carsentation man-Kozeny equation [S] seems to be a more suitable tool for the extension of fluidization theory to twocomponent beds, since it clearly states the role of mean particle diameter, solid density and bed voidage in determining u,f. Trends of UMversus mixture composition presented m Figs. 3 to 6, and the good agreement with experimental results for all conditions tested as shown

in Fig. 7, seem to demonstrate that eqns. (10) and (ll), together with proper assumptions of bed void fractions, can provide reliable estimates of minimum fluidization velocity, at least for well-mixed beds, well beyond those obtained by Chiba et al. [5]. In addition to their assumption of constant voidage, also using eqn. (8) for defining the average mixture size appears questtonable, as the generally accepted way of applying equations such as Carman-Kozeny’s to a bed of particles having a size distrtbution (namely a multicomponent mixture of equal-density solids) utilizes d,, as the smtable mean diameter definition [9]. The successful apphcation of eqn. (10) to the calculation of uM enables interpretatton of the rapid fall of minimum fluidization velocity of a given solid (as, for instance, in the case of the GB483-GB173 mixture, reported in Fig. 4) by adding to it a small amount of fine particles. As a matter of fact, the

264

voidage reduction accompanying the mixing of the two particulate species increases at high d,/d, ratios, giving rise to an increase of intestitial gas velocity and, thus, of the drag force acting on the particles which promotes fluidizatlon at a lower superficial gas velocity.

AP Re,i u UF,

UP

UFF

Conclusions

11mf

bed pressure drop, N/m2 Reynolds number at minimum tion = pfumfdlp superficial gas velocity, m/s mmlmum fluldlzation velocity of dized, packed component, m/s full fluidization velocity of a binary m/s minimum fluldlzatlon velocity m

fluidiza-

the fltnmtxture, general,

m/s

In a well-mixed bed of two solids, the void fraction depends strongly on the mean size ratio and volumetric fractions of its components, and its values can be significantly lower than for a monosized bed of particles. The mmlmum fluidizatlon velocity of a binary mutture of solids of equal density can be calculated by utilizing a classical result such as the Carman-Kozeny equation, if the voidage reduction IS correctly accounted for, and by utilizing the average mutture diameter defined as in eqn. (11). The considerable lowering of minimum fluidlzation velocity that the addition of a small amount of fines can promote in a bed of coarser particles can be explamed by the resulting voidage reduction, which causes a corresponding increase in interstitial gas velocity.

wF,

WP

xF,

xP

Pf

PS PF> Pp u

uld, List of symbols

A, B Ar d

ci

drn d

S”

iF7 g fNP

H

parameters in eqn. (4), Archimedes numbers =d3pr(ps - pJgl$, particle diameter, m mean particle diameter of a binary mixture, m particle diameter of fluidized, packed component, m median particle diameter, size at 50% of cumulative distribution, m volume to surface mean particle diameter, m fluidization column diameter, m number fraction of particles of fluidized, packed component, acceleration due to gravity, m/s2 bed height, m

minimum fluldlzatlon velocity of a completely mixed, segregated binary mucture, m/s weight fraction of the fluidlzed, packed component, volume fraction of the fluldized, packed component, voidage at mmlmum flutdlzatlon, fluid vlscoslty, kg/(m . s) mean particle density of a bmary mixture, kg/m3 fluid density, kg/m3 particle density in general, kg/m3 particle density of fluldized, packed component, kg/m3 distribution spread = (dgqs -d16%)/2, m relative distribution spread, -

References

C. Y. Wcn and Y. H. Yu, Chem. Eng Progr Symp Ser, 62 (1966) 100. W. R. A. Goossens, G. L. Dumont and G _I Spaepen, Chem Eng Progr. Symp Ser, 67 (1971) 38 V Thonghmp, N Hlquily and C Laguerle, Powder Technol, 39 (1984) 223 K. Noda, S. Uchlda, T Maklno and H Kamo, Powder Technol., 46 (1986) 149 S Chlba, T. Chlba, A. W Nlcnow and I-1 Kobayashl, Powder Technol, 22 (1979) 255. L Y. Cheung, A W. Nlenow and P. N Rowe, Cllefn Eng scz, 29 (1974) 1301. A. B Yu and N StandIsh, Powder Technol, 52 (1987) 233. J F. Davldson and D HarrIson, Flulduatron, Acadcmlc Press, London, 1971, p 34. D. Gcldart, Gas Flutdrzatlon Technology, Wiley, Chrchester, 1986, p. 20