Segregation of solid particles of two sizes in bubble columns

Powder

Technology,

68 (lW1)

Segregation Toshitatsu Deparrmenr

(Received

of solid particles

Matsumoto”, of Chemical

and Shigeharu Department

Nobuyuki

Engbleering,

Kagoshima

of two sizes in bubble

Hidaka, Universiry,

Hiroshi Kagoshima

columns

Takenouchi 890 (Japan)

Morooka

of Chemical

September

131

131-136

Science

and

Technology,

Kyushu

Universiry

Fukuoka

812 (Japan)

24, 1990; in revised form May 22, 1991)

Abstract

Binary mixtures of solid particles were fluidized by a two-phase flow of gas and liquid. The changes in holdup of the two components with axial position in the column were determined. The experiments were conducted with three combinations of sieved glass beads (118 and 243 pm; 118 and 465 pm; and 243 and 465 pm diameter) in vertical columns of 7 cm diameter X 4.85 m height and 15 cm diameter X 2.7 m height under batch operation with respect to the solid phase. A sedimentation-dispersion model developed on the basis of the experiments

gives a semi-empirical of the column.

description of the axial distributions

Introduction When solid particles of different sizes and densities are fluidized, segregation of the respective components

occurs in the bed. The segregation pattern for liquid-solid systems has been studied phenomenologically by a number of authors [l-3]. Al-Dibouni and Garside [2], for instance, reported that binary mixtures with a particle diameter ratio of 2.0 were uniform throughout the bed while those with a ratio greater than about 2.2 were classified. Moritomi and Chiba [4] studied the fundamental mechanism of segregation in a liquid-solid fluidized bed consisting of hollow char particles and glass beads, the latter being heavier and smaller than the former. They predicted patterns of stratified layers from the balance between drag and buoyant forces, assuming perfect mixing in each segregation layer and no mixing between adjacent layers. It was clearly shown that the segregation of particles is affected by the properties of components in the mixture as well as the properties of the particles. In a gas-liquid-solid fluidization column with a binary mixture of solid particles, the axial change in solid holdup becomes very complicated. Previous works indicate that the three-phase fluidized bed is roughly divided into two regions: the lower part with a dense and nearly constant solid holdup and the upper part *Author

to whom correspondence

0032-5910/91/$3.50

should be addressed.

of segregation and solid holdup over the whole range

with a dilute solid holdup that decreases with increasing height. The latter part is formed by ascending gas bubbles which transport solids from the dense region to the freeboard. Several authors have described the axial distribution of solid holdup assuming gravitational settling of particles relative to liquid flow and turbulent dispersion [5-71, as summarized by Jean et al. [S]. Most of their models, however, cover either the dense region or the lean region, even though these regions are interrelated. It is evident that both concentration and composition of particles vary continuously according to axial position. Fan et al. [9] conducted experiments in a 10.2 cmdiameter column with coarse glass beads of 3 and 4 mm and of 3 and 6 mm in diameter. They divided the column into three discrete regions, assuming that the concentration of small and large particles was constant in the bottom and top regions and varied with height in the middle region. Murray and Fan [lo] studied the holdup distribution of each solid in binary mixtures of 97 and 163 pm glass beads in a slurry bubble column. Their model was valid only in the case of very dilute solid holdups. On the other hand, the model developed by Matsumoto el al. [ll] is applicable to the whole length of a column, including the dense and lean regions; however, the situations investigated are restricted to cases where particles of the same size, shape and density are treated.

0 1991 -

Elsevier Sequoia, Lausanne

132

In the present study, binary mixtures of glass beads are fluidized by the flow of gas and liquid in a vertical column, and the axial change in solid holdup of each component is thoroughly investigated. An empirical model that can be applied over the whole column is derived on the basis of a one-dimensional diffusion model. The slip velocity between particles and liquid velocities and axial dispersion coefficient involved in the model are experimentally evaluated.

Experimental

Figure 1 shows a schematic diagram of the experimental apparatus. The fluidization column is made of acrylic resin pipe with an i.d. of 7 cm and a height of 4.85 m, and is vertical. The gas distributor is a spiral copper tube of 6 mm o.d., with six 2-mm holes pointing downwards, and is installed horizontally at a height of 0.105 m from the bottom. The liquid distributor is a packed bed of 10 mm-diameter glass spheres, a bronze

Fig. 1. Experimental apparatus (7-cm diameter column). 1 compressor, 2 oil-mist separator, 3 orifice meter, 4 gas distributor, 5 bronze net, 6 pump, 7 reservoir, 8 shutter plate, 9 shutter case, 10 solids withdrawal tap, 11 wire and pulley, 12 device for pulling wire.

net of 145 mesh being placed at the upper face of the packed layer. The shutter plates, made of stainless steel 3 mm thick, are installed horizontally at 0.2-m intervals and are interconnected with wire rope. The fluidization column is also made of a pipe 15 cm in diameter x 2.7 m in height. The other features are fundamentally the same as those of the 7-cm diameter column. All the experiments were conducted batchwise with respect to the solid particles. At the top of the column, a divergent section of bronze net was used to prevent entrainment of particles from the column. Air and tap water at room temperature were used as the gas and liquid phases, respectively. Three kinds of binary mixtures of sieved glass beads (118 and 243 pm; 118 and 465 pm; and 243 and 465 pm in diameter; density= 2 500 kg m-“) were used for the solid phase. The size distributions are shown in Fig. 2. After continuous running of N 1 h to reach steady state, local values of solid holdup were measured. This was done by a shutter method. Ten shutter plates were pulled closed by a wire, and the feeds of gas and liquid were stopped simultaneously. By this action, the column was partitioned into 11 parts almost instantaneously. The solid particles settling onto each shutter plate were withdrawn through a tap after measuring the volume of slurry in each section, and were separated by sieving after drying. The local values of solid holdup of each component in the slurry phase, & and c#+,~,were determined by weighing the particles. The solid holdup is defined as the volume fraction of either the smaller or larger particles suspended in the slurry. The mean gas holdup is calculated from the total volume of gas in each section. The axial position of the shutter plates was changed to measure the solid holdup over the whole column.

Fig. 2. Size distribution

of glass beads used in experiments.

133

Results Typical results of solid holdup in the 7-cm diameter column are plotted as a function of axial distance for the binary mixture of 243 and 465 pm in Fig. 3 and for 118 and 243 pm in Fig. 4. Diagrams (a) and (b) indicate the effect of the gas holdup (or the gas velocity) while the liquid velocity and the mass of the solids are mostly the same, and diagrams (b) and (c) show the influence of the mass of solids in the column while the gas and liquid velocities are nearly unchanged. As can be seen in Figs. 3 and 4, the holdup of the larger particles decreases simply with an increase in the axial position, but the axial holdup distribution of the smaller particles varies widely with the operating conditions, such as the combination of particles, the solids mass in the column, the velocities of gas and liquid and the gas holdup. There is a maximum value of solid holdup for the smaller particles in the case of Figs. 3(a) and 3(b). The results for the binary mixture of 118 and 465 wrn show the same tendencies as the other mixtures.

, 0.1

L----

(b)

I

I

t

Cc)

Eg,o.213 Ug=O.l52mls II =O.OlOm/s

n‘ P

0

I’m:

t 0

1.

13

9

&:3.37kg

52kg

1

I

2

I

2

3

[ml

Fig. 4. Experimental and calculated results of axial changes solid holdup for the mixture of 11% and 243.pm diameter 7-cm diameter column.

0.011

Fig. 3. Experimental and calculated results of axial changes solid holdup for the mixture of 243- and 465pm diameter 7-cm diameter column.

in in

0

I 2

I 1 L

in in

I

[ml

Fig. 5. Experimental and calculated results solid holdup in 15cm diameter column.

of axial

changes

in

134

Figure 5 shows the solid holdup in the 15cm diameter column for the binary mixture of 243 and 465 pm and that of 118 and 243 pm. The axial distribution of &,,_ in the E-cm column is flatter than in the 7-cm column.

of U,=O.O1-0.3 m s-l, U,=O-O.15 m s-l, 4++ 4,,=0-0.3 and d,= 661 300 pm. In the case of air-water systems (4ps+4pL=O), eqn. (6) gives a good description of gas holdup in columns of D, < 1.07 m

P11. Discussion For a binary mixture of solid particles in a gas-liquid-solid system, the axial change in the solid holdup of each component is analyzed with a onedimensional dispersion model. At steady state and in batch operation with respect to solids, the basic equations in terms of the axial coordinate z are: 4psups - E,, %

4pspL-&

=0

d4PL =o z

(2)

where 4+ and 4+ are the particle holdups, E,, and EPs are the axial dispersion coefficients, and the subscripts S and L refer to small and large particles respectively. The time-averaged particle velocities with respect to fixed coordinates are taken as: U PS

=u,--u,s

(3)

U pL=uI-utL

(4)

where u, is a time-averaged velocity of liquid related to the superficial liquid velocity by: UI= W(I

- c&l -

4,s- 4&l

and

is

(3

where U, is the superficial liquid velocity, Ed is the volume fraction of gas, and u,~ and u,,_ are slip velocities between the particles and liquid velocities. In a case of quiescent fluid, these correspond to terminal settling velocities. If the particle velocity is negative, the particles tend to sediment and the holdup of the particles decreases with an increase in the axial position. In binary systems, direct determinations of the slip velocities and the axial dispersion coefficients are rather difficult. Therefore, the following assumptions are made, referring to the results for single-component systems

UllGas holdup The local gas holdup in a column for a gas-liquidsolid system with binary particles is weakly dependent on the particle size and is calculated from: Ep= v&J1 -R)/{0.29[

+ l.W,(l

-R)}

1+

2.5(4ps + 4,,)"~"'] (6)

where R = +,/[(l - @J,]. Equation (6) was originally developed for monocomponent systems in the range

Axial dispersion coeficient of solid particles The axial dispersion coefficient of liquid air-water system is expressed by: E,=0.3[1 x

+17.3(e,UJ3”][(1

for

the

-R)

(gDT3)~J2/(1 - Q>

(7)

This equation can be used over a wide range of variables: Ug=0.01-0.3 m s-‘, U, [email protected] m SK’, and D,=O.O7-1.07 m. The verification of eqn. (7) against experimental data has been demonstrated elsewhere [ll, 121. The axial dispersion of monocomponent iparticles, E,,, is directly related to E, as reported by Matsumoto et al. [ll]. Their equation is complicated and can be simplified as: E,,,/E,

= 1 - 0.01(Re,*)2’3

(i = S and L)

(8)

for Re,* = d,Jc,(l - R)(gD,/2)]“*/u< 500. Since the difference between EPso and EpLO, which are values for single component systems calculated from eqns. (7) and (S), is not large, the axial dispersion coefficient of solids for the binary system of S- and Lparticles is expressed by an average value of E,,, and E PLO: 4s

=EpL=

( 4ps:;pJEpso+

( 4ps$L4P,)EPLo

Slip velocity The slip velocity of monocomponent i-particles gas-liquid-solid systems is expressed as:

(9)

in

l& =fiv,i

(IO)

f;=((1-4pi)ni-'

(11)

where5 is the void function and V, the terminal velocity of a single i-particle. According to Matsumoto et al. [ll], the value of ni is correlated by the following equation: (ni - 2)/(5 - ni) = 6.0Gaie1”

(i = S and L)

(12)

where Ga,=d,,‘g(p,/p,l)/ti. Equation (12) gives a slightly smaller value than that predicted by Garside and Al-Dibouni [13] for liquid-solid systems and is in better agreement with the experimental data for threephase systems [ll]. The value of V, of an isolated particle falling in a liquid is expressed by Stokes’, Allen’s, and Newton’s laws. To simplify the analysis, the following equation

135

is adopted of -2%.

VJ, _ v

for the whole region,

with a maximum

Ga,

error

(13)

[18“‘“+ (Ga,/3.0)2’5]“4

When monocomponent i-particles (i=S and L) fall through a three-phase flow, eqn. (13) should be corrected as:

4iq.G -=-v

hi&

_

fiGa;& [l@”

Y

+

(Gai~/3.0)2’5]5’4

(14)

(b)

7ii

-

where 6.5[~,(1 -R)]“2Ga,“3

’ = 1+

1+ {[Q( 1 -R)]“2Gai”3/15}2 I

3nGai_Z,3 (15)

These equations were obtained experimentally by Matsumoto et al. [ll]. All the phenomenological constants appearing in eqns. (14) and (15) can be unequivocally calculated from the preceding equations. For binary systems of S- and L-particles in threephase flow, the slip velocity of each component is affected by &_ as well as &. Thus f; of eqn. (10) should be a function of c#J,,~and &L and is determined as follows: For S-particles: fs=(l-~pS-~pL)nS-‘(l--~L)nL-“S

OO-

3 2 [ml

Fig. 6. Changes in gas and solid cm diameter column.

holdup

and slip velocities

in 7-

(16)

For L-particles: fL=(l-~pS-~pL~L-‘(l-~pS)nS-“L

(17)

where (1 - (Pp,J’--nS and (1 - &)nS-“’ are introduced to express the interaction between S- and L-particles, and both are unity in the case of monocomponent systems. The values of n, and n,_ in eqns. (16) and (17) are given by eqn. (12) for S- and L-particles. The values of u,~ and utL for binary component systems are calculated from eqn. (10) using eqns. (14)-(17). From the set of eqns. (l)-(10) and (12)-(17), &,,s and &,,_ at a given z value can be calculated as functions of U,, U,. DT, and the properties of the liquid and solids. The computation was carried out here by the Runge-Kutta-Gill method. A few other expressions for fi were tried, and the axial changes in & and &,,_ were calculated and compared with the data. Equations (16) and (17) g ave the best results under the present experimental conditions. Axial changes in the solid holdup are shown in Figs. 6(a) and 7(a). Figure 6(a) shows the case in which c#+ has a maximum, and Fig. 7(a) shows the case in which c#J,~increases with an increase in the axial height. The lines in Figs. 6 and 7 as well as Figs. 3, 4 and 5 are calculated from the present model and are in agreement with the data. Figure 6(b) shows that the slip velocity of the S-component in the bed, z+_, increases gradually

0

2

1

z

3

[ml

Fig. 7. Changes in gas and solid holdup cm diameter column.

and slip velocities

in 7-

with increasing axial height And then becomes larger than u,. This is primarily caused by the axial change in the solid holdup which strongly influences fs and f,_. Thus, d&&iz takes positive values at the axial position lower than about 2 m, and then becomes negative because of c#+u~~ 2 m. In Fig. 7(b), on the other hand, uks does not cross the liquid velocity at any axial position. As can be seen in Figs. 6(a) and 7(a), the gas holdup calculated from eqn. (6) also changes axially.

136

The present experiment was carried out using tall columns of 7 and 15 cm in diameter. If the column diameter increases, the dispersion of particles increases in accordance with eqns. (7)-(9). The axial distribution of solid holdup will be less notable due to intermixing, which becomes dominant compared with sedimentation. In larger columns, therefore, the particle segregation pattern is less dependent on ups and uPL, which are very sensitive to the experimental conditions, and can be simulated more easily with the model proposed.

time-averaged linear velocity of i-particles with respect to fixed coordinate, m s-’ slip velocity of i-particles between u,- and u,, m s-’ terminal velocity of single i-particle, m s-’ mass of solid particles in column, kg axial distance from gas distributor, m

upi

uti ?)ti

W

z

Greek letters

gas holdup in column correction factor defined by eqn. (15) kinematic viscosity of liquid, m2 SK’ density of liquid, kg mW3 density of solid particles, kg m-3 time-averaged holdup of i-particles defined by volume fraction in slurry

%

& V m

Conclusions

PP

In a gas-liquid-solid fluidized bed containing a binary mixture of solid particles of two sizes, the axial distribution in solid holdup of each component is well expressed by eqns. (l)-(4). The parameters used in the model are correlated by eqns. (6)-(9) and (12)-(17) as functions of particle size, mass of particles in the column, and liquid and gas velocities.

&

g Ga, ni R Re,*

diameter of column, m diameter of i-particle, m axial dispersion coefficient of liquid, m* s-l axial dispersion coefficient of i-particles, defined by us&@&,&), where I& is the fluctuation linear velocity of i-particles with respect to the fixed coordinate, & is the fluctuation holdup from c$* and Z&C& is the time-averaged value of Z&C&, m2 SC’ gravitational acceleration, m SC’ modified Galilei number of i-particles defined by d,3g(pp/p, - 1)/y* exponent in eqn. (11) dimensionless parameter defined by- E-U,/ m-

[Cl- %)Ugl

Subsctipts 0 monocomponent i S or L

S L

system

small particles large particles

References

List of symbols

DT dpi 4

&

-

Reynolds number defined by d,{e,( 1 - R)(gD,l 2))‘“lY

superficial velocity of gas, m s-r superficial velocity of liquid, m s-’ time-averaged linear velocity of liquid with respect to fixed coordinate, m s-’

S. C. Kennedy and R. H. Bretton, AIChE J., 12 (1966) 24. M. R. Al-Dibouni and J. Garside, Trans. Inst. Chem. Eng., 57 (1979)

94.

A. K. M. Jumma and J. F. Richardson, (1983)

Chem.

Eng. Sci., 38

955.

H. Moritomi

and T. Chiba, in N. P. Cheremisinoff (ed.), Mechanics, Vol. 6, Gulf Publishing, Houston, 1987, p. 477. 5 Y. Kato, A. Nishiwaki, T. Fukuda and S. Tanaka, .7. Chem. Encyclopedia

of Fluid

Eng. Jpn., 18 (1972)

308.

6 S. Morooka, T. Mizoguchi, T. Kago, Y. Kato and N. Hidaka, J. Chem. Eng. Jpn., 19 (1986) 507. 7 D. N. Smith and J. A. Ruether, Chem. Eng. Sci., 40 (1985) 741. 8 R. H. Jean, W.-T. Tang and L.-S. Fan, AIChE J., 35 (1989) 662.

9 L.-S. Fan, T. Yamashita and R. H. Jean, Chem. Eng. Sci., 42 (1987) 17. 10 P. Murray and L.-S. Fan, Ind. Eng. Chem. Rex, 28 (1989) 1697. 11 T. Matsumoto, N. Hidaka and S. Morooka, AIChE J., 35 (1989)

1701.

12 T. Matsumoto, N. Hidaka, H. Kamimura, M. Tsuchiya, T. Shimizu and S. Morooka, J. Chem. Eng. Jpn., 21 (1988) 256. 13 J. Garside and M. R. AI-Dibouni, Ind. Eng. Proc. Des. Dev., 16 (1977) 206.