Expansion of solid—liquid spouted beds

The Chemical Engineering Journal, 10 (1975) 219-223 @ Elsevier Sequoia S.A., Lausanne. Printed in the Netherlands

219

Expansion of Solid-Liquid Spouted Beds ANDRZEJ KMIEb Institute of Chemical Engineering and Heating Equipment, 50-370 Wroeiizw, Wybrzeie Wyspiariskiego 27 (Poland)

Technical University of WroCtaw,

(Received 25 June 1975)

Abstract The results of a study of solid-liquid spouted bed expansion, using an 8.8 cm i.d. column with a 30”, 60” or 180” conical base, are reported. Two regions of overall bed voidage have been found: a region with bed voidages up to 0.85 and a region with bed voidages over 0.85. In the region of bed voidages up to 0.85, the overall bed voidage is found to be dependent on the ratio of inertial to gravitationalforces and the geometrical parameters of the bed. In the region of bed voidages over 0.85, the bed voidage is found to be dependent on the superficial liquid velocity and the geometrical parameters of the bed. the mechanics of spouted beds have attracted the interest of many researchers, relatively few papers have been published on bed expansion. Kolar l studied the expansion of solid-liquid fluidized beds in tapered columns with base angles of lo”, 20” and 30”. He found that the average bed voidage could be correlated with the superficial liquid velocity by equations similar to those of Richardson and Zaki*: Although

E = 1 .O~~(U/U~)~.*~~

Richardsons, however, pointed out that the expansion of non-homogeneous solid-liquid fluidized beds was no longer linear; it diverged from the theoretical straight line at voidages between 0.45 and. 0.95. In this paper some experimental results on the expansion of solid-liquid spouted beds are reported.

EXPERIMENTAL

The apparatus is shown in Fig. 1. The column, shown in detail in Fig. 2, consisted of a glass tube, 8.8 cm in internal diameter and 50 cm high, on a 30”, 60” or 180’ conical base with a 1.5 cm inlet nozzle. The materials investigated consisted of glass beads, two fractions of silica gel, a fraction of ion-exchange

-I

(1)

for a 10” base angle and E = 1 .O~(U/U~)~.~ **

(2)

for a 20” base angle. The exponent has slightly different values for different cone angles. Koloini and Farkas3 also found that for tapered columns the superficial liquid velocity plotted against average bed voidage in double logarithmic coordinates was linear, and that the slope depended on the column and particle geometry. Muchlenow and Gorsztejn4 successfully correlated the average bed voidage of solid-gas spouted beds by the equation E = 2.17 (E)“,, ,I

(2)-‘.’ \-I

(tan $y)-“.6

(3)

l-7

$1 Fig. 1. Schematic diagram of the apparatus: 1, pressure tank; 2, rotameters; 3, fluidizing column; 4, scale; 5, tank; 6, valve.

220

A. KMIEk RESULTS

Experimental data for the average spouted bed voidage are plotted against the superficial liquid velocity in Figs. 3-5 for cone angles of 30°, 60’ and 180” respectively. These figures show that there are two distinct regions of bed voidage: the region of low voidages up to 0.85 and the region of high voidages above 0.85. It is interesting to note that at high voidages the data for the various materials lie on one line. The slopes of the lines in these two regions differ markedly, that for voidages above 0.85 having the higher value. In the region of low voidages the lines for different kinds of materials are shifted upwards as the minimum

Fig. 2. Cross-sectional view of the test column with a 60” conical base: 1, inlet orifice; 2, conical base; 3, cylindrical

particles and a fraction of sand. The physical properties are summarized in Table 1. The solid density was determined pycnometrically with water. The particle diameter dp was calculated from the geometrical average of the diameters of adjacent screens. The particle density was calculated from measurements of the weight and geometrical parameters of several chosen spheres. The liquid investigated was water.

Fig. 3. Dependence of the superficial liquid velocity on the overall bed voidage for y = 30’ and H,J = 0.115 m. ooo glass (Ho = 0.06 m); AA~silica gel, dp = 3.32 x 10-s m; nob silica gel, dp = 2.24 x 10-s m; n oe sand; e e B ion-exchange particles.

TABLE 1 Properties of the particles Material

Particle dhmeter (x 10m3 m)

Particle density PP &g mm3)

Terminal velocity Utt (m SW1 )

Minimum spouting velocity ums (her Ho = 0.074 m), ~=60”(ms-*)

6.17

2451

0.437

4.4-2.5 2.5-2.0

3.32 2.24

1293 1293

0.134 0.0982

0.03 (Ho = 0.055) 0.0164 0.00959

1.2-1.02 1.02-0.75

1.11 0.875

1264 2646

0.0483 0.129

0.0114 0.00434

Fraction (x low3 m)

Glass Silicagel Ion-exchange particles Sand

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EXPANSION OF SPOUTED BEDS

and applying a dimensionless analysis the following correlation, similar to that of Muchlenow and Gorsztejn4, was developed: E = czRenArb(HO/~P)d(dc/dp)Cye

(5)

For voidages E > 0.85 a simple form is proposed: E = CjU~(kf&)by=

(6)

The following correlations squares fits:

were obtained

from least

for E < 0.85 E = 0.838

~~0.182~~-0.0866(H,/&)-0.243y-0.067 (7)

Fig. 4. Dependence of the superficial liquid velocity on the overall bed voidage for y = 60’ and Ho = 0.074 m; labelling as for Fig. 3.

and for E > 0.85 (8) The

spouting velocity increases, illustrating the need for higher liquid velocities in order to obtain the same average bed voidage. Assuming that the average bed voidage is a function such as E = c,uad~d$H$rePf/.@‘@p

- Pf)’

(4)

mean absolute deviation between experimental and calculated values was 7% for eqn. (7) and 1.7% for eqn. (8); maximum deviations did not exceed 18% and 6% respectively. The dimensionless factors varied in the following ranges: 3.5 < Re < 350 0.19
2.1 x lo3 < Ar < 2.6 x lo6

< 1.55

0.523 < y < 3.14

0.023 < u < 0.095 (m s-l )

DISCUSSION

It is interesting to note that the magnitude of the exponent of Re in eqn. (7) is approximately twice the value of the exponent of Ar. Thus eqn. (7) can be transformed to the form

(9) where Re2_ X

inertial forces

- gravitational

forces

=--=112 Pf gdp PP - pf Fig. 5. Dependence of the superficial liquid velocity on overall bed porosity for 7 = 180° and Ho = 0.034 m (glass, Ho = 0.038 m); labelling as for Fig. 3.

Fr -= pf

PP - Pf

Frm

Hence eqn. (9) becomes E = cs Frf,,(Ho/dc)byc

(10)

222

A. KMIEti

forces represent the momentum transfer rate and the fluid motion while the gravitational forces represent the counter-factor for bed expansion. Viscous forces do not appear to play any part in the expansion. This, however surprising, has some support in the MathurGishler equation’ for minimum spouting velocity, which does not include fluid viscosity. Furthermore, the Mathur-Gishler equation

0.4

0.5

0.6

0,6

0.7

E theor.

0.9

Fig. 6. Comparison of experimental overall bed voidages with those from eqn. (11): o glass; A silica gel, dp = 3.32 x 10-J m; o silica gel, dp = 2.24 x 1O-3 m; 0 sand; 0 ionexchange particles; .y=180°;Oy=600;oy=300.

and a least squares fit gave E = 0.878 F&.091 (~o/~,)-0.253y-0.072

(11)

The mean absolute deviation between experimental and calculated values was 7.4% and the maximum deviation was 18%. A comparison of the experimental and calculated values of the voidages is shown in Fig. 6. A modified Froude number Frm was also developed by Balakrishnan and Pei6. They pointed out that Frm has a considerable significance for heat transfer between particles and fluid in packed beds. In order to prove the validity of the general character of eqn. (11) it is useful to show that the equation of Richardson and Zaki2can be transformed to this form for the region where inertial forces play a substantial role. For the Newton’s region (Ar > 105) Ar=$

Rep

and the Richardson-Zaki

(12) equation

U/U~ =E2e4 becomes Re/(3Ar)*12 = E2”

(13)

can be transformed Frms

to the similar form

=u;fis pf

-=2(3(3(;~'" -Pf

(16)

@PPP

Equation (16) states that at minimum spouting velocity the inertial force of the fluid is equal to the gravitational force on a particle with a coefficient which has a constant value for a given geometrical system. Moreover, the Mathur-Gishler equation can be expressed as a correlation:

Rems

=

ArO.5

(2z(2r’3r’5

(17)

The role of the rate of momentum transfer on fluid and particle mechanics in spouted beds has been discussed by Velzen et al. 8 They pointed out that the average gas velocity in the spout is a function of momentum transfer rate but does not depend on the particle properties. The data presented here show that the expansion of spouted beds at high voidages does not depend on particle properties but on the superficial liquid velocity. For constant liquid density and column diameter the momentum transfer rate can be introduced instead of the liquid velocity. Thus it appears that the expansion of spouted beds at high voidages is controlled by the momentum transfer rate and does not depend on particle properties, as was found earlier for the case of average spout velocity.

giving E = (3)’ /‘r*s(Rea /Ar)r /4.s =

&l/4.8Frfii4.8

CONCLUSIONS

(14)

Equation (11) shows that the expansion of spouted bedsat voidages up to 0.85 is determined by inertial and gravitational forces on the one hand and geometrical factors (Ho, d,, y) on the other. The inertial

The expansion of solid-liquid spouted beds can be described by the following correlations: for E < 0.85

EXPANSION OF SPOUTED BEDS

and for E > 0.85 /j’ = 1 ~l()2u0.0774(~o/&)-0.105y-o.047

Inertial and gravitational forces play an important part in expansion, but viscous forces do not appear to have any influence.

ACKNOWLEDGMENT

223

Subscripts column C f fluid i inlet orifice modified m minimum for spouting ms particle P t terminal of a single particle terminal of a particle in a fluidized bed ti

The author is grateful to the Polish Academy of Sciences for financial assistance. NOMENCLATURE

Ar d E Fr Frm LO

Re U Y P P

gd;(Pp - ~&hfz diameter, m voidage fraction fi2/&, (u2/&) @f/Co, - pf)) acceleration due to gravity, m sm2 bed depth, m 4&~f superficial liquid velocity, m s-l an angle of conical base, rad liquid viscosity, kg m-l s-r density, kg mm3

REFERENCES V. Kolar, Collect. Czech. Chem. Commun., 28 (1963) 1224. J. F. Richardson and W. N. Zaki, Trans. Inst. Chem. Eng., 32 (1954) 3.5. T. Koloiniand E. J. Farkas, Can. J. Chem. Eng., 51 (1973) 499. J. P. Muchlenow and A. E. Gorsztejn, Chim. Prom., Moscow, 6 (1965) 443.

J. F. Richardson, in J. F. Davidson and D. Harrison (eds.), Academic Press, London, 1971. Chap. 2. A. R. Balakrishnan and D. C.-T. Pei, Iid. Eni. Chem. ProCessDes. Dev., 13 (1974) 441. K. B. Mathur and P. E. Gishler, A.I.Ch.E. J., I (1955) 157. D. V. Velzen, H. J. Flamm and L. Langenkamp, Can. J. Chem. Eng., 52 (1974) 145. Fluidization,