The Chemical Enginee?-ing Journal, 51 (1993) 45-52 45

Expansion of spouted beds in conical contactors

M. J. San Jose, M. Olazar, A. T. Aguayo, J. M. Arandes and J. Bilbao Departamento de Ingenkr.?.~ Q&mica, Universidad de1 Pati Vasco, Apartado 644, 48080 Bilbao [Spain)

(Received February 25, 1992; in final form May 25, 1992)

Abstract

The expansion of conical spouted beds has been studied on a wide experimental base (using contactors of different geometries and solids of different diameters and sphericities). The correlation obtained for calculating the global voidage from the operation conditions is of a more general application than those previously proposed in the literature, which are generally centred on the study of voidage in the spout. The global incipient voidages are delimited for both stable regimes corresponding to two voidage ranges: spouting and jet spouting. While the correlation for calculation of expansion can be applied for the calculation of global minimum jet spouting voidage, a correlation is proposed for the calculation of the global minimum spouting voidage. This equation is applicable in a wide range of operation conditions.

1. Introduction

The interest in the use of the spouted bed of exclusively conical geometry lies in its capacity for handling solids that are diihcult to treat, i.e. solids that are adherent and/or with a particle size dis- tribution, because vigorous gas-solid contact is attained [l-3]. The expansion of the spouted bed leads to a different regime, of jet spouting, with a peculiar hydrodynamic behaviour [ 4 1. This gas-solid regime, which is even more vigorous, combines the advantages of the cyclic movement of the particles, characteristic of the spouted bed, with a high gas velocity, within the velocity range of innovative design reactors [ 5-81.

The study of the expansion is of special interest for the design of spouted beds and of jet spouted beds, in conical contactors, because flexibility of operation is one of the main qualities of both regimes and their application limit will lie precisely in the voidage and consequently in the gas flow rate. The minimum bed voidage under conditions of stable operation is a basic parameter for the calculation of the contactor minimum volume necessary for treating a given amount of solid, and in general to design the operation or process to be carried out.

For the expansion of cylindrical spouted beds, the fulfilment of the correlations proposed by Kmiec [ 9, lo], for liquid-solid and gas-solid contact, is much discussed in the literature. In these studies, the expansion of spouted beds was compared with

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the phenomenon of jet penetration in flmdized beds by using the empirical equation of Merry [ 111 that was established for this phenomenon. Thus, for gas-solid contact

for e-CO.85

E= 0.798(F&,) 004!3(&')-"~070($j-o~'20~-0.022 (2) .

for ~>0.85

The existence of these two equations is, according to Damronglerd et al. [ 121, due to a change in the mechanism of momentum transfer for voidage values between 0.8 and 0.85. In order to prove this, Kmiec [ 9 ] , by fitting his data to the modified Leva equation, obtained the following correlations:

for E O.85

For the expansion of conical beds, there are few references in the literature and they have been contrasted on the basis of a very limited experimental

0 1993 - Elsevier Sequoia. All rights reserved

46 M. J. San Jo& et al. / Expansion of spouted beds in conical co-ntactcn-s

base. Mukhlenov and Gorshtein [ 13 ] proposed

Later, Markowski and Kaminski [ 141 correlated their experimental data to an equation similar to that of Kmiec [9]:

(6)

where the ranges of the dimensionless numbers are ~x~O-~~F~/F,

M. J. San Jo& et al. / Expansion of spouted beds in conical cmtactors 47

TABLE 1. Properties of the solids used

Material

Glass spheres

Beans Rice Chickpeas Peas Lentils Ceramics Extruded polystyrene

d, PS (mm) (kg m-Y

1 2420 2 2420 3 2420 4 2420 6 2420 8 2420 9.6 1140 3 1250 9.2 1130 6.8 1110 4.4 1190 6.1 3520 3.5 960

4

1 1 1 1 1 1 0.65 0.60 0.90 0.70 0.40 0.90 0.70

CO

0.322 0.328 0.345 0.355 0.361 0.378 0.405 0.449 0.412 0.446 0.490 0.501 0.395

Geldart classification

B D D D D D D D D D D D D

The pressure and velocity readings are carried out using four probes whose radial and longitudinal positions can be established at will inside the con- tactor by means of a displacement device controlled with a computer, which establishes the coordinates of the point to be measured by each probe following a given sequence. The displacement device, outlined in the upper part of Pig. 1, consists of three step- by-step motors (MX, MY and MZ) which by means of mechanical thongs displace the probe runner in the 5, y, and z coordinates. The probes are Prandtl tubes that consist of concentric tubes whose external diameters are 0.004 and 0.0016 m. The outer tube has four inlet orifices of 0.002 m diameter situated at 0.01 m from its end. The signals of total pressure taken by the internal tubes of the four probes go to a four-way valve and those of static pressure taken by the external tubes to another four-way valve. Prom here they go to a differential pressure meter, where the difference between the two pres- sures measured (total and static, or two static) is shown. The output signal of the differential pressure meters, O-20 mA, goes to a SIPAR DR20 indica- tor-regulator, which gives the pressure differences in a O-100 range. The absolute error range for the dynamic pressure measurement is below 0.1 Pa and that for the static pressure measurement below 1 Pa. The Tandon 386/20 computer is provided with a PC-Lab-718 data acquisition card with PCLS-701 software that permits us to obtain the fluid interstitial velocity in a given position and continuous curves (80 measures per second) of total pressure drop VS. velocity. The total pressure drop is determined from the static pressure difference between the inlet and the exit of the bed by taking into account the correction proposed by Mathur and Epstein [24] to eliminate the grid pressure drop.

The experimental measurement of bed voidage has been carried out by determining the upper level of the expanded bed by means of a photographic technique and by visual observation.

3. Expansion

The states of incipient spouting and jet spouting have been determined in detail from the total bed pressure drop vs. air velocity curves. In Fig. 3, a general outline of these curves is shown and in Pig. 4 the different states in the expansion of a conical spouted bed have been sketched. After the stable regime of spouting (Pig. 4(a)), on increasing the velocity, both annular and spout zones characteristic of classical spouting become progressively confused (transition zone in Pig. 3) and the particle movement

600

400

Incipient 0 Increasing u A Decreasing u

OY 8 I 1 I / L 0 4 6 12 16 20

U(m/s)

Fig. 3. Pressure drop evolution with velocity for the different regimes.

48 M. J. San Jo& et al. / Expansion of spouted beds in conical contactcn-s

Fig. 4. Particle state in the contactor for the different regimes.

outlined in Fig. 4(b) is obtained. The transition evolves until the spout and annular zones are no longer differentiated and the bed voidage is uniform, a new situation that corresponds to incipient jet spouting (Fig. 4(c)). This regime stays stable at higher velocities, with a constant value of pressure drop in a velocity range and then it begins to decrease gradually.

The fitting of our experimental data of voidage obtained in the expansion corresponding to the whole range (from fixed bed to jet spouted bed) to eqns. (5) and (6) is, in general, awkward. Equation (5) gives values of voidage smaller than the ex- perimental values and eqn. (6) on the contrary, gives higher values. The application of both leads to standard deviations greater than 50%. An ex- ception should be made about the application of eqn. (6) for contactor angles of 36 and 39 (Mar- kowski and Kaminski [ 141 proposed eqn. (6) on the basis of an experimental study using an angle of 37) and for voidages higher than 85%, for which it gives results that agree with our experimental data. In Fig. 5, the validity of eqn. (6) is shown for 36 and 39 cone angles.

In view of the fact that the equations in the literature have been proved not to be valid for our experimental data, another equation has been pro- posed taking into account the same dimensionless moduli as Kmiec [9], eqns. (3) and (4), with the contactor angle instead of the angle of the conical base. In this case, the equation obtained by non- linear regression fitting of the experimental data is (with a square regression coefficient ti of 0.90 and maximum standard deviation of 12%)

(7)

It is noteworthy that, when Db/Do (ratio of the In the curve in Fig. 6, the positions corresponding upper diameter of the stagnated bed to the contactor to the beginning of the spouting and jet spouting inlet diameter) and the angle are taken into account, regimes have been indicated, from which the values the stagnated bed height and the contactor base of the minimum voidages can be read for the systems diameter are fixed for any value of these ratios; so taken as example. For the other materials in Table

0.90

0.85

. l . . 11 . &=o.O3m I n,=o.o4m . ~:0_05m I

0.85 0.90 0.95 1.0 &experimental

Fig. 5. Comparison of experimental results of bed voidage with those calculated using eqn. (6).

they are variables that will be implicitly considered in the correlation.

The value of FD/FG depends on the drag coefficient C,, and the Reynolds number. In conical beds, when the section is varied, the velocity also varies; for this reason, the intermediate Reynolds number cor- responding to the upper diameter D, of the stagnated bed height has been taken into account in the previous expression.

The fitting of the experimental data of voidage to the equation proposed is shown in Fig. 6 for contactor angles of 28, 36 and 45, which have been taken as examples to show the fitting accuracy as they correspond to the extreme and mean values of those studied.

For each angle, the data corresponding to the stagnated bed height for 0.06 m (Fig. 6(a) and 6(b)), and for 0.06 and 0.028 m (Fig. 6(c)) have been plotted. The experimental points correspond to the inlet diameter of 0.05 m and glass spheres with particle diameters of 0.003, 0.004 and 0.008 m, which are values adopted as an example.

M. J. San Jo& et al. / Expansion of spouted beds in conical contactors 49

0.6

7=28'

LLL 10-2 lo-'

(a> h/F,)

0.6

10-Z lo-' (&j/F,)

0.6

0.4

cc>

10-z %, /F, )

Fig. 6. Expansion of spouted beds of conical geometry: -, calculated with eqn. (7); 0, experimental, glass spheres with d,=3 mm; n , experimental, glass spheres with d,= 4 mm; A, experimental, glass spheres with dP= 8 mm.

1 the fitting of the experimental data to eqn. (7) is similarly satisfactory.

In order to compare the expansion of conical beds with the expansion of other beds studied in the literature, the expansion curves deduced for flmdized beds 13 1, for cylindrical spouted beds of conical base [ 91, for spouted beds of flat base [ 1 ] and for conical spouted beds have been plotted in Fig. 7. In this figure, contactors of different ge- ometries are compared. Nevertheless, the expansion curves plotted have been calculated using the same values of the common geometric factors: for fluidized beds and for spouted beds of different geometries, I&=0.105 m and D,=O.13 m; for a cylindrical

10-J 1u-' 1".

t&/F,) '

Fig. 7. Bed expansion for different gas-solid contact regimes.

spouted bed of conical base, y,, = 36; for a conical spouted bed, y= 36.

The great advantage of plotting the expansion of spouted beds with only one equation for the whole range of voidage values should be noted. The in- definiteness of the expansion in the transition zone when using the correlations of Kmiec [9], eqns. (5) and (6), for both voidage ranges is avoided. In the same way, the applicability of eqn. (7) is noteworthy as the conical geometry allows us to carry out the experimental study with high values of voidage (near to unity), which are inadmissible for cylindrical spouted beds.

4. Minimum porosity

For the spouted bed in either cylindrical contactors or conical contactors, several workers [ 19-261 have considered that the voidage in the annular zone is constant and equal to that of the loose 6xed bed; so attention will be centred on the spout zone.

This consideration, neglecting the volume of the spout zone, is not valid in the contact forms studied in this paper; consequently the equations previously set out are not applicable when the calculation of global porosity is the objective.

In the expansion of conical beds, two stable regimes, namely spouting and jet spouting, to which different values of minimum voidage correspond, are established. As is observed in the expansion curves, the difference between the values of min- imum voidage of both regimes depends on the contactor geometry and on the characteristics of the solid particles.

4.1. Spouting regirn.43 The experimental data corresponding to the in-

cipient spouting regime for small values of stagnated bed high (less than 0.06 m) fit acceptably to eqn. (7) proposed for bed expansion (r2 = 0.72 and a

50 M. J. San Jo& et al. / Expansion of spouted beds in conical contactors

standard deviation of 12%). Nevertheless, for stag- nated bed heights between 0.06 and 0.4 m, the fitting is awkward (r2 < 0.50). The following expres- sion is proposed, which is specific for the minimum voidage and is obtained by fitting the experimental data corresponding to this particular situation in the expansion:

The fitting of all the experimental data has a regression coefficient r2 = 0.84 and a standard de- viation of 4%. The adequacy of the fitting is shown in Fig. 8, where the voidage values calculated with eqn. (8) are compared with the experimental values for some contactor-particle systems taken as ex- amples. Anyway, it is noteworthy that this equation is not valid for other than incipient spouting con- ditions.

The values of voidage modulus [(E- eo)/ (1 - E)]ms(~rJ!&,-o.272 calculated with eqn. (8) VS. stagnated bed height and for different values, taken as an example, of angle and contactor inlet diameter have been plotted in Fig. 9, once the effect of the particle characteristics has been isolated, so that

P J 0.7 Y=36 .z

3 a mO.6

0

(a>

0.4 0.5 0.6 0.7 & ms experimental

?=28, 33,45

ILL- . I 0.4 0.5 0.6 0.7

@I 8 ms experimental

Fig. 8. Values calculated with eqn. (8) and experimental values of minimum spouting voidage in conical co&actors for (a) glass spheres and (b) other materials (Table 1) (I, beans; A, chickpeas; 0, peas; +, rice; X, lentils; 0, ceramics; +, extruded poly- styrene).

0.5 . 0 2 4 6 8 10

102H, (m)

Fig. 9. Effect of contactor geometry onvoidage modulus [(E - co)/ (1 - E)]~~(F~/F~)-~~~~~ of incipient spouting.

ii 18 c--

10 -

6 - I, I, I , I

0 2 4 6 8 10

lo% (ml Fig. 10. Effect of contactor geometry on the minimum spouting voidage.

the plot is valid for any particle diameter. In order to delimit stable operation ranges in this system, the broken curves correspond to ranges in which the operation is unstable for particles of 0.004 m diameter. The bed stability depends on the geometric factors of the contactor-particle system and has been studied in a previous paper [ 271, in which the stable operation maps and the ranges of the geo- metric factors corresponding to stable operation are shown. It is observed in Fig. 9 that the effect of the inlet diameter is more pronounced than that of the angle and, when both increase, the value of the modulus studied increases.

In Fig. 10, values of [(~--~)/(l --E)],, corre- sponding to stable operation vs. stagnated bed height for an angle of 36 have been plotted as an example. Each curve corresponds to a value of inlet diameter and particle diameter. It is observed in this figure that, when the stagnated bed height increases, the minimum voidage decreases. The effect of inlet

M. J. San Jo& et al. / Elcpansion of spouted beds in conical wntactors 51

0.80 /

2

l . l u .

. l .

.

l . . . 4=0.03m .

. r&.=0.04 m

l l&=O.O5m

0.80 0.85 0.90 0.95

c 1

I

1.0

0.85 t

0.80 0.85 0.90 0.95 1.0

@I &mj experimental

Fig. 11. Values calculated with eqn. (7) and experimental values of minimum jet spouting voidage in conical beds for (a) glass spheres and @) other materials (Table 1) (W, beans; A, chickpeas; 0, peas; +, rice; x , lentils; 0, ceramics; + , extruded poly- styrene) .

g. 1.0, , I

d,=O.O04m ./I'

0.0 . 0 2 4 6 8 10

102H. (m)

Fig. 12. Effect of contactor geometry on the voidage modulus I(e- l o)/(l - l )lmj(~DIFD)- 1 of incipient jet spouting.

diameter and particle diameter is pronounced. When the former increases, so does the minimum voidage while, when the latter increases, the voidage de- creases.

4.2. Jet spouting regime For the calculation of the minimum jet spouting

voidage, eqn. (7) proposed for expansion can be used, as it fits the experimental data with a regression

0 2 4 6 8 10

102H, (m)

Fig. 13. Effect of contactor geometry on minimum voidage of jet spouting.

coefficient r2 = 0.89 and with a standard deviation of 3%. In Fig. 11, the validity of eqn. (7) for this purpose is shown, with a 36 angle as an example.

In order to analyse the effect of the contactor geometric factors, within the ranges used in this study, the values of [(E- eo)/(l - )],&iu/Fe)~~~.~~ (the effect of particle characteristics is isolated) calculated with eqn. (7) vs. stagnated bed height have been plotted in Fig. 12 for different values of angle and contactor inlet diameter taken as ex- amples. In this regime, the operation is stable for all the contactor-particle systems and for the whole range of values of Ho in the figure. The broken curves correspond to ranges where the bed partially occupies the upper zone of the contactor out of the conical section for particles of 0.004 m diameter.

It can be noted that, when the stagnated bed height increases, the voidage modulus increases and to a greater measure as the angle becomes larger and the inlet diameter smaller. The voidage modulus is substantially affected by both geometric factors; for a given stagnated bed height it increases with increasing angle and decreases with increasing inlet diameter.

The values of [(E- eo)/(l - E)]~ calculated with eqn. (7) for an angle of 36 vs. stagnated bed height have been plotted in Fig. 13. Each curve corresponds to one value of particle diameter and inlet diameter and the broken curves correspond to the operation with part of the bed out of the conical section. It is observed that the minimum voidage decreases with increasing stagnated bed height and that this decrease is sharper as the inlet diameter becomes larger and the particle diameter smaller. It is noted in this figure that, as the particle diameter increases, the minimum voidage decreases noticeably. The effect of inlet diameter is smaller and the minimum porosity increases when the inlet diameter increases.

52 M. J. San Jo& et al. / Expansion of spouted beds in conical contactors

6. Conclusions

The expansion of spouted beds in conical con- tactors has different characteristics from those cor- responding to conventional cylindrical contactors. The more important peculiarity lies in the fact that from the spouting regime it passes to another stable regime, of jet spouting, after an intermediate regime (transition). The jet spouted bed has voidage levels similar to those of transport fluidized beds; so the applications of this new regime lie in the treatment of solids of large size (typical of the spouting regime) with a gas-solid contact similar to those in transport beds.

Equation (7) for the calculation of the bed global voidage suitably fits the experimental results cor- responding to a wide range of contactor geometric factors and particle properties, in the whole voidage range in which conical contactors can be applied.

Equation (8) for the calculation of the minimum global voidage of spouting has also been determined with an accurate definition of incipient spouting, from knowledge of the complete curves of pressure drop VUS. velocity obtained in the bed expansion.

References

1 M. J. San Jose, Ph.D. Thesis, Universidad de1 Pais Vasco, Bilbao, 1991.

2 M. J. San Jose, M. Olazar, A. T. Aguayo, J. M. Arandes and J. BiIbao, in C. Laguerie and P. Guigon (eds.), Rt%ents

3

4

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8 9

10 11 12

13

14

Progds en GEnie des Proc&i&, Vol. 5, La Fluidisation, Lavoisier Technique et Documentation, Paris, 1991, p. 146. M. J. San Jose, M. Olaaar, A. T. Aguayo, J. M. Arandes and J. BiIbao, Can. J. Chem. Eng., in the press. M. J. Jose, M. Olaaar, A. T. Aguayo, J. M. Arandes and J. Bilbao, Proc. 4th World Cony. on Chemical Engineering, 1991, Chemische Technik und Biotechnologie, FrankfuN Main, 1991, 9.5-13. A. Kmiec and K. Leschonski, Chem. Eng. J., 45 (199 1) 137. T. A. Gauthier, C. L. Briens, M. A. Bergougnou and P. A. Galtier, in C. Laguerie and P. Guigon (eds.), R&ents Progrtk en Gt?nie des Proc&%s, Vol. 5, La Fluidisation, Lavoisier Technique et Documentation, Paris, 1991, p. 47. D. Sonnet, S. Afara, C. L. Briens, J. F. Large and M. A. Bergougnou, in P. Basu and J. F. Large (eds.), Circulating FluzU.zed Bed Technolom LI, Pergamon, Oxford, 1988, p. 565. A. Tamir, Ch.em. Eng. Prog., 9 (1989) 53. A. Kmiec, Chem. Eng. J., 10 (1975) 219. A. Kmiec, Chem. Eng. J., 13 (1977) 143. J. M. D. Merry, AIChJZ J., 21 (1975) 507. S. Damronglerd, J. P. Couderc and H. Angelino, Trans. Inst. Chem. Eng. J., II (1976) 237. I. P. MukhIenov and A. E. Gorshtein, Zh. Prikl. Khim. (Leningrad), 37 (1964) 609. A. Markowski and W. Kaminski, Can. J. Chem. Eng., 61 (1983) 377.

15 A. D. Goltsiker, Doctoral Dissertation, Lensovet Techno- logical Institute, Leningrad, 1967.

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17 P. G. Romankov, N. B. Rashkovskaya, A. D. Goltsiker and V. A. SebaIIo, Heat Transfer Sov. Res., 3 (1971) 133.

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Appendix A: Nomenclature

Ar

CD

4 Db, D,, Di, DO

FDIFG

Hc, Ho

Re u AP

gd,3p(p, - p)/p Archimedes number (24/Re)( 1 + 0.15 Re0.687)drag coefficient particle diameter (m) upper diameter of the stagnated bed height, diameter of the column, diameter of the contactor base and diameter of the inlet respectively (m) $ CD Re/Ar, ratio of the drag force to the gravitational force u/gd,, Froude modulus for the minimum spouting velocity height of the column and height of the stagnated bed respectively (m) Reynolds modulus referred to Db air velocity referred to Di (m s- ) pressure drop (Pa)

Greek letters

yi2, 3/b contactor angle and contactor base angle in cylindrical contactors with conical base respectively (rad)

e, 6 voidage of bed and of voidage static bed, respectively

P, Ps density of the gas and particle density Og me3)

4 particle shape

Subscripts ms related to the state of incipient spouting mi related to the state of incipient jet

spouting