HYDRODYNAMIC CHARACTERISTICS OF FLUIDIZED BEDS CONTAINING LARGE POLYDISPERSED PARTICLES

HYDRODYNAMIC CHARACTERISTICS OF FLUIDIZED BEDS CONTAINING LARGE POLYDISPERSED PARTICLES

K. TANNOUS1,^*, M. HEMATI² and C. LAGUERIE2, ^f

¹Universidade Estadual de Campinas - UNICAMP, Faculdade de Engenharia Química, Departamento de Termofluidodinâmica - C.P.: 6066, CEP 13083-970 Campinas, SP, Brazil

Phone : (55) (19) 239-7781 - Fax : (55) (19) 239-4717 - e-mail : [e-mail]

²Laboratoire de Génie Chimique (URA CNRS 192), Ecole Nationale Supérieure d’Ingénieurs en Génie Chimique, Institut National Polytechnique de Toulouse - 18, Chemin de la Loge - 31078 Toulouse Cedex – France

(Received: August 5, 1997; Accepted: December 15, 1997)

Abstract - This paper presents a hydrodynamic study of fluidized beds containing large polydispersed particles (B and D categories of Geldart’s classification). The experiments have been carried out with particle samples characterized by the Rosin-Rammler-Sperling (RRS) size distribution. The parameters analyzed in this study are the dispersion index and the average particle diameter obtained from the RRS size distribution model. Correlations to estimate the initial and complete fluidization velocities and the segregation velocity as a function of these two size distribution parameters have been established.

Keywords: Fluidized bed, large polydispersed particles, gas velocity.

INTRODUCTION

The prediction of the hydrodynamics in fluidized beds of heterogeneous particles is of fundamental importance in designing the equipments and in evaluating the efficiency of physical and/or chemical operations, e.g. the gasification and combustion of coal, catalytic reactions, drying, coating and granulation, mixing, etc..

In literature, studies related to the analysis and to the determination of these parameters are rare. Most of the correlations have been developed for predicting the apparent minimum fluidization velocity in beds of binary particle mixtures. These correlations are similar to those obtained in beds of homogenous particles, derived from Ergun’s equation or from the dimensional analysis. Some of these correlations have been described and discussed in detail by Thonglimp (1981), Baleato (1986) and Chyang et al. (1986), but only two can be applied to a fluidized bed of polydispersed particles (Rowe and Nienow, 1975 and Obata, 1982). According to our research, no correlation has been proposed for a fluidized bed of large polydispersed particles.

The objective of this study is to characterize the hydrodynamics in fluidized beds of polydispersed particles belonging to B and D categories of Geldart’s classification, with the same density.

EXPERIMENTAL

Experimental Apparatus

A schematic diagram of the experimental apparatus is shown in Figure 1. This consists of two methyl-metacrylate columns of a circular cross-section which is 2 m high and 0.094 m and 0.192 m in diameter. These columns have been equipped with perforated plate distributors with a free area of 5%. During the experiments, dry air from a compressor (delivery pressure of seven bars and a maximum flow rate of 400 m³/h) was injected into the column. The air flow rate was measured using previously calibrated rotameters.

The differential pressure measurements along the columns were taken by membrane pressure transducers at different axial positions below and above the distributor. The response time of these transducers is lower than 2 milliseconds. The voltage signals transmitted by the transducers were treated by a data acquisition system at a frequency of 50Hz. The acquisition time was fixed at 50 seconds. From the 2500 pressure signals registered, the data treatment program calculated the mean pressure differential

and standard deviation of pressure fluctuations (s ). These parameters were determined by the following expressions:

and (1)

Solids Used and Preparation of Mixtures

Sand particles belonging to B and D categories of Geldart’s classification are used in this work. Their physical properties are listed in Table 1. The particles density (r _p) was obtained by the displacement of water in a Candlot-Le Chatelier densimeter. The particles sphericity (j ) was evaluated from a pressure drop measurements across a fixed bed of these particles where air flows in a laminar regime (Re_p<10, by supposing an uniforme particle arrangement into the bed. The equation of Kozeny and Carman could be applied for estimating the particle sphericity.

The polydispersed particle mixtures (nine components) were prepared by mixing different four samples of sand particles which are reported in Figure 2. It shows that these four samples present an average particle size between 450 and 715, 715 and 1125, 1125 and 1800, 1800 and 2825 m m respectively. These samples were chosen in such a way that the granulometric distribution did not superpose. Each one of these samples can be considered as a lot of homogeneous particles according to the uniformity criteria suggested by Shannon (1961) and Bena (1968).

The Rosin-Rammler-Sperling (RRS) distribution model was used to prepare the particle mixtures in the following way:

(2)

where d_po is the characteristic diameter of the particle size corresponding to a mass fraction accumulated of 0.63 and m is the dispersion index.

The parameters chosen for this study were, from one side, the dispersion index, ranging from 0.01 to 10 while maintaining the average diameter of the mixtures as the constant 1130 m m. From the other side, the average diameter of the mixtures ranging between 750 and 1520 m m while maintaining the dispersion index constant at as 2.

The size distributions of the prepared mixtures are shown in Table 2. In this table, X_i (i=1 to 9) corresponds to the mass percentages of nine sizes successively obtained by sieving between 400 and 3125 m m.

The average particle diameters of mixtures presented in Table 2 were determined by Sauter diameter in the following way :

(3)

Figure 1:
Experimental apparatus scheme: 1- fluidization columns, 2- rotameters, 3- throttle valves, 4- spheric valves, 5- compressor, 6- relief valve, 7- flow rate automatic regulator, 8- cyclone.

Definition of the Characteristic Velocities

Before describing the methods used for the determination of the three characteristic velocities for the mixtures of polydispersed particles, it is important to define each one of these velocities. The initial fluidization velocity (U_fi) is the minimum velocity above which the lowest size particles begin to fluidize; the segregation velocity (U_s) is the one corresponding to the apparition of a totally defluidized zone at the bottom of the bed, constituted essentially by the largest particles; the complete fluidization velocity (U_fc) is the minimum one above which all particles are suspended in the bed by the fluid.

These three characteristic velocities were determined by measuring the total pressure drop, the differential pressure fluctuations in different bed layers (50-100, 150-200, and 200-250mm of the distributor), and the total and differential standard deviation pressure fluctuations.

The defluidized layer height was measured by a rule fixed in the wall of the columns.

Figure 2:
Particle size distributions of four samples of sand.

RESULTS AND DISCUSSION

Figure 3 presents, for the mixture M1(see table 1), the total pressure drop across the bed as a function of the air velocity increasing and decreasing the air flow rates through the initially well mixed bed. As shown, for the air velocity higher than the complete fluidization velocity, the total pressure drop maintains constant and equal to the apparent bed weight by the cross-sectional area of the column. For the air velocity between the complete (U_fc) and segregation (U_s) velocities, a decrease of the total pressure drop is observed for both, the fluidization and defluidization curves. For the air velocity below the segregation velocity, the total pressure drop oscillates when the air flow rate is increased (fluidization curve) and decreases regularly when the air flow rate is decreased (defluidization curve).

These oscillations of the pressure drop in the fluidization curve can be attributed to the change in the bed structure due to the entrainment into the bed surface of fine particles trapped by the large ones. These oscillations in the pressure drop disappear at air velocities lower than the initial fluidization velocity (U_fi). This velocity can be determined by the interception of the plateau pressure drop and the straight line corresponding to the static state of the bed at increasing flow rate. It is also possible to determine this velocity by measuring the pressure drop at increasing and decreasing flow rates through a layer placed in the neighboring surface (Tannous, 1993).

The initial fluidization velocity defined in this work corresponds to the minimum apparent fluidization velocity proposed by Rowe and Nienow (1972), for beds of binary particle mixture.

Figure 4 presents the standard deviation of the total pressure fluctuation and of the differential pressure fluctuations for a bed layer close to the surface (200-250mm) as a function of the air velocity for decreasing air flow rate. It can be observed that the inflection points of these curves correspond exactly to the three characteristic velocities of fluidization, U_fi, U_s, U_fc. Thus, these velocities delimit four zones corresponding to the fixed bed, well and intermediate segregation and the perfect mixed, as displayed in Figure 3.

For each air velocity during the progressive defluidization, the height of the defluidized layer was measured by visual observation. In Figure 5, it can be observed that this height of the defluidized layer decreases drastically for air velocities just above U_fi, moderately, for air velocities between U_fi and U_s, and drastically again for air velocities close to U_s to reach a null value of U_fc.

For the air velocity lower than U_s, the bed can be divided into two regions: the first one, close to the distributor where large particles exist in a stationary state; the second one, close to the bed surface, where fine particles exist in a fluidized state. The static bed height corresponds to the height of the bed region occupied by the large particles of the mixture.

For the air velocity just above U_s, the bubble intensity in the upper part of the bed becomes high enough to trap a partial flotation of large particles and the height of the fluidized layer is reduced. In this case, the bed is in a intermediate segregation state.

For air velocities higher than U_s, the defluidized layer tends to disappear, and particles become perfectly mixed.

Figure 3: Evolution of total pressure drop as a function of gas velocity: 1- fixed bed, 2- well segregated, 3- intermediate, 4- perfectly mixed =1130m m, m=0.01, D_c=0.192m, M_s=14Kg, H_o=0.31m.

Table 1.a:
Detailed granulometric distributions of mixtures of sand used

Mixture	r (kg/m3)		j	m	Retained mass percentages (%)
					X1	X2	X3	X4
M1 M2 M3 M4 M5 M6 M7 M8 M9	2650	1130 750 943 1320 1520	0.8-0.86	0.01 1.5 2.0 2.5 10 2.0	5.23 3.64 3.14 2.81 0.89 8.27 4.80 2.15 1.49	14.71 9.41 8.01 7.25 0.45 21.72 12.21 5.35 3.63	18.48 12.36 10.73 9.79 2.36 28.17 16.20 7.23 4.92	0.29 9.81 12.10 12.48 32.13 16.52 15.93 9.35 6.66

Mixture r (kg/m3) j m Retained mass percentages (%) X5 X6 X7 X8 X9 M1 M2 M3 M4 M5 M6 M7 M8 M9 2650 1130 750 943 1320 1520 0.8-0.86 0.01 1.5 2.0 2.5 10 2.0 0.21 7.75 9.60 9.98 24.87 12.52 12.40 7.51 5.43 0.14 13.90 18.75 22.30 22.30 6.70 16.75 16.82 13.95 2.77 12.01 15.10 17.79 17.00 5.14 13.15 14.52 12.97 24.10 12.92 9.41 7.31 0.00 0.40 3.53 15.29 21.01 34.07 18.27 13.41 10.33 0.00 0.56 5.03 21.78 29.94

Mixture	r (kg/m3)		j	m	Retained mass percentages (%)
					X5	X6	X7	X8	X9
M1 M2 M3 M4 M5 M6 M7 M8 M9	2650	1130 750 943 1320 1520	0.8-0.86	0.01 1.5 2.0 2.5 10 2.0	0.21 7.75 9.60 9.98 24.87 12.52 12.40 7.51 5.43	0.14 13.90 18.75 22.30 22.30 6.70 16.75 16.82 13.95	2.77 12.01 15.10 17.79 17.00 5.14 13.15 14.52 12.97	24.10 12.92 9.41 7.31 0.00 0.40 3.53 15.29 21.01	34.07 18.27 13.41 10.33 0.00 0.56 5.03 21.78 29.94

Table 1.b: Detailed granulometric distributions of mixtures of sand used

Figure 4: Evolution of starndard deviation of pressure fluctuation as a function of decreasing total differential (200-250mm belong of distributor), =1130m m, m=0.01, D_c=0.192m, M_s=14Kg, H_o=0.31m.

Figure 5: Evolution of defluidized layer height as a function of gas velocity: =1130m m, m=0.01, D_c=0.192m, M_s=14Kg, H_o=0.31m.

Characteristic Velocities of Mixtures

Experimental results concerning the dependence of three characteristic velocities on the column diameter and the static bed height, the dispersion index and average particle diameter are the presented in table 2 and Figures 6 and 7:

Table 2:
Characteristic velocities of fluidization for different particles populations

No.	Dc (m)	Ho (m)		m	Ufi (m/s)	US (m/s)	Ufc (m/s)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17	0.192 0.094 0.192 0.094	0.31 0.15 0.21 0.31 0.23	1130 750 943 1130 1320 1520 750 1130 1520	0.01 1.5 2.0 2.5 10 2.5 0.01 1.5 10 2.0 2.0	0.36 0.47 0.51 0.55 0.70 0.53 0.36 0.50 0.70 0.37 0.40 0.51 0.55 0.70 0.37 0.50 0.70	1.06 0.85 0.80 0.76 0.74 0.75 1.08 0.80 0.70 0.49 0.68 0.80 0.88 1.05 0.50 0.80 0.95	1.45 1.15 1.10 1.00 0.75 0.95 1.50 1.12 0.74 0.78 0.90 1.10 1.20 1.40 0.80 1.10 1.45

Figure 6: Evolution of characteristic velocities as a function of m: =1130m m, D_c=0.192m, M_s=14Kg, H_o=0.31m.

Figure 7:
Evolution of U_fi, U_s and U_fc as a function of avarage particle diameter: m=2.0 , D_c=0.192m, M_s=14Kg, H_o=0.31m.

These results show that:

- U_fi, U_s and U_fc are not influenced neither by the column diameter nor by the static bed height.

- The increase of the dispersion index leads to an increase in U_fi and to a decrease in U_fc and U_s. As a consequence, the segregation interval (U_fc - U_fi) tends is become smaller as the dispersion index increases. For values of m which are equal to 10, the three characteristic velocities are, in effect, identical.

- The difference between these three velocities and segregation interval increase with the average particle diameter of the mixture.

Establishment of New Correlations

From all the results presented here, the following empirical correlations are proposed for the predicting fluidization characteristic velocities in beds of polydispersed particle mixtures:

Initial fluidization velocity:

(E=1.79% and s _E=0.029)

Segregation velocity:

(5)

(E=1.64% and s _E=0.041)

and

Complete fluidization velocity:

(6)

(E=3.01% and s _E=0.054)

In equations (4) to (6), U_mf represents the minimum fluidization velocity calculated from the correlation six with average diameter equal to the Sauter diameter (Tannous, 1994).

(7)

(E=1.2% and s _E=0.097)

The correlation seven is valid for 10 < Re_mf < 486 and 0.14 10⁵ < Ar < 181 10⁵.

Comparison Between the Experimental and Calculated Results for the Complete Velocity Fluidization (U_fc)

The experimental results related to the fluidization of mixtures of polydispersed particles are not very frequent in the literature. However, we compare the predictions of equation five relative to the complete fluidization velocity with experimental results of some available works (Cobbinah, 1986; Fayolle, 1988; Raillard, 1988).

Figure 8:
Comparison between calculated and experimental results of complete fluidization.

The greatest part of the experiments were carried out with solid particles of low density such as polyethylene and polystyrene.

Figure 8 shows the comparison between the measured and calculated values of U_fc for the available experimental results. It was observed that this correlation represents the results in a satisfactory way with an maximum average relative error of 10%.

CONCLUSIONS

In this work, hydrodynamic parameters were determined (U_fi, U_s, U_fc) from fluidized beds containing large polydispersed particles of the B and D categories of Geldart’s classification.

The parameters studied were the dispersion index and the average particle diameter of mixtures. From the experimental results, the following can be concluded:

1) As the mixture dispersion index increases, the polydispersed particles tend to decrease the segregation phenomenon;

2) For a dispersion index greater than or equal to four, the particle mixture can be considered to be equivalent to a lot of identical particles;

3) For a given dispersion index, a reduction of the average diameter leads to a reduction of the segregation phenomena;

4) Three correlations established to determine the initial, complete fluidization, and segregation velocities suitably represent our experimental results and also the results from other authors.

NOMENCLATURE

dp Aperture size of the sieve, m

d_pi Average diameter of one "i" lot, m

_o Characteristic diameter of distribution corresponding to a 0,63 accumulated mass fraction, m

Average particle diameter (Sauter diameter), m

d_p Arithmetic mean of the aperture sizes consecutives sieves , m

D_c Bed diameter, m

E Relative error, %

F(d_pi) Accumulated mass fraction passing through a sieve of d_pi, -

H_o Fixed bed height, m

D Pi Instantaneous differential pression, Pa

D P Average pressure drop through the bed, Pa

m Dispersion index, -

N Samples number, -

U Superficial gas velocity, m s^-1

U_fc Complete fluidization velocity, m s^-1

U_fi Initial fluidization velocity, m s^-1

U_mf Minimum fluidization velocity, m s^-1

U_s Segregation velocity, m s^-1

X_i Mass percentage of a granulometric class, -

Greek letters

m g Gas viscosity, kg m^-1 s^-1

r g, r p Gas and solid density, kg m^-3

s Standard deviation of total pressure fluctuations, Pa

s _d Differential standard deviation of pressure fluctuations, Pa

s _E Standard deviation, -

Dimensionless Numbers

Ar Archimedes number

Re Reynolds number

REFERENCES

Bena, J.; Havalde I.; Bafrnec M. and Ilavsky J., Coll. Czechoslov. Chem., 33, 2620 (1968).

Barleato, F. Z., Analyse des Phénomène de Mélange et de Ségrégation de Deux Populations Différents de Particules Solides dans un Lit Fluidisés par un Gaz. PhD Thesis, ENSIGC-INPT, France (1986).

Chyang, C.S.; Kuo C.C. and Chen M.Y., Minimum Fluidization Velovity of Binary Mixtures. Can. J. of Chem. Eng., 67 (4), 344-7 (1989).

Cobbinah, S., Fluidisation de Polyèthyléne. Classic Report realized on cooperation between ENSIGC GRL and ATOCHEM (Mont.), ENSIGC-INPT, France (1987).

Fayolle, P., Etude de Poudres en Lit Fluidisé. Classic Report, ENSIGC-INPT, France (1988).

Geldart, D., Gas Fluidisation Technology , John Wiley & Sons, New York, USA (1986).

Obata, E., Watanabe H. and Endo N., Measurement of Size and Size Distribution of Particles by Fluidization. J. Chem. Eng. of Japan, 15 (1), 23-8 (1982).

Raillard, J.C., Etude du Minimum de Fluidisation de Couches Polydispersées. Classic Report, ENSIGC-INPT, France (1988).

Rowe, R.N. and Nienow A. W., The Mecanisms by Which Particles Segregate in Gas Fluidised Beds-Binary Systems of Near-Spherical Particules. Trans. Instn. Chem. Engrs., 50, 310-23 (1972).

Rowe, R.N. and Nienow A. W., Minimum Fluidisation Velocity of Multi-component Particle Mixtures. Chem. Eng. Sci., 30, 1365-9 (1975).

Shannon, P.T., PhD Thesis, Illinois Inst. Technol., Chicago, USA (1961).

Tannous, K., Contribution à l’Etude Hydrodynamique des Lits Fluidisés de Grosses Particules. PhD Thesis, ENSIGC-INPT, France (1993).

Tannous, K.; Hemati M. and Laguerie C., Caractéristiques au Minimum de Fluidisation et Expansion des Couches Fluidisées de Particules de la Catégorie D de Geldart. Powder Technology, 80, 55-72 (1994).

Thonglimp, V., Contribution à l’Etude Hydrodynamique des Couches Fluidisées par un Gaz-Vitesse Minimale de Fluidisation et Expansion. PhD Thesis, ENSIGC-INP, France (1981).

Table 1.a: Detailed granulometric distributions of mixtures of sand used

Mixture

r (kg/m3)

j

m

Retained mass percentages (%)

X1

X2

X3

X4

M1

M2

M3

M4

M5

M6

M7

M8

M9

2650

1130

750

943

1320

1520

0.8-0.86

0.01

1.5

2.0

2.5

10

2.0

5.23

3.64

3.14

2.81

0.89

8.27

4.80

2.15

1.49

14.71

9.41

8.01

7.25

0.45

21.72

12.21

5.35

3.63

18.48

12.36

10.73

9.79

2.36

28.17

16.20

7.23

4.92

0.29

9.81

12.10

12.48

32.13

16.52

15.93

9.35

6.66

Table 1.b: Detailed granulometric distributions of mixtures of sand used

Mixture

r (kg/m3)

j

m

Retained mass percentages (%)

X5

X6

X7

X8

X9

M1

M2

M3

M4

M5

M6

M7

M8

M9

2650

1130

750

943

1320

1520

0.8-0.86

0.01

1.5

2.0

2.5

10

2.0

0.21

7.75

9.60

9.98

24.87

12.52

12.40

7.51

5.43

0.14

13.90

18.75

22.30

22.30

6.70

16.75

16.82

13.95

2.77

12.01

15.10

17.79

17.00

5.14

13.15

14.52

12.97

24.10

12.92

9.41

7.31

0.00

0.40

3.53

15.29

21.01

34.07

18.27

13.41

10.33

0.00

0.56

5.03

21.78

29.94

* To whom correspondence should be addressed.

To whom correspondence should be addressed.

^f In Memorium

Publication Dates

• Publication in this collection
  09 Oct 1998
• Date of issue
  Mar 1998

History

• Received
  05 Aug 1997
• Accepted
  15 Dec 1997