A simple correlation for solids holdup in a gas-liquid-solid fluidized bed

Chemical Engineering Science, Vol. 41, No. Printed in Great Britain.

I I, pp. 2823-2828,

1986.

OCW-250!9/86 53.00 + O.Ml Pergamon Journals Ltd.

A SIMPLE CORRELATION GAS-LIQUID-SOLID

FOR SOLIDS FLUIDIZED

RONG-HER

HOLDUP BED

IN A

JEAN

and LIANG-SHIH

FAN?

Department of Chemical Engineering, The Ohio State University, Columbus, OH 43210, U. S. A.

(Received 31 May 1985) Abstract-A simple empirical model was established which allows solids holdup in a gas-liquid-solid fluidized bed containing large and dense particles to be readily predicted based on the equation of Richardson and Zaki (1954, Trans. Inst. Chem. Engrs 32, 35) for liquid-solid Auidized bed systems. The approach is applicable both to monocomponent particle systems and to binary mixtures of particles. For a monocomponent system, a correlation for model parameters was proposed which is expressed as a function of particle diameter, particle density, bed diameter and liquid density. For a binary mixture of particles, the averaging and serial approaches were shown to predict the solids holdup equally well within the range of the gas and liquid velocities considered. Experiments were also performed using eight solid particles for the monocomponent system and five binary mixtures of particles differing in diameter and/or density for the mixture system to substantiate the model.

INTROI)UCIION

Gas-liquid-solid fluidized beds have evolved in recent years as one of the most promising devices for threephase operation. Such a device is of considerable industrial importance as evidenced in its use in the Hail process for hydrogenation and hydrodesulfurization of residual oil, the H-coal process for coal liquefaction, and the bio-oxidation process for wastewater treatment. The fundamental characteristics of a three-phase fluidized bed were recently extensively reviewed by Muroyama and Fan (1985). The review indicated the importance of the information of phase holdup, specifically, solids holdup, in the optimal design of a three-phase fluidized bed reactor. Classical correlations for the solids holdup or bed expansion for monocomponent systems have resorted to two approaches. One is based on the totally empirical correlation of the solids holdup as functions of physical properties of particles, gas and liquid and operating conditions (e.g. Dakshinamurty et al., 1971, 1972; Kim et al., 1972, 1975; Razumov et al., 1973; Soung, 1978; Begovich and Watson, 1978). The other is based on semi-empirical correlations established on the wake model, which takes into account the behaviour of the bubble wake (e.g. Ostergaard, 1965; Efremov and Vakhrushev, 1970; Rigby and Capes, 1970; Bhatia and Epstein, 1974; Darton and Harrison, 1975; ElTemtamy and Epstein, 1978). The former approach has a strict range limitation for the correlation while the latter requires knowledge of such model parameters as ratio of wake volume to bubble volume and

~To whom correspondence

should

be addressed. 2823

ratio of solids holdup in the wake to that in the liquid-solid fluidized region, and gas holdup. In contrast to the monocomponent system, little is known regarding overall solids holdup or bed expansion for mixed particles in a three-phase fluidized bed. Fan et al. (1982a) analysed the variation of bed expansion characteristics with solids mixing states for a binary mixture using the averaging model and serial model proposed by Epstein et al. (1981). They indicated that similar to a two-phase (liquid-solid) fluidized bed (Epstein et al., 1981) prediction of the porosity based on the serial model is satisfactory for a three-phase fluidized bed, even when the bed is at the complete intermixing state. Fan et al. (1984) studied the qualitative solids mixing behaviour in a threephase fluidized bed containing a binary mixture of particles. They reported a strong correlation between the flow regimes, i.e. dispersed bubble regime, coalesced bubble regime and slugging regime, and solids mixing states. Sinha et al. (1984) examined the effect of polydispersity of solids on bed stratification, bed expansion and bed contraction for a three-phase fluidized bed. They correlated the porosity as a function of four dimensionless groups in which the median diameter was employed to characterize the particle property. They also reported the bed contraction behaviour, which is similar to that observed for monocomponent systems. This study presents a simple unified empirical relationship for the prediction of solids holdup in both liquid-solid and gas-liquid-solid fluidized beds. The relationship for a three-phase fluidized bed is established via the introduction of a parameter, the “equivalent liquid velocity” for the two-phase fluidized bed. The “equivalent velocity” was found to be cor-

2824

RONGHER JEAN and LIANGSHIH FAN

relatable with the ratio of velocity for two-phase and Both the monocomponent of particles are considered

the minimum Auidization three-phase fluidized beds. system and binary mixture in this study.

EXPERIMENTAL A schematic diagram of the experimental apparatus is shown in Fig. 1. The vertical Plexiglas column was of 76.2 mm i.d. and 2.73 m in length. The column consisted of three sections, namely, the gas-liquid distributor section, the test section, and the gas-liquid disengagement section. The gas-liquid distributor was of the tube-shell type, which provides a uniform distribution of gas and liquid flow through the distributor. Details of the distributor design are given elsewhere (Fan et al., 1982b). Water and air were used as the liquid and gas phases, respectively. Manometer taps were axially spaced at 51 mm intervals along the column. The height of bed expansion was determined based on the axial pressure profile. The superficial velocities of the gas and liquid used ranged from 0 to 15 cm/s and from 6 to 25 cm/s,

Eight solid particles differing in diameter and/or density were used in the experiments. The physical properties of the particles are summarized in Table 1. All the particles were spherical or near spherical. Both nonporous and porous particles were used in the study. The wet density of the porous alumina beads was measured using specific gravity bottles under the same condition as in the bed. The Richardson-Zaki index and the extrapolated terminal velocity as the bed voidage approaches unity for a liquid-solid fluidized bed were determined experimentally. Five binary mixtures of particles were considered in this study. Three particle weight ratios, i.e. 1:1, 3:1 and 1:3, were also examined. Details of the particle mixture properties are given in Table 2. MATHEMATICAL

u, = u, (EL)n. To

Water

MODEL

(A) Monocomponent systems The bed voidage in a liquid-solid fluidized bed has been well represented by the Richardson and Zaki equation (1954): (1)

eq. (1) to a three-phase fluidized bed requires that U, be replaced by an “equivalent liquid velocity” in a two-phase system, ULi, and Edbe replaced by the bed porosity or holdups of gas and liquid phase combined, sir where the subscript i refers to type i particle. Thus, for an equivalent two-phase (liquid-solid) system for three-phase (gas-liquid-solid) fluidized bed, we heave

. 1 Ii__.!

extend

U’Li = uei (Ei)n,.

(2)

It was found that ULi can be simply empirically related to the superficial liquid velocity, U, the minimum fluidization velocity in a three-phase system, Urnfi, and the minimum Ruidization velocity in a two-phase system, UmfiO, according to

06

u;i

=

u/,

umfi

‘i

( UmfiO >

Fig. 1. Experimental apparatus. 1, Test section; 2, gas-liquid distributor; 3, manometer tap; 4, disengagement section; 5, pressure gauge; 6, liquid flow meters; 7, gas rotameters; 8, pump; 9, liquid reservoir; 10, particle sieve.

Table

1.

where yi is the correlation parameter. It should be noted that Umfi in eq. (3) is a function of the gas velocity and particle and fluid properties. Furthermore, for a given liquid velocity and particle

Properties of the solid particles

Particle notation

Type of particles

d, (mm)

pp (g/cm3)

LJ,(cm/s)

Pl P2 P3 P4 P5 P6 P7 ~8

Glass beads Glass beads Glass beads Alumina beads Alumina beads Alumina beads Alumina beads Lead particle

3.04 3.99 6.11 2.27 2.53 5.50 6.69 3.33

2.525 2.53 2.20 3.69+ 3.69+ 3.69+ 3.644+ 11.075

24.8 30.1 34.2 26.8 30.0 49.6 54.1 65.9

t Wet density.

?I 2.43 2.40 2.31 2.40 2.56 2.47 2.50 2.11

2825

Solids holdup Table 2. Compositions Mixture notation

P3, P2, P2, P2, P2, P3, P3,

P5 P4 Pl PI Pl Pl P2

arithmetic

1:l 1:l 1:l 3:l 1:3 1:l 1:l

Xl&l

P,l(l

--d+&*w-2)

where

G

(4)

GnfiO

The above equation was found to be correlatable with the data obtained using the particles in this study. Substituting eq. (3) into eq. (2) and taking the logarithm of both sides gives In { Uei &i“I} = y, In

Umfi ___

i Umf i0 1

+ln(U,).

( >

(B) Binary mixture of particles For solids holdup prediction, there are two approaches which can conveniently be used to obtain the “equivalent liquid velocity” for a three-phase fluidized bed containing a binary mixture of particles; one is the averaging approach, the other is the serial approach. For these two approaches, the “equivalent liquid velocity” similar to that in eq. (3) can be defined as: U;m=Ut

Ym U mf U mfD

( >

are the minimum fluidization for where Umf and U,, the binary mixture in a three-phase and a two-phase system, respectively, and Y, is the correlation parameter for the binary mixture. U,f/Umfl, can be determined by the correlation of Fan et al. (1982a):

Note that for a binary mixture of particles, subscript 1 refers to the particle with a larger U, whereas subscript 2 refers to the particle with a small U,. Umfi/ UmfiO in eq. (7) can be evaluated by eq. (4). For the averaging approach, ym is expressed as a

3

1,2

i=

(10)

where ULi is obtained from eq. (3). The “equivalent liquid velocity” for the mixture can thus be evaluated by

Uem&“m

=

(11)

where E is obtained by eqs (9) and (lo), and n, and U,, are given based on the harmonic average of n, and n2, and U,, and U,,, respectively as:

2+x’ n,

Psl

=

(5)

A plot of In { Uei &i “i} vs. In { Umfi/UmfiO) would result in a straight line with yi as the slope of the line and In (U,) as the intercept of the line. Thus, eqs (2), (3) and (4) can be used to determine solids holdups or bed expansion if the value of y, is known.

114

U’

Ei=c

UL, d,0.598(p,_pL)-0.305.

(9) x2

Xl

properties, Uti in eq. (3) varies soleiy with the gas velocity. For a three-phase Auidized bed containing large or dense particles, Begovich and Watson (1978) reported the correlation given in the following equation which can be utilized to predict the minimum fluidization velocity: &227

X2&2

E=Ps,(f--61)+PS2(1-EZ)

and liquid

1 _ ~9.436

(8)

For the serial approach, one relates the bed height of the mixture as if it were the sum of individual expanded bed heights from monocomponents fluidized alone with different “equivalent liquid velocity” for each particle. Hence,

TDefmed as the weight of large particles over the weight of small particles.

u mfr _

average of y, and yZr i.e.

Ytll = XlYl +xzyz.

Weight ratio?

Types of particles

I II IIIa IIIb IIIC IV V

weighted

of the binary mixtures

Ps2

(12)

Xl -++

x2

Pslnl

Ps2n2 x’+x2

U em=

Psi

Xl p+p Psi

Ps2

(13)

x2

U.?I

Ps2 ue2

It should be noted that this approach relates Y, in a very complex way to yi via eqs (3), (4), (6), (7), (9), lo), (ll), (12) and (13). After obtaining the “equivalent liquid velocity” for the mixture by either the averaging approach from eqs (6)-(8) or the serial approach from eqs (9E(13), the solids holdup of a binary particle mixture in a threephase fluidized bed can be predicted by one of the wellestablished relationships for a two-phase fluidized bed containing a binary mixture, such as the empirical correlation by Sinha et al. (1984) or the serial model by Epstein et al. (1981). For example, applying the serial model, E can be evaluated by eq. (9), where ei is calculated by eq. (10) with ULi replaced by UL, as given below:

It should be noted that in the serial approach, Ecan also be obtained simply from eqs (9) and (10) if the approach involving the “equivalent liquid velocity” for the mixture is not employed. RESULTS

AND

DISCUSSION

Figure 2 shows the linear In { U,iEn’} and In { Umfi/Umfio}

relationship between as a function of UL_

2826

RONG-HER

r*

.

8..

-2.00~1.60

8..

-1.20

1..

.

.

Ln ( Umfi/Umfio)

1.

-0.40

-0.00

‘,

JEAN and LIANGSHIH

-0.00

-0.

FAN

JO -0.40

-0.30

-0.20

Ln(Umfi/UmftO)

[-I

-0.10

-0.00

[-I

Fig. 2. Relationship between In (Ueieni) and In (V,ri/U,r& for 6 mm glass heads.

Fig. 4. Relationship between In ( V,j~“‘) and In ( U,,i/U,f,) for 3.33 mm lead particles.

The particle used in the figure is a 6 mm glass bead. Note that variation of In {U,,i/U,,,) reflects the variation of U,. Thus, the plot covers both the twophase (liquid-solid) and the three-phase (gasliquid-solid) fluidized beds. Based on eq. (S), the slope and intercept correspond to yi and In (Vi), respectively. It is seen in the figure that yj for each line is almost constant, with an average value of - 0.154, and is independent of the liquid velocity. The intercept corresponds well to the liquid velocity for each line. A similar relationship between ln(U,is”i) and In (U,fi/U,fjo) is also observed for 5.5 mm alumina beads, as shown in Fig. 3, and for 3.33 mm lead particles, as shown in Fig. 4. It should be noted that experiments involving low-density particles, i.e. PVC cylindrical with density (3mmx3mm shape 1.47 g/cm’) and nylon beads (2.5 mm with density 1.15 g/cm3), were also attempted. However, a considerably large dilute region above the dense region is observed for these particles. Apparently, the pressure drop method is no longer feasible in this case for characterizing the height of bed expansion, as pointed out by Begovich and Watson (1978). Furthermore, it appears that one single region is not adequate to

characterize the bed behaviour and two distinct regions in the bed, i.e. dense region and dilute region, must be accounted for separately. The present analysis is, thus, not extended to the light-particle system. Figure 5 shows a correlation of y with a dimensionless function defined as (d,/,D) (p,/(p, --pr,)) for all eight types of particles used m the experiments. It is seen that the correlation can be well represented by

5

[D

y = -0.0869

(&)3~o]-osg6.

(15)

Note that eq. (15) is verified over a wide range of gas and liquid velocities, i.e. 0 < U, < 15 cm/s, 6.0 < U, c 25.0 cm/s, which covers three distinct flow regimes including dispersed, coalesced and slugging regimes. Comparisons of the sotids holdup obtained experimentally and predicted based on the model equations are given in Fig. 6. It is seen that the agreement is satisfactory. It should be noted that the model equations used in obtaining Fig. 6 are eqs (2), (3), (4) and (15). Comparisons are also made for the solids holdup in a fluidized bed containing a binary mixture of particles. As indicated previously, there are two approaches

3

1 -

9. -1

..l....l....I,...LI.,.

.oo-0.60

-0.60

-0.40

Ln(Umfi/Umflo)

-0.20

I

-0.00

c-1

Fig. 3. Relationship between In (U& and In ( Umri/Umrio) for 5.5 mm alumina beads.

0

7:i

.

.

.,,I

,--yyy -I

10-2 do

/

D. ( &‘s

10° - A$“*

c-1

Fig. 5. Correlation of y as a function of particle properties for glass, alumina and lead particles.

2827

Solids holdup

zz .-i

I---‘ ’I’.’’ .’.. .’

2

Go

0.0

<

L&

<

12.0

(cm/s)

6.0

<

4

c

i6.6

(cm/s)

Z%

.A

.

-0 if?

-“z

d

\y”

E d

iz

d

0.00

0.20

Es

(experimental)

CS

0.40 0.60 [experimental)

o.eo

1.00

Fig. 6. Comparisons of the solids holdup obtained experimentally and predicted based on the model with y calculated by eq. (15) for monocomponent systems.

Fig. 8. Comparisons of the solids holdup obtained experimentally and predicted based on the serial approach for five binary mixtures of particles.

which can be used to obtain the “equivalent liquid velocity”, namely, the averaging approach and the serial approach. In the averaging approach, the solids holdup is calculated from eqs (9) and (14), with UL, evaluated by eqs (6~(8) and (15). In the serial approach, the solids holdup is obtained from eqs (9)and (14), with U>.,.,calculated by eqs (9)-( 13) and (15). Figures 7 and 8 show the comparisons of experimental data with the prediction based on the averaging approach and serial approach, respectively, for all five binary mixtures of particles considered in this study. It is seen that the agreement in both figures is practically equally satisfactory over the entire ranges of gas and liquid velocities employed. Thus, due to its relative simplicity, the averaging approach is adopted successfully by Fan et al. (1986) to account for the segregation velocity of a binary mixture of particles.

ponent particle system or a binary mixture of particles which are large and dense. The model was established based on successful introduction of the “equivalent liquid velocity” as given in eq. (3), and the correlation for the model parameter as given in eq. (15). The model also holds for the two-phase (liquid-solid) fluidized bed. It has been shown that the solids holdup in a threephase fluidized bed containing a binary mixture of particles can be predicted satisfactorily by the model via both the averaging and the serial approach. Both the averaging and the serial approach yielded a similar prediction accuracy over the wide range of gas and liquid velocities employed in this study. Acknowledgement-The Science Foundation,

NOTATION

dP CONCLUDING

REMARKS

A simple empirical model has been developed to account for the solids holdup or bed expansion in a three-phase fluidized bed containing a monocom-

is

<

12.0

(cm/s)

c

16.6

[cm/s)

z” E,o -Vi

D n

UL .

P” k.0 -V 6 G R d L3 d 0.00

u mf u mm umfi

0.20

0.40 FS

0.60

texperimentall

0.60

1.00

Fig. 7. Comparisons of the solids holdup obtained experimentally and predicted based on the averaging approach for five binary mixtures of particles.

work was supported by the National Grant No. CPE-8219160.

UmfiO

particle

diameter,

cm

bed diameter, cm Richardson and Zaki index; ni, for a monocomponent bed of particle i; nm, for a mixture, defined by eq. (12) superficial liquid velocity, cm/s extrapolated terminal velocity as the voidage approaches unity for the liquid-solid fluidized bed, cm/s; Ue, for a monocomponent i, cm/s; U,,, for a binary mixture, defined by eq. (13), cm/s “equivalent liquid velocity” defined in eq. bed of (31%cm/s; U’L,, for a monocomponent particle i, cm/s; V;,, for a binary mixture, cm/s minimum fluid&&ion velocity for a binary mixture in a three-phase fluidized bed, cm/s minimum fluidization velocity for a binary mixture in a liquid-solid fluidized bed, cm/s minimum fluidization velocity for a monocomponent bed of particle i in a three-phase fluidized bed, cm/s minimum fluidization velocity for a monocomponent bed of particle i in a liquid-solid fluidized bed, cm/s

2828 x

RONG-HER JEAN and LIANG-SHIH weight

fraction

particle Y

of a binary

model

parameter

defined

i; y,,

monocomponent Greek &

mixture;

xi, for

i in eq.

(3); yi, for

for a binary mixture

letters

bed porosity

or

mixture

an

in

bed

voidage

“equivalent”

of

a binary two-phase

bed; Ed, for a monocomponent bed of particle i bed voidage in a solid-liquid system density, g/cm3; psb for particle i in a monocomponent bed, g/cm’ viscosity, g/cm s fluidtied

EL

P cc

Subscripts G gas phase monocomponent ;.

liquid

m

binary

P

solid particle

S

i; i =

1,2

phase mixture

solid phase REFERENCES

Begovich, J. M. and Watson, J. S., 1978, Hydrodynamic characteristics ofthree-phase fluidized beds. In Fluidizotion (Edited by Davidson, J. F. and Keairns, D. L.), pp. 190-195. Cambridge University Press, Cambridge. Bhatia, V. K. and Epstein, N., 1974, Three phase fluidization: a generalized wake model.Fluidization and Its Applications (Edited by Angelino, H. et al.), pp. 380-392. Cepadues Editions, Toulouse. Dakshinamurty, P., Subrahmanyam, V. and Rao, J. N., 1971, Bed porosities in gas-liquid ffuidization. Ind. Enana _ I Chem. Proc. Des. Dev. 10, 3221328. Dakshinamurtv. P.. Rao. K. V.. Subbaraiu. R. V. and Subrahman&m, V., 1932, Bed- porosities in gas-liquid fluidization. Ind. Engng Chem. Proc. Des. Dev. 11,318-319. Darton, R. C. and Harrison, D., 1975, Gas and liquid holdup in three-phase fluidization. Chem. Engng Sci. 30, 581-586.

FAN

Efremov, G. I. and Vakhrushev, I. A., 1970, A study of the hydrodynamics of three-phase fluidized beds. Inr. them. Engng 10, 3741. El-Tern&my, S. A. and Epstein, N., 1978, Bubble wake solids content in three-phase fluid&d beds. Int. J. Multiphase Flow 4, 19-3 1. Epstein, N., Leclair, B. P. and Pruden, B. B., 1981, Liquid fluidization of binary particle mixtures-I. Overall bed expansion. Chem. Engng Sci. 34, 1803-1809. Fan, L. S., Matsuura, A. and Chern, S. H., 1982a, Hydrodynamic characteristics of a gas-liquid-solid fluidized bed containing a binary mixture of particles. Paper Sic, presented at the A.1.Ch.E. Annual Meeting, Los Angeles, l&18 Nov.; 1985, A.I.Ch.E. J. 31, 1801-1810. Fan, L. S., Muroyama, K. and Chern, S. H., 1982b. Hydrodynamics of inverse fluidization in liquid&solid and gas-liquid-solid systems. Chem. Engng J. 24, 143-150. Fan, L. S., Chern S. H. and Muroyama, K., 1984, Solids mixing in a gas-liquid-solid fluid&d bed containing a binary mixture of particles. A.I.Ch.E. J. 30, 858-860. Fan, L. S., Yamashita, T. and Jean, R. H., 1986, Solids mixing and segregation in a gas-liquid-solid fluidized bed. Chem. Engng Sci. (in press). Kim, S. D., Baker, C. G. J. and Bergougnou, M. A., 1972, Hold-up and axial mixing characteristics of two and three phase &idized beds. C& J. them. Engng 50, 695-700. Kim, S. D., Baker, C. G. J. and Beraouenou. M. A.. 1975. Phase holdup characteristics of three phase kuidized beds: Con. J. them. Enana - - 53. 134-139. Muroyama, K. and Fan, L. S., 1985, Fundamentals of gas-liquid-solid fluidization. A.1.Ch.E. J. 31. l-34. OGergaaid, K., 1965, On bed porosity in gas-liquid fluidization. Chem. Engng Sci. 20, 165167. Razumov, I. M., Manshilin, V. V. and Nemets, L. L., 1973, The structure of three-phase fluid&d beds. Inr. Chem. Engng. 13, 5741. Richardson, J. F. and Zaki, W. N., 1954, Sedimentation and fluidization: Part I. Trans. Inst. Chem. Engrs 32, 35-52. Rigby, G. R. and Capes, C. E., 1970, Bed expansionand bubble wakes in three-phase fiuidization. Can. J. them. Engng 48, 343-348. Sinha, V. T., Rutensky, N. and Nyman, D., 1984, Three-phase fluidization of polydisperse beads. Paper presented at the A.1.Ch.E. Annual Meeting, San Francisco, 25-30 Nov. Soung, W. Y., 1978, Bed expansion in three-phase fluidization. Ind. Engng Chem. Proc. Des. Dev. 17, 33-36.