coltters, rivas - minimum fluidation velocity correlations in particulate systems

8/18/2019 Coltters, Rivas - Minimum Fluidation Velocity Correlations in Particulate Systems

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Minimum fluidation velocity correlations in particulate systems

R. Coltters*, A.L. Rivas

Department of Materials Science, Universidad Simon Bolivar, Caracas ,Venezuela

Received 26 February 2004; accepted 21 June 2004

Available online 12 November 2004

Abstract

A new relationship for the prediction of minimum fluidization velocity is proposed. It has been made a comprehensive critical review,concluding that in order to apply, some of these correlations additional experimental data is required, such as bed voidage and shape

factors. It is found a strong dependency of the physical and chemical properties of the particle surface on the minimum fluidization

velocity. This influence of the nature of the particle surface allows that empirical equations are applicable in specific cases, but cannot be

generalized. The original equation presented in this paper allows the predicting minimum fluidization velocity in a very simple way

without the need of experimental determination of bed voidages and shape factors. The new correlation was tested using 189

measurements reported in the literature on about 90 different materials. The results shown that the new correlation is in very well

agreement with the experimental data.

D 2004 Elsevier B.V. All rights reserved.

Keywords: Gas–solid fluidization; Particle size; Minimum fluidization velocity

1. Introduction

Among the various factors affecting the dynamic con-

ditions of fluidized beds, one of the most significant is the

fluid velocity at incipient fluidization. The velocity at which

this behavior develops is called the minimum fluidization

velocity. This is an important variable in the design of

fluidized beds [1–4]. Knowledge of the minimum fluid-

ization velocity facilitates the study of reaction kinetics

because it allows a rational use of the gas in the gas phase as

an excess over that required for minimum fluidization. It

would therefore be useful to be able to predict this velocity

instead of having to measure it for each new situation. Untilnow, many equations for calculating this variable have been

obtained for glass beads, metallic shots, sands, cracking

catalysts, etc., all of them of fairly well-known particle size

distribution and shape.

However, with the increasing interest in the use of

fluidized beds for ore treatment in extractive metallurgy, the

number of systems in which fluidized beds are finding practical application is rapidly expanding. For such beds,

which are formed by a wide number of combinations of

particle size and shape, no information is available for the

predictions of the minimum fluidization velocities. Disagree-

ments among these predictions, which are on different

correlations, reflect the problem of making allowances for

effects such as: particle shape, size distribution, and

interparticle forces, etc. Thus, it seems that most of the actual

correlations appears to be inadequate. Accordingly, a new

general correlation has been developed based on the available

published experimental data in this field, that fits the data

quite well.This paper deals with gas–solid systems and reviews the

previous publications and the empirical arguments support-

ing the new general correlation.

2. Literature survey

Several equations are available for predicting the

minimum fluidization velocity, based mainly on particle

and gas properties; densities of solid and gas (qs, qg),

0032-5910/$ - see front matter D 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.powtec.2004.06.013

* Corresponding author.

E-mail address: [email protected] (R. Coltters).

Powder Technology 147 (2004) 34 – 48

www.elsevier.com/locate/powtec


2/15

sphericity (/), particle diameter ( D p) and voidage at

minimum fluidization velocity (emf ). The correlations

proposed in the literature [5–28], containing similar fluid-

ization parameters, differ in the values of their coefficients

and exponents, which usually were determined for a

particular fluidization system.

Some correlations appear to be equivalent. For example,Wen and Yu’s correlation [29] is given by the following

expression:

U mf ¼ e4:7mf

18 C DS

C DS stokes

gD2Pðqs qgÞ

l ð1Þ

where

C DS

C DS stokes¼

C D Remf

24 ðaÞ

C D ¼ 18:5

Re3=5mf

ð bÞ

Substituting Eq. (b) in (a), we arrive at:

C DS

C DS stokes ¼

18:5Remf

24Re:3=5mf

¼ 0:0771Re0:4mf ðcÞ

and combining with Eq. (1) gives

U mf ¼e4:7mf

18 0:771Re0:4mf

dD2pðqs qg Þ

l ðdÞ

This equation can be simplified and rearranged into the

following form:

U mf ¼ 0:072e4:7mf Re

0:4mf

dD2 pðqs qgÞ

l ð2Þ

It seems that, the Wen and Yu correlation (1) coincides with

Schiller’s Eq. (2) [30].

Other [6,9–18] are of the Ergun equation type [31],

Lippens and Mulder [28] showed that they have a general

form, which can be written as:

Ar

Remf ¼ f emf ;/ s

þ g emf ;/ s

Remf

ð3Þ

and

Remf ¼ C 21 þ C 2Ar

1=2 C 1

h ð4Þ

from which U mf may be calculated according to Eq. (5).

U mf ¼ l Remf

d Pqgð5Þ

These expressions require information of the / and emf parameters, which are difficult to measure experimentally.

This is particularly true of incipient bed voidage bemf Q at low

pressure using dense materials and big bed heights. In this

case, only a fraction of the bed appears to approach

fluidization at the minimum fluidization velocities, whereas

the rest of the volume remains undisturbed. In this situation,usually the true value of bemf Q can be approximated by the

value of beP Q obtained by pouring the particles slowly from

one container into another [32].

The deduction of these equations has been carried out by

experimental data fitting. Fletcher et al. [33] concluded that to

apply these relations, experimental data have to be extracted

from the literature to calculate Remf , but each experimental

point requires specific values of C 1 and C 2. Therefore,

calculations based on simple values of C 1 and C 2 introduce a

significant error into the prediction of U mf . Also it can be

emphasize, the knowledge of the voidage emf at incipient

fluidization and the sphericity /s is needed to apply Eq. (5).Additionally in the fitting procedure, in order to obtain a

linear dependence of Ar/ Remf on Remf , emf and /s must be

constant, which it may no be true.

The purpose of this paper is search for a simple

correlation to predict U mf without the necessity of exper-

imental determination of bed voidages and shape factors.

3. Development of the new correlation

It is well known that the minimum fluidization

velocity U mf is sensitive to parameters such as solid

and fluid densities, the nature of solids and fluids, etc. In

addition, gas viscosity is usually considered independent

of pressure [34,35], but density is not. It is widely known

that U mf is quite sensitive to the density difference

(qsqf ) due to the buoyancy. Additionally, the particle– fluid density ratio can be related to the drag exerted from

the fluid on the particles and to the void fraction [36,37].

Therefore, dimensional analysis of the independent

variables suggests that there may be a functional relation-

ship among the following parameters affecting the

minimum fluidization velocity:

qsqg

; D p; qs qg; l

Or assuming simple power relationships:

U mf ¼ K

qsqg

m; Dn p; ðqs qgÞ

p; g ;lqa

ð6Þ

where K and a are constants and are functions of the solid–

fluid system, and m, n, p and q are exponents. This equation

has the form

U mf ¼ KX a ð7Þ

R. Coltters, A.L. Rivas / Powder Technology 147 (2004) 34–48 35


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and

X ¼ u

qsqg

m; Dn p; ðqs qgÞ

p; g ; lqa

ð8Þ

The exponents of Eq. (8) have been evaluated using

dimensional analysis and by experimental data fitting fromthe literature. After substitution of these exponents, Eq. (8)

becomes

X ¼ D2 pðqs qgÞ g

l

qsqg

1:23ð9Þ

combining Eqs. (7) and (9), the minimum fluidizing velocity

yields

U fm ¼ K

D2 pðqs qgÞ g

l

qsqg

1:23að10Þ

Eq. (10) is a general expression that may be used to

estimate the minimum fluidization velocity in a system. The

precise knowledge of emf and /s is avoided, which is very

important given the experimental difficulties in determining

those parameters, especially when beds of irregular shape

and coarse particles are handled.

4. Evaluation of the correlation

To test the relation (10), experimental results have been

extracted from the literature. The literature data have been

selected according to the following criteria:

(a) The particle diameter used to test the correlation were

those defined by the relation: d̄ d p ¼ 1P

xd a

where x is the

weight fraction of particles in each size range and the

average particle diameter d ¯ p usually was obtained from

sieve analysis

(b) The minimum fluidizing velocity strongly depends on

the surface characteristics of the solid particles.

The first condition excludes rod- or disc-shaped particles

because the interpretation of their characteristic length

measurement is ambiguous. The last selection criteria

demands select data from solids of similar surface morphol-ogy or crystallographic structures at ambient temperature and

atmospheric pressure. Therefore, the correlation will be tested

against experimental values of U mf for the following groups

of materials: metals, alumina, glass, sand, coal, catalysts,

metallic ores, polymers and minerals. Table 1 shows the bed

material and fluidizing gas of the systems studied.

5. Results

The experimental data reported with all the groups

selected has been plotted in Figs. 1–10. If Eq. (10) applies,

a plot of log U mf vs. log X should yield to a straight line,

where K and a can be determined.

5.1. Metals

Nineteen sets of experimental data have been tested. Fig.

1 shows the relation between the experimental data of U mf and the calculated values of X as a logU mf vs. log X . The

experimental data points can be approximated by the

following expression resulting from the best linear fit to

Eq. (10). The relationship has been correlated as

U mf ¼ 4:7673 106 X 0:71635F0:02213ð Þ

ð11Þ

From this figure, it can be seen that the equation fits

the experimental data in an excellent manner. Closer

scatter of the data points around this line is seen.

Nevertheless, the correlation is applicable over a wide

range of particle size (3 AmV D pV900 Am) and particledensity (2.7VqsV11.37 [g/cm

3]). The fitti ng of the

experimental data to Eq. (11) has a correlation coefficient

of R =0.990.

Also shown in this figure are three points, mar ked

with arrows, from experiments of Turton et al. [38] and

Kusakabe et al. [43], in both studies the results yield

values for U mf higher than those obtained in the other

metal–gas systems.

Turton et al. [38] measure the heat transfer coef-

ficients between fluidized beds and immersed current-

carrying Alumel wires. The beds particles consisted of

uniformly-sized aluminum from 105 to 454 Am. The

fluidizing gas used was house air at a total pressure of 1

atm, the oxygen partial pressure in the fluidizing air was

0.21 atm.

Kusakabe et al. [43] used ultra-fine aluminum powder

(d P=134 Am). High-purity nitrogen as the fluidizing gas

was used and the bed was evacuated with a rotary pump.

Under these conditions and assuming a vacuum of 105

mm Hg, the oxygen partial pressure in the fluidizing

nitrogen probably was c2.64109 atm (this, of course,ignores vacuum pump vapours, etc.). Because at room

temperature the standard free energy of formation for

Al2O3 is about 975 kJ and the equilibrium oxygen partial

pressure is c1095

atm [144], it is thermodynamically possible that the bare aluminum surface of the particles

exposed to an oxygen containing atmosphere a very thin

layer of alumina (far too thin to be visible to the naked

eye) was formed very quickly. Thus, it is conceivable that

alumina was formed on the aluminum particle surface by

oxygen from the fluidizing gas and they actually were

measuring the U mf of Al2O3/air and Al2O3/N2 instead of

that for Al/air and Al/N2 systems.

Therefore, the surface geometry of the aluminum

particles probably was significantly modified after the

particle was coated with a film of alumina and this coating

containing pores with diameters in the range from 4 to 100

R. Coltters, A.L. Rivas / Powder Technology 147 (2004) 34–4836


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Table 1

Data from the literature for calculating the minimum fluidization velocity

Ref. Solid-air Symbol Fig.

[1,59] Glass beads 3

Hollow silica ballons 3

Cooper powder 1

Cooper shot (spherical) 1[2] Glass spheres 3

Glass Balls 1/16? 3

[34] Glass beads 3

FCC 6

Silica sand 4

[38] Aluminum powder 1

Aluminum powder 2

Polyethylene beads 8

Glass spheres 3

Sand 4

[40] Steel shot (spherical) 1

Alumina powder 2

Glass spherical 3

[41] Steel shot (spherical) 1

Copper shot (spherical) 1Polystyrene beads 8

Ballotini 6

[44] Copper powder 1

Glass beads 3

FCC catalyst 6

[50] Sand 4

[42] Copper (/s=0.56) 1

Copper shot (/s=1) 1

Bronze shot (/s=1) 1

Polystyrene spheres 8

Ballotini 6

Glass 3

Sand 4

Carbon 9

[45] Bronze 1Ballotini 6

[46] Lead shot (spherical) 1

Bellotini 6

Diakon 6

[47] Sand 4

Rock salt (NaCl) 10

Glass balls 3

[48] Alumina powder 2

Corindon particles 2

[49] Corindon 2


Glass spheres 3

Iron ore particles 7

[52] Glass powder 3

Petroleum coke particles 5Ballotini 6

[53] Alumina powders 2


Magnetite (Fe3o4) particles 10

[55] Silica sand 4

CaF2MgF2 particles 10

[56] Fused alumina powder 2

CaCO3 particles 9

[57] Ballotini 6

[58] Glass beads 3

Silica sand 4

Dolomite particles 9

SiC particles 10

Alumina 2


[59] Hollow char 5

[60] Glass beads 3

Sand 4

Coal particles 5

Polyethylene (PE) particles 8[61] Glass beads 3

Sand 4

[62] Glass beads 3

Sand 4

Catalytic FCC 6

Polypropylene 8

[63] Glass beads 3

Sand 4

[64] Glass beads 3

Cracking catalyst 6

[65] Glass beads 3

[66] Glass beads 3

[67] Glass powder 3

Sand 4

Catalytic powder FCC 6[68] Glass spheres 3

Hollow plastic spheres 8

CaCO3 particles 9

[69] Glass spherical 3

[70] Glass spheres 3

Sand 4


[72] Glass balls 3

[73] Glass balls 3

[74] Glass beads 3


Silica sand 4

[76] Glass beads 3

[77] Glass beads 3

[78] Glass beads 3[79] Sand 4

[80] Silica sand 4

Petroleum coke 5

[81] Sand 4

[82] Sand 4

[83] Sand 4

[84] Sand B 4

Sand T 4

[85] Sand 4

[86] Glass beads 3

[87] Sand 4

[88] Sand 4

[89,90] Silica sand 4

FCC particles 6

[91] Sand 4[92] Sand 4

[93] Sand 4

[94] Sand 4

[95] Sand 4

Ballotini 6

[96] Sand 4

[97] Sand 4

Synclyst particles 6

[98] Silica sand 4

FCC particles 6

[99] Sand 4

[100] Sand 4

[101] Sand 4

[102] Sand 4

Table 1 (continued )

(continued on next page)



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nm [145] possibly increases the surface area and roughnessand promotes close contact among particles, and obviously,

originates in the increasing relative magnitude of the

cohesive forces between the particles leading to a higher

than expected U mf . This was also shown by the work done

by Luo et al. [39]; they measured the heat transfer

coefficient in fluidized bed of Ni and Ni alloy powders.

The fluidizing gas was Nitrogen. Two types of nickel

powder of the same spherical shape were employed, Ni-

1 consisted of spheres with flat surface and Ni-2

consisted of spheres with acicular surface. They found

that Ni-2 was easier to fluidize and they explained by

differences in surface roughness; the acicular surface of

Ni-2 powder limits close contact between the particles,

while the flat surface of Ni-1 powder promotes close

contact among the particles, so that the cohesive forces

of Ni-1 powder was stronger than that of Ni-2 powder,

this was reflected by the high value of U mf . Thus, this

conclusion drawn from the fitting of experimental results

of Turton and Kusakabe studies, appears to be justified

because the U mf could be related to the interparticle

adhesive force.

5.2. Alumina

Aluminium hydroxides are common sources of alumi-nium oxide (Al2O3), which itself exists in various

metastable polymorphs (transition Aluminas) in addition

to the thermodynamically stable a Al2O3 form (corun-

dum). The transition aluminas v, g, d, j, h, c and q

(especially c form) have fine particle sizes and high

surface areas with enhanced surface/gas interactions.

These alumina phases are produced during the heat

treatment of aluminum hydroxide. This means that a

series of morphological forms develops the surface

properties which are determined by the structure and

impurity content of the starting material (aluminum

hydroxide) and the temperature of calcination. Therefore,


[104] Sand 4

[105] Sand 4

[106] Silica sand 4

FCC 6

[107] Sand 4PVC beads 8

[108] Sand 4

[109] Sand 4

[110] Coal particles 5

Limestone 9

CaSO4 particles 10

Partially sulphated lime 9

[111] Diakon 6

Fresh catalyst 6

Spent catalyst 6

[112] Ballotini 6

[113] Ballotin 6

Catalyst 6

Diakon 6

[114] Reformer catalyst 6[115] FCC 6

[116] Microspherical catalyst 6

FCC 6

[117] Cracking catalyst 1 6

Cracking catalyst 2 6

[118] Alumina catalyst 6

[120] Catalyst sand 6

[121] Engelhard FCC catalyst 6

[122] Alumina cracking catalyst 6

[123] FCC 6

Polyethylene Resin (PE) 8

[124] Iron ore particles 7

[127] 1/8 Nylon spheres 8

Plastic particles 8

Acrylic particles 8[128] Polyethylene 8

Plypropylene 8

[129] Polyvinyl acetate 8

[130] PVC particles 8

[131] Dolomite particles 9

[132] SiC particles 9

[133] CaCO3 particles 9

[134] ZnO particles 9

[135] Ballotini 6

[136] Si3 N4 particles 9

[137] Alumina beads 2

[138] Silica sand 4

[139] Sand 4

Alumina 2

[141] Sand 4[140] Glass beads 3

[143] Silica sand 4

FCC 6

Ref. Solid-gas Symbol Fig.

[39] Nickel-1/Helium 1

(Nickel-1/Nickel-2)/H2 1

[104] Sand/natural gas 4

Sand/Acetylene 4

Sand/H2 4

[115] FCC/Argon 6

FCC/Neon 6

Ref. Solid-Nitrogen Symbol Fig.

[21] Nickel powder 1

Alumina powder 2

[39] Nickel-1 (spherical) 1

[43] Iron powder 1

Aluminum powder 1Aluminum powder 2


Pyrrhotite particles 10

[103] Sand 4

CaCO3 particles 9

[119] Li/MgO catalyst 6

[125] Iron ore particles 7

[126] Copper concentrate 7

[135] Si3 N4 particles 9


Silica sand 4

FCC particles 6

Table 1 (continued ) Table 1 (continued )



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alumina can be manufactured by many different routes,

and the different nature and morphology of alumina

particles result in differences in the behavior of fluidized

beds. The fact that the same material has different surface

properties, as particle–particle interactions is believed to

be quite important.

Commercially for industrial applications, for the catalyst

and abrasive industries, high-purity alumina powders can be

classified as high density and low–medium density [146].

Sixteen sets of experimental data have been tested. The

correlation of U mf

for alumina was better addressed taking

into account the differences in alumina densities than

particles size. Then, according to the alumina densities

ranges, it was found that the experimental values of U mf are

much better fitted by two separated lines than by a simple

correlation. These correlations are shown in Fig. 2. The

equations of the best fitting are:

Low–medium density

U mf ¼ 2:7568 106 X 0:81455F0:02845ð Þ

ð12Þ

0.768VqsV2.8 [g/cm3]

High-density

U mf ¼ 3:7774 105 X 0:63012F0:03064ð Þ

ð13Þ

3.3VqsV4.015 [g/cm3].

Fig. 1. Comparison of the predictions of Eq. (10) with the experimental U mf data for Metal–Gas fluidized beds.

Fig. 2. Comparison of the predictions of Eq. (10) with the experimental U mf data for Alumina–Gas fluidized beds.



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The fitting of the experimental data to Eqs. (12) and (13)

have a correlation coefficient of R=0.991 and R=0.991,

respectively.

Fig. 2 shows that there is a good agreement between the

calculated values and the experimental one. Also these

results indicate that beds of particles of low-medium density

and high density have similar fluidization behavior, respec-

tively, over a wide range of particle size.

Also shown in this figure, are the values of U mf reported

by Turton et al. [38] and Kusakabe et al. [43] which fit

better on the linear relationship for low-medium density

than in Fig. 1. Therefore, it seems that the oxide-coated

aluminum particles showed a similar fluidization behavior

as pure alumina particles.

5.3. Glass

Thirty-three sets of experimental data have been tested.

It was found t hat t wo l ines fit much bet ter the

experimental values of U mf with different slope than by

Fig. 3. Comparison of the predictions of Eq. (10) with the experimental U mf data for Glass–Gas fluidized beds.

Fig. 4. Comparison of the predictions of Eq. (10) with the experimental U mf data for Sand–Gas fluidized beds.



8/15

a simple correlation. These correlations are shown in Fig.

3. The equations of the best fitting are:

U mf ¼ 4:3384 107 X 0:89029F0:1888ð Þ

ð14Þ

23 AmV D pV569 Am

U mf ¼ 2:4624 103 X 0:46943F0:01190ð Þ ð15Þ

569 AmV D pV3000 Am.



respectively.

These correlations suggest that in glass beads ranging

from a mean particle size of 23 to 569 Am, the effect of

particle interactions and viscous forces predominate. For

glass beads ranging from a mean particle size of 569 to 3000

Am where the slope of the straight line decreases, turbulence

becomes a factor and the support of the particle is no longer due to a simple viscous drag.

Fig. 5. Comparison of the predictions of Eq. (10) with the experimental U mf data for Coal–Gas fluidized beds.

Fig. 6. Comparison of the predictions of Eq. (10) with the experimental U mf data for Catalyst–Gas fluidized beds.



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5.4. Sand

Forty-eight sets of experimental data have been tested. It

was found that the experimental values of U mf are much

better fitted by two lines with different slope than by a

simple correlation. These correlations are shown in Fig. 4.

The equations of the best fitting are:

U mf ¼ 9:7119 107

X 0:84268F0:01601ð Þ

ð16Þ

95 mmV D pV800 mm.

U mf ¼ 6:4051 103 X 0:4252F0:01339ð Þ

ð17Þ



have correlation coefficients of R=0.993 and R=0.992,

respectively. The plot of sand data (Fig. 4) was similar to

that of Fig. 3.

5.5. Coal

Six sets of experimental data have been tested. It was

found that the experimental values of U mf are much better

fitted by two lines with different slope than by a simple

correlation.

These correlations are shown in Fig. 5. The equations of

the best fitting are:

U mf ¼ 4:7731 106 X 0:87117F0:01513ð Þ

ð18Þ

Fig. 7. Comparison of the predictions of Eq. (10) with the experimental U mf data for Ores–Gas fluidized beds.

Fig. 8. Comparison of the predictions of Eq. (10) with the experimental U mf data for Polymers–Gas fluidized beds.



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710 AmV D pV1000 Am

U mf ¼ 8:5557 103 X 0:46093F0:28872ð Þ

ð19Þ

1000 AmV D pV3578 Am.



respectively. The Eqs. (18) and (19) were generally similar

to those of glass and sand correlations.

Arguments similar to those used in Fig. 3 to explain the

fluidization behavior apply to Figs. 4 and 5. The trends in

these data could be explained in terms of the balance of

viscous and turbulent forces for each particle size range with

reference to Eqs. (18) and (19).

5.6. Catalyst

Thirty-eight sets of experimental data have been tested. It

was found that the data could be correlated on a single

straight line by plotting logU mf versus the calculated values

of log X . This relationship is shown in Fig. 6. The equation

of the best fitting is:

U mf ¼ 1:145 105 X 0:71957F01422ð Þ ð20Þ

25AmV D pV2250 Am.

The fitting of the experimental data to Eq. (21) has a

correlation coefficient of R =0.991.

Fig. 9. Comparison of the predictions of Eq. (10) with the experimental U mf data for Orthorhombic and Hexagonal minerals–Gas fluidized beds.

Fig. 10. Comparison of the predictions of Eq. (10) with the experimental U mf data for Cubic minerals–Gas fluidized beds.



11/15

Good agreement between the calculated and experimental

results was obtained, as revealed in Fig. 6. The results suggest

that particle density has been shown to be an unimportant

parameter, at least in the range 0.79–2.95 [g/cm3].

5.7. Metallic ores

Four sets of experimental data with different particle size

and shape have been tested. It was found also that the

experimental data could be correlat ed on a single straight

line. This relationship is shown in Fig. 7. The equation of

the best fitting is:

U mf 3:1108 108 X 0:93283F0:03451ð Þ

ð21Þ

101AmV D pV1250 Am.


correlation coefficient of R=0.994, indicating a good

agreement between the calculated values and the exper-imental one, such as can be seen in Fig. 7.

It is important to notice that metallic ores and concentrates

are generally of irregular particle size and shape and comprise

a wide spectrum of size distribution. Therefore, the correla-

tion is valid over a wide spectrum of size distribution. This is

so because the correlation has been derived from experi-

mental data predominantly for particles of irregular shapes.

5.8. Polymer

Fourteen sets of experimental data were tested. Here also,

it was found that the experimental data could be corr elatedon a single straight line. This relationship is shown in Fig. 8.

The equation of the best fitting is:

U mf ¼ 2:1308 104 X 0:59460F0:01730ð Þ

ð22Þ

116AmV D pV1000 Am.


correlation coefficient of R=0.995. Fig. 7 also shows good

agreement between the calculated values and the exper-

imental one. The plot of polymer data (Fig. 8) was similar

to those of metal (Fig. 1), catalyst (Fig. 6) and ores (Fig.

7). The results suggest similar fluidization behavior of the

beds. These correlations would indicate that U mf is directly proportional to the diameter of the particle squared, to the

difference in solid and gas density, and inversely proportional

to the first power of the gas viscosity. Figs. 1, 6, 7 and 8 also

suggest that the effect of particle size interaction and viscous

forces predominate and that the particle size distribution does

not appear to have a significant effect on U mf . This is

particularly evident for the polymer beds because a character-

istic property of polymeric particles is the superficial

dielectric properties. When two particles are in contact,

movement of electric charges occur through their surface

leading to a formation of a double electric layer and strong

particle–particle interaction.

5.9. Minerals

Seventeen sets of experimental data were tested. It was

found that the experimental values of U mf are much

Table 2

Values of K , a and R for the equation U mf = KX a applied to the published

fluidization data

Fluidizing system K a Correlation

coefficient R

Metal–Gas

3 Amb DPb900 Am

4.7673106 0.71635F0.02213 0.990

Alumina–Gas

Low–medium

density

0.768VqsV2.8

[gr/cm3

]

2.7568106 0.81455F0.02845 0.991

High density

3.3VqsV4.015

[gr/cm3]

3.7774105 0.6301F0.03064 0.991

Glass–Gas

23 Amb DPb569 Am

4.3384107 0.89029F0.01888 0.992

569 Amb DPb3000 Am

2.4624103 0.46943F0.01190 0.991

Sand–Gas

95 Amb DPb800 Am

9.7119107 0.84268F0.01601 0.993

800 Amb DP

b2800 Am

6.4051103 0.42520F0.01339 0.992

Coal–Gas

710 Amb DPb1000 Am

4.7731106 0.87117F0.01513 0.998

1000 Amb DPb3578 Am

8.5557103 0.46093F0.28872 0.996

Catalysts–Gas

25 Amb DPb2250 Am

1.145105 0.71957F0.01422 0.991

Metallic Ores–Gas

101 Amb DPb1250 Am

3.1108108 0.93283F0.03451 0.994

Polymer–Air

116 Amb DPb1000 Am

2.1308104 0.59460F0.01730 0.995

Mineral–Gas

Orthorhombic

502 Amb DPb2828 Am

4.427103 0.47851F0.03930 0.992

Hexagonal

0.89 Amb DPb2300 Am

7.926510 4 0.50953F0.01379 0.991

Cubic

106 Amb DPb2474 Am

7.1187105 0.61787F0.04099 0.994



12/15


13/15

better fitted by three separate lines than by a simple

correlation.

These correlations are shown in Figs. 9 and 10. The

equations of the best fitting are:

Orthorhombic System

U mf ¼ 4:427 103 X 0:47851F0:03930ð Þ

ð23Þ


Hexagonal System

U mf ¼ 7:9265 104 X 0:50953F0:01379ð Þ

ð24Þ

0.89 AmV D pV2300 Am.

Cubic System

U mf ¼ 7:1187 105 X 0:61787F0:04099ð Þ

ð25Þ


The fitting of the experimental data to Eqs. Eqs. (23)–

(25) have a correlation coefficient of R=0.992, R =0.991 and

R=0.994, respect ively.

Figs. 9 and 10 show that there is good agreement between

the calculated values and the experimental one. These results

indicate that the properties of the particle surface are key

factors for predicting U mf . In addition, these results indicate

that beds of particles of the same crystal structure have similar

fluidization behavior. This is confirmed by the data where the

minimum fluidizing velocity is well predicted by three linear

relationships corresponding to three different crystal systems.

This is because minerals often occur in geometrical forms

bounded by plane surfaces. Those of the same crystal systems

should have similar physical surface properties, which are

constant within narrow limits.

The values of K , a and the correlation coefficient R of

the curve fitting for each of the nine different fluidizing

systems are listed in Table 2.

In Table 3, using the equations drawn from the literature,

the experimental values of U mf given in column 1 are

compared with values calculated from various existing

correlations and those obtained applying Eq. (10). Column17 shows the calculated values of U mf applying Eq. (10) for

each particular system and column 18 shows the calculated

values of U mf applying the general Eq. (10) of the form

shown in Table 2. The results shown in Table 3 indicate that

the correlation of Babu et al. [11] yielded the greatest mean

error and standard deviation of errors probably because it

was developed from data for coals.

Based on the data selected from the literature the Eq. (10)

has been shown to be the most suitable for estimating the

minimum fluidization velocity. According to Table 3, the

deviation caused by using either Eq. (10) for a particular

systemorthegeneralEq. (10) given in Table2 are the smallest.

The most striking feature of Figs. 1–10 is the fact that, if

we consider the diverse materials and fluids used by several

investigators, there is excellent agreement between the

experimental data and the calculated values with a

correlation coefficient better than 0.99.

6. Conclusions

In this paper, a novel criterion for the selection of

fluidizing beds has been proposed to estimate the minimum

fluidization velocities.

It is found that the proposed correlation predicts values of

U mf , which are in excellent agreement with the experimental

data reported in the literature over a wide range of gas–solid

fluidized systems.

From the comparative analysis of the results shown in

Table 3, Eq. (10) emerges best for estimating the minimum

fluidization velocities of tested systems.Eq. (10) is useful for predicting U mf without the

necessity of experimentally determining bed voidages and

shape factors.

List of symbols

D p Particle size [cm]

G Gravitation constant 980 [cm/s]

K Constant in Eq. (10), dimensionless

U mf Minimum fluidization velocity [cm/s]

a Exponent in the power law on Eq. (10), dimensionless

emf bed voidage at minimum fluidization velocity,

dimensionless

l Viscosity of fluidizing gas [g/cm s]

qs Density of particle [g/cm3]

qg Density of fluidizing gas [g/cm3]

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coltters, rivas - minimum fluidation velocity correlations in particulate systems

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