Epstein N., Grace J.R. Spouted and Spout-Fluid Beds: Fundamentals and Applications

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Hydrodynamics of spout-ﬂuid beds 107

Figure 6.2. Regime map of a small spout-ﬂuid bed

(D = 152 mm, D

= 19.1 mm, H = 0.6 m,

θ = 60

◦

, d

= 2.9 mm, ρ

= 1040 kg/m

,airat20

◦

C and 1.03 bar, G–ﬂuidization at minimum

condition, A–spouting at minimum condition, C–spout-ﬂuidization at minimum condition).

Figure 6.3. Regime map of a large spout-ﬂuid bed

(D = 0.91 m, D

= 88.9 mm, θ = 60

◦

, H

1.5 m, d

= 3.25 mm, polystyrene particles, air at 20

◦

C and 1.03 bar, G–minimum ﬂuidization,

A–minimum spouting, C–spout-ﬂuidization at minimum condition).

6.1.2 Pressure drop and pressure distribution

The bed pressure drops in spout-ﬂuid beds depend on the ﬂows of both spouting gas and

ﬂuidizing gas. As shown in Figure 6.4, the pressure drop of a spout-ﬂuid bed shares the

characteristics of a conventional spouted bed when the spouting gas velocity is increased

at a constant auxiliary gas velocity,

9–12

whereas the pressure drop across a spout-ﬂuid

bed varies in a manner similar to that of a ﬂuidized bed when increasing the auxiliary

108 Wenqi Zhong, Baosheng Jin, Mingyao Zhang, and Rui Xiao

Figure 6.4. Pressure drop versus spouting gas velocity

(A = 0.3 m × 0.03 m, A

= 0.03 m ×

0.03 m, θ = 60

◦

, U

= 0.39, d

= 3.2 mm, ρ

= 1640 kg/m

Figure 6.5. Pressure drop versus auxiliary (“ﬂuidizing”) gas velocity

(A = 0.3 m × 0.03 m, A

0.03 m × 0.03 m, θ = 60

◦

, u

= 10 m/s, d

= 3.2 mm, and ρ

= 1640 kg/m

gas velocity while maintaining the spouting gas velocity constant.

11,12

As illustrated in

Figure 6.5, the pressure drop increases gradually with increasing ﬂuidizing gas velocity

and then approaches a constant level.

In a spout-ﬂuid bed, the maximum pressure drop required to initiate spouting increases

with increasing static bed height, spout nozzle diameter, and particle density, but

decreases with increasing particle diameter. These tendencies are similar to those of

conventional spouted beds. Furthermore, the maximum pressure drop across a spout-

ﬂuid bed decreases with increasing ﬂuidizing gas velocity.

Hydrodynamics of spout-ﬂuid beds 109

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Dimensionless Height, Z

Dimensionless radius, R

0.7 0.8 0.9 1.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Dimensionless Height, Z

0.7 0.8 0.9 1.0

0.0 0.2 0.4

(a)

0.6

Streamline

Isobar

Streamline

Isobar

0.8 1.0

Dimensionless radius, R

0.0 0.2 0.4

(b)

0.6 0.8 1.0

0.680

0.645

0.610

0.575

0.540

0.505

0.470

0.435

0.400

0.365

0.330

0.295

0.260

0.225

0.190

0.155

0.120

0.085

0.95

0.90

0.85

0.80

0.75

0.70

0.65

0.60

0.55

0.50

0.45

0.40

0.35

0.30

0.25

0.20

0.15

0.10

0.05

0.680

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

0.60

0.65

0.085

0.120

0.155

0.190

0.225

0.260

0.295

0.330

0.365

0.409

0.645

0.610

0.575

0.540

0.505

0.470

0.435

0.95

0.90

0.85

0.80

0.75

0.70

Figure 6.6. Comparison of ﬂuid ﬂow and pressure distribution of a conventional spouted bed and

a spout-ﬂuid bed

(D = 0.91 m, D

= 88.9 mm, θ = 60

◦

, H

= 2 m, polystyrene, d

= 3.25 mm):

(a) Q

= 0; (b) Q

= 0.2 m

/s.

Addition of auxiliary gas causes the pressure distribution to be more uniform in the

radial direction, even in the conical lower part of the column. The pressure gradient in the

vertical direction is substantially higher with auxiliary ﬂow present because of increased

interstitial ﬂow through the annulus.

3,11

The Epstein-Levine

and Lefroy-Davidson

equations have been found to be in reasonable agreement with experimental pressure

proﬁles in the annulus.

A computer model that involves ﬁnite difference solutions of the vector form of the

Ergun

equation gives useful qualitative predictions of the ﬂuid ﬂow distribution and

good predictions of the pressure proﬁles in the annulus. A typical comparison of ﬂuid

ﬂow and pressure distribution of a spouted bed with a spout-ﬂuid bed based on the vector

form

of the Ergun equation i s shown in Figure 6.6. Solid curves represent streamlines,

whereas dashed lines represent predicted isobars in the annulus. The distribution of ﬂow

leaving the bed through the top of the annulus is virtually the same for the conventional

spouted bed and the spout-ﬂuid bed. However, more gas enters the annulus from the

spout near the central inlet for the spouted bed. As the auxiliary ﬂow rate increases,

some gas even enters the spout from the annulus.

110 Wenqi Zhong, Baosheng Jin, Mingyao Zhang, and Rui Xiao

0.0 0.1 0.2 0.3 0.4

150

200

260

(m/s)

msi

(m/s)

(mm)

0.5 0.6 0.7

Figure 6.7. Variation of minimum spouting velocity with ﬂuidizing gas velocity

(D = 0.125 m,

= 18 mm, θ = 60

◦

, d

= 1.62 mm, ρ

= 2490 kg/m

6.1.3 Minimum spouting velocity and minimum spout-ﬂuidizing velocity

The minimum spouting velocity of a spout-ﬂuid bed can be deﬁned as the spout nozzle-

based spouting gas velocity, u

msi

or as the column-based superﬁcial spouting gas

velocity, U

16,17

when spouting is initiated in the central spout region at a certain

auxiliary gas velocity. Both deﬁnitions share the characteristics of a conventional spouted

bed

18,19

in that both u

msi

and U

increase with increasing static bed height, particle

density, particle diameter, and spout nozzle diameter. However, they also decrease with

increasing ﬂuidizing gas velocity, as indicated in Figure 6.7.

The minimum spout-ﬂuidizing velocity, U

msf

, of a spout-ﬂuid bed, deﬁned as the

minimum total superﬁcial gas velocity when spouting is initiated in the central spout

region and the annulus is aerated, also increases with increasing static bed height, particle

density, particle diameter, and spout nozzle diameter.

12,16,17

An increase in auxiliary gas

velocity also leads to increasing U

msf

as plotted in Figure 6.8. The bed diameter and

perforated distributor conﬁguration (e.g., cone angle, gas distribution geometry, and hole

orientation angle) all affect U

msf

. By comparing U

msf

for a small column

with a large

column,

it is found that U

msf

decreases with increasing column diameter. Moreover,

msf

decreases with increasing included cone angle, but increases with increasing hole

orientation angle (angle from the horizontal).

The correlation of Tang and Zhang

based on 590 groups of experimental data,

1 − ε

= cos(θ/6) sin(θ/2) tan(ϕ) f (D/D

cref

)





0.43





1.90





0.33



ρ(ρ

− ρ)gD



0.65



0.051 − 0.00046





0.83



, (6.1)

Hydrodynamics of spout-ﬂuid beds 111

5.0

4.5

4.0

3.5

3.0

0.7 0.8 0.8 1.0 1.1

0.03 × 0.03

)

0.07 × 0.03

0.10 × 0.03

1.2 1.3 1.4 1.5

(m/s)

msf

(m/s)

Figure 6.8. Variation of minimum spout-ﬂuidizing velocity with ﬂuidizing gas velocity

(A = 0.3 m × 0.03 m, θ = 60

◦

, H

/D = 1.72, d

= 2.8 mm, ρ

= 1018 kg/m

can predict reasonable trends for U

in terms of cone angle, θ , gas distribution geometry,

hole orientation angle, ϕ (angle between ﬂuidizing gas inlet line and distributor plane),

bed diameter, D, and reference diameter,

ref

, by using modiﬁed functions of cos(θ/6),

sin(θ/2), tan (ϕ), and f (D/D

ref

The spout-nozzle-based u

msi

correlation of Zhong et al.,

based on 314 groups of

experimental data, can also be used. This correlation has a similar form to that of Choi

and Meisen,

but adds the term (1 + U

) to cover the effect of ﬂuidizing gas,

giving

msi

= 24.5

(

2gH

)

0.5





0.472





0.183





0.208



1 +



−0.284



− ρ



0.225

≥ 0.

(6.2)

To determine the minimum spout-ﬂuidizing velocity, U

msf

, the correlations of Nagarkatti

and Chatterjee

and Zhong et al.

predict the right trends. However, these correlations

still need to be further tested and improved based on additional experimental data.

6.1.4 Voidage and particle velocity

Typical radial proﬁles of local voidage measured by an optical probe

are presented

in Figure 6.9. Spout voidage decreases with increasing auxiliary airﬂow; this ﬁnding

is nearly independent of particle size. The local voidage in the annulus increases with

increasing height, whereas there is no consistent trend with increasing auxiliary airﬂow.

Spout shapes, determined from voidage proﬁles and plotted in Figure 6.10, are similar

to those in conventional spouted beds.

The spout diameter increases with increasing

particle size. The proportion of auxiliary air has remarkably little inﬂuence on the spout

diameter.

20,22

112 Wenqi Zhong, Baosheng Jin, Mingyao Zhang, and Rui Xiao

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0102030405060

Radial distance from spout axis (mm)

= 0.15

= 0.43

Voidage(-)

70 80 0 10

168

218

268

z (mm)

20 30 40 50 60 70 80

Figure 6.9. Radial proﬁles of local voidage at different heights

(D =0.152 m, D

=19.1 mm, θ =

◦

, H

= 0.28 m, d

= 1.33 mm, ρ

= 2493 kg/m

, U

= 0.672 m/s, Q

= Q

+ Q

= 1.2Q

300

250

200

150

100

0 5 10 15 20

= 1.33 mm

= 1.84 mm

= 2.53 mm

25 30 0 5 10 15 20 25 30 0 5 10

0.00

0.15

0.28

0.43

15 20 25 30

Radial distance from spout axis (mm)

Height above orifice z (mm)

Figure 6.10. Vertical proﬁles of spout radii for three particle sizes

(D = 0.152 m, D

= 19.1 mm,

θ = 60

◦

, H

= 0.28 m, glass beads, Q

= Q

+ Q

= 1.2Q

The particle velocity proﬁles in the spout are of similar shape to those in conventional

spouted beds,

as shown in Figure 6.11. A maximum velocity is reached at some

distance above the oriﬁce, above which the particle velocity generally decreases with

increasing height. Increasing the proportion of auxiliary gas, Q

, may reduce the

local particle velocity in the spout and reduce the difference in local particle velocity

between the bottom and top of the bed. Velocity proﬁles in the annulus for a spout-ﬂuid

bed resemble those reported by He et al.

for a conventional spouted bed. The vertical

Hydrodynamics of spout-ﬂuid beds 113

4.0

3.5

3.0

= 0.15

= 0.43

2.5

2.0

1.5

1.0

0.5

0.0

0 5 10 15 20

z (mm)

168

218

268

Radial distance from spout axis (mm)

Particle velocity V

(m/s)

0 5 10 15 20

Figure 6.11. Radial proﬁles of par ticle velocities in the spout

(D = 0.152 m, D

= 19.1 mm, θ =

◦

, H

= 0.28 m, d

= 1.84 mm, ρ

= 2485 kg/m

, U

= 0.795 m/s, Q

= Q

+ Q

= 1.2Q

10 20 30 40

z (mm)

50 60 70 10

Radial distance from spout axis (mm)

Particle velocity V

(mm/s)

20 30

168

218

268

40 50 60 70

= 0.15

= 0.39

Figure 6.12. Radial proﬁles of particle velocities in the annulus

(D = 0.152 m, D

= 19.1 mm,

θ = 60

◦

, H

= 0.28 m, d

= 1.84 mm, ρ

= 2485 kg/m

, U

= 0.795 m/s, Q

= Q

+ Q

1.2Q

particle velocities decrease with decreasing height. Particles also travel more slowly

near the outer wall of the column and there is limited inﬂuence of the proportion of gas

entering as auxiliary gas, as portrayed in Figure 6.12.

Time-average solids mass ﬂowrates in the spout and annulus of spout-ﬂuid beds can be

calculated by integrating the voidage and particle velocity proﬁles, based on the steady

state requirement that the upward-moving solids mass ﬂow in the spout should equal the

downward-moving solids mass ﬂow in the annulus (see He et al.

). As for conventional

114 Wenqi Zhong, Baosheng Jin, Mingyao Zhang, and Rui Xiao

1.0

0.8

0.6

0.4

0.2

0.0

0.0 0.3 0.6

Zhong et al.

Rao et al.

Grbavcic et al.

0.9 1.2 1.5

msf

Figure 6.13. Effect of auxiliary gas ﬂowrate on H

msf

(D = 90 mm, D

= 10.3 mm, d

1.84–2.42 mm, ρ

= 2600 kg/m

)

;(D = 144 mm, D

= 25 mm, d

= 2.03–4.12 mm, ρ

2511–2573 kg/m

)

;(A = 0.3 m × 0.03 m, A

= 0.03 m × 0.03 m, d

= 1.3–3.2 mm, ρ

1018–2600 kg/m

spouted beds, the solids mass ﬂowrates in the spout and annulus increase with increasing

height, with particles entering the spout over its entire height. As reported by Pianarosa

et al.,

with increasing auxiliar y gas ﬂow there is some decrease in net solids circulation

owing to less entrainment of particles by the centrally injected spouting gas.

6.1.5 Spoutable bed height

The maximum spoutable bed height, H

, is an important characteristic of both conven-

tional spouted beds and spout-ﬂuid beds, because it is directly related to t he amount of

material that can be processed by spouting. In spout-ﬂuid beds, H

can be determined

by adding particles stepwise until periodic and incoherent spouting can no longer be

achieved for any spouting gas velocity at a given auxiliary gas ﬂowrate.

for a spout-ﬂuid bed decreases with increasing particle size and increasing spout

oriﬁce diameter.

24–27

Increasing the ﬂuidizing gas ﬂowrate leads to a sharp decrease

in H

, as presented in Figure 6.13, where H

msf

and H

are the maximum spoutable

bed heights with and without ﬂuidizing gas, respectively. Existing H

correlations for

conventional spouted beds

24,25,27

are subject to large discrepancies when used to predict

for spout-ﬂuid beds, because they neglect the effect of the auxiliary gas.

When bed materials are tested with bed depth exceeding the maximum spoutable

bed height, the region of stable ﬂow patter n is narrow, and a stable coherent spout

or fountain cannot be obtained. Instead, periodic and incoherent spouting and spout-

ﬂuidizing occur.

A stable ﬂow pattern of JFB may form; this is of special interest for

some applications, such as coal gasiﬁcation.

In this case, the spout-ﬂuid bed resembles

a jetting ﬂuidized bed, as described by Yang.

28,29

Hydrodynamics of spout-ﬂuid beds 115

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Particles

Mung bean

Millet

Polystyrene

15 470

470

515

(m/s)

(mm)

Figure 6.14. Effect of ﬂuidizing gas ﬂowrate on jet penetration depth L

(A = 0.3 m × 0.03 m,

= 0.03 m × 0.03 m, θ = 60

◦

6.1.6 Jet penetration depth

One of the features of gas injection into a spout-ﬂuid bed is the distance to which ﬂuid

dynamic disturbances associated with the injection extend, known as the jet penetration

depth. The jet penetration depth of spout-ﬂuid beds operated in the ﬂow regime of JFB

is similar to that in a jetting ﬂuidized bed.

29–34

The jet penetration depth increases with

increasing spouting gas velocity and with increasing spout oriﬁce diameter, whereas

it decreases with increasing particle density, particle diameter, static bed height, and

auxiliary gas ﬂowrate.

Figure 6.14 shows the typical variation of jet penetration depth

with auxiliary gas ﬂowrate.

6.1.7 Gas mixing

Mixing of spouting gas and auxiliary gas of spout-ﬂuid beds has been investigated

by tracer techniques. Experiments found that transfer of spouting gas into the annulus

and of auxiliary gas into the spout take place simultaneously,

29 ,36–41

leading to mixing

of spouting and auxiliary gases. Increasing the spouting gas velocity and ﬂuidizing

gas ﬂowrate can promote both axial and radial gas mixing in spout-ﬂuid beds,

38–40

but increasing the auxiliary gas ﬂowrate is more effective.

40,41

The axial and radial gas

mixing become poor when the ﬂow pattern undergoes a transition from stable to unstable

ﬂow, and it is difﬁcult to obtain effective mixing in the wall layers.

The mechanism of gas mixing in spout-ﬂuid beds is complex, according to the ﬁndings

in the literature on diffusive mixing, on convective transport

29,37,38

owing to pressure

gradient, and on combined convection and diffusion

39–41

because of pressure and con-

centration gradients. Based on different gas mixing mechanisms, different models have

been proposed.

37,39,41

The probabilistic model of Freychet et al.

indicates that the gas

exchange rate between the spout jet and annulus increases rapidly with increasing auxil-

iary gas velocity. Similar results have been predicted by a three-region mixing model.

116 Wenqi Zhong, Baosheng Jin, Mingyao Zhang, and Rui Xiao

(a) (b) (c) (d)

(e) (f) (g) (h)

Figure 6.15. Sequential stages of particle mixing

(A = 0.1 m × 0.03 m, A

= 0.01 m × 0.03 m,

ﬂat-bottom spout-ﬂuid bed, d

= 0.5 mm, ρ

= 2650 kg/m

, u

msi

= 1.4, U

≥ 0):

(a) t = 0s;(b)t = 2s;(c)t = 4s;(d)t = 6s;(e)t = 10 s; (f ) t = 15 s; (g) t = 20 s;

(h) t = 30 s.

6.1.8 Particle mixing

Particle tracer and digital image processing have been used to investigate particle mixing

in spout-ﬂuid beds. Increasing both the spouting velocity and the auxiliary gas velocity

can promote mixing.

42,43

Axial mixing varies more than radial mixing with increas-

ing spouting gas velocity, whereas this is reversed when increasing the auxiliary gas

velocity.

The initial tracer location affects the rate of mixing. For example, in one

study,

mixing was much faster for middle loading than for top, side, and bottom

loading, b ut the ﬁnal degree of mixing was independent of the initial tracer location.

The particle mixing process can be divided into three sequential stages: a macromix-

ing stage, a micromixing stage, and a stable mixing stage.

In the macromixing stage

(Figures 6.15a–c), the mixing speed is high, but the degree of mixing is low; in the

micromixing stage (Figures 6.15d,e), tracer particles mix with the bed material at the

individual particle level; in the stable mixing stage (Figures 6.15f–h), a dynamic equilib-

rium is achieved. Particle mixing in spout-ﬂuid beds is caused by diffusion, transporta-

tion, circulation, and the action of bubbles.

43,44

Diffusion, transportation, and circulation

dominate solids mixing at high spouting gas ﬂowrates, whereas bubble action becomes

dominant at large auxiliary gas ﬂowrates.