Epstein N., Grace J.R. Spouted and Spout-Fluid Beds: Fundamentals and Applications
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2 Initiation of spouting
Xiaotao Bi
2.1 Introduction
In a bed packed with particles, the introduction of an upward-flowing fluid stream into
the column through a nozzle or opening in a flat or conical base creates a drag force and
a buoyancy force on the particles. A cavity forms when the fluid velocity is high enough
to push particles aside from the opening, as illustrated in Figure 2.1(a). A permanent
and stable vertical jet is established if the nozzle-to-par ticle-diameter ratio is less than
25 to 30.
1
Further increase in fluid flow rate expands the jet, and an “internal spout” is
established, as in Figure 2.1(b). Eventually, the internal spout breaks through the upper
bed surface, leading to the formation of an external spout or fountain, as in Figure 2.1(c).
Such an evolution process to a spouted bed, involving cavity formation, internal
spout/jet expansion, and formation of an external spout, was well documented in the
1960s.
2
Figure 2.2 shows the evolution of measured total pressure drop in a half-circular
conical bed
3
for 1.16-mm-diameter glass beads and ambient air, starting with a loosely
packed bed, Run 1. It is seen that the total pressure drop increases with increasing gas
velocity in the gas flow ascending process (shown by closed squares), and reaches a
peak value before decreasing to approximately a constant value with a further increase
in the gas velocity. When the gas velocity is decreased (closed triangles), after the bed
is operated at stable spouting along a gas flow ascending process, the total pressure drop
decreases, following a quite different path, with a much lower pressure drop than for
the ascending process. Such a pressure-drop-versus-gas-flow hysteresis appears to be
a reproducible phenomenon, as shown by repeated runs performed on the same day.
3
For the initially compacted bed, the pressure drop was much higher than for the loosely
packed bed in the ascending process, but the results in the descending process were the
same as for t he other runs. This indicates that the hysteresis is affected by the initial
particle packing state, but cannot be eliminated by changing the initial packing state.
Such a pressure drop hysteresis is quite different from that observed in a fluidized bed
using fine Geldart Group A powders,
4
in which t he interparticle forces play the key role
and the higher pressure drop in the ascending process is associated with the strength of
these forces.
Spouted and Spout-Fluid Beds: Fundamentals and Applications, eds. Norman Epstein and John R. Grace.
Published by Cambridge University Press.
C
Cambridge University Press 2011.
18 Xiaotao Bi
(a) (b) (c)
Figure 2.1. Evolution of the spouting process. (a) Formation of small cavity; (b) development of
internal spout; and (c) onset of external spout.
8.0
6.0
P
4.0
2.0
0.0
010
1
2
8
Collapse of external spout
Onset of external spout
7
6
5
4
3
2
8
7
6
1
5
4
3
20
Run 1, normal flow increase
to spouting
Run 1, normal flow decrease
from spouting
Run 2, prespouting, u
i
<u
msi
Run 3, postspouting, u
i
<u
msi
3040
u
i
(m/s)
Figure 2.2. Deviation of total pressure drops from the normal ascending or descending process in
a semicircular conical spouted bed. Adapted from Wang et al.
3
(D
i
= 0.019 m, D
0
= 0.0381 m,
H
0
= 0.396 m, θ = 45
◦
, d
p
= 1.16 mm, ρ
p
= 2490 kg/m
3
.)
The nature of the flow hysteresis phenomenon is fur t her demonstrated in Figure 2.2.
In Run 2 (open squares), the gas flowrate first increased to point ➀, and then passed the
peak pressure drop region to ➁, just as in Run 1. Before arriving at external spouting,
however, the flow rate was decreased from ➁ to ➂, giving a pressure drop at ➂ much
lower than in the original ascending process because of the collapse of the internal cavity.
When the gas flowrate was increased again from point ➂, the pressure drop climbed back
to the values achieved in the originally ascending process (points ➆ and ➇). Similarly,
Initiation of spouting 19
0.5
0.4
Flow ascending
Flow descending
0.3
0.2
Collapse of external spout
Onset of external spout
0.1
0.0
01020304050
u
, m/s
i
Height of internal spout, m
Figure 2.3. Variation of internal spout height with increasing and decreasing gas flowrate in a
semicircular conical spouted bed. Closed symbols for increasing u
i
; open symbols for decreasing
u
i
. Adapted from Wang et al.
3
(D
i
= 0.019 m, D
0
= 0.0381 m, H
0
= 0.468 m, θ = 45
◦
, d
p
=
1.16 mm, ρ
p
= 2490 kg/m
3
.)
interrupting the gas flow descending process of Run 3 (open triangles) after the external
spout collapsed when the flow rate was decreased from ➊ to ➋,thegasflowratewas
increased from ➋ to ➌. The pressure drop then increased to a value much higher than
in the normal descending path (closed triangles) because of the compaction created by
the collapsed internal spout. The pressure drop returned to the normal values (points ➏
to ➑) when the gas flowrate was decreased again. This confirms that the development
of the gas cavity and the internal spout is responsible for the pressure drop versus flow
hysteresis in spouted beds.
2.2 Evolution of internal spout
The higher total pressure drop in the ascending process has been explained by the com-
paction of the curvature region right above the roof of the internal spout,
2
as the region
above the jet is in a packed-bed state and particles pushed aside by the gas cavity/jet
compact the vicinity around the jet. An additional pressure drop is thus created. Associ-
ated with the pressure drop hysteresis, there also exists hysteresis in the development of
the internal spout in the ascending and descending processes. As shown in Figure 2.3,
the inter nal spout in the gas ascending process is much shorter than the one in the
descending process at the same gas flowrate, as a consequence of the compacted dome
region in the ascending process, which imposes an extra stress to suppress the vertical
20 Xiaotao Bi
180
160
140
z = 38-89 mm
z = 89-140 mm
z = 140-242 mm
z = 242-343 mm
120
100
80
DP /DZ, kPa/m
60
40
20
0
01020304050
u
i
, m/s
Figure 2.4. Axial pressure gradients measured incrementally at different axial locations of a
conical spouted bed for decreasing gas flow. Data from Wang.
27
(D
i
= 0.019 m, D
0
= 0.0381 m,
H
0
= 0.468 m, θ = 45
◦
, d
p
= 1.16 mm, ρ
p
= 2490 kg/m
3
.)
penetration of the fluid jet. The difference in pressure drops between the flow ascending
and descending processes is thus a combined contribution of the extra resistance created
by the particle compaction and the longer packed section above the internal spout in the
flow ascending process.
The development of the inter nal spout is also captured by the evolution of pressure
gradients at different levels of the bed. As the gas flowrate increases in the flow ascending
process, Figure 2.4 shows that the pressure drop per unit length at the bottom inlet
region rises quickly to a peak value several times higher than that required for full
suspension of t he particles. Such a maximum peak, however, decreases with distance
above the inlet, and the peak point at higher elevations is reached at higher gas velocities.
The implication is that the “breakup” resistance imposed by the interlocked particles
in the compacted zone is weakened as the internal jet or spout develops upward. This
“breakup” resistance is thus expected to be smaller in a shallower bed.
The evolution of the axial pressure profiles in the spouted bed is shown in Figure 2.5
(a) and (b) for the flow ascending and descending processes, respectively. It is seen
that the pressure drop is much steeper in the lower section at low gas velocities. The
high-pressure gradient zone at a given gas velocity shifts upward as the internal spout
develops upward with increasing gas flow, and eventually reaches the upper section
of the column when the internal spout erupts from the upper bed surface, giving rise
to external spouting (u
msia
= 37.3 m/s). In the flow descending process, as shown in
Figure 2.5(b), the pressure variation with gas velocity is generally smaller than in the
flow ascending process because of the absence of the extra “breakup” resistance.
Initiation of spouting 21
1.0
0.8
2.2
u
i
(m/s)
8.2
14.6
21.6
28.0
37.3 (u
msia
)
39.4
0.6
0.4
0.2
0.0
0.0 0.2 0.4 0.6 0.8 1.0
z /H
0
(P – P
H
)/(P
0
– P
H
)
(a)
1.0
0.8
38.3
u
i
(m/s)
20.5
14.3
10.3
6.3
4.1
28.9 (u
msid
)
0.6
0.4
0.2
0.0
0.0 0.2 0.4 0.6 0.8 1.0
z /H
0
(P – P
H
)/(P
0
– P
H
)
(b)
Figure 2.5. Axial pressure distribution for (a) ascending and (b) descending processes in a
conical spouted bed. Data from Wang.
27
(Semicircular column, D
i
= 0.019 m, D
0
=
0.0381 m, H
0
= 0.468 m, θ = 45
◦
, d
p
= 1.16 mm, ρ
p
= 2490 kg/m
3
, u
msia
= 37.3 m/s,
u
msid
= 28.9 m/s).
22 Xiaotao Bi
6
5
30
12.7
θ (°) D
i
(mm)
12.7
12.7
19.0
19.0
19.0
25.4
30
45
45
45
60
60
4
3
2
1
0
0.0 0.1 0.2 0.3 0.4 0.5
H
0
, m
DP
M,a
/ DP
M,d
Figure 2.6. P
M,a
/P
M,d
as a function of the static bed height in conical spouted beds. Adapted
from Wang et al.
3
(D
0
= 0.0381 m, H
0
= 0.468 m, d
p
= 1.16 mm, ρ
p
= 2490 kg/m
3
.)
2.3 Peak pressure drop
As shown in Figure 2.2, there exists a unique peak pressure drop in spouted beds, which
is reproducible in a loosely packed bed without precompaction or from repeated spouting
runs. Such a peak pressure drop has been measured extensively in spouted bed columns
of different geometries (conical and cylindrical, both flat-based and conical-based) with
different types of particles and fluids. The peak pressure drop is found to be generally
higher than that corresponding to full suspension of bed particles in a cylindrical fluidized
bed. The extra pressure drop is attributed to compaction or interlocking of par ticles above
the internal jet, represented by a “breakup” force.
5
As shown in both Figure 2.6 and
the correlations of Table 2.1, the peak pressure drop increases with increasing static
bed height in conical spouted beds. The Mukhlenov-Gorshtein
6
correlation predicts that
peak pressure drop in conical spouted beds increases with increasing cone angle for
a given static bed height, whereas the opposite trend is predicted by the correlations
of Gelperin et al.
7
and Olazar et al.
8
The recent data of Wang et al.,
3
Figure 2.6, with
included cone angles of 30
◦
to 60
◦
, did not show a clear effect of cone angle on the
peak pressure drop. The implication is that the cone angle may play only a secondary
role, if any. The Manurung
9
correlation predicts that the peak pressure drop increases
with decreasing coefficient of internal friction of the particles, tan γ , suggesting that
the interlocking is likely less severe for particles of poor flowability. This prediction
appears to contradict the general interpretation of the particle interlocking phenomenon,
and thus requires further investigation. Because the two correlations of Olazar et al.
8,14
were developed from data covering very broad ranges of bed geometry and particle
Initiation of spouting 23
Table 2.1. Correlations for peak pressure drop in spouted beds.
Authors Equations Geometry
Gelperin et al. (1961)
7
−P
M
ρ
b
gH
= 1 + 0.062(D
H
/D
i
)
2.54
× Conical
[
(D
H
/D
i
) − 1
]
tan
θ
2
−0.18
Manurung (1964)
9
−P
M
ρ
b
gH
=
0.8 +
6.8
tan γ
D
i
D
− 34.4
d
p
H
Cylindrical
Mukhlenov and Gorshtein
(1965)
6
−P
M
P
s
= 1 + 6.65(H/D
i
)
1.2
tan
θ
2
0.5
Ar
0.2
Conical
Yokogawa and Isaka (1971)
10
−P
M
(1 − ε)(ρ
p
− ρ)gH
=
D
i
D
0.14(D−D
i
)/H
Cylindrical
Asenjo et al. (1977)
11
−P
M
ρ
b
gH
= 1 + 2.8exp(−0.312H/D) Cylindrical
Kmiec (1980)
12
−P
M
ρ
b
gH
= 1 + 0.206 exp(1.24H/D) Conical
Ogino et al. (1993)
13
−P
M
(1 − ε)(ρ
p
− ρ)gH
= 1.15(H/D)
1/2
D
i
D
1/3
Cylindrical
Olazar et al. (1993)
8
−
P
M
P
s
= 1 + 0.116(H/D
i
)
0.5
tan
θ
2
−0.8
Ar
0.0125
Conical
Olazar et al. (1994)
14
−
P
M
P
s
= 1 + 0.35(H/D)
0.1
(D
i
/D)
1.1
Ar
0.1
Cylindrical
Rocha et al. (1995)
23
−P
M
ρ
b
gH
= 1 + 0.0006(D
H
/D
i
)
5.04
[d
p
/(φ D
H
) − 1]
−1.92
where D and D
i
are equivalent diameters
Slot-Rectangular
properties, they are recommended for the estimation of the maximum pressure drop in
conical and cylindrical columns, respectively, in combination with measured pressure
drop in stable spouting. In the absence of information on stable spouting pressure drops,
the correlations of Gelperin et al.
7
(conical column) and Ogino et al.
13
(cylindrical
column) can be used.
2.4 Onset of external spouting and minimum spouting velocity
External spouting is reached after the internal spout or jet breaks the packed bed upper
surface with increasing gas flowrate. That condition has been called incipient spouting.
2
The onset of spouting, on the other hand, has been defined as the neighboring state when
the total pressure drop falls to a lower, roughly constant value. External spouting can be
maintained at a significantly lower gas velocity when the flow rate is decreased from a
stable spouting state, as indicated by Figure 2.2. The gas velocity corresponding to the
24 Xiaotao Bi
Table 2.2. Summary of correlations for minimum spouting velocity in conical spouted beds.
Authors Correlation
Nikolaev and Golubev (1964)
15
(Re
ms H
)
a
= 0.051 Ar
0.59
(H/D
H
)
0.25
(D
i
/D
H
)
0.1
Gorshtein and Mukhlenov (1964)
16
(Re
msi
)
a
= 0.174 Ar
0.5
(D
H
/D
i
)
0.85
tan(θ/2)
−1.25
Mukhlenov and Gorshtein (1965)
6
(Re
msi
)
a
= 1.35 Ar
0.45
(H/D
i
)
1.25
tan(θ/2)
0.58
Tsvik et al. (1967)
17
(Re
msi
)
a
= 0.4 Ar
0.52
(H/D
i
)
1.24
tan(θ/2)
0.42
Wan-Fyong et al. (1969)
18
(Re
msi
)
a
= 1.24Re
t
(H/D
i
)
0.82
tan(θ/2)
0.92
for 16
◦
<θ<70
◦
(Re
msi
)
a
= 0.465Re
t
(H/D
i
)
0.82
tan(θ/2)
0.49
for 10
◦
<θ<16
◦
Kmiec (1977)
19,5
(Re
ms
)
a
= 0.0176 Ar
0.714
(H/D)
1.535
θ
0.714
ε
2.21
ms
, θ in radians
Markowski and Kaminski (1983)
20
(Re
msi
)
d
= 0.028 Ar
0.57
(H/D
i
)
0.48
(D/D
i
)
1.27
Kmiec (1983)
5
(Re
msi
)
2
a
[1.75 + 150(1 − ε
ms
)/(Re
msi
)
a
] =
31.3Ar(H/D
i
)
1.757
(D
i
/D)
0.029
tan(θ/2)
2.073
ε
3
ms
Choi and Meisen (1992)
21
(U
ms
)
d
/
√
2gH = 0.147(
ρ
p
−ρ
ρ
)
0.477
(d
p
/D)
0.61
(H/D)
0.508
(D
i
/D)
0.243
Olazar et al. (1992)
22
(Re
msi
)
d
= 0.126 Ar
0.5
(D
H
/D
i
)
1.68
tan(θ/2)
−0.57
Olazar et al. (1996)
24
(Re
msi
)
d
= 0.126 Ar
0.39
(D
H
/D
i
)
1.68
tan(θ/2)
−0.57
for d
p
≤ 1mm
Bi et al. (1997)
25
(Re
msi
)
d
= [0.30 − 0.27/(D
H
/D
i
)
2
] ×
Ar(D
H
/D
i
)[(D
H
/D
i
)
2
+ (D
H
/D
i
) + 1]/3
0.5
for D
H
/D
i
≥ 1.66
(Re
msi
)
d
= 0.202[ Ar (D
H
/D
i
)[(D
H
/D
i
)
2
+ (D
H
/D
i
) + 1]/3]
0.5
for D
H
/D
i
< 1.66
Jing et al. (2000)
26
A(D
i
/D
H
)
2
(u
msi
)
a
+ B(D
i
/D
H
)
4
(u
msi
)
2
a
− (1 − ε)(ρ
p
− ρ)g = 0
A = 150(1 − ε)
2
μ/[ε
3
(φd
p
)
2
]andB = 1.75(1 − ε)ρ/[ε
3
φd
p
]
point at which stable external spouting collapses with decreasing gas flowrate has been
defined, especially for cylindrical beds, as the minimum spouting velocity, U
ms
.
It should be noted, however, that in early studies of shallow conical spouted beds, the
minimum spouting velocity was commonly determined following the velocity ascending
process, with the reported u
msi
values thus being generally higher than those from the
velocity descending process. To distinguish u
msi
obtained from ascending and descending
processes, the former is subscripted by a and the latter by d in the equations shown in
Table 2.2. It should be noted that the use of an upper cylinder diameter D in correlations
for conical beds, as with Kmiec
12
in Table 2.1 and with four equations
19,20,5,21
in
Table 2.2 (two of which
19,21
also generate U
ms
based on D rather than U
msi
based on
D
i
), limits each of these correlations more than ever to the specific geometries and other
conditions on which they are based.
To predict the minimum spouting velocity in conical spouted beds, the Ergun equa-
tion
40
has been applied by introducing a “breaking force coefficient”
5
or a data-fitted
constant
25
to correct the pressure drop at the onset or collapse, respectively, of the
Initiation of spouting 25
Table 2.3. List of selected equations for predicting
U
ms
in flat- and cone-based cylindrical spouted beds.
Authors Correlation
Mathur and Gishler (1955)
28
U
ms
= (d
p
/D)(D
i
/D)
1/3
2gH(ρ
p
− ρ)/ρ
Grbavcic et al. (1976)
41
U
ms
/U
mf
= 1 − (1 − H/H
m
)
3
Fane and Mitchell (1984)
33
U
ms
= 2.0D
1−exp(−7D
2
)
(d
p
/D)(D
i
/D)
1/3
2gH(ρ
p
− ρ)/ρ
for D > 0.4 m, with D in meters
Choi and Meisen (1992)
21
U
ms
= 18.5
ρ
p
− ρ
ρ
0.263
(H/D)
−0.103
(d
p
/D)
1.19
(D
i
/D)
0.373
√
2gH
Anabtawi et al. (1992)
36
U
ms
= 2.44(d
p
/D)
0.7
(D
0
/D)
0.58
(H/D)
0.5
[2gH(ρ
p
− ρ)/ρ]
0.28
for square column
Olazar et al. (1994)
14
U
ms
= (d
p
/D)(D
i
/D)
0.1
2gH(ρ
p
− ρ)/ρ
Li et al. (1996)
37
U
ms
= 1.63U
t
d
p
D
0.414
D
i
D
0.127
H
m
D
0.452
ρ
p
− ρ
ρ
−0.149
based on high temperature data
Du et al. (2009)
39
U
ms
= 0.2
0.5
U
mf
H
0.2H
m
1−
(
2.5H/H
m
)
assuming U
mf
= U
m
Applicable range: 0 < (H/H
m
) ≤ 0.2
external spout. For Geldart
4
Group B and Group D particles, the following relationship
was obtained
25
:
Re
msi
= kAr
0.5
(D
H
/D
i
)[(D
H
/D
i
)
2
+ (D
H
/D
i
) + 1]/3. (2.1)
The relationship Re
msi
= ρu
msi
d
p
/μ ∝ Ar
0.5
and the fact that U
mf
is approximately pro-
portional to Ar
0.5
for large Geldart Group D particles implies that u
msi
/U
mf
is independent
of gas and particle properties, which seems to agree with experimental data.
25
The influ-
ence of column geometry includes inlet diameter, bed height, and included cone angle.
Experiments in cylindrical spouted beds have commonly been conducted in columns
with a flat base or with a conical base of total included angles ranging from 45
◦
to 90
◦
.
A number of correlations have been developed as summarized in Table 2.3, with the
Mathur-Gishler
28
correlation being the most widely used.
Some attempts to theoretically
29,31,32
predict U
ms
have resulted in a net exponent of
unity or larger on D
i
, but Thorley et al.
30
and Olazar et al.
14
found experimentally that
U
ms
was proportional to D
i
0.1–0.33
. All these equations, however, fail to predict the data
obtained from columns of diameter larger than 0.5 m,
33–35
where U
ms
data were reported
to be roughly proportional to H. Fane and Mitchell
33
therefore dimensionally modified
the Mathur-Gishler equation for the prediction of U
ms
in large columns.
Applicability of the correlations relating jet velocity and vertical upward jet pene-
tration length for the prediction of minimum spouting velocity has also been exam-
ined.
35,38,42
It was found that commonly used jet penetration correlations, two of which
are listed in Table 2.4, gave reasonable agreement with U
ms
data in spouted beds, espe-
cially in shallow beds in which a coherent jet was expected.
26 Xiaotao Bi
Table 2.4. Two empirical equations for predicting vertical upward jet penetration length in gas-solid fluidized beds.
Authors Correlation
Merry (1975)
43
ρ
ρ
p
− ρ
u
2
j
gD
i
1/2
= 0.0084
L
j
D
i
ρ
p
ρ
0.3
d
p
D
i
0.3
+ 5.2
2.5
ρ
ρ
p
− ρ
1/2
Yang and Keairns (1978)
44
ρ
ρ
p
− ρ
u
2
j
gD
i
1/2
= 0.154
L
j
D
i
The applicability of the Mathur-Gishler equation to spouted beds of particle mixtures
has also been evaluated. It was found
45
that the Mathur-Gishler equation could be used
to predict U
ms
approximately for beds of solids mixtures when a mean particle size and
an average particle density were calculated by
¯
d
p
= 1
(x
i
/d
pi
) (2.2)
and
¯ρ
p
= 1
(x
i
/ρ
pi
), (2.3)
respectively, with x
i
being the mass fraction of species i.
Further discussion of the minimum spouting velocity is given in Chapter 3.
Chapter-specific nomenclature
Ar Archimedes number = d
3
p
ρ(ρ
p
− ρ)g/μ
2
k dimensionless coefficient in Eq. (2.1), evaluated
25
in Table 2.2
L
j
vertical jet penetration length, m
Re
ms
particle Reynolds number in cylindrical section at minimum spouting =
d
p
U
ms
ρ/μ
Re
ms H
particle Reynolds number at upper bed surface at minimum spouting =
d
p
U
ms H
ρ/μ
Re
msi
particle Reynolds number at fluid inlet at minimum spouting = d
p
u
msi
ρ/μ
Re
t
particle Reynolds number based on U
t
= d
p
U
t
ρ/μ
U
ms H
minimum superficial spouting velocity based on D
H
,m/s
U
t
free settling terminal velocity of particles, m/s
u
j
jet velocity based on diameter at jet inlet, m/s
x
i
mass fraction of species i
Greek letters
γ angle of internal friction, degrees
ε
ms
fractional void volume at minimum spouting
ρ
b
bulk density of bed, kg/m
3
φ sphericity of particles