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Advanced Powder Technol., Vol. 00, No. 0, pp. 1– 14 (2005)
 VSP and Society of Powder Technology, Japan 2005.
Also available online - www.vsppub.com
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Original paper
Transition velocities in the riser of a circulating
fluidized bed
N. BALASUBRAMANIAN 1,∗ , C. SRINIVASAKANNAN 2
and C. AHMED BASHA 1
1 Central Electrochemical Research Institute, Karaikudi 630 006, India
2 School of Chemical Engineering, University Sains Malaysia, 14300 Nibong
Received 17 June 2004; accepted 1 September 2004
Tebal,
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Palau Penang, Malaysia
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Abstract—We attempted to study the hydrodynamics and flow regime transitions in a circulating
fluidized bed (CFB). In conventional gas–solids fluidization, the flow regimes include the fixed bed,
bubbling fluidization and turbulent fluidization, in which the regimes mainly depend on the gas
velocity. However, in a CFB, the flow regime depends on both the solids circulation rate and gas
velocity. The flow regimes in a CFB include the high-velocity fluidized bed and pneumatic conveying.
Experiments were conducted in a column of 0.052 m internal diameter and 1.2 m long covering
a wide range of operating conditions. The transport velocity was estimated by emptying time and
extrapolation techniques. It was noticed from the present experimental observations that Geldart Btype particles move more or less as individual particles, while Geldart A-type particles have a tendency
to form clusters. Empirical correlations have been proposed for the transport velocity Utr and the
chocking velocity Uch . A qualitative map of different flow regimes of a gas–solid fluidized bed has
been proposed based transition velocities.
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Keywords: Circulating fluidized bed; flow regime transition; transport velocity; chocking velocity.
NOMENCLATURE
Archimedes number,
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Ar
c
CD
ρg (ρs − ρg )gdp3
µ2g
correction factor for effective particle diameter
4gdp3 ρg (ρs − ρg )
drag coefficient,
3µ2g
∗ To whom correspondence should be addressed at: Department of Chemical Engineering, Alagappa
College of Technology, Anna University, Chennai 600 025, India. E-mail: [email protected]
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particle diameter (m)
solids rate (kg/m2 /s)
acceleration due to gravity (m2 /s)
index
index
index
Reynolds number
Reynolds number at the chocking condition
Reynolds number at terminal velocity
minimum fluidization velocity (m/s)
characteristic velocity (m/s)
superficial solids velocity (m/s)
terminal gas velocity (m/s)
slip velocity (m/s)
D
dp
Gs
g
k
m
n
Re
Rech
Ret
Umf
Uo
Us
Ut
Uslip
N. Balasubramanian et al.
1. INTRODUCTION
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average bed porosity
viscosity of gas (kg/m/s)
gas density (kg/m3 )
solids density (kg/m3 )
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Greek
ε
µg
ρg
ρs
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2
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Fluidized bed reactors have been widely used in the chemical and petroleum industries, e.g. include fluidized catalytic cracking (FCC); fluidized bed combustion,
calcination, etc. The bed has different flow regimes as a function of the operating
gas velocity [1, 2]. Understanding of the flow regimes in circulating fluidized bed
(CFB) risers is the key for successful design and scale-up of CFB reactors. Numerous studies have been carried out to define the flow regimes of bubbling and
turbulent fluidization. However, studies on high-velocity fluidization are comparatively sparse and hence the hydrodynamics of high velocity fluidization are not well
understood [3]. The present investigation attempts to study the hydrodynamics and
flow regimes in a CFB. The objective of the work is to (i) identify the flow regimes
in a CFB, and (ii) estimate the transition and chocking velocities.
2. LITERATURE ON HIGH-VELOCITY FLUIDIZATION
Over the last few decades, extensive work has been devoted to the study of highvelocity fluidization, which is characterized by entrained solids flow, high slip
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Transition velocities in the riser of a CFB
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velocity, and dependence of riser pressure drop on both solids circulation rate and
gas velocity. The flow regime of fast fluidization has been defined by several
investigators. Yerushalmi and Cankurt [4] defined the fast fluidization regime
as the bed operated above the transport velocity without choking which can be
characterized by relatively high solids concentration with the presence of solid
clusters and extensive back mixing of solids. Li and Kwauk [5] reported that the
regime of fluidization shifted from turbulent fluidization to fast fluidization when
the gas velocity approached the transport velocity. The authors also observed that in
the fast fluidization regime, the riser should have an inflection point which separates
a dense phase at the bottom and a dilute region at the top of the riser. Avidan and
Yerushalmi [6] experimentally investigated the bed expansion in a fluidized bed and
introduced cluster terminal velocity instead of terminal velocity of a single particle
in the Richardson–Zaki [7] equation to describe the bed expansion and noted a
sharp change in the slope of the expansion curve associated with a change in the
fluidization regime. The authors reported that the effect of particle size on cluster
terminal velocity was significant.
Takeuchi et al. [8] presented the regime classification of fluidization differently
from the earlier investigators. The authors observed that the superficial gas
velocity and solids circulation rate should be controlled independently in order to
understand the fluidization behavior of various regimes. Kuwak et al. [9] gave
an empirical equation for regime transition in fluidization. Grace [10, 11] presented
a quantitative fluidization map with dimensional gas velocity against dimensional
particle diameter and identified the different regimes with minimum fluidization
velocity, i.e. terminal velocity. The authors observed a considerable overlapping of
operating region of the CFB with other regimes of gas–solid fluidization.
Drahos et al. [12] characterized the regimes of fluidization with pressure
drop fluctuation. The authors proposed a regime diagram from their experimented
observation and reported that in a fast fluidized bed a thin layer of particles was
moving down in the vicinity of the well. Smolders and Baeyens [13] reviewed
the literature data on fluidization regimes at high velocities, and clarified the
contradictory situation and unambiguously defined that (i) the CFB operates at
gas velocities above the transport velocity, (ii) the axial density profiles can be
classified into three types: a dilute phase transport regime exponential shape, the
fast fluidization regime S-shape and the dense transport regime straight line, and
(iii) the existence of an S-shaped profile mainly depends on the design of the recycle
loop and on the solids circulation rate being in excess of the saturation carrying
capacity. Esmail et al. [14] presented a transient technique to delineate different
regimes fluidizations. The method is based on transient pressure drop measurement
across the riser during a solids flow cut-off experiment while maintaining constant
gas flow.
It can be concluded from the experimental and theoretical observations that
the transport velocity plays an important role in the CFB. However, research
devoted to transport velocity has been rather scarce when compared with work
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reported on other transition velocities such as minimum fluidization velocity Umf
and terminal velocity Ut . The objective of the present investigation was to study
the hydrodynamics of a CFB, which includes examination of pressure drop profiles
along the riser, analysis of slip velocity characteristics, and estimation of transport
velocity and chocking velocity.
3. EXPERIMENTAL
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Experiments were carried out in a Plexiglas column of 52 mm internal diameter
and 1200 mm high (Fig. 1). The column consists of a riser (1) with a provision for
continuously feeding the solids at a controlled rate from the hopper (3). A gas–
solids separator (2) and a bag filter were provided at the top of the riser for
separating solids and gas. For the movement of the solids co-current upward with
air introduced at the bottom of the column, air for fluidization was drawn from a
centrifugal blower (5) through a surge tank (4) and a flow meter (7). Quick closing
valves (6) were provided at the solids feed point to facilitate the measurement
of solids concentration in the riser. The solids particle properties are given in
Table 1. The solids circulation rate (which can be varied by controlling valve 9)
was measured by collecting the solids for a period of time. The solid particles
Figure 1. Schematic diagram of the experimental set-up: 1, riser; 2, gas–solid separator; 3, solids
hopper; 4, surge tank; 5, air blower; 6, quick closing valves; 7, orifice meter; 8, pressure tappings;
9, solids control valve.
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Transition velocities in the riser of a CFB
5
Table 1.
Properties of the materials used in the present study
Size
(µm)
Density
(kg/m3 )
Ar
Geldart
classification
Sand
Sand
Resin
Resin
Silica gel
FCC
412
177
530
385
384
81
2650
2650
1480
1480
676
900
6681
529
7941
3044
1378
17.2
B
B
B
B
B
A
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Material
4. RESULTS AND DISCUSSIONS
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were supported on a perforated plate distributor situated at the bottom of the
riser. Pressure tappings were provided at different locations on the riser for the
measurement of the pressure drop across the riser. Solids were admitted into the
riser at a low rate and gradually increased in small increments to the desired value.
The pressure drop across the riser was measured for various solids circulation rates,
and gas velocities.
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The pressure drop at different solids circulation rates is given in Fig. 2. It can be
ascertained that the pressure drop is less at low solids rate and increases gradually
with solids circulation rate. The pressure drop is high and approaches an asymptotic
value at high solids circulation rate. In between these boundaries, the pressure
drop increases sharply with the solids circulation rate. It can be ascertained that
the pressure drop decreases with increasing gas velocity for a given solids rate.
These observations are in qualitative agreement with the observations reported in
the literature [15, 16].
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4.1. Transport velocity
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The transport velocity (Utr ) is the transition velocity between the turbulent and fast
fluidized bed, and has been determined by various methods [17, 18]. In this study,
Utr is determined by emptying time and extrapolation techniques. In the linear
extrapolation technique, the maximum solids flux for a particular gas velocity has
been noted and plotted against the gas velocity (see Fig. 3). Referring to Fig. 2,
the maximum solids flux for a given gas rate is obtained, where P /L approaches
an asymptotic value. The tangent of the curve gives the transport velocity Utr as
given in Fig. 3. As can be seen from the figure, the resulting Utr value for resin
particles of 530 µm is 3.19 m/s. The transport velocities for all the solid particles
used in the present study have been measured using this linear extrapolation and are
listed in Table 2.
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Figure 2. The pressure drop with solids and gas flow rate. Material: resin; dp : 385 µm.
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Figure 3. Estimation of transport velocity by the extrapolation technique.
dp : 530 µm.
Material: resin;
Table 2.
Minimum fluidization velocity, free fall terminal velocity, transport velocity and the intercept of (10)
for the materials investigated in the present study
412
177
530
385
384
81
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Sand
Sand
Resin
Resin
Silica gel
FCC
Size
(µm)
Ar
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Material
6681
529
7941
3044
1378
17.2
Umf
(m/s)
Ut
(m/s)
Utr (m/s)
Emptying time
Extrapolation
14.20
2.76
13.00
7.10
3.28
0.196
3.43
1.47
2.99
2.17
1.28
0.32
3.47
2.56
3.19
2.47
1.86
1.35
3.48
2.68
3.25
2.41
1.97
1.40
k
3.26
2.34
3.00
2.55
2.12
1.41
For cross-verification, the transport velocity has also been measured using the
emptying time technique. The time required for all solid particles to leave the
bed as a function of gas velocity (Ug ) is considered. As Ug is increased, the bed
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Transition velocities in the riser of a CFB
Figure 4. Estimation of transport velocity by the emptying time technique. Material: silica gel;
dp : 384 µm.
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material could be emptied in a short period of time due to a sharp increase of
particle carryover in the absence of solid recycle (Fig. 4). As can be seen in Fig. 4,
two lines have different slopes at lower and higher Ug . The intersection of these
two lines gives Utr . The resulting value of Utr is found to be 1.86 m/s for silicagel particles. Transition velocities have been estimated by both techniques for all
the solid particles used in the present study and the estimated values are given in
Table 2. It can be observed from Table 2 that the values of the transport velocity
estimated by both techniques match satisfactorily within 10%. It is also noted from
Table 2 that the transport velocity Utr is approximately equal to the free fall velocity
when the Archimedes number is high.
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4.2. Slip velocity
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Slip velocity is defined as the relative velocity difference between the phases.
The solids concentration may be considered to depend upon the relative velocity
between the phases [19]. Slip velocity between the two-phase co-current up flow
system may be defined as:
Uslip =
Ug
Us
−
.
ε
(1 − ε)
(1)
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Equation (1) is further improved to incorporate buoyancy, hindrance and momentum
effects as [20]:
Uslip
=
Uo
ε
([1 + (1 −
ε)1/3 ] exp
5(1 − ε)
)
3ε
.
(2)
The terms ε, [1 + (1 − ε)1/3 ] and exponential represent buoyancy, hindrance and
momentum effects, respectively. Since the momentum transfer effect and hindrance
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N. Balasubramanian et al.
effect are shown in terms of solids concentration, (2) may be modified as:
Uslip
εn
=
,
Uo
[1 + (1 − ε)1/3 ]m
(3)
and
Uslip
4(ρs − ρg )g
=
30ρg0.5 µg
2/3
dp
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where n = 1 for creeping flow and n = 2/3 for an intermediate range of Reynolds
number [1 < Re < 103 ]. Substituting the single particle free fall velocity in a finite
medium for Uo in (3) and rewriting for Stokes and intermediate Reynolds numbers:
(ρs − ρg )gdp2
εn
, Re 1,
(4)
Uslip =
18µg
[1 + (1 − ε)1/3 ]m
ε2/3
,
[1 + (1 − ε)1/3 ]2m/3
1 Re 103 .
(5)
and
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Formation of agglomerates is reported to be present in a CFB, which results in an
increase in the effective particle diameter. Taking these facts into consideration, (4)
and (5) have been improved as given below [21];
(ρs − ρg )g(cdp )2
εn
,
(6)
Uslip =
18µg
[1 + (1 − ε)1/3 ]m
2/3
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Uslip
4(ρs − ρg )g
=
30ρg0.5 µg
cdp
ε2/3
,
[1 + (1 − ε)1/3 ]2m/3
(7)
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where c is the correction factor accounting for particle agglomeration, and m is
an index to account for particle–particle and particle–wall effects. The corresponding drag equation is written as:
4(ρs − ρg )g(cdp )
ε
.
(8)
CD =
2
[1 + (1 − ε)1/3 ]m
3ρg Uslip
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The index m and correction factor c may be evaluated from the present experimental
data. It can be noted from the present study that the factor c is found to depend on the
material characteristics, correlated with particle properties in terms of Archimedes
number as given below:
c = 5.2Ar−0.172 .
(9)
Figure 5 shows the variation of factor c with Archimedes number. It can be seen
from Fig. 5 that the factor c decreases with an increase in Archimedes number
— it is approximately 1 for coarse particles (i.e. Ar > 103 ) and nearly 3.5 for
finer particles. It indicates that coarse material moves more or less as individual
particles, while fine materials have a tendency to form agglomerates. Uslip and CD
are evaluated using (6)–(8) (Fig. 6) along with the CD –Re curve, where the Reynolds
number is defined as Re ≡ (cdp )ρg Uslip /µg .
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Transition velocities in the riser of a CFB
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Figure 5. Variation of the factor c with Archimedes number.
Figure 6. Comparison of experimental data with the CD –Re relationship.
Figure 7 presents the experimental data plotted as [log Uslip ] versus [log ε]. In
Fig. 7, the variation of slip velocity with bed porosity is given for two solids
particles. Similar observations have been recorded for all the materials used in the
present study. It can be seen from Fig. 7 that the data may be represented by lines
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Figure 7. Variation of lip velocity with bed porosity. Material: resin; dp : 385 µm.
of the same slope, but of different intercept for the materials covered in the study,
i.e.:
Uslip = kε−1.5 .
(10)
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The value k depends on the material characteristics. It has been observed from the
present investigation that the intercept k is equal to the transport velocity Utr for all
the materials used in the present study. The intercept k along with the transition
velocities (transport velocity, terminal velocity and minimum fluidization velocity)
for the materials investigated in the present study is plotted against Archimedes
number as given in Fig. 8. The minimum fluidization velocity, terminal velocity
and drag coefficient are estimated using the following equations [22, 23]:
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Minimum fluidization velocity:
dp3 ρg (ρs − ρg )g 1/2
dp ρg Umf
2
= (33.7) + 0.0408
− 33.7.
µg
µ2g
(11)
Terminal velocity:
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Ut =
g(ρs − ρg )dp2
18µg
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4 (ρs − ρg )2 g 2
Ut =
225
ρg µg
for Re < 0.4,
,
(12)
1/3
3.1(ρs − ρg )gdp
Ut =
ρg
for 0.4 < Re < 500,
dp ,
(13)
1/2
,
for 500 < Re .
(14)
Drag coefficient:
CD Re =
2
4gdp3 ρg (ρs − ρg )
3µ2g
.
(15)
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Transition velocities in the riser of a CFB
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Figure 8. Variation of intercept k, terminal free fall velocity Ut and transport velocity Utr with
Archimedes number.
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An important observation has been noticed from Fig. 8 that the transport velocity Utr
for Geldart B-type material (except FCC in the present study) is approximately
equal to the terminal velocity of a single particle, whereas the transport velocity
is much higher than the terminal velocity for Geldart A-type materials (FCC).
It can also be ascertained from Fig. 8 that the intercept k [of (11)] for the materials
investigated in the present study matches satisfactorily with the transport velocity
for Geldart B-type materials; the transport velocity and the terminal free fall velocity
of a single particle are close to each other for these materials. However, for
Geldart A-type material (FCC), the transport velocity and terminal velocity differ
considerably. Figure 9 presents Utr /Ut and Ut /Umf against CD Re2t . It can be
ascertained from the Fig. 9 that Utr /Ut decreases with an increase in CD Re2t . This
observation validates the earlier statement that finer particles (Geldart A) tend to
form agglomerates, while Geldart B-type materials move more or less as individual
particles in the high-velocity fluidization regime.
4.3. Chocking velocity
The chocking velocity Uch can be defined as the gas velocity at which solids can be
transported in dilute flowing suspension without any axial mixing for a given solids
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Figure 9. Variation of Utr /Ut and Ut /Umf with CD Re2t .
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rate. In this case, a slight decrease in gas velocity will lead to a sudden fluctuation
in the pressure drop and extensive back mixing of solids. Hence, the chocking
velocity Uch in a CFB is considered as the transition velocity from pneumatic
transport to the fast fluidization regime. The chocking velocity can be estimated by
decreasing the gas velocity from a high value for a given solids rate. The chocking
velocity has been estimated for the present study, and related empirically with the
Archimedes number and dimensionless solids circulation rate as
ReCh = 0.48Ar0.53
Gs
ρg Ut
0.412
.
(16)
4.4. Fluidization map
A flow regime map for gas–solid fluidization consisting of the above transition
velocities is given in Fig. 10. The dimensionless parameters U ∗ and Ar∗ are
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Transition velocities in the riser of a CFB
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Figure 10. Flow regime map of gas–solids flow in a CFB.
calculated as U ∗ = Re /Ar1/3 and Ar∗ = Ar1/3 , where
dp ρg U
µg
and Ar =
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Re =
ρg (ρs − ρg )gdp3
µ2g
.
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The transition velocities have been estimated using the equations given above. It can
be noticed from Fig. 10 that there is an overlap on the regime transition for Geldart
B-type material, whereas the transition is very wide for Geldart A-type particles.
This observation is in qualitative agreement with the observation reported in the
literature [24].
5. CONCLUSION
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Experiments were conducted for the total pressure drop covering a wide range of
operating conditions. Slip velocity has been estimated for all the solids particles
used in the present study. Transport velocity has been estimated by emptying time
and extrapolation techniques. It has been observed from the present experimentation
that the transport velocity for Geldart A-type particles is much higher than the
terminal velocity of single particles, while the transport velocity is more or less
close to the terminal velocity of solids particles for Geldart B-type materials.
The intercept k obtained for slip velocity versus bed voidage correlation matches
satisfactorily with the transport velocity Utr for Geldart B-type materials.
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