Powder Technology 274 (2015) 146–153

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Powder Technology
journal homepage: www.elsevier.com/locate/powtec

A hydrodynamic model for circulating fluidized beds with low riser and
tall riser
Xin Mo, Peining Wang, Hairui Yang ⁎, Junfu Lv, Man Zhang, Qing Liu
Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, China
Beijing Key Laboratory of CO2 Utilization and Reduction Technology, China
Department of Thermal Engineering, Tsinghua University, Beijing 100084, China

a r t i c l e i n f o a b s t r a c t

Article history: Based on different flow regimes classified by the saturation carrying capacity in the riser, a comprehensive
Received 4 September 2014 hydrodynamic model for circulating fluidized beds was proposed and validated with experimental data. The
Received in revised form 4 January 2015 model can describe the different axial solids distributions or regimes in previous literatures, especially the
Accepted 12 January 2015
boundaries among them. The calculation of model shows good agreement with experiments not just for gas
Available online 17 January 2015
solids behavior in riser, but also for that in standpipe.
Keywords:
The influences of the riser height on the axial solids distribution in riser were discussed. With the increase of the
Circulating fluidized beds model distance between the upper end of dense phase and the bottom of riser, the axial solids distribution in low riser
Transport detached height appears as the exponential profile, the quasi exponential profile and the quasi S-shaped profile continuously. For
Saturation carrying capacity the tall riser, the quasi exponential profile is replaced by the S-shaped profile due to the dilute phase in the upper.
In addition, the saturation carrying capacity prevails in the tall riser, and with greater inventory solids circulation
rate would exceed the saturation carrying capacity to form the quasi S-shape profile.
© 2015 Published by Elsevier B.V.

1. Introduction when the opening of butterfly valve is great, while the variation of
inventory has no impact on the distribution when the opening is
Hydrodynamic model is a useful tool to describe the gas solids flow small, similarly found by Xu et al. [8]. If a screw feeder exists in the
in circulating fluidized beds (CFB) reactors, especially in the riser, and is external loop, the variation of pressure drop across standpipe had
of significant importance for design and performance of CFB reactors. no effect on the pressure drop across riser [8]. In Rhodes and
The hydrodynamic model integrates the pressure balance and the Lasussmann's experiments [14], it was found the difference of pressure
material mass balance around the whole loop, and the most difficult is drop between the standpipe and the butterfly valve was almost the
the proper identification of axial solids distribution in the riser. constant during the variation of inventory. The opening of mechanical
The axial solids distribution is influenced by many factors. Except for valve was reduced to keep the constant of Gs. Therefore the increased
material properties [1], the influencing factors include the height and pressure drop in standpipe was offset by the increased pressure drop
diameter of the riser [1], inlet and outlet restrictions [1–5], and operating of butterfly valve, which led to no variation in the pressure drop across
conditions (fluidizing gas velocity, solids circulating rate and material riser.
inventory) [1,6–14]. At certain fluidizing gas velocity and solids circula- The circulating fluidized bed boiler is widely used in the coal
tion rate, the effect of inventory is still a controversy. Weinstein et al. combustion and electric generation, which belongs to the type B CFB
[10], Mori et al. [11] and Li et al. [13] found that the interface between due to the following characteristics [15].
the dense phase and the dilute phase moves up with the increase of
inventory; however Hirama et al. [9,12], Rhodes and Lasussmann [14] (1) There is no hopper or screw feeder in the external loop, and the
did not observe this phenomenon. The controversy may result from loop satisfies pressure balance. The variation of inventory influ-
the differences of experimental structures, especially the discrepancies ences axial solids distribution in the riser.
in external loop including the standpipe and the mechanical valve. Bai (2) The diameter of standpipe is small; therefore unit mass of mate-
et al. [1] found that the axial solids distribution is related to inventory rial in standpipe produces greater pressure drop.
(3) The butterfly valve is replaced by loop seal. Loop seal has small
⁎ Corresponding author at: Key Laboratory for Thermal Science and Power Engineering
flow resistance and good gas sealing ability.
of Ministry of Education, China. Tel.: +86 10 62773384. (4) The solids circulation rate is influenced by fluidizing gas velocity,
E-mail address: yhr@mail.tsinghua.edu.cn (H. Yang). aeration rate in loop seal and material inventory.

http://dx.doi.org/10.1016/j.powtec.2015.01.022
0032-5910/© 2015 Published by Elsevier B.V.
 X. Mo et al. / Powder Technology 274 (2015) 146–153 147

solids circulation rate and axial solids distribution is summarized in

Nomenclature
Table 1.
The dilute phase in the upper of riser is restricted by the riser height
ΔP pressure drop, Pa
[17]. If the riser height is smaller than the transport detached height
M material mass, kg
(TDH), the dilute phase is very difficult to form, and solids circulation
Mt total inventory, kg
rate is normally greater than Gssat [13]. On the contrary, it is much easier
dp diameter of solid particles, μm
to form dilute phase in the tall risers [18]. Therefore, according to
φp sphericity of solid particles
TDH at certain fluidizing gas velocity, the riser of different heights
Q0 aeration rate in supply chamber, m3/h
can be classified into the so-called low riser and tall riser. Compared
Qv gas volume flow rate in the standpipe, m3/s (positive
with low riser, the S-shaped profile prevails in tall riser [13].
when gas flow upward)
However, it should be realized the definition of low riser and tall
Qh gas volume flow rate in passage, m3/h
riser is a relative one, which depends upon fluidizing gas velocity
Gs solids circulation rate based on the sectional area of
and the solids properties. The decay factor of axial solids holdup
riser, kg/m2/s
distribution is reduced with the increase of fluidizing gas velocity
Gssat saturation carrying capacity, kg/m2/s
[19,20], which leads to the increase of TDH. In other words, when
Ρ density, kg/m3
the fluidizing gas velocity increases, the tall riser at low fluidizing gas
U velocity, m/s
velocity would change to the low riser. Xu et al. [8] found low fluidizing
Ug superficial fluidizing gas velocity in riser, m/s
gas velocity is beneficial to observe the saturation carrying capacity,
Usl gas solids slip velocity in standpipe, m/s
which proves the effect of gas velocity on TDH.
g gravitational acceleration, m/s2
As mentioned above, the axial solids distribution in riser is very
H height, m
complicated, which is not only influenced by solid properties and
Z height, m
operating conditions, but also related to the riser height. Based on
Zd distance between the upper end of dense phase and the
the pressure balance and material balance, Kim et al. [21], Pasu and
bottom of riser, m
Cheng [22], Lei and Horio [23] proposed their hydrodynamic models
TDH transport detach height, m
for circulating fluidized bed reactors; however the axial solids distribu-
Dpas diameter of passage, m
tion in riser and the gas solids behavior in standpipe are too simplified,
Lpas length of passage, m
which restricts the application of models. In summary, there are three
A area, m2
major simplifications:
Ci inlet dust loading, kg/m3
(1) The dense phase is always assumed in the bottom of riser.
Actually as shown in Table 1, the dense phase depends upon
Greek letters solids circulation rate, inventory and riser height [1,13,24].
ξ solids holdup (2) The effect of riser height on saturation carrying capacity is not
ε voidage considered.
α decay factor (3) The gas solids behavior in the standpipe is normally assumed
as the minimum fluidization; however it may be the stick
slip state at low aeration rate in the loop seal [6,25].
Subscript
R riser Based on the pressure balance and material balance, a comprehensive
c cyclone hydrodynamic model is proposed in this paper. The model can describe
ls loop seal the different axial solids distributions listed in Table 1, especially the
rc recycle chamber boundaries among them. The feasibility of model is validated with
sc supply chamber experimental data conducted in the riser of low height. In addition,
pas passage axial solids distributions in the low riser and the tall riser are analyzed.
sp standpipe
dil dilute phase 2. Hydrodynamic model of circulating fluidized beds
den dense phase
p particle As shown in Eq. (1), assuming that the pressure drop in the
g gas connecting pipes is zero, the algebraic sum of pressure drop in riser,
t terminal cyclone and loop seal equals to the pressure drop in standpipe. Similarly,
mf minimum fluidization neglecting the solids mass in cyclone and the connecting pipes, the sum
pb packed bed of solids mass in each section should equal to the total inventory as
sp stick slip state shown in Eq. (2).

ΔP sp ¼ ΔP r þ ΔP c þ ΔP ls ð1Þ

Mt ¼ M r þ Mls þ M sp ð2Þ
Saturation carrying capacity, Gssat, is one of the important
parameters to distinguish gas solids flow regimes in the riser [16].
Li et al. [13] classified the flow condition in the riser into three 2.1. Hydrodynamic model in riser
cases, i.e. Gs b G ssat , G s = Gssat and G s N G ssat , in which the case of
Gs = Gssat prevails in the tall risers. With respect to the riser with As mentioned above, the gas solids distributions in different cases
weak restriction, Xu et al. [8] found saturation carrying capacity is classified by comparing Gs with Gssat are different.
easy to keep in low fluidizing gas velocity for the riser of certain
height. By neglecting the acceleration region in the bottom of riser
and solids back-mixing influence near the exit, the relation between Case 1. Gs b Gssat
148 X. Mo et al. / Powder Technology 274 (2015) 146–153

Table 1
Characteristics of different axial solids distributions.

Uniform Exponential S-shaped Quasi exponential Quasi S-shaped

profile profile profile profile profile

Solids circulation rate Gs b Gssat Gs = Gssat Gs = Gssat Gs N Gssat Gs N Gssat

Dilute phase Y Y Y N N
Transition phase N Y Y Y Y
Dense phase N N Y N Y

Notes: Y—included, N—excluded.

When neglecting the effects of solids acceleration, gas solids friction, limited, and the deviation between the value calculated by Eq. (3) and
the axial solids distribution is uniform, which is defined as the dilute the measured value is small [27].
pneumatic conveying. Solids holdup calculated by the Eq. (3) is the
terminal solids concentration [26], and it is more acceptable for the G
ξdil ¼
s  ð3Þ
CFB with low solids circulation rate. For the low solids circulation rate
ρp U g −U t
and high fluidizing gas velocity, the formation of clusters would be

Fig. 1. Calculation procedure.

 X. Mo et al. / Powder Technology 274 (2015) 146–153 149

If ξ − ξdil is smaller than 1% of ξdil, assume that the gas solids flow is
at the dilute state. Therefore the length of transition state, namely the
transport detached height, is expressed as

TDH ¼ − ln ð0:01ξdil =ðξden −ξdil ÞÞ=α ð8Þ

Zd is negative for the exponential profile, and it is positive for the

S-shape profile; therefore the pressure drops for exponential profile
and S-shaped profile are expressed as Eqs. (9) and (10) respectively.
Z Hr
ΔP r ¼ ρp g ξdZ ð9Þ
0

Z !
Hr
ΔP r ¼ ρp g ξden Z d þ ξdZ ð10Þ
Zd

Case 3. Gs N Gssat
The characteristic of the case of Gs N Gssat is the disappearance of
dilute phase in the upper of riser. The solids holdup in dense phase
changes little with solids circulation rate when Gs N Gssat [8,29], and it
is assumed as Eq. (6). We assume that the dilute phase is beyond the
top of riser, and its solids holdup is set as Eq. (3).
Fig. 2. Schematic diagram of circulating fluidized beds. The solids holdup at the riser exit is expressed as Gs / (ρp(Ug − Ut))
and substitutes it for ξ in Eq. (7); the relation between Zd and Gs is
expressed as
The exit structures influences the axial solids holdup distribution,
especially the solids holdup in the upper of riser. The back-mixing 00 1 1
would be intensive with high fluidizing gas velocity and high solids Gs
Z d ¼ H r þ ln @@
 −ξdil A=ðξden −ξdil ÞA=α ð11Þ
circulation rate [3,28], and the axial solids holdup distribution is ρp U g −U t
the so-called C-shaped distribution. Because the gas velocity and
the solids circulating rate in this paper is not much high, therefore
If Zd is positive, the axial solids distribution is the quasi S-shaped
the effect of abrupt exit should be not much obvious. Moreover, the
profile; otherwise it would be the quasi exponential profile.
back-mixing especially in the low riser could confuse the relation
between the axial solids holdup distribution and the saturation carrying
2.2. Hydrodynamic model in cyclone
capacity; therefore the effect of abrupt exit is not considered.
The pressure drop across riser and the material mass can be calculated
Inlet dust loading at the inlet of cyclone significantly influences the
with Eqs. (4) and (5) respectively.
pressure drop of cyclone [31–34]. The pressure drop at first shows a
ΔP r ¼ ρp gH r ξdil ð4Þ descending trend with the increase of inlet dust loading, then increases
gradually after a turning point. Therefore the effect of solids concentration
could not be ignored during the calculation of pressure drop of cyclone.
Mr ¼ ΔP r Ar =g ð5Þ
Few correlations could properly reflect the effect of inlet solids load-
ing on the cyclone pressure drop. Chen and Shi [31] analyzed the
pressure drop and proposed a model based on the cyclone structures;
Case 2. Gs = Gssat however the model is complicated, which limits its application. A
more universal model as Eq. (12) shown was first proposed by Baskakov
The solids holdup in dilute phase can be calculated with Eq. (3), and
et al. [32]. Then it was adopted to fit the variation of pressure drop with
the solids holdup of dense phase [29] is set as
the inlet solids loading by others [33,34], and the results showed good
!−0:013 ! agreement between the measured pressure drop and the calculated
 
U g ρp 1:13 ρp −ρg G pressure drop in different inlet solids loadings.
ξden ¼ 1 þ 0:103  
s  ð6Þ
Gs ρg ρp U g −U t !
2 1
ΔP c ¼ 0:5kρg U g a þ a3 C i ð12Þ
1 þ a1 C i 2
The solids holdup in transition state exponentially decays with the
increase of height. The decay factor is influenced by operating conditions,
The coefficients of k, a1, a2 and a3 depend on the cyclone structures.
design parameters, and properties of material and gas [19,20,23].
For the cyclone in this paper, the coefficients are calculated according to
Although numerous empirical correlations for predicting decay
the experiment data conducted in the same cyclone [34]. In addition,
factor have been proposed, there are great deviations among them
[23]. In this paper, the decay factor is adjusted to better predict the
variation in pressure drop across riser. Given the decay factor, the Table 2
Material properties.
solids holdup in the transition state is calculated by [30]
Real density Particle diameter Bulk Minimum
(kg/m3) (μm) voidage fluidizing voidage
ξ−ξdil
¼ expð−α ðZ−Z d ÞÞ ð7Þ Quartz sands 2600 160 0.52 0.56
ξden −ξdil
150 X. Mo et al. / Powder Technology 274 (2015) 146–153



Mls ¼ ρp H rc Arc 1−εm f þ ρp Lpas Apas 1−εpas : ð17Þ

2.4. Hydrodynamic model in standpipe

The gas solids distribution in the standpipe includes a dilute region

in the upper, and a dense region in the bottom. The pressure drop
produced by the dilute region could be ignored in the low solids flux
due to much low solids holdup in the dilute region; however the
contribution of dilute region to the total pressure drop in the
standpipe may be great in the high solids flux [35]. For the gas solids
flow with relative low solids flux, the gas solids slip velocity and
voidage satisfy the following correlations [36]:

G Qv
U sl ¼
s þ ð18Þ
ρp 1−εsp εsp Asp

U sl

ε sp ¼ εpb þ εm f −εpb ð19Þ
Fig. 3. Variation of solids circulation rate with aeration rate in the supply chamber. U m f =εm f
 
 ε −ε
due to the great voidage of gas solids mixture in cyclone, the material ΔP sp pb
¼ ρp g 1−εm f  ð20Þ
mass in cyclone is assumed to zero. ΔL sp εm f −εpb

2.3. Hydrodynamic model in loop seal The material mass in standpipe is expressed as


The loop seal consists of the supply chamber connecting the bottom Msp ¼ Ls ρp 1−εsp Asp ð21Þ
of standpipe, the recycle chamber connecting the riser and the horizontal
passage between the two chambers. Compared with the minimum fluid-
where Ls is the solids height in standpipe.
ization, the voidage of the mixture and the solids height in the recycle
chamber would increase with the increase of fluidizing gas velocity in
2.5. Calculation procedure
the bubbling regime; however it is difficult to predict the increased solids
height. Assuming the minimum fluidization and the solids height equal
Fig. 1 shows the calculation procedures for different cases classified
to the height of recycle chamber would not cause great deviation of
by Gssat. For all cases, gas solids behaviors in the riser, the standpipe
pressure drop for the recycle chamber with low height. For the industrial
and the passage of loop seal are the variables of hydrodynamic model,
CFB boilers, the height of the recycle chamber is much high, and the
and the pressure balance and material balance are the controlling
hypothesis of minimum fluidization may lead to great deviation.
equations. Three variables and two controlling equations make the
Therefore the pressure drop in the recycle chamber is simply
direct solution impossible. We adopt an indirectly way to calculate
assumed as
the gas solids flow in CFB. The first step ignores the effects of passage

 to obtain the gas flux and solids flux in the passage, then the pressure
ΔP rc ¼ ρp gH rc 1−εm f : ð13Þ drop and material mass in the passage could be calculated. The calculated
pressure drop and material mass in the passage are input to conduct the
The pressure drop in passage influences the solids circulation second step. If the pressure drop of passage approaches the constant,
especially in the CFB boilers with long passage. Although the inclined the calculation is finished. The differences among the three cases are
passage has been proposed to reduce the flow resistance in the loop
seal, the majority of loop seal adopt the horizontal passage due to the
simple structure. The gas solids behaviors in the horizontal passage
are different from that in the inclined passage due to the different
effects of gravity. Kim et al. [21] fitted the experimental data conducted
in the loop seal with horizontal passage, and proposed an empirical
correlation for the pressure drop across the horizontal passage.
0 0 0 10:43 11 = 1
3
1 B μρp U pas
ε pas ¼ @0:4 þ @4@
 A A C A ð14Þ
2:1 d2p ρg ρp −ρg φ2p g

 
ΔP 0:51 2:01 −0:97 −0:76
¼ 0:0056Gs;pas ρbulk dp Dpas ð15Þ
ΔL pas

Assume that the gas solids behavior in supply chamber is the same
to that in standpipe, the pressure drop of supply chamber is normally
considered as the part of pressure drop of standpipe. The pressure
drop and material mass in loop seal are set as

ΔP ls ¼ ΔP rc þ ΔP pas ð16Þ Fig. 4. Pressure drop of each section.

 X. Mo et al. / Powder Technology 274 (2015) 146–153 151

Fig. 5. Gas solids behaviors in the standpipe.

the identification of axial solids distribution. For the case of Gs b Gssat, the the results of calculation, and dots with different shapes are the
axial solids distribution is uniform, and the solids holdup depends upon experimental data. Due to the increase of solids circulation rate,
Gs. For the case of Gs N Gssat, Zd could be obtained according to Eq. (11); more materials are suspended in the riser. At low aeration rate,
however Zd should be given for the case of Gs = Gssat. the calculation has good agreement with the experiments. After
3.7 m3/h of aeration rate, the pressure drop of loop seal drops; however
3. Experiments the calculated values by Eq. (16) do not show a decreasing trend.
Actually the gas solids mixture in the upper of lateral passage is dilute;
As Fig. 2 showed, the circulating fluidized bed for calculation consists however it is dense in the bottom [37]. The voidage in Eq. (14) is the
of a riser with weak exit restriction to avoid solids back-mixing, a average value in the passage, which may lead to the deviation of
cyclone, a standpipe and a loop seal. More details about the circulating pressure drop between calculation and experiments.
fluidized bed can be found in the previous study [25]. The riser height Fig. 5 shows the gas solids behaviors in standpipe. With the increase
and standpipe height are adjusted to calculate the axial solids distribution of solids circulation rate, the pressure drop across riser is increased. In
in the CFB with low riser and tall riser. order to keep the pressure balance with less material, the pressure
The bed material is quartz sand, of which properties are listed in drop gradient in standpipe is increased with decreasing solids height,
Table 2. The superficial fluidizing gas velocity in riser is 6 m/s, and the which leads to the increase of voidage in standpipe. The voidage calcu-
total inventory is 11 kg. The aeration rate in loop seal is adjusted to lated is lower than that of experiments, which is deduced from the
change solids circulation rate. pressure drop gradient according to ERGUN model [36]. The deviations
in sphericity and diameter of solid particles may cause the deviation of
4. Model validation voidage. The material mass in elbow and cyclone are ignored for calcu-
lation, which makes the calculated solids height always higher than the
Yao et al. [25] investigates the gas solids flow in a riser with a height experimental value. When the gas solids flow in standpipe is at the stick
of 4.5 m. Due to the very high fluidizing gas velocity (6 m/s), TDH is slip state, the gas flows downward, and the gas flux increases with
almost 9.76 m. Therefore the gas solids flow in riser is at the case of solids circulation rate. When the aeration rate is greater than 4.7 m3/h,
Gs N Gssat. As Fig. 3 showed, the solids circulation rate increases with the solids in standpipe would be fluidized. In the fluidization state, the
the aeration rate in bottom of supply chamber. The variation of pressure gas bypassing upward was found, while the calculation cannot simulate
drop of each section is shown in Fig. 4. Curves with different colors mark such phenomenon.
152 X. Mo et al. / Powder Technology 274 (2015) 146–153

Fig. 6. Axial solids distributions in low riser and tall riser. (a. low riser, b. tall riser.)

5. Axial solids distribution in low riser and tall riser Lower boundary in case of

Li and Kwauk [24] regarded the exponential profile and the state of Gs ¼ Gssat : Z d ¼ −TDH; Gs ¼ Gssat ð27Þ
Gs N Gssat as the S-shaped profile by assuming the dense phase under
the bottom of riser or the dilute phase above the top respectively. The Upper boundary in case of
assumptions proposed by Li and Kwauk [24] are adopted in this paper.
Gs ¼ Gssat : Z d ¼ H r −TDH; Gs ¼ Gssat ð28Þ
The distance between the upper end of dense phase and bottom of
riser, Zd, is adopted to reflect the change of axial solids distribution.
At fixed solids circulation rate in the state of Gs N Gssat, the pressure The axial solids distributions in a low riser and in a tall riser are
drop across riser does not change with the variation of total inventory summarized as Fig. 6. The axial solids distribution of dilute pneumatic
[6,38], which indicates that Zd depends upon solids circulation rate. conveying is uniform and it is not shown here. Fig. 6a corresponds to
Axial solids distribution in case of the distributions in a low riser, while Fig. 6b shows the distributions in
a tall riser. The curves indicate boundaries to distinguish different
Gs N Gssat : F ðGs Þ ð22Þ solid distributions, and the dash curves represent the assumed section
that is beyond the top or under the bottom. With the increase of Zd,
where Gs is related to the total inventory and gas solids behavior in the axial solids distribution in a low riser firstly presents as the expo-
standpipe [6,25] nential profile, then changes to the quasi exponential profile and finally
evolves to the quasi S-shaped profile. For the tall riser, the quasi expo-


nential profile is replaced by the S-shaped profile due to the dilute
Gs ¼ G M t ; εsp : ð23Þ
phase in the upper of riser.
The saturation carrying capacity prevails in the tall riser according to
The lower boundary for state of G s N Gssat corresponds to the Fig. 6. The range for saturation carrying capacity in the low riser is very
disappearance of dilute phase in the upper of riser, and it is set as limited, which indicates that it is hard to keep saturation carrying capac-
Eq. (24). The maximum of solids circulation rate corresponds to the ity. For the tall riser, over the limited range of pressure drop provided by
maximum of Z d which is restricted by the maximum of pressure the external loop, there exists the dilute phase in the upper of riser, and
drop across standpipe. Gs is equal to Gssat. If the total inventory is greater than a critical value at
Lower boundary in case of which Zd is Hr − TDH, Gs would be greater than Gssat to form the quasi
S-shaped profile.
Gs N Gssat : Z d ¼ H r −TDH; Gs ¼ Gssat ð24Þ
6. Conclusions
Upper boundary in case of

 A comprehensive model is proposed based on the pressure balance
Gs N Gssat : Gsmax ¼ Φ H sp ð25Þ and material balance for circulating fluidized beds. The sub-model for
axial solids distribution in riser is classified by the saturation carrying
capacity. The model is verified with experiments conducted in a low
For the case of Gs = Gssat, Zd depends upon the total inventory and
riser, which shows good agreement not only for the pressure drop of
gas solids behaviors in standpipe. Greater total inventory and greater
each section in the circulating fluidized bed, but also for gas solids
voidage in standpipe lead to the increase of pressure drop across riser
behaviors in standpipe.
[18].
The riser height has a significant influence on the axial solids distri-
Axial solids distribution in case of
bution in CFB riser. With the increase of Zd, the axial solids distribution
in low riser appears as the exponential profile, the quasi exponential

 profile and the quasi S-shaped profile continuously. For the tall riser,
Gs ¼ Gssat : F Mt ; ε sp ð26Þ
the quasi exponential profile is replaced by the S-shaped profile due
 X. Mo et al. / Powder Technology 274 (2015) 146–153 153

to the dilute phase in the upper of riser. In addition, the saturation [16] J. Li, G. Xu, W. Ge, The coexistence of two different steady states in circulating fluidized
beds, in: J. Werther, M. Kwauk, J. Li (Eds.), Abstracts for WorkshopIIon Modeling and
carrying capacity prevails in the tall riser, and with greater inventory Control of Fluidized Bed Systems, Beijing, 1996, p. 14.
Gs would exceed the Gssat to form the quasi S-shaped profile. [17] D. Bai, K. Kato, Saturation carrying capacity of gas and flow regimes in CFB, J. Chem.
Eng. Jpn 28 (1995) 179–185.
[18] N. Hu, H. Zhang, H. Yang, S. Yang, G. Yue, J. Lu, Q. Liu, Effects of riser height and total
Acknowledgments solids inventory on the gas–solids in an ultra-tall CFB riser, Powder Technol. 196
(2009) 8–13.
Financial support of this work by the Key Project of the National [19] D. Kunii, O. Levenspiel, Fluidization Engineering, Second ed. Butterworth-
Heinemann, U.S.A., 1991
twelve-Five Year Research Program of China (2012BAA02B01) [20] J. Adanez, P. Gayan, F. Garcia-Labiano, L.F. de Diego, Axial voidage profiles in fast
and the National Basic Research Program of China (973 Program) fluidized beds, Powder Technol. 81 (1994) 259–268.
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with a loop-seal, Ind. Eng. Chem. Res. 41 (2002) 4949–4956.
[22] P. Basu, L. Cheng, An analysis of loop seal operations in a circulating fluidized bed,
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