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Energy 24 (1999) 633–653
www.elsevier.com/locate/energy
A mathematical model for a circulating fluidized bed (CFB)
boiler
Qinhui Wang*, Zhongyang Luo, Xuantian Li, Mengxiang Fang, Mingjiang Ni,
Kefa Cen
Institute for Thermal Power Engineering, Zhejiang University, Hangzhou, 310027, People’s Republic of China
Received 3 November 1997
Abstract
In developing a mathematical model for a CFB boiler we use earlier work. Our model includes mathematical descriptions of the underlying physical and chemical processes. It has been applied to simulation of
a 12 MW CFB boiler. The calculations agree well with test results.  1999 Elsevier Science Ltd. All
rights reserved.
Nomenclature
A
Ci
CO2,⬁
Dac
Dca
Dh
Dl
Dspi
Dt
f
F
F0
Fd1
Cross-sectional area, m2
Concentration of particles of size i, kg/m3
Oxygen concentration in the bed, kg/m3
Dispersion coefficient from the annulus to the core, m/s
Dispersion coefficient from the core to the annulus, m/s
Diffusion coefficient of oxygen in the ash shell, m2/s
Axial dispersion coefficient, m2/s
Axial dispersion coefficient in the cyclone, m/s
Furnace equivalent diameter, m
Mass fraction of solid particle
Interface between the core and the annulus
Mass flow rate of feed, kg/s
Bed material drain rate, kg/s
* Corresponding author. Fax: ⫹ 86-571-795-1616; e-mail: ccctasun.zju.edu.cn
0360-5442/99/$ - see front matter  1999 Elsevier Science Ltd. All rights reserved.
PII: S 0 3 6 0 - 5 4 4 2 ( 9 9 ) 0 0 0 0 8 - 0
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Fd2
Mass flow rate of back down the dense bed from the dilute region, kg/s
Total heat transfer coefficient
ht
Chemical reaction rate constant, m/s
kc
Specific combustion rate of char particle, kg/m3/s
Ks
Fragmentation constant
kt
l
Length of the spiral in the cyclone, m
Bed material inventory in the dense bed, kg
M1
Particle distribution function
P(R, ␳)
Particle distribution function of feed mass
P0(R,␳)
Pd1(R,␳) Particle distribution function of drained bed material
Pd2(R,␳) Particle distribution function of mass flow that back down the dense bed
Natural size distribution
Pf(R)
Particle distribution function of recycle solids
Pin(R,␳)
Pnew(dp,new) Size distribution after fragmentation
Pold(dp,new) Size distribution before fragmentation
Pu1(R,␳) Particle distribution function of mass flow that elutriated into dilute region
Fin
Recycle solids rate, kg/s
ith mass component flowing into the cell, kg/s
Fin,i
ith mass component flowing out of the cell, kg/s
Fout,i
Ratio of weight consumption of char to that of oxygen
fs
Mass flow rate of elutriated into the dilute region, kg/s
Fu1
Generating rate of i particle in the annulus, kg/s
Gai
Generating rate of i particle in the core, kg/s
Gci
Net solids circulation rate, kg/m2/s
Gs
Generating rate of particle group i in the cyclone, kg/s
Gspi
H
Furnace height, m
h
Height above the distributor, m
Convective heat transfer coefficient for the cluster, W/m2s
hc
Convective heat transfer coefficient for the dispersed phase, W/m2s
hd
Radiative heat transfer coefficient for the cluster, W/m2s
Hrc
Radiative heat transfer coefficient for the dispersed phase, W/m2s
hrd
Heat coming from other regions, kJ/s
Qin
Heat going to other regions, kJ/s
Qout
Heat produced in the cell, kJ/s
Qrelease
R
Particle diameter, m
Maximum particle diameter, m
Rmax
r
Fine particle diameter, m
Radius of char particle, m;
R1
Re
Renault number
Upper size limit of the fines, m
Rfi
U
Gas velocity, m/s
Superficial gas velocity, m/s
U0
V
Particle velocity, m/s
Particle velocity; m/s
Vpi
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W
Z
dmi
d␶
⌬Ri
635
Downward solids flux, kg/m2/s
Height, m
Variation rate of i component in the cell, kg/s
i component generated or consumed in the cell, kg/s
Greek symbols
␳
␶
␦
␨
␤0
Suspension density or particle density, kg/m3
Time, s
Thickness of annulus
Thickness of the ash shell, m
Mass transfer coefficient, m/s
Subscripts
i
c
a
Particle size increment
Core
Annulus
1. Introduction
The CFB represents an improvement over traditional systems used for coal combustion and is
widely applied in industry. Previous studies may be found in Refs [1–6]. Although published
models have a similar structure, significant differences are found in the sub-models.
Our model includes following constraints: (i) The physical and chemical processes occurring
in the boiler are described but include empirical models for poorly understood processes. (ii) The
model should be applicable to different applications of CFB boilers. (iii) The computer code
should be modular to allow users to update component modules easily as new findings become
available. The model is shown schematically in Fig. 1.
2. Brief description of main sub-models
This paper only gives a brief description of the sub-models. For more detailed information
readers may refer to Ref. [7].
2.1. Particle properties
The bed material in the furnace consists of fuel particles (burned or burning), inert particles and
sulfur sorbent, such as limestone. Fuel particles’ behavior during gas–solid reactions is assumed to
be described in terms of three limiting types: (i) shrinking core with attriting shell i.e. the dual
shrinking-core model, (ii) shrinking core with non-attriting shell i.e. the single shrinking-core
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Fig. 1. Structure of the mathematical model for CFB boilers.
model and (iii) uniform reaction. These three reaction modes may occur within a CFB boiler,
and different particles may be in different modes. Hence, the particle population should be
described by particle size and/or density. The two dimensional particle distribution functions may
be given as P(R,␳). Here, R is the particle diameter and ␳ is the particle density.
2.2. Hydrodynamics model
Fig. 2 shows the hydrodynamic structure in CFB boilers with a square cross-section furnace.
In this paper, on the basis of previous researches [8–11], a model is suggested to describe the
core–annulus flow structure in a CFB boiler furnace with a bed material of wide size distribution.
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Fig. 2.
637
Gas–solid flow structure in the CFB boiler and overall balance of gas and solid.
The principal assumptions are: (i) the furnace is characterized by two flow regimes: a dense
phase at the bottom and a dilute phase above the solid entry or secondary air inlet. The dense
phase operates in turbulent fluidized bed regime while in dilute phase core–annulus solids flow
structure is established. Particles travel upward in the core and downward in the annulus. (ii)
Both the thickness of the annulus and the suspension density vary with the furnace height. (iii)
Within the core and the annulus there are no radial suspension density gradients, while the lateral
dispersion between the core and the annulus is considered. (iv) The flow pattern in the furnace
is assumed to be symmetric. (v) While moving in the boiler, the char particle burns and undergoes
attrition, and the gases participate in homogeneous reactions; (vi) The gas phase is modeled as
only flowing upward, backmixing of gas is neglected.
The model used in this paper to determine the voidage in the dense bed is suggested by Hannes
et al. [1].
Bed materials may be divided into size groups. For every solid particle group i in the core or
annulus of the dilute region, a one-dimensional axial dispersion model is used to characterize
solid behavior. For the core,
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冋
册
(1)
冋
册
(2)
d(Vci␳cfciAc)
d
d(␳cfci)
⫽
AcDlci
⫹ (Daci·␳afai ⫺ Dcai␳cfci)F ⫹ Gci.
dZ
dZ
dZ
For the annulus,
d
d(␳afai)
d(Vai␳afaiAa)
⫽
AaDla
⫹ (Dcai␳cfci ⫺ Daci·␳afai)F ⫹ Gai,
dZ
dZ
dZ
where V is the particle velocity, ␳ the suspension density in the furnace, f the mass fraction of
size i particle, F the interface between core and annulus, Dl the axial dispersion coefficient, Dac
the dispersion coefficient from annulus to core, and A stands for cross-section area, Gci and Gai
are the generating rate of i particle in the core and the annulus, to be calculated by the attrition
and the reactions of solid particles.
Subscript c stands for the core, a for the annulus, and i for particle group.
The thickness of annulus ␦ is given by Werther [12] as
冉冊 冉 冊
␦
H
⫽ 0.55Re−0.22
Dt
Dt
0.21
H⫺h
H
0.73
,
(3)
where Dt is the furnace equivalent diameter, H the furnace height and h the height above the distributor.
The downward solids velocity in the annulus maintains constant, about 1.2–1.5 m/s [13,14].
The upward solids velocity in the dilute core can be taken as:
Vci ⫽ Ugc ⫺ Vti,
(4)
where Vti is the terminal velocity of particle group i, the gas velocity in the core, Ugc, is given
by Bai et al. [15].
The dispersion coefficients Dlci, Dlai, Daci, Dcai can be obtained from previous literature [15–18].
Similarly, the balance equations for the gas phases can be given [7].
2.3. Particle population model for the dense bed
Fig. 3 shows the solid balance in the dense bed. In this paper, a particle population model has
been developed by properly accounting for the attrition and reaction, in which the particle size
distribution is divided into two size range, one is from 0 to Rfi (the upper size limit of fines) for
fines, and the other one from Rfi to the maximal size of feed particles Rmax for mother particles.
By considering the population of a given solid particle group (R,␳), the solid mass balance for
mother particles is given as
F0·P0(R,␳) ⫺ Fd1Pd1(R,␳) ⫺ Fu1Pu1(R,␳) ⫹ Fd2·Pd2(R,␳) ⫹ FinPin(R,␳)
⫹ M1·
冉
冊
(5)
∂P1(R,␳) dR
∂P1(R,␳) d␳
3 dR 1 d␳
⫹ M1·
⫺ M1·P1(R·␳)
⫹
⫽ 0,
∂R
dt
∂p
dt
R dt
␳ dt
where F0, Fd1, Fu1, Fd2 and Fin are mass flow rates of feed, bed material drain, elutriated into
dilute region, back down the dense bed from the dilute region and recycle solids, respectively.
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Fig. 3.
639
Flow chart of the numerical solution.
The fines generated will react further but not subject to further attrition, and it is assumed that
the fines have a known size distribution (natural grain size) Pf(r). So, for the fine particle (Rfi >
r > 0), the following item should be added to the population equation, i.e.:
dR
R
max
3·P(R,␳) latt
dt
dR·Pf(r).
(6)
R
冕冤
Rfi
冥
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In addition, the normalization of the distribution function requires,
R
␳
冕 冕
max
0
max
P1(R,␳)d␳dR ⫽ 1.
(7)
␳min
2.4. Coal combustion model
The combustion of coal particles may be modeled as: (i) devolatilization and volatiles combustion, (ii) primary fragmentation, (iii) char combustion with attrition and (iv) homogeneous gas
reaction.
2.4.1. Devolatilization and volatile combustion
Because of the rapid mixing in CFB furnace, the volatile fraction of coal is completely and
instantaneously released in the gas phase in the dense bed. To simplify the volatiles combustion
model, the hydrocarbons in the volatiles may be treated as one gas species, and its molecular
formula may be written as CnHm. So the overall chemical reaction of volatile with oxygen can
be assumed to be
C n Hm ⫹
1
1
nO2→ mH2 ⫹ nCO.
2
2
(8)
The nitrogen and sulfur in the volatiles are considered in the models of NO and N2O formation
and sulfur retention.
2.4.2. Fragmentation
Fragmentation can be treated as happening immediately at feed port. An empirical model has
been proposed by Bellgardt et al. [19] as
1/3
Pnew(dp,new) ⫽ Pold(dp,new·K 1/3
f )K f ,
(9)
where Kf is the fragmentation constant.
2.4.3. Char combustion
The main assumptions for char combustion are: (i) both CO and CO2 are primary products;
(ii) CO burns after leaving the char particle surface; (iii) coal particles with high ash content burn
according to the dual shrinking-core model, but for those with low ash content the single shrinking-core model is applied, and for fine particle the uniform reaction model should be employed.
(iv) The combustion rate of the char particle is determined by reaction kinetics, gaseous and
intraparietal diffusion resistance.
So, the specific combustion rate of char particle Ks may be given as
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fsCO2,⬁
冉冊
Ks ⫽
1
1 R
⫹
kc ␤0 R1
2
␨ R
⫹
Dh R 1
,
641
(10)
where fs is the ratio of weight consumption of char to that of oxygen, ranging from 0.375 to 0.75,
R1 is the radius of the char particle, ␨ represents the thickness of the ash shell, ␨ ⫽ R ⫺ R1, kc
the chemical reaction rate constant, Dh diffusion coefficient of oxygen in ash shell, m2/s.
2.4.4. Homogeneous gas reaction
The main homogeneous reactions for combustible gases are given below:
1
O →CO2;
2 2
(11)
1
O →H2O;
2 2
(12)
CO ⫹
H2 ⫹
CO ⫹ H2O ⫽ CO2 ⫹ H2.
(13)
2.5. Particle attrition
For each bed material having its own attrition characteristics, different empirical models for
the attrition rate of the individual components should be applied. The particle material may be
divided into two types: one is coal/char particles with low ash content, and the other one includes
coal/char particles with high ash content and limestone particles.
2.6. Heat transfer
Based on the special hydrodynamics of the CFB boiler, the cluster renewal model of the bed
to membrane wall heat transfer process has been described in the literature [20]. The dilute phase
comprises of a continuous upflowing gas phase with thinly dispersed solids (dispersed phased)
and relatively denser cluster moving downward along the wall. Any part of the wall comes in
alternate contact with the cluster and the dispersed phase. If ␦c is the average fraction of the wall
area covered by the clusters, the time-averaged overall heat transfer coefficient, ht, may be written
as the sum of the convective and radiative heat transfer coefficients,
ht ⫽ ␦chc ⫹ (1 ⫺ ␦c)hd ⫹ ␦chrc ⫹ (1 ⫺ ␦c)hrd,
(14)
where hc and hd stand for the convective heat transfer coefficient for the cluster or the dispersed
phase respectively, hrc and hrd for the radiative heat transfer coefficient for the cluster or the
dispersed phase respectively.
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2.7. Emission
An improved model for evaluating the performance of sulfur retention by limestone in the CFB
boiler is established based on the model developed by Li et al. [21]. Meanwhile, a simplified
kinetic model for the formation and reduction of NO and N2O is developed on the basis of the
previous research works [22–25].
2.8. Boiler components
A simplified model is established to simulate the gas–solid flow structure in the cyclone. The
basic assumptions are: (i) gas and solid move together in plug flow around a helical path in the
cyclone body. (ii) The cross-sectional area of the spiral is the same as that of the cross-sectional
area at the entry point of the cyclone, and the gas–solid slip velocity entering the cyclone also
depends on the entry area of the cyclone. (iii) Gas–solid separation takes place only at the end
of the spiral. (iv) The combustion of char and combustible gases also takes place in the cyclone
due to the rapid mixing between gas and solid.
So, the balance equation for every solid particle group i may be described as
d 2C i
d(VpiCi)
⫽ Dspi 2 ⫹ Gspi,
dl
dl
(15)
where Ci is the concentration of particles of size i, Vpi the particle velocity, Dspi the axial dispersion
coefficient, Gspi the generating rate of particle group i in the cyclone; l the length of the spiral.
Because there is no suitable model for the cyclone of CFB boiler, traditional calculation models
of grade separation efficiency, overall separation efficiency and the pressure drop are used.
In addition, the models of other CFB boiler components such as inertial separator, external
heat exchanger, recycle device valves and heat transfer surfaces are developed.
3. Numerical results
The CFB boiler may be divided into cells along gas and solid flow path for solving the model.
The cells are treated as balance sections (control volumes), and mass balance and enthalpy balance
are drawn up. While the dense bed is treated as the first cell, the dilute region is divided into a
number of cells. Each cell of the dilute region is divided horizontally into two parts: core and
annulus, and each part is treated as one balance section. Cyclone, external heat exchanger, recycle
device and each type of heating surfaces in the back-pass are treated as one cell, respectively.
In each balance section, the balance equation for one component of gases or solids may be
written as
dmi
⫽ Fin,i ⫺ Fout,i ⫹ ⌬Ri,
d␶
(16)
where Fin,i is the ith mass component flowing into the cell, including that coming from other
regions and the external; Fout,i the ith mass component flowing out of the cell, including going
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643
to other regions and the external; ⌬Ri the i component generated or consumed in the cell by
dmi
physical and chemical processes;
the variation rate of i component in the cell, and it is zero
d␶
under steady state.
The balance equation of energy for one balance section may be given as
dHi
⫽ Qin ⫹ Qrelease ⫺ Qout,
d␶
(17)
where Qin is the heat coming from section outside, Qout the heat going to section outside, Qrelease
the heat released in the cell.
dHi
⫽ 0.
The enthalpy of gas and ash is invariant with time under steady state. So,
d␶
According to the balance equations for each balance section, the flow chart of the numerical
solution of the model is given in Fig. 3.
4. Simulation results and model validation
4.1. Introduction of a 12 MW CFB boiler
Fig. 4 shows the scheme of a 12 MW bituminous-fired CFB boiler which has an external heat
exchanger. The furnace is 21.0 m high and has a square cross-section measuring 5.45 ⫻ 2.45 m
in the water-wall region and 1.5 ⫻ 5.45 m in the bottom refractory-lined section. It is equipped
with two cyclones. Part of the solids separated by the cyclones is cooled by the external heat
exchanger, and the rest is recycled into the furnace by a pair of recycle devices [7,26].
Our model is applied to the simulation of the 12 MW CFB boiler, and the simulation results
are compared with the detailed performance test results.
4.2. Simulation results and comparison with the test results
The particles in the furnace are divided into 70 classes, i.e. 10 size classes from 0 to 8 mm
and seven density classes from 1100 to 2400 kg/m3. The furnace is divided into 30 cells, i.e. one
for dense bed and 29 cells for the dilute region. The model input data shown in Table 1 are
obtained from the operation parameters of the boiler. The temperature of feed water dropped to
105°C from the designed temperature, 150°C, and no limestone is fed.
Tables 2 and 3 show the ultimate analysis and the size distribution of the test coal respectively.
The feed coal is mixed with the fly ash of a stoker boiler. The stoker fly ash is very fine with
high carbon content but almost no volatility.
4.2.1. Main performance parameters
Table 4 shows the predictions and the measurements of main performance parameters. Table
4 shows that, in general, the predictions of main performance parameters except the carbon content
in fly ash are in good agreement with the tested results. Because the blending of fly ash of the
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Q. Wang et al. / Energy 24 (1999) 633–653
Fig. 4. The scheme of the 12 MW CFB boiler.
stoker boiler is not considered in the model, the prediction of residual carbon content is much
lower than measurement and the calculated boiler efficiency is slightly higher.
4.2.2. Temperature profile
Fig. 5 shows that close agreement is observed between the predicted and measured temperature
profile throughout boiler system. In Fig. 6 the predicted temperature profile and the measured
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Table 1
The model input data
Item
Parameter
Item
Parameter
Rated capacity
Main steam pressure
Main steam temperature
Feed water temperature
73 t/h
3.82 MPa
450°C
105°C
Air temperature
Combustion air flow rate
Primary air flow rate
Primary air ratio
25°C
苲 70 500 Nm3/h
苲 42 000 Nm3/h
苲 60%
Ultimate analysis, air dry
Test coal
Table 2
The ultimate analysis of the test coal
Ultimate analysis, air dry
Mt,ar, moisture, as-received,
wt%
Cad, carbon, wt%
Had, hydrogen, wt%
Oad, oxygen, wt%
Nad, nitrogen, wt%
Test coal
5.72
Sad, sulfur, wt%
63.01
3.59
6.23
1.15
0.85
Aad, ash, wt%
Mad, moisture, wt%
Vad, volatile, wt%
Qad, heating value, MJ/kg
23.74
1.43
24.035
24.45
Table 3
The size distribution of the test coal
Diameter 0–0.1
(mm)
Mass
0.5
fraction
(%)
0.1–0.3
0.3–0.5
0.5–1
1–1.5
1.5–2.0
2.0–3.5
3.5–5.0
5–6.5
6.5–8
2
6
16
9
10
13
18
12
13.5
Table 4
Comparison between prediction and test of the main performance parameters
Item
Unit
Prediction
Measurement
Boiler efficiency
Carbon content in fly ash
Fraction of fly ash in total ash
Solids recycle rate
Stack gas temperature
Carbon content in the bottom ash
%
%
%
kg/s
°C
%
89.6
4.8
73
47.5
154
1.8
88.3
11
74.6
苲 50
159.6
1.4
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Fig. 5. Profile of gas temperature in the boiler system; (•) measurement; the solid line is the calculation.
Fig. 6. Temperature profile in the furnace; (䊏) measurement; the thick line is the calculated temperature profile in
the core and the thin line is that in the annulus.
temperature in the core region are given. The model predictions show that the temperature in the
core is clearly higher than that in the annulus, and the temperature in the annulus decreases along
the furnace height but increases slightly near the furnace exit. The reasons for this are that most
of the heat transferring to the membrane wall is from the annulus region and the combustion
reactions in the thin annulus are much lower than that in the core. Fig. 6 also shows model
predictions are in agreement with that measured in the core.
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4.2.3. Profile of solid particle flux
Fig. 7 shows the predictions and measurement results of the solid particle flux in the core and
annulus. The particle flux in the annulus is much higher than that in the core. The particle flux
decreases along the furnace height both in the core region and in the annulus region, but the
particle flux in the annulus increases slightly near the furnace exit. It is caused by the solids
backmixing at the tee and downward flow in the thin annulus region. In this region, the net solids
exchange between the core and the annulus is towards the core. Fig. 7 also shows the close
agreement observed between predicted and measured results at 13 m above the distributor.
4.2.4. Particle population
As seen in Fig. 8, the mean size of solid particles decreases along the vertical position in the
furnace in both core and annulus, and decreases slower in the upper furnace. The model predictions are in agreement with that measured in the furnace.
The particle population varies with height in the furnace. Here only the particle population of
the core region at the middle part of the furnace (above 13 m the distributor) is given in Fig. 9,
which shows most of the bed material particles are the ash particles with low carbon content
from 0.3 to 1.0 mm. In Fig. 10 a comparison between the predicted size distribution and the
measurements in the core region at the same place are given.
In general, the model predictions of particles population are reasonable and in good agreement
with the measurement results.
4.2.5. Profile of carbon content
Here, only the comparison between the measured residual carbon content in particles in the
core region at the middle part of the furnace (13 m above the distributor) and those predicted by
the models are given in Fig. 11, which shows the model predictions for carbon content in small
Fig. 7. Profile of the particle flux in the furnace; (䊐) and (•) are the average measured particle flux in the core
and annulus respectively; the thick line and thin line represent the calculation of the particle flux in the core and
annulus respectively.
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Fig. 8. Profile of the particle mean diameter in the furnace; (䊏) and (䊐) are the average measured particle mean
diameter in the core and annulus respectively; the thick line and thin line denote the calculation of the particle mean
diameter in the core and annulus respectively.
Fig. 9. Population of particles at 13 m above the distributor (in the core region).
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Fig. 10. The size distribution of particles collected at 13 m above the distributor (in the core region);(䊏) the measurement; the solid line is the calculation.
Fig. 11. Residual carbon content in particles sampled at 13 m above the distributor in the furnace (in the core region);
(䊏) the measurement; the solid line is the calculation.
particle (0 苲 1 mm) agree well with the measurement data, whereas there exists great deviation
for coarse particles ( > 1 mm). This difference may be attributed to the model assumptions that
large particles are less likely to be entrained to the upper part of the furnace and to the effects
of particle sampling in the test as well. However, because of the low occurrence of coarse particles
( > 1 mm) in the dilute region, the influences of the deviation may be ignored.
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As seen in Fig. 12, the carbon content decreases slightly along the furnace height and is slightly
lower in the annulus region. This indicates that the combustion of char particles takes place
throughout the height of the furnace. There exists a sharp peak above the dense bed (around 1.5
m). This may be explained as the following: due to the higher density, the elutriated char particles
return more easily back down to the dense bed at the bottom of the dilute region. So the mass
fraction of char particles is higher in this region.
The model predictions of carbon content profile do not fit very well to the measurement data.
The calculated carbon content in the bottom bed material is higher than the measurement data.
This can be due to the fact that the measured carbon content in the bottom material is the residual
carbon content in the drained bed material. In fact, the residual carbon content in drained bed
material is lower than the average carbon content in the bottom material in this CFB boiler. This
may be explained by the following two reasons: (i) two draining ports are arranged in the rear
of the furnace and far away from the feeding ports. (ii) There exists slight segregation in the
dense bed, i.e. the mass fraction of coarse particles is higher near the distributor.
4.2.6. Profile of O2, SO2, NO and N2O concentration
Here, the profiles of several gas species in the furnace are given. Fig. 13 shows the calculated
and measured profiles of O2 concentration both in the core region and in the annulus region. The
model predictions of O2 concentration are slightly higher than the experimental data. Due to the
secondary air injection, the O2 concentration changes rapidly in the secondary air inlet region
(about 2 m), and forms a peak. The profiles of SO2, NO and N2O in the furnace and the average
tested concentrations of SO2 and NO at gas exit are given in Figs. 14 and 15. In general, model
predictions are in agreement with measurement data. Because the violent char combustion formats
a great deal of NO and the dilution of secondary air is not considered in the code, the NO
Fig. 12. Profile of residual carbon content in particles along the furnace height; (䊏) and (䊐) are the average measured
residual carbon content in particles in the core and annulus respectively; the thick line and thin line represent the
calculation of residual carbon content in particles in the core and annulus respectively.
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651
Fig. 13. Profile of O2 concentration; (䊏) measured O2 concentration; the thick line and thin line represent the calculation of O2 concentration in the core and annulus respectively.
Fig. 14. Profile of SO2 concentration; (䊏) is the measured SO2 concentration at the gas exit; the thick line and thin
line represent the calculation of SO2 concentration in the core and annulus respectively.
concentration in the annulus near the secondary air inlet is very high. But it decreases rapidly
owing to the NO reduction along the furnace height.
It should be noted that, because of the small area fraction of annulus and low gas velocity, the
gas flux in the annulus region is very low and accounts for only a small fraction of total crosssection gas flux in the furnace.
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Q. Wang et al. / Energy 24 (1999) 633–653
Fig. 15. Profile of NO and N2O concentration along the furnace height; (䊏) is the measured NOx concentration at
the gas exit of the boiler; Lines 1 and 2 denote the calculation of NO and N2O concentration in the core respectively;
lines 3 and 4 represent the calculation of NO and N2O concentration in the annulus respectively.
4.2.7. Heat transfer coefficient
Fig. 16 shows a comparison between the predicted overall heat transfer coefficient and the
measurement result together with the profiles of convective and radiative heat transfer coefficients
in the furnace. The range of the calculated heat transfer coefficient is from 160 to 190 W/m2/°C,
and decreases along with the furnace height. The average heat transfer coefficient measured is
168 W/m2/°C and is in agreement with the model prediction.
Fig. 16. Profile of heat transfer coefficient in the furnace. Line 1 is the calculation of heat transfer coefficient in the
furnace; line 2 refers to the tested heat transfer coefficient; lines 3 and 4 represent the calculation of radiative heat
transfer coefficient and convetive heat transfer coefficient respectively.
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653
5. Conclusions
A mathematical model for a CFB boiler including the mathematical descriptions of the underlying physical and chemical processes has been developed. These processes are hydrodynamics,
coal combustion, particle attrition, heat transfer, formation and reduction of NO and N2O, sulfur
retention and operation of boiler components such as gas–solid separator, external heat exchanger,
non-mechanical valves and heat transfer surfaces. The model is applied to the simulation of a
12 MW CFB boiler and the predictions are reasonable and agree well with the performance
test results.
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