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Mathematical Modeling of the Prereduction Process of Iron Ore in a Circulating Fluidized Bed.

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Mathematical Modeling of the
Prereduction Process of Iron Ore in a
Circulating Fluidized Bed
Y. B. Hahn,' Y. H. Im, K. J. Kim, D. G. Park,+l. 0. Lee,'
1. S. Nam" and K. S. Chang"
Department of Chemical Engineering, Chonbuk National
KOREA
University, 664-74 Duckjn-dong 1 Gal Chonju 567-756,
~~
A malhematical model has been developed to describe the various subprocesses
occurring in a circulating fruidized bed (CFB) used for pre-reduction of iron ore
particles in the smelting reductwn iron-making process. The model incorporates
hydrodynamics, iron reduction kinetics, and heat and mass transfer. One of the key
features is the inclusion of a wall-to-bed heat transfer model to describe the heat
transfer phenomena occurring in the CFB. The predicted and measured heat transfer
coeficients showed a minima in the lower par1 of the bed due lo the irregular
up-and-down movement of ore particles. The model predictions of the reduction
degree of iron oxides based on shrinking-unreacted-corechemical reaclwn control
mode showed satisfactory overall agreement with measured data. The performance of
the CFB reactor has been tested extensively in terms of gas oxidation degree, inlet
temperature,particle size and mean particle residence time. It was confirmed that the
reduction degree is signifiantly affected by gas oxidation degree, wall temperature
and particle size.
Introduction
CFB reactorshave been u t i l d extensively in both catalytic and noncatalpc gas-solid
reactions, such as in the catalytic cracking of crude oil, the combustion of low-grade.
fuels to meet strict environmental standards,and the gasification of wood and biomass.
However, little work has been done on the behavior of fluidizing iron ore particles in
the CFB for the purpose of iron ore reduction.
In recent years, various smelting/reductionprocesses have been under development
to replace the conventional iron-making process, i.e. the blast furnace process. The
smelting- reduction iron-making ~ X O C ~ S Smay be required to satisfy criteria such as
the use of different coals, simplified material preparation, hot metal with little impurities,
*
+
Author to whom correspondence should be addressed.
Research Institute of Industrial Science and Technology, b h a n g 790-600,KOREA.
i-+
Depamnent of Chemical Engineering, Pohang Institute of Science and Technology,
Pohang 79@600, KOREA.
23
Y.B. Hahn, et al.
independent process steps, dosed energy system, efficient pollution conUoJ and no
generation of wastes. The smelting/reduction process that combines a smelting furnace
and a CFB pre-reduction reacm has been highlighted as one of promising processes
that meet the above requirements [I, 21.
For the pre-reduction stage, there is an increasing interest in using a CFB because
of its ability for the pre-reduction of iron oxides.The CFB reactor has seveml advantages
including no agglomeration of the feed, excellent heat and mass transfer, temperature
uniformity through the whole reactor circuit, excellent thermal efficiency. low
investment cost, and efficient pollution control. An understanding of the overail
phenomena occurring in a CFB is important, but very little work has been done based
on first principles. This is mainly due to the complexity of the system.
In this work, a mathematical model has been developed to describe the various
subprocesses occumng in the CFB used for pre-reduction of iron ores in the
smeltinglreductionim-making process. The model incorporates hydrodynamics, iron
reduction kinetics, and heat and mass transfer. The model predictions were compared
with experimental data and showed good agreement. The performance of the CFE3
reactor has been extensively tested in terms of various operating conditions such as
superficial gas velocity, particle size, gas oxidation degree, inlet temperature, and
mean parucle residence time.
Mathematical Models
The circulating fluidized bed consists of a gas inlet, iiser, cyclone, downcomer and
solid discharge, as shown in Figure 1. The specified particles are charged into the
riser, and the reducing gases are blown in through a perforated bottom plate. The
particles are then fluidzed. separated in a recycling cyclone, and circulated through
0 Downcorner(or Circulation tube)
0 Cyclone
@ Gas exit
0 Blower
8
0 Aeration tube
Electric heater
Figure 1. Schematic diagram of a c i r c W g jluidized bed.
24
Mathematical Modeling of Prereduction Process of Iron Ore
the downcomer into the bed to maintain the amount of solid in the CFB reactor. The
riser in which the pre-reduction reaction of iron ores occurs is important. Fbr efficient
operation, stable fluidization of ore panicles has to be maintained in the riser. Model
equations basedon first principles may be obtained by considering m a s and momentum
balances, gas-solid-wall interactions, and heat and mass transfer for both the gas and
solid phases.
Hyddynunaic model
To describe the fluidizing behavior of solid partides in a CFB,s e v e d hydrodynamic
models have been proposed by many research groups. The models can be divided
largely into two main groups: entrainment models [3,4] and inviscid models for two
fluids [57].
Hahn et al. in 1995 showed that the inviscid model can be adequately
used to describe the hydrodynamic behavior of iron ore particles in a CFB [7]. Hence,
in this study, the inviscid model in which both phases are considered to be continuous
and fully interpenetrating has been used to describe the behavior of fluidizing iron ore
in the CFB riser. Detailed descriptions of the hydrodynamic model equations are
available elsewhere [ST.
Heat transfer model
The conservation equation of energy includes conduction, convection and radiation.
Based on the assumption of onedmensional steady state, the energy equations for
both gas and solid phases can be expressed, respectively, in the following forms :
The boundary conditions for solving Equations (1) and (2) are obtained from the
inlet values of T8 and T,, The inlet values of ef E,, u8 and usare also used as boundary
conditions for solving the hydrodynamic model equations.
The gas-solid interphase heat-transfer coefficient (hJ can be obtained from the
following equation [8,9]:
6Eh
hi =-
(3)
dP
where the gas-solid heat transfer coefficient (h) can be obtained from the following
empirical cornlation f9]:
25
Y.B. Hahn, et al,
Nu = nd =h( 7 - 1 0 ~ g +%:)[I
k8
+0.7R,Q 2 P,1pI
a7 Ip
+(133 - 2 4 + 12&,+ l.2&i)Re
P,
(4)
where
In Equations (1)and (2). the thermal conductivities %and K , represent contributions
due to the gas and solid phases, respectively, and they pose some difficulty in solving
the energy equations because they are effective transfort properties. Bauer and SchlUnder
[ 101 developed an approximate model for the effective thermal conductivity in packed
beds. Kuipers et al. [9] and Biyikli et al. [ 111 applied this model to estimate the
effective thermal conductivity in fluidized beds. In this work, based on Bauer and
Schliinder's model,K,and K, can be obtained from :
K,represents the contribution of thermal radiation, and can be expressed as [12J:
26
Mathemaricai Modeling of Prereduction Process of Iron Ore
In order to obtain the volumetric wall-to-bed heat transfer coefficients, Hahn et al.
in 1994 have developed a wall-to-bed heat transfer model based on core-annulus flow
structure [13].where qgand 4, are obtained based on the wall-to-bed heat transfer
model :
where
Reduction Kinetics of Iron Ore Particles
The iron ores are reduced by the two major reducing agents, i.e. carbon monoxide and
hydrogen. The reduction involves the following steps :
Fe30,
AH",
+ co(m
= 9.7;
H2)
3FeO + W 2 ( m H,O)
Hl = 195 (M
I md)
+
FeO+CO(m H2) + F e + W 2 ( u r H 2 0 )
AH",, =-4.4; AM&Hl =5.4(kcallml)
The above reactions occur in series depending on reduction degree (RD), that is,
reaction (17) when RD e 11%. reaction (18)when 11 5 RD s 308, and reaction (19)
when RD > 30%.The overall reduction reaction is written as :
27
Y.B. Hahn, et al.
Fe203+3C5(or 3H2) + 2Fe +3C02(a3H20)
AI-&,
=-6.l; A I $ m H , = 2 3 . 4 ( k C a l I t d )
Iron ore pamcles in the CFB system are much small compared with the conventional
blast furnace iron-makmg process in which sintered pellets are reduced. In general,
the reducing gases are fed into the reactor in a large excess amount. The CFB system
also can be characterized by efficient contact between gas and solid particles, and
rapid rate of mass and heat transfer. Hence, it is assumed that mass transfer resistance
of gases from the bulk to the surface can be neglected. Based on this assumption, the
reduction of nonporous iron ore particles can be described by a chemical reaction
control scheme under using the shrinlung unreacted-core model [14]. The conversion
is then given by :
where the dimensionless time is defined as :
The reduction rate is obtained from :
Since the reduction of iron oxides is affected by the solids residence time, the
residence time distribution of the solids in the bed has to be considered for a continuous
fluidized bed reactor. The residence time distribution of soIids at dinlensionless time
is given by [Is] :
E(f*) = T1e x p [
tR
-$]
where
-
kC
r',=-T;;
PBrP
and
-
iR =
W
mean residence time = 9
F,
28
Mathematical Modeling of Prereduction Process of Iron Ore
By combining Equations (21) and (24),the mean conversion of iron oxides leaving
the CFB reactor is :
The energy source for the energy equation of the solid phase is :
where V,, and G , represent the control cell volume and the solid mass flux in the
fluidized bed, respectively. The corresponding equation for the gas-phase energy is :
h
sp*
=-sph
In Equation (B),A@ is obtained from :
RESULTS A N D DISCUSSION
Predictions of Heat Transfer in a CFB
In our previous work [13],a wall-tdxd heat transfer model was developed based on
the core-annulus flow structure. To verify the heat transfer model, model predictions
were compared with measured data obtained by Wu et al. [16] They obtained heat
transfer data from two heat transfer surfaces, each 1.53 m long and 148 nvn wide,
located on one wall of the rectangular column and beginning 1.22 and 4.27 m above
the distributor plate. The profiles for the heat vansfer coefficient as a function of
height measured downward along the upper and lower heat transfer surfaces are
shown in Figures 2 and 3, respectively, together with the model predictions Ilepresented
by the solid lines. From Figure 2 the developed wall-to-bed heat transfer model
produces satisfactory prediction of the heat transfer coefficient in the upper part of the
bed.
The model predictions in the lower part of the bed are less satisfactory (see Figure
3). However, the model predicts almost the same trend as the experimental
measurements. The prehcted and measured data show a minima in the heat transfer
coefficient in the lower surface region. The particle motion in the lower part of the
CFB is likely to be less regular than that in the upper part Particles move sometimes
upward and sometimes downward in the lower part of the bed. The upand-down
motion of particles may explain the minima in the heat transfer coefficient in the
lower part of the bed [16]. Figure 3 also shows sharp increase in the predicted and
measured heat transfer coefficient possibly because the suspension density increases
29
Y.B. Hahn, et al.
400
1
350
-
I
I
0 G,,
= 28 kg/m
s
250
loo
t
n
50 I
0.0
W
I
1 .o
0.5
Distance along Heat Transfer Surface(m)
Figure 2. Effect of solid circurCrrionftux on the Iocai hear trunsfer coefficient along
the upper heat transfer surface ( 0 0 measuremenfsby Wu el al. [MI;prediction of this work).
4
tl
.r(
0
450
I
400
-
150
-
.rl
I
k
rn
0
-
0
0
0
I 4
100
0.0
I
0.5
I
1 .o
Distance along the Heat Transfer Surtace(m)
Figure 3. EBect of solid circulation flux on the local heat trawfer coeficient along
the lower heat transfer surfwe ( 0 measurements by Wu et al. [16];prediction of this work).
30
Mathematical Modeling of Prereduction Process of Iron Ore
over the lower part of the heat transfer surface. In spite of the complexityand differences
between the upper part (orthe dilute-phase region) and the lower part (or the dense-phase
region), the model pmhctions are satisfactory overall.
Based on the wall-to-bed heat transfer model, p h c t i o n s were made to explain
the heat transfer phenomena occurring in a CFB. The test CFB is 10 rn high and 0.31
rn &meter. Test particles are iron ores with a size distribution of 40% 2ooo pm, 20%
3000 p, 12% 4OOO p and 28% so00 pm. The fluidizing medium is a reducing gas
having composition of 54% CO, 5%Ar, 20% CO, and 21% H,. A typical example of
the model predrctions in terms of effect of inlet temperature is shown in Figure 4 for
the case of an ore inventory of 130 kg, superficial gas velocity of 4 m/s and solid
circulation rate of 11.5 kg/rn2.s.For calculations, the wall temperature was fixed at
1073K. The temperature of solid is higher than the gas along the riser height, in spite
of feedlng solids at temperatures lower than the gas. This indicates that the solid
particles are heated up first,and followed by the gas. This result may be because the
heat transfer rate from the wall surface to the solid particles is greater than that to the
gas phase. This also may be due to the large heat capacity and conductivity of the iron
ores compared to the reducing gas.
Reduction of Iron Ores in a CFB
Iron ore particles are pre-reduced in the CFB reactor to increase the productivity of
the smeltinglreduction furnace, to decrease the consumption of coal as a primary
energy source, and to suppress the generation of gas. The gas generated in the
smelting/reduction furnace is utilized as a reducing gas in the pre-reduction stage.
The reduction rate of iron oxides is significantly affected by the gas oxidation degree
(GOD) and the bed temperature. Although the reaction kinetics of iron oxides in the
CFB reactor are of importance, very little work has been reported.
As described in previous section, the reduction reaction of iron oxides occurs in
series dependmg on reduction degree. However, it is v e q difficult to explicitly obtain
kinetic data for each reaction step. Hence, apparent experimental kinetic data were
used to express the rate constants in Arrhenius form. In a series of experiments with
varying temperature and particle size, the reduction of iron oxides with CO was able
to be described as chemical reaction control in the shnnlung urueacted-core model as
shown in Figure 5. Although not illustrated, similar behavior was obtained for the
case of reducing iron oxides with %. The apparent rate constants for reducing iron
oxides with CO and % are expressed, respectively, as follows :
kco = 1 5 . 4 6 e x p10,412
(-y)
It is assumed that the a p p n t kinetic data obtained from Equations (31) and (32)
can be used to quantitatively describe the individual reduction steps. This assumption
31
Y.B. Hahn, et al.
-
700
700
I
Tgo= 573K. TIO= 473K
P
Tgo= TSo= 473K
k4
W
Q)
s
600
600
f
4
ld
k
Q)
8
500
500
Q)
b
Solid temperature
400
400
0
2
4
6
8
1012
1200
n
x
1000
0
2
4
6
8 1 0 1 2
11200
T = 773K, Tao= 473K
PO
1000
Tgo= 1073K, Tao= 300K
W
600
800
600
600
3
4
ld
2
E^
Q)
b
400
200
0
Gas temperature
40 0
1
'
200
-
Figure 4. Temperature profile ahng the riser height with varying inlet temperatures
(Tw= 1073K).
32
Mathematical Modeling of Prereduction Process of Iron Ore
0.8
I
I
I
I
I
I
10
20
30
40
50
60
m
0.6
\
d
n
x
I
4
0.4
W
I
0.2
4
0.0
0
70
1.0
m
0.6
\
d
n
x
I
0.6
4
W
0.4
I
4
0.2
0.0
0
10
20
30
40
50
Time (min)
Figure 5. Reduction degtee versus time with CO reduelion of 1223 K ((a)particle
size 0.125-0.25mm; ( b )particle size 0.25-0.5mm I.
was verified with Figure 6 in which model predctions based on this assumption
showed good agreement with measurements (0)in terms of reduction degree versus
time.
Prereduction of iron ore particles (size 1-5mm) was carried out in a laboratory-scale
circulating fluidized bed (3 m high; 0.08 m diameter). The gas oxidation degree
defined as (CO, + H,O)/(CO + CO,+ H, + $0) was maintained at 21% for the first
30 minutes, and at 5% for the next 30 minutes. The prerduction results obtained at a
wall temperature 1073K are shown in Figure 6. The sudden increase of reduction
degree at 30 minutes is due to switching the gas oxidation degree from 21% to 5%.
The solid cuwes (a) and (b) in Figure 6 represent the predicted reduction degree in
the riser itself, and in the whole CFB system including cyclone and downcomer,
respectively. It is seen that the agreement between the predicted and measured results
are satisfactory overall.
The effect of wall temperatures on the reduction of iron oxides was predicted and
is shown in Figure 7.The reduction rate is greatly affected by the wall temperature.
33
Y.B. Hahn, et al.
The reduction of iron ores is also affected by the gas oxidation degree. Predictions
were made at a wall temperature 1073K with varying GOD values as given in Table
I . Table 1 shows inlet gas compositions for the first 30 minutes of reduction
(prereduction)and for the next 30 minutes (final reduction). The predicted results are
shown in Figure 8 where the reduction of iron oxides is significantly affected by the
gas oxidation degree.
The effect of particle size was predicted at the wall temperature of 1073K with
switching the GOD from 21 to 5% after 30 minutes reduction time. It is seen from
Figure 9 that iron ore parucles smaller than 1 nrm are quickly reduced to 90% reduction
degree within 30 minutes. The predicted results may be used to estimate the feed rate
of iron ores because the mean residence time is determined depending on the mean
reduction degree.
Table 1 . Composition of reducing gases.
1.o
0.8
0.8
0.7
0.6
0.5
0 -4
0.3
0.2
0.1
0.0
0
10
20
30
40
50
60
70
Time (min)
Figure 6. Comparison of predicted and measured reduction degree versus time [(a)
reduction degree in the riser ( ): (b)reduction degree in the whole CFB
sysrern f 0 ) I .
34
Mathematical Modeling of Prereduction Process of Iron Ore
1.o
0.9
0.8
-
0.7
-
0.6
(a) 1023
K
0.5
(b) 1073 K
0.4
(c) 1123
K
(a)
K
0.3
1173
-
-
0.2
0.1
0.0
0
10 20 30 40 50 60
70
80 90 100 110
Time (min)
Figure 7. Effect of wall temperature on the reduction rate of iron ore (particle size
1-5 m).
Time (min)
Figure 8. Effect of gas oxidation degree on reduction rate of iron ore: a, b. c and d
arefrom Table I (T,= 1073K)
35
Y.B. Hahn. et al.
CONCLUSIONS
The numerical predictions of the prereduction of iron ores in a circulating fluidized
bed show satisfactory overall agreement with experimentaldata in spite of the bmplex
nature of the system. This leads to the following conclusions.
1. The developed wall-Wbed heat transfer model produd good prediction of the
heat transfer coefficient in the upper part of the bed, and less satisfactory but the
same trend in the lower part of the bed. The predicted and measured data showed a
minima in the heat transfer coefficient in the lower part of the bed due to the irregular
up-anddown movement of parbcles.
2. The reduction of iron oxides in the CFB can be described by chemical reaction
control using a shrinking unreacted-core model.The model predictions of reduction
degree showed satisfactory overall agreement with measured data
3. The reduction degree is significantly affected by the gas oxidation degree, wall
temperature and particle size.
80
I
I
I
I
I
I
I
I
1
1
-
80
-
Particle Size
70
-
(a) 0.25-0.5
'O
-
mm
(b) 0.5-1 m m
(c) 1 - 3 mm
50
-
(d) 3
40
-
( c )-
30
-
-
20
-
-
-
(dl
-
5 mm
(b)
-
(4
0.0
0.1
0.2
0.3
0.4
0.6
0.8
0.7
0.8
0.9
1.0
Mean Reduction Degree
Figure 9. Mean residence time versus mean reduction degree with varying particle
size (Tw= 1073K).
36
Mathematical Modeling of Prereduction Process of Iron Ore
NOMENCLATURE
C&
‘P8
Bulk concentration of reducing gas [mOUm?.
Heat capacity of gas [JlkgeKJ.
Heat capacity of solid [Jlkg-KJ.
Particle drameter [ m].
Solid feed rate [kglh].
Fs
h
Gas-solid heat transfer coefficient [ Jlm’sK 1.
Volumetric heat transfer coefficient [ J/m2.sK ] .
h,
hwg,h, Wall-&bed heat hansfer coefficientsof gas and solid [ J/m2.sK 1.
Thermal conductivity of gas [ J l m s K 1.
kg
Thermal conductivity of solid [JlmsK 1.
4
Defined in Equation (6) [JlmAsK I.
K/
Radiation contribution to heat conductivity, Equation (12) [Jlrn.s.K].
KR
Defined in Equation (7) [Jlm-sK 1.
KS
P
Pressure [N/m2]
P
Radius of parhcle.
Rates of enthalpy change due to the reaction of iron ore. Muation (28).
t
Dimensionless time, Equation (22).
c&=
dP
tPg,
s”,
-
1;
Ts
TS
T*.
%
US
X
X
X
Dimensionlessmean residence time of particles, Equation (25).
Gas temperature [ 4.
Solid temperature
Wall temperature [a.
Gas velocity [mls].
Solid velocity [ d s ] .
Average falling velocity of emulsion [ d s ] .
Mole fraction.
Conversion
Mean conversion, Equation (27).
Bed weight [kg].
[a.
W,
Greek Symbols
awg,
am Volumetricwall-@bed heat transfer coefficientsof gas and solid, respectively
[J/m2.sK 1.
B
Gas-solid friction coefficient.
ax
Thcbess of emulsion layer [m].
Voidage.
5
Volume fraction of solid.
5
PB
Molar density of iron oxide [mUmq.
Gas
density [kg/m3].
’8
Solid density [kglm’ 1.
P*
0
Stephan-Boltzmannconstant.
@S
Sphericity of solid particle.
ACKNOWLEDGEMENTS
Parttal financial support from Korea Science and Engineering Foundation through the
37
Y.B. Hahn, er al.
Automation Research Center at POSTECH is gratefully acknowledged.
REFERENCES
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in Smelting Reduction." Metallurgical Plant and Technology International. 3.28-32.
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Partides in a Circulating Fluidized Bed." in press, Metals and Materials, 1. No. 2.
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Mass Transfer. 21,467476.
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Heat-Transfer Coefficients in Gas-Fluidized Beds," AIChE J., 38. 1079-1091.
10. Bauer and Schliinder. 1978. "EffectiveRadial Thermal Conductivity of Packing in Gas Flow. Part U:
Thermal conductivity of the Packing Fraction without Gas Flow," Int. Chem. Eng., 18,189-204.
11. Biyikli, S.. Tuzla K. and Chen. T. C. 1589. "A PhenomenologicalModel for Hear Transfer in Freeboard
of Fluidized Beds,"Can. J. Chem. Eng.,67.230-210.
12. Matbur. A. and Saxena. S. C. 1987. "Total and Radiatjvc Heat Transfer to an Immersed Surface in a
Gas-FlUidkd Bed." AIchE J.. 33,1124-1 135.
13 Im. Y . H., Kim. K J. and Hahn. Y . B. 1944. "Heat Transfer in a Circulating Fluidized Bed of Iron Ore
Particles" In: Yosliida K. and Momka, S. (4.).
ASCOh: F.BR '54 Fluidized-Red & Three-Phase
Reaaors. 8592.
14. Szekely. J., Evans, J. W. and Sohn. H. Y. 1976. In: Gas-Solid Reactions, Academic Press, New York,
73 88.
15. Kunii. D. and Levenspiel, 0. 1991. In: Fluidization Engineering. (2nd ed.) Butterworth- Heinemann.
Boston.337-339.365-367.
16. WU.R L.. Lim, C. J., Chaouki. J. and Grace, J. R. 1987. "Heat Transfer from a Circulating Fluidized
Bed to Membmne Waterwall Surface," AIChE J., 33.1888-1894.
Received: 7 July 1995:Accepted after revision: 13 February 1996.
38
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