Materials Sciences and Applications, 2011, 2, 370-380
doi:10.4236/msa.2011.25048 Published Online May 2011 (
Copyright © 2011 SciRes. MSA
Application of Intra-Particle Combustion Model
for Iron Ore Sintering Bed
Pingli Hou1, Sangmin Choi 1*, Won Yang2, Eungsoo Choi3, Heejin Kang1
1Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Daejeon, Korea (South); 2Korea
Institute of Industrial Technology, Chungnam, Korea (South); 3Technology Research Lab, Ironmaking Research Group, OSCO,
Gyeongbuk, Korea (South).
Received February 16th, 2011; revised March 21st, 2011; accepted April 12th, 2011.
In order to quantitatively predict the behavior of the material in the packed bed, a single particle model is developed to
describe the combustion and sintering process inside an individual particle composed of multiple solid material fines,
including iron ore, coke and limestone, and is applied to the combustion modeling of an iron ore sintering. By analyz-
ing three typical fuel distribution cases using the developed single particle combustion model, the effects of temperature
and oxygen concentration gradient inside the particle on heat and mass transfer and the combustion behavior of the
iron ore sintering process are investigated. Considering the various combustion rates which are highly dependent on
the fuel distribution methods, correction factor for single particle model is also introduced and systematically analyzed.
The aim of this research is to supplement particle technology to conventional approach and it is found that the oxygen
concentration gradient inside the particle is significantly affected from the mixing method thereby changing the com-
pletion times of sintering process.
Keywords: Iron Ore Sintering Bed, Porous Materials, Coating, Melting, Computer Simulation
1. Introduction
In the iron ore sintering process, a raw mix of fine par-
ticles of iron ore, limestone, and fuel coke fines form
pseudo-particles after being mixed with water and these
pseudo particles are then fed to the traveling grate to
form a bed. After the feed material is introduced to the
bed, combustion starts from the top of the bed by the
ignition burner, and then the combustion front propagates
downward into the bed while the entire bed is travelling.
During the sintering process, the bed material expe-
riences thermal drying, propagating combustion and var-
ious physicochemical and thermal phenomena.
In order to quantitatively predict the behavior of the
material involved in the sintering process, mathematical
models for the iron ore sintering bed have been devel-
oped. Previous studies [1-7] have attempted to describe-
the complicated phenomena of combustion and heat and
mass transfer in the sintering bed, but there is still
enough room for improvement. Numerical model based
on sound physics could be effective in understanding the
physicochemical mechanisms involved in the sintering
process and ultimately in optimizing the sintering
Muchi and Higuchi [1] used the Ranz equation for heat
transfer in packed beds and principally took into account
heat transfer, drying and coke combustion in their one
dimensional modeling, and primarily focused on the coke
combustion and predicted gas compositions with temper-
ature distribution in the bed. Young [2] produced a ma-
thematical model that allows the dynamic behavior of the
bed to be studied when gas flow and properties of the
mixture change as sintering proceeds. Cumming and
Thurlby [3] and Patisson et al. [4] considered the change
of the bed height and treated void fraction in detail that
resulted from the surface melting of the iron ore by in-
troducing shrinkage factor. In the model of Cumming
and Thurlby [3], the surface and core of granules are at
different temperatures. Nath et al. [5] developed a mathe-
matical model which can be used to simulate both the
static bed of the laboratory and the moving bed condition
used in actual industrial plants. Mitterlehner [6] devel-
oped a model for the iron ore sintering process with a
special focus on heat front propagation through the packed
Application of Intra-Particle Combustion Model for Iron Ore Sintering Bed
Copyright © 2011 SciRes. MSA
bed. In the model, coke particles and the other particles
are treated separately to take into account the change of
void volume as the diameter of a coke particle gradually
shrinks with combustion. Yang et al. [7] developed a
unified approach that can be applied to a variety of com-
bustors. Base on the assumption that the bed materials
are homogeneous and continuum, the governing me-
chanisms of the solid and the gas phases are modeled,
and particularly, the solid materials are treated as mul-
tiple solid phases. Each component of solid materials that
have different temperatures, physical properties and
chemical compositions is applied with the consideration
of radiative heat transfer. Komarov et al. [8] employed
commercial CFD software package Phoenics which in-
corporates self-developed numerical code.
An essential simplification in previous investigations
was the assumption of homogeneity inside a particle.
Those studies only focused on the ideal case of surface
reactions on a particle without considering the tempera-
ture and species profiles inside. A single solid particle is
assumed to have one representative value, which means
that there is no temperature and species concentration
gradient inside the single particle. However, especially in
the case of large particles, the processes are strongly
controlled by heat and mass transfer inside the particle.
Penetration of the reaction gas is influenced by in-
tra-particle mass transfer. Tests [3] have proved that
simple modeling assumption would be insufficient to
simulate conditions near the top of the bed under the ig-
nition hood with the low gas flow rates. Resistance to
gaseous diffusion within the granules can greatly affect
the reaction rates, particularly that of coke combustion.
Granule surface temperatures, which affect convective
heat transfer rates, may be considerably higher or lower
than that of the mean granule temperature assumed [3].
Perters [9] proposed a numerical model for the packed
bed moving on a forward acting grate by a discrete par-
ticle model considering the conversion process of a sin-
gle particle. This approach considers the packed bed to
be composed of a finite number of individual particles.
Wurzenberger et al. [10] developed a combined transient
single particle and a fuel-bed model for the thermal con-
version of biomass in a packed bed furnace. A represent-
ative particle is chosen to be discretized in a radial direc-
tion at each grid point. Mass, momentum and energy
balances are solved for the entire system. R. Johansson et
al. [11] considered intra particle gradients to compare the
impact of using a porous media approximation for mod-
eling fixed bed combustion. By introducing two-dimen-
sional particle model, intra particle gradients were taken
into account. The particle model provides information on
the internal heating of the solid particles and the internal
rate of drying and devolatilizatioin. An important aspect
of the three above works provided insight on the thermal
processes in packed bed for single porous particles.
Figure 1(a) shows a simplified bed model from an
actual fuel bed to an unsteady 1-D model. [12] The hori-
zontal location of the fuel layer can be transformed from
the elapsed time and the moving speed. Figure 1(b)
conceptualizes the extension of the model from the pre-
viously developed iron ore sintering bed model to the
present improved model. Yang et al. [7] proposed an
unsteady 1D model of multiple solid phase materials for
the numerical analysis of an iron ore sintering bed. In the
model, the solid material is treated as multiple solid
phases, which makes it possible to consider characteris-
tics of different solid materials such as limestone, coke
and iron ore. The objective of this paper is to develop an
iron ore sintering bed model which takes the single par-
ticle into consideration and incorporates more informa-
tion on individual particles in terms of the entire iron ore
sintering bed.
2. Modeling Approach
2.1. Intra-Particle Combustion Model
Unlike previously proposed single particle model in
which the particle was composed of a single solid phase,
the single particle model proposed in this paper describes
the combustion and sintering process inside an individual
pseudo particle composed of multiple fines of solid ma-
terial within the iron ore sintering bed (as shown in Fig-
ure 1). It is assumed that the size of the solid particle
remains constant, while the particle density decreases as
the conversion progresses.
The mathematical modeling of these phenomena in-
volves constructing system equations and determining
the sub-models required for each term of the governing
equations. Governing equations have a form of unsteady
1-dimensional partial differential equations for spherical
particles. For the gas phase, an oxygen transport equation
is employed without the convection term for simplifica-
tion. The source terms of each controlling equations are
closely combined through the interaction between phases.
2.2. Governing Equations for the Single Solid
2.2.1. Gas Phase
1) Oxygen diffusion
The oxygen diffusion equation is employed to take in-
to account the influence of the oxide concentration gra-
dient on char combustion. Conservation of oxygen de-
pends on a chemical term and a diffusive flux.
,O O
fC C
tr r
 
Application of Intra-Particle Combustion Model for Iron Ore Sintering Bed
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Figure 1. Schematic of the of sintering bed model concept. (a) Simplification of bed model from actual fuel bed to unsteady
1-D model; (b) Extension from previously de ve lope d iron ore sintering bed mode l to the improved model.
where f is particle porosity, C is oxygen concentration, D
is the effective diffusion coefficient of oxygen consider-
ing the porosity and the influence of tortuosity on the
diffusion, and 2
is the consumed mass by combustion
with char.
2.2.2. Sol id Phase
1) Mass
is the volume factor of solid in the particle,
s the overall density of the particle, ,Sr
is the
mass loss of the solid phase through reactions,
r is the
reaction number.
2) Energy
spss s
Sr r
 
Application of Intra-Particle Combustion Model for Iron Ore Sintering Bed
Copyright © 2011 SciRes. MSA
where Ts is the local particle temperature, Cp,s is the
over- all heat capacity of the particle, and
is the
overall heat conductivity. Heat of the heterogeneous
reactions is
. The second term on the right-hand
side of this equation is the reaction heat absorbed by sol-
ids where y is the fraction of reaction heat absorbed by
the solids. The third term is the sensible heat loss of
evolved gas.
3) Component
is the component factor of the solid phase, and
is the mass loss of the components of the solid
phase through reactions.
2.3. Sub-Model
2.3.1. Dr ying
Boiling is considered as the main process above the tem-
perature of 373 K. The process of drying is described
based on energy balance
evap p
ch evap
2.3.2. Ch a r Reactions
The rates of carbon oxidation by stream and carbon dio-
xide are of the same order of magnitude, and are gener-
ally much slower than that with oxygen [13]. A differen-
tial approach of intrinsic modeling yields more accurate
results than postulating a reacting or a shrinking core
mode in advance [9].
The rate of char reaction with oxygen can be calcu-
lated as follows [7]:
exp2.3 eT
Cr r
  
 (6)
After being transported across the outer annulus of the
porous sintered part, the gas phase reactant diffuses to
the surface of the unreacted char core or into the pores in
the core. Oxygen reacts with the carbon of the char ac-
cording to the following reaction scheme based on a
combustion model by Hobbs et al. [14].
2.3.3. Limestone Decomposition
Limestone is one of the main components of sinter mix
material. Its thermal decomposition is an endothermic
process that occurs at the temperature of 600˚C.
The reaction equation can be expressed as
CaCOCO CaO (8)
The reaction rate [6] is given as,
1.75 10eRT
 
2.3.4. Physical Propertie s
Properties of the solid particle components such as fuel,
iron ore and limestone are adopted from the literature [7].
As a result of the averaging process and the influence of
tortuosity on the diffusion, an effective diffusion coeffi-
cient is used.
,O O
,:porosity and tortuosity
Tortuosity is employed to consider the contribution of
Knudsen diffusion, and porosity is the volume factor of
the gas phase inside the particle.
The special heat of the mixture is given as,
sk sk
Cpm Cp (11)
The density of the mixture is given as,
sk sk
The conductivity of the mixture is given as,
sk sk
2.3.5. Boundary Condition
The boundary condition for the individual particle is,
where h is the convective heat transfer coefficient be-
tween the particle surface and the outer gas flow.
2.4. Application of Intra-Particle Combustion
Model-Fuel Distribution inside a
Pseudo Particle
To examine the adaptability of the developed model,
typical single iron ore particles with various fuel distri-
butions were chosen. Those are one of the various tech-
nologies which were developed to optimize the melting
reaction by controlling quasi-particle structure as well as
late coke addition [15]. From Method 1 to Method 4 (as
shown in Figure 2), coke breezes are gradually trans-
ferred toward the particle surface and the diffusion dis-
tance of oxygen subsequently becomes shorter. By
changing the mode of operation of the mixing drum, the
fuel distribution pattern inside the pseudo-particles can
Application of Intra-Particle Combustion Model for Iron Ore Sintering Bed
Copyright © 2011 SciRes. MSA
(a) (b) (c) (d)
Figure 2. Schematic diagram of four different methods of adding fuel(total amount of fuel is constant), (a) Method 1: Homo-
geneous distribution; (b) Method 2: Layered fuel distribution 1.1%, 0 < r < 0.8R; 7.15%, 0.8R < r < R; (c) Method 3: Layered
fuel distribution 2.0%, 0 < r < 0.8R; 8.197%, 0.8R < r < R; (d) Method 4: Adding fuel entirely outside.
be controlled. The total amount of coke was kept con-
stant to compare the sole effect of fuel adding methods.
For the simplicity, the assumption that all of the fuel
grains are inserted into the outer layer of a solid particle
was made as shown in Figure 3, contrary to the O2 con-
centration which was kept constant.
3. Simulation Results and Discussion
3.1. Simulation Case and Results
Table 1 presents the components of the bed material. For
the single particle model, the physical properties of the
solid phase can be determined by varying the composi-
tion of these components. For the entire bed model, these
components can be divided into three solid phases [7].
Table 2 summarizes the initial calculation parameters
used in this simulation. In an actual sintering plant, the
diameter of pseudo particles ranges from 0.5 mm to 8
mm [4] and that of coke particles is 1 mm to 2 mm. For
convenience of simulation, the diameters of pseudo and
coke particle are taken as 6 mm, 1mm respectively. Ini-
tially, the temperature throughout the interior of the
pseudo particle is 300 K, while the particle is instant-
taneously surrounded by an environment of 1373 K.
Figure 3. An approximate equivalent assumption for the
modeling of Method 4.
Figure 4 shows the temperature and oxygen concen-
tration distribution during the sintering process of a sin-
gle solid particle. The developed single solid particle
model properly describes the drying, limestone decom-
position and coke combustion during the sintering
process. The temperature gradient inside the particle is
not obvious, but the oxygen concentration gradient inside
the particle is significant. The reason is that the solid
conductivity is sufficient to conduct heat quickly, while
the effective diffusion coefficient of oxygen produces a
resistance to oxygen diffusion inside the particle. In the
sensitivity analysis, the effects of variations of solid
conductivity and the oxygen effective diffusion coeffi-
cient for temperature and oxygen concentration are fur-
ther discussed Figure 5 shows temperature profiles as a
function of radius and time for the different fuel distribu-
tion methods inside a pseudo particle. In addition, a
comparison of sintering times for each distribution me-
thods is given in Table 3. The sintering time for a single
particle is taken as the time that elapses before the par-
ticle reaches its maximum temperature.
In the case of fuel distribution only at the outer surface
(Method 4), sintering process is clearly promoted where
it shows higher temperature and faster combustion speed.
This result can be attributed to the relatively higher oxy-
gen diffusivity generated from the adding fuel outside
only method. In other words, oxygen diffusion is re-
strained when the fuel is placed inside pseudo particles.
The effect of bonding and melting disturb the reaction
between oxygen and fuel, thereby reduces the fuel com-
bustion rate.
Figure 6 shows a comparison of oxygen concentration
distributions for two modes of fuel distribution. The
oxygen concentration inside the particle of Method 1 is
much lower than that of Method 3 which is similar to
Method 4. Also, it can be found that in the Method 3, the
oxygen concentration gradient exists only in the outer
layer where all the fuel is placed. Lower oxygen concen-
Application of Intra-Particle Combustion Model for Iron Ore Sintering Bed
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Table 1. Initial composition of the bed material.
Components Moisture Coke Fe2O3 CaCO3 CaO Inertmaterial
Concentrtion(mass%) 7 4 52.29 9.75 1 25.96
Figure 4. Particle temperature andoxygen concentration as a function of radius and time for sintering process of a single solid
particle, (a) Temperature gradient distribution (K); (b) Oxygen concentration gradient distribution (kg/m3).
Table 2. Other simulation parameters.
Pseudo-particle diameter (mm) 6
Coke breeze diameter(mm) 1
Velocity of outer flow(m/s) 0.4
Heating up temperature(K) 1373
Oxygen concentration in heating gas(mass%) 23.3
Table 3. Comparison of sintering time of various fuel add-
ing methods.
Fuel addition
method Method 1 Method 2 Method 3 Method 4
Sintering Time
(s) 275 255 251 235
tration levels would enhance reductive reactions (Equa-
tion (15)). When the fuel is located only at the outer sur-
face, the FeO content can also be reduced according to
the following relation.
2334 2
34 2
 
  (15)
From the Figures 5 and 6, the temperature gradient in-
side the single solid particle is appeared to be negligible.
However, those results show that significant oxygen con-
centration gradient exists along the radius of pseudo par-
3.2. Sensitivity Analysis
In this numerical model, some calculation parameters
were arbitrarily selected since those were not able to be
decided by experimental approach. Therefore, their value
should be checked carefully, because variations in their
values can affect simulation results significantly. For this
reason, a sensitivity analysis was performed for two ma-
jor parameters. Those include the thermal conductivity of
the solid particle and the effective diffusion coefficient of
oxygen through the particle medium.
Solid conductivity is related to the heat transfer inside
the pseudo-particle. Temperature distributions for vari-
ous values of solid conductivity λs are considered and it
is found that this parameter has a meaningful effect on
the temperature distribution when its value is very low,
compare to the normal range of solid conductivity. Add-
ing to that, the effective diffusion coefficient is examined
and it is basically related to the oxygen concentration
distribution inside the pseudo particle. Therefore, this
study has analyzed the various values of the effective
Application of Intra-Particle Combustion Model for Iron Ore Sintering Bed
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Figure 5. Particle temperature as a function of radius and time for the sintering process for different fuel adding methods (K).
(a) Method 1: Homogeneous distribution; (b) Method 2: Layered fuel distribution1: 1%, 0 < r < 0.8 R; 7.15%, 0.8 R < r < R;
(c) Method 3: Layered fuel distribution 2: 0%, 0 < r < 0.8 R; 8.197%, 0.8 R < r < R; (d) Method 4: Adding all fuel outside.
diffusion coefficient 2
. The diffusion parameter plays
a significant role on the oxygen concentration distribu-
tion, as well as on the sintering time, which implies that
this parameter should be carefully determined in the
model studies.
4. Extension of the Intra-Particle Model to
the Bed Combustion
4.1. Extension of Intra-Particle Combustion
In the case of the normal mode of fuel distribution, in
Application of Intra-Particle Combustion Model for Iron Ore Sintering Bed
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Figure 6. Comparison of oxygen concentration distributions (kg/m3). (a) Method 1; (b) Method 3.
which the fuel is evenly distributed inside a particle, the
speed of the sintering process is determined by the coke
combustion speed [14] which is in turn influenced by
factors including oxygen concentration, char combusti-
bility, char particle size, char mass fraction and gas ve-
locity. The reaction rate of char combustion is de-
ter-mined from the kinetic rate, diffusion rate and inter-
nal mass transport in the ash layer of the particle. It can
be expressed as in Equation (16) [14]
11 1
where π,exp
, 2
s scharg
VI r
sp rr
peff eff
kk k
kdk D
The single particle model discussed above clearly shows
that the fuel combustion conditions where the various
fuel distributions were applied differ from each other.
Figure 7 shows the oxygen concentration profile in the
neighborhood of a coke particle and it indicates that the
oxygen diffusion process inside a pseudo particle is
slightly different from that of a separate coke particle.
Considering the various combustion rates which are
highly dependent on the fuel distribution methods, it can
be an appropriate measure introducing the correction
factor. Since the speed of the sintering process may re-
flect the fuel combustion speed, the correction factor for
the coke combustion rate can be determined according to
the sintering time. Here, based on the coke combustion
rate value of Method 1, thecoke combustion rate of Me-
thod 4 can be expressed as
, where
11 1
s scharg
kk k
In the equation shown above, kml and ξ are the diffu-
sion rate in the iron ore particle layer, and the correction
factor respectively. From the sintering times of the Me-
thod 1 and Method 4 which are brought from completion
of sintering process, the correction factor for Method 4
can be traced as 1.4 in comparison with the Method 1. It
should be also noted that increased or decreased combus-
tion temperature due to the different coating method in-
fluences diffusion rate [17], and suggested correction
factor would be slightly different if the change of per-
meability is considered. Several studies have been done
on the permeability of mixtures of raw materials and it is
found that the method of the separate coke addition leads
to more permeable condition [18]. However, oxygen dif-
fusion is primarily discussed in this research and newly
adopted factor seems to reflect the time interval between
Method 1 and Method 4. Under the condition where the
enhanced permeability is applied, comparatively lowered
correction factor is expected and this consequence can be
attributed to the increased air flow rate.
Application of Intra-Particle Combustion Model for Iron Ore Sintering Bed
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(a) (b)
Figure 7. Oxygen concentration profile in coke particle neighborhood. (a) Separ ate coke particle [15]; (b) Coke Particle
inside a pseudo particle.
4.2. Results and Discussion
In the Figure 8, the simulation results of temperature
distribution are presented, and the fuel distribution cases
Figure 8. Temperature distribution for Method 1 (a) and
4(b) (570 mm H). (a) Method 1; (b) Method 1.
for Method 1 and 4 are generally discussed. To compare
the combustion speed, y = 100 mm is chosen to be a base
level, and the time when each flame front reaches the
point are calculated which are obtained as 1040 s, 950 s
respectively. From the consequence, it is attained that the
front of the combustion zone of Method 4 penetrates the
bottom quicker than that of Method 1. In other word, the
propagation of combustion of Method 4 is faster and the
difference between the total sintering times of the two
methods is: (1040 950)/1040 = 8.6%.
An immediate cause for the above results can be ex-
plained by the different oxygen diffusion processes, and
it should be noted that the surrounding environment of
coke surface is one of the most influential factors in dif-
ferent fuel adding methods. The oxygen diffusivity of
Method 4, late coke addition, is supposed to be higher
than that of Method 1. Having the difference in the na-
ture of diffusivity between Method 1 and 4 consequently
results in the reduction of sintering time for the late coke
addition. For the variation of diffusivity, newly adopted
correction factor was employed and it reflects different
modes of fuel distribution. In conclusion, the approach
described in this research is one example of the cases
where the improved model could be used to simulate the
sintering process with different modes of fuel distribu-
5. Conclusions
Adding to the previously developed combustion bed
model, a refined mathematical model for the iron ore
sintering process is proposed. The aim of this research is
Application of Intra-Particle Combustion Model for Iron Ore Sintering Bed
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to supplement particle technology to conventional ap-
proach where the assumption of homogeneity inside a
particle is applied. The presented single particle model
isincorporated into the previously constructed entire
combustion bed model and it successfully describes the
drying, limestone decomposition and coke combustion in
the sintering process.
It is found that the temperature gradient inside the par-
ticle is not obvious, but the oxygen concentration gra-
dient inside the particle is significant. A sensitivity anal-
ysis was performed and it revealed that the oxygen con-
centration gradient inside the particle is significant, while
the temperature gradient inside the particle can be neg-
lected. The simulation results for the different mode of
fuel distribution are also presented and the prediction for
the completion times of sintering process is discussed.
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Application of Intra-Particle Combustion Model for Iron Ore Sintering Bed
Copyright © 2011 SciRes. MSA
C molar concentration, kmol/m3
E activation energy, J/kmol
fip ratio of internal pore generation
H heat of reaction or combustion, J/kmol
h enthalpy, J; convection coefficient, W/m2K
k rate constant, s1; conductivity, W/mK; mass trans-
fer coefficient, m/s
M volumetric mass generation rate, kg/m3s
m mass fraction
q volumetric heat generation rate, J/m3s
R universal gas constant
R reaction rate, kmol/m3s
T temperature, K
t time, s
V volume, m3
v superficial velocity, m/s
W molecular weight, kg/kmol
y vertical coordinate, m
absorption coefficient, m1
stoichiometric coefficient
ρ density, kg/m3
general scalar quantity
eff diffusion through the ash layer
g gas phase
ip internal pore
j chemical species of the solid phase
k reaction or combustion process
m mass transfer
o initial value
r kinetic