Mathematical model of thermal processes in an iron ore sintering bed

Abstract

An unsteady one-dimensional model of an iron ore sintering bed with multiple solid phases was proposed. The proposed model
confers a phase on each solid material. The present model was established with a series of conservation equations in the form
of a partial differential equation for each solid phase and gas phase. Coke combustion, limestone decomposition, gaseous reaction,
heat transfers in/between each phase, and geometric changes of the solid particles are reflected by each term of the governing
equations. Simulation results are compared with the limited experimental data set of sintering pot tests. Parametric studies
for various initial water contents and coke diameters have also been performed. The simulation results predict the experimental
results well and show physically reasonable trends for various parameters.

Full text

METALS AND MATERIALS International, Vol. 10, No. 5 (2004), pp. 493~500
Mathematical Model of Thermal Processes in an Iron Ore Sinterin
g
Bed
Won Yan
g
1, Chan
g
kook R
y
u2, San
g
min Choi1,*, Eun
g
soo Choi3, Deo
g
Won Ri3, and Wanwook Huh3
1Department of Mechanical Engineering
Korea Advanced Institute of Science and Technology
373-1 Guseong-dong, Yuseong-gu, Daejeon 305-701, Korea
2Department of Chemical Process Engineering, University of Sheffield
3Technical Research Laboratory, POSCO
5 Dongchon-dong, Nam-gu, Pohang 790-785, Korea
An unsteady one-dimensional model of an iron ore sintering bed with multiple solid phases was proposed.
The proposed model confers a phase on each solid material. The present model was established with a series
of conservation equations in the form of a partial differential equation for each solid phase and gas phase.
Coke combustion, limestone decomposition, gaseous reaction, heat transfers in/between each phase, and geo-
metric changes of the solid particles are reflected by each term of the governing equations. Simulation results
are compared with the limited experimental data set of sintering pot tests. Parametric studies for various
initial water contents and coke diameters have also been performed. The simulation results predict the exper-
imental results well and show physically reasonable trends for various parameters.
Keywords: iron ore sintering, coke combustion, heat transfer, modeling, sintering pot test
1. INTRODUCTION
Computational analyses of iron-making facilities, which
are comprised of a coke oven and sintering and blast furnace
processes, constitute one of the major research fields in the
steel industry for improvement of operating conditions, pro-
ductivity, and energy efficiency [1,2]. An iron ore sintering
process is applied to produce large particles (>~5 mm) of
iron ore agglomerates with appropriate metallurgical proper-
ties required in the blast furnace. A raw mix of iron ores,
limestone, and fuel coke fines forms a bed on a traveling
grate. Fig. 1 shows a conceptual version of the process in the
iron ore sintering bed. Once ignited by a coke oven gas
(COG) burner, coke combustion progresses downward very
slowly, and iron ores are sintered in the high temperature
(combustion) zone. Air is supplied to the bed by a down
draft suction fan. The combustion commences at the top of
the bed by a hot gas jet from the ignition burners for a few
minutes after the feed material is introduced into the bed,
and propagates into the bed with sintering near the combus-
tion front.
Many researchers have strived to build an accurate mathe-
matical model of coke combustion and heat transfer in the
iron ore sintering bed [3-10]. However, there is still room for
improvement of the models in terms of solid fuel combus-
tion and heat transfer in a porous media, whereas the pro-
posed models adequately describe these complicated pheno-
mena in the sintering bed. In addition, effects of variation of
the solid composition and operating parameters should be ana-
lyzed carefully. In this research, simulations of the iron ore
sintering process have been developed, considering multiple
solid phases and employing a series of conservation equa-
tions for each phase. Reactions and heat transfer in/between
identical/different solid phases are developed for calculating
source terms of the conservation equations. Geometrical
changes of the solid particles and structural change of the
bed are modeled in an improved manner. Simulations are
performed for various compositions of solid material and
coke diameters. The computed results are compared with the
limited set of sintering pot test results.
2. COMPUTATIONAL MODELING
The sintering bed consists of a gas phase and multiple
solid phases including iron ores, coke, limestone, and other
minor additives. The mixture of the solid phases can be con-
sidered as a homogeneous medium of all the component spe-
cies. Each solid phase may be of a different particle size and
chemical composition. When heated by a hot gas stream
generated by a gas burner, solid material experiences drying,
coke reactions, limestone decomposition, or reduction of the
iron oxide. For large particles, multiple kinds of reactions
*Corresponding author: smchoi@kaist.ac.kr


Won Yang et al.
can occur in a single particle due to the temperature gradient.
Through these processes, heat and mass exchange between
the solid and gas phase occur.
Geometrical change is also an important parameter in the
model. Changes of the particle sizes during combustion, melt-
ing, or sintering cause a change of bed structure, which can
be represented by bed height and porosity. Generation of
internal pores during drying and coke combustion changes
the particle densities and other physical properties, which
should be modeled carefully because they can significantly
influence the combustion process and quality of the sintered
ore.
Mathematical modeling of these phenomena is composed
of constructing system equations of conservation form based
on the assumption that the solid and gas in the bed are con-
tinuum. Sub-models are also required to determine each term of
the governing equations.
Governing equations have a form of unsteady and one-
dimensional partial differential equations. Unsteady terms of
the equations can be transformed to a location along the
direction of the moving grate, which progresses at constant
speed. This process is shown in Fig. 2. Velocity v is a super-
ficial velocity based on the assumption of a plug flow. Vol-
ume fractions of each phase are reflected in the generalized
form of the transport equation of scalar quantity ϕ. The fol-
lowing is a generalized 1-dimensional form of the governing
equations for each phase.
Solid phases, for solid phase I,
(1)
Gas phase,
(2)
The solid phases and gas phase influence each other
through the pressure drop as well as heat and mass transfer.
These effects are reflected in the source terms of the equa-
tions. Table 1 shows the detailed governing equations for
each phase. The terms on the right hand side of the energy
equation for the solid phase I are defined as follows; a diffu-
sion term including conduction, heat transfer from other
solid phases, convective heat transfer from the gas phase,
radiation, heat of various reactions, and heat loss by release
of gas produced by reactions.
Sub-models are employed to determine each term of the
governing equations, considering chemical reactions, vari-
ous modes of heat transfer, and geometrical changes of the
solid particles. Table 2 summarizes the phenomena and cor-
responding sub-models. The major solid-gas reactions in an
iron ore sintering bed are coke combustion and limestone
calcination. Gas species participate in these reactions as
reactant or product. From this point of view, drying and con-
densation also can be regarded as solid-gas reactions. Heat
transfer in the iron ore sintering bed is summarized as fol-
lows: convection/radiation between gas and solid phases,
conduction/radiation between solid phases, conduction/radi-
ation between solid particles (in the same solid phases), and
conduction in the gas phase. One solid particle is assumed to
have one representative value of temperature, which means
that there is no temperature gradient in a single particle.
∂ρ
sI
, fVsI
,,φsI
,
()
∂t
---------------------------------- ∂ρ
sI
,vsI
,φsI
,
()
∂y
------------------------------
+∂
∂y
----- fVsI
,,ΓsI
,∂φsI
,
∂y
---------- SφsI
,
+=
∂ρ
gεφg
()
∂t
---------------------∂ρ
gvgφg
()
∂y
-----------------------
+∂
∂y
----- εΓg∂φg
∂y
--------Sφg
+=
Fi
g
. 1. Major phenomena in an iron ore sintering bed.
Fi
g
. 2. Extension of 1-D unsteady model to the 2-D model.

Mathematical Model of Thermal Processes in an Iron Ore Sintering Bed

Modeling of geometrical changes is categorized into three
parts: (1) change of the particle sizes, (2) generation of inter-
nal pores, and (3) bed structural changes. Finally, physical
properties such as density, specific heat, thermal conductiv-
ity, diffusivity, and viscosity of the solid component or gas
species should be modeled carefully since they can directly
influence the simulation results. They are obtained by sum-
mation of the properties of each component multiplied by
the components mass fraction. Chapman-Enskog Theory
[15] is employed for estimating gas diffusivity and the Mer-
rick Model [16] is used for setting the properties of coke.
3. RESULTS
3.1. Sinterin
g
p
ot
A sintering pot of laboratory scale is used for validation of
the numerical model. Fig. 3 shows a schematic diagram of
the pot, which has a bed 205 mm in diameter and 600 mm in
Tabl e 1. Governing equations for each solid phase and gas phase
Solid phase, I Gas Phase
Mass
Energy
Component
Tabl e 2. Sub-models used in this study
Categories Phenomenon Equations
Reactions
Solid-gas
reactions
Char
reactions [11]
Limestone
calcination
[4]
Gaseous
reactions
CO
oxidation [12]
Heat transfer
Conduction Included in the energy equations
Convection [13]
Radiation Two-flux model [12]
Heat exchange btw. solid phases [2,14]
Geometrical
changes
Particle diameters [11]
Generation of the internal pores [10]
Bed structural changes [10]
∂ρ
sI
,
f
VI
,
()
∂t
---------------------∂ρ
sI
,vsI
,
()
∂
y
---------------------
+M
·rsI
,J
→
phaseJ
IJ
≠
∑
=∂ρgε
∂t
-----------∂ρgvg
∂
y
------------
+M
·sIr
s
,,
rs
∑
I
∑
–=
∂
f
VsI
,,hsI
,
()
∂t
----------------------- ∂vsI
,hsI
,
∂
y
---------------- ∂
∂
y
-----
f
VsI
,,ksI
,∂TsI
,
∂
y
----------
⎝⎠
⎛⎞
=+
+h
JIAsI
,TsJ
,TsI
,
–
()
J
∑hconv g 1–
,AsI
,TgTsI
,
–
()
I
∑
+
+
f
vI
,
1ε
–
----------
q
rad
y
1M
·sIr
s
,, ΔHrM
·sIr
s
,,
rs
∑
⎝⎠
⎛⎞
CpI
,TsI
,
–
rs
∑
+
where AsI
,npI
,ApI
,
=
∂ε
hg
()
∂t
---------------∂vghg
()
∂
y
-----------------
+∂
∂
y
----- εkg∂Tg
∂
y
--------
⎝⎠
⎛⎞
=
+h
conv g I
–
,AsI
,TsI
,Tg
–
()
I
∑
+1
y
I
–
()
M
·sIr
s
,, ΔHrs+M
·sIr
s
,,
rs
∑
⎝⎠
⎛⎞
CpI
,TsI
,
rs
∑
∂ρ
sI
,
f
VI
,msIk
,,
()
∂t
-------------------------------- ∂ρ
sI
,vsI
,msIk
,,
()
∂
y
--------------------------------
+M
·sIkr
s
,,,
rs
∑
=∂ρ
gεmgk
,
()
∂t
------------------------ ∂ρ
gvgmgk
,
()
∂
y
--------------------------
+M
·sIkr
s
,,,
I
∑
rs
∑M
·gkr
g
,,
rs
∑
+=
Ri
og
,AsvsWcharCgi
,dp
1krζ()⁄1km
⁄1keff
⁄
++
---------------------------------------------------
=
Rl
nlπdlCCO2
*CCO2
–
()
1
km
-----dpdpdl
–
()
dlDs
-----------------------2Kl4.1868
⋅
klRTs
----------------------------dp
dl
----
⎝⎠
⎛⎞
++
-----------------------------------------------------------------------------
=
dCCO
dt
------------1.3 1011CCOCH2O
0.5 CO2
0.5ex
p
15 105
,
Tg
-----------------
–
⎝⎠
⎛⎞
×
=
q
ss IJ
,hIJAsI
,TsJ
,TsI
,
–
()
=
where hIJ 2
π
-------
f
VI
,ksI
,ρsCps
()
IεkgρgCpg
+
I
∑
f
VI
,tsεtg
+
I
∑
----------------------------------------------------------------
f
VJ
,
f
VI
,
------
=
dp1F
–
()
du
3Fdr
3
+
[]
13
⁄
=
∂
f
VI
,εip I
,
∂t
----------------- ∂vsεip I
,
∂
y
---------------
+
f
ip i
,M
·comb i
,
ρi
---------------+ε
·ip loss I
,,
i
∑
–=
f
v
f
s
1n
–
f
v
o
=


Won Yang et al.
height. Three R-type thermocouples are installed along the
y-direction of the bed. Hearth ores having a diameter of
approximately 10 mm are placed at the bottom of the pot in
order to improve gas permeability. Iron ores, coke, lime-
stone, and other additives are mixed with water in the cham-
ber and form various sizes of pseudo particles in a rolling
drum. After a selected amount of raw material is fed into the
pot, the material is exposed to a LPG burner for 90~120 s
and then ignited. The pressure difference of the suction fan is set
to 1000 mmAq during ignition and approximately 1500 mmAq
after ignition. Gas inlet velocity, flow rates, and flue gas
compositions including O2, CO2, CO, NO, and SO2 can be
measured.
3.2. Simulation conditions
Table 3 summarizes the compositions of the solid phases
and gas phase. The components, species, and initial compo-
sition for the reference case are also listed. Three solid
phases of iron ore, coke, and limestone are considered. Other
additives, which are not involved in the solid-gas reactions,
are considered as part of the inert material. Each solid phase
consists of solid components such as moisture, coke, iron
ore, CaCO3, CaO, and inert material. Each of them has spe-
cific physical properties such as density, specific heat, and
thermal conductivity. O2, H2O, CO2, CO, H2, and N2 are
selected as the gas species considered in the simulation.
Fig. 4 shows the typical trends of the pressure difference
and gas flow rate in the sintering pot used in this study. The
initial pressure drop represents the air suction rate. After set-
ting the initial value, the suction pressure varies with the
progress of the coke combustion and the sintering of iron
ore. Considering these variations, air inlet velocity, which is
a function of time, can be considered as a second order poly-
nomial, while pressure difference is not reflected in the cal-
culations.
Table 4 summarizes other major inputs and calculation
parameters used in the simulation. Particle diameters of the
iron ore, coke, and limestone are adopted from measured
Fig. 3. Schematic diagram of the sintering pot.
Table 3. Phases and their initial composition considered in the simulation (Reference case)
Solid components Moisture Coke Iron CaCO3CaO Inert
Solid phases
Iron ore (%) 7.0 0.0 63.0 0.0 0.0 30.0
Coke (%) 7.0 85.0 0.0 0.0 0.0 8.0
Limestone (%) 7.0 0.0 0.0 75.0 8.5 9.5
Gas species O2H2OCO
2CO H2N2
Gas phase (mass %) 23.3 0.3 0.0 0.0 0.0 76.4

Mathematical Model of Thermal Processes in an Iron Ore Sintering Bed

data obtained during the test. Fractions of the internal pores
for each solid phase are difficult determine in a real situation,
and therefore they are estimated from a simple calculation
considering the total weights of the material, volume of the
pot, solid densities, and porosity of the bed.
Table 4 also shows some calculation parameters that can-
not be measured; fraction of reaction heat absorbed by solid
(expressed as y), particle area factor to account for internal
surface burning (expressed as ζ), and packing parameter
(expressed as n). Their values should be selected with con-
sideration of the physical phenomena and previous studies.
In this simulation, the value of ζ is selected from a previous
work [9] and y is determined by considering the physical
phenomena. Decrease of the bed height is tuned by setting
the value of the packing parameter based on the pot test
results, which indicated that the bed height is decreased by
approximately 7 cm. Solid-gas reactions also affect the poros-
ity of the bed, which is increased to about 0.43~0.44 after the
sintering process; this value is similar to the selected value
from previous researchers’ work [4].
Flame front speed (FFS) [12] is introduced as a quantified
parameter for analysis of the results. It is defined as
This parameter is mainly influenced by char combustion
rate and parameters involved in heat transfer within the bed.
In this study, the numerator is defined as the distance
between the location of y = 490 mm and that of y = 110 mm,
where the thermocouples are installed.
3.3. Results and discussion
Fig. 5 shows the simulation results of the temperature dis-
tribution and melt fraction within the bed [10]. Once ignited,
the combustion is sustained by coke reactions. As the com-
bustion zone proceeds downward, combustion thickness and
maximum temperature increase. This is because the temper-
ature of air supplied to the combustion zone increases due to
the convection heat transfer from the solid particles and coke
combustion rate also increases as the solid temperature increases.
Gas temperature distribution has a similar trend compared
with the solid temperature distribution. When the tempera-
ture of the iron ore reaches a certain point, which is assumed
to be 1373 K in this study [9], iron ores start to melt. Melt
fraction, which can be obtained from a previous study [9],
also increases as the solid temperature increases, as illus-
trated in Fig. 5(c).
Simulation data is compared with the pot test data, as pre-
sented in Fig. 6. Fig. 6(a) shows the average temperature dis-
tribution of the solid phase. Particle diameter and surface
FFS(Flame Front Speed)= Distance between two points
Time consumed for propagation
Fig. 4. Typical trends of the pressure difference and gas flow rate in
the sintering pot [10].
Tabl e 4. Major input parameters (Reference case)
Parameters Value Parameters Value
Mass fractions (%) of Number of cells 57
Iron ore 83.2 Δy (cm) 1
Coke 3.8 Time step (s) 1
Limestone 13.0
Ignition condition
Temperature (K) 1400
Particle diameters (mm) of Time (sec) 90
Iron ore 3.2 Inlet gas velocity (m/s) 4
Coke 1.6 ΔP during ignition (mmAq) 1000
Limestone 1.6 Setting value of ΔP after ignition (mmAq) 1500
Pseudo particle 3.0 Particle area factor, ζ0.5
Initial internal porosities of Packing parameter, n 0.6
Iron ore 0.025 Air inlet velocity = 0.35+7.5585×10-6t+1.5853×10-7t2
Coke 0.025 Fraction of reaction heat absorbed by solid, y
Limestone 0.025 Drying 0.9
Water contents (%) 7.0 Coke reactions 0.6
Porosity of the bed 0.4 Lime decomposition 0.7


Won Yang et al.
area of each solid material can be reflected to the calculation,
and the results are close to the experimental data with regard
to maximum temperature, thickness of the combustion zone,
and time of the temperature increase. Fig. 6(b) shows the gas
compositions of O2, CO2, and CO, which are major combus-
tion reactants and products. The values remain constant after
ignition and they also are in agreement with the experimen-
tal data.
Simulation for various water contents is performed and the
results are presented in Figs. 7 and 8. Water content in raw
material is set by operators in making pseudo particles, and it
can directly influence the combustion rate, thickness of the
combustion zone, and flame propagation. The case of 6 %
water content is compared with the case of 8 %, because
initial water content in the solid material is usually in this
range for effective operation of the sintering machine. Fig. 7
shows the gas compositions for various water contents in the
raw material. It appears that the gas composition is not sig-
nificantly changed by the water content, indicating that coke
combustion rate is also not changed by this parameter. The
change occurs by the decrease of the amount of coke in the
case of 8 % water content. This is supported by the observa-
tion that the flame front speed in the case of 6 % water con-
tent is 2.82 cm/min, while it is 2.79 cm/min for 8 % water
content. However, temperature distribution is significantly
changed to a meaningful extent for various water content.
Fig. 8 shows the temperature distributions for the two extreme
cases of water content in the raw material. Water content in
the raw material affects the thickness of the combustion zone
and the maximum temperature. For 6 % water content (Fig.
Fi
g
. 5. Simulation results of the sintering bed (Reference case): (a)
Solid temperature (K), (b) Gas temperature (K), and (c) Melt fraction.
Fi
g
. 6. Comparison between the measured data and simulation results
of coke3.8: (a) Temperature profiles of solid material and (b) Flue gas
compositions.

Mathematical Model of Thermal Processes in an Iron Ore Sintering Bed

8(a)), the combustion zone is thicker than that of 8 % water
content (Fig. 8(b)) due to the heat of evaporation, which
affects the melt fraction and permeability of the bed. This
result shows that drying is an important parameter in the sin-
tering bed and water content in the raw material should be
determined carefully.
Fig. 9 shows temperature profiles and gas compositions
for various coke diameters. Fine coke of under 2 mm in
diameter, which is a by-product of the coke-making process,
is used for the sintering process. Since coke diameters deter-
mine the surface area and influence the combustion rate,
they should be set carefully by operators. Maximum temper-
atures of each point, duration time at high temperature, and
CO2 concentration are increased for smaller coke particle
sizes. Increase in coke diameters significantly decelerates the
coke combustion rate due to the decrease in the surface area
of coke.
4. CONCLUSIONS
An improved model of the thermal process is proposed for
iron ore sintering beds. The model considers multiple solid
phases, radiative heat transfer, and various kinds of geomet-
Fi
g
. 7. Simulated gas compositions for various water content in the
raw material.
Fi
g
. 8. Simulated temperature distributions for various water content
in the raw material: (a) Water content in raw material: 6 % and (b)
Water content in raw material: 8 %.
Fi
g
. 9. Simulation results for various coke diameters: (a) Temperature
profiles and (b) Gas compositions.


Won Yang et al.
rical changes. It is comprised of a series of conservation
equations with the forms of partial differential equations,
with sub-models of reactions, various modes of heat transfer,
and geometrical changes of the bed. This model can predict
temperature distributions within the bed and flue gas compo-
sitions. The simulation results show good agreement with
the results obtained from pot sinter tests. Parametric studies
are performed for various water contents and coke diame-
ters. They have a reasonable trend and demonstrated that the
operating parameters should be carefully determined during
operation of the sintering bed.
ACKNOWLEDGMENTS
The presented work was a part of the program of Interna-
tional Collaborative Research, financially supported by the
Korea Ministry of Science and Technology.
NOMENCLATURE
A : volumetric surface area, m2/m3; pre-exponential fac-
tor, s-1
C : molar concentration, kmol/m3
dp: particle size, m
E : activation energy, J/kmol
fshrink : shrink factor
fip : ratio of internal pore generation
H : heat of reaction or combustion, J/kmol
h : enthalpy, J; convection coefficient, W/m2K
I+,I-: radiation intensity upward or downward, W/m2s
k : rate constant, s-1; conductivity, W/mK; mass transfer
coefficient, m/s
M : volumetric mass generation rate, kg/m3s
m : mass fraction
np: particle number density, 1/m3
p: pressure, N/m
2
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
y : fraction of heat absorbed by solid
Greek
ε: porosity
τ: transmissivity
ζ: particle area factor
κ: absorption coefficient, m−1
ν: stoichiometric coefficient
ρ: density, kg/m3
φ: general scalar quantity
Su
p
erscri
p
ts
a : exponent of temperature
b : exponent of pressure
Subscri
p
ts
b : black body
eff : diffusion through the ash layer
g : gas phase
I : index of solid phase
i : component of the solid phase
ip : internal pore
j : chemical species of the solid phase
k : reaction or combustion process
m : mass transfer
o : initial value
r : kinetic
s : solid phase
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