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PRODUCTION OF MgO IN AN ELECTRIC ARC
FURNACE.
THERMAL ANALYSIS
U. Ortiz, J. Aguilar, C. Esparza, C. Guerrero
Universidad Autónoma de Nuevo León
Facultad de Ingeniería Mecánica y Eléctrica
Doctorado en Ingeniería de Materiales
A.P. 076 "F", Monterrey, N.L. 66450, México
ABSTRACT
The computer simulation that is presented here is the response of
an industrial challenge about how the electric arc furnace, where
the smelting process of magnesium oxide (MgO) is taking place,
should be charged for avoiding shell overheating. If solid MgO is
charged at a very high rate, the processing time becomes very
long; on the other hand, if the feed rate is too slow, external
shell made of steel reaches temperatures above its melting point.
Thus, it is necessary to reduce the electrode current or to charge
more material for avoiding shell overheat. With the aid of this
model, a charge scheme for the furnace could be proposed, in order
to have the maximum production without shell overheat.
Validation of the model has been made with temperature
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measurements along the external shell while the process was being
conducted; the size and shape of the smelted zone after the fusion
were also compared with information obtained from the graphic
results predicted by the model. Results from the model are in good
agreement with the measurements done. Calculation of the specific
energy consumption can be provided with the input energy rate and
the mass of the smelted MgO.
1. INTRODUCTION
At the present time one way for producing smelted magnesium oxide
is by using an electric arc furnace [1,2]. Production of this kind
of materials is carried out by smelting high purity briquettes of
sinterized magnesium oxide. The electric arc furnace is used for
conducting the smelting process that takes place with the radiant
energy that comes from an electric arc. While the charged material
is being smelted, more briquettes are being fed to cover the arc.
The wall of the furnace is naked (it does not have any refractory
material), but the briquettes that have not been smelted insulates
the wall from the heat that is being produced in the arc. As the
material is charged the electrodes must vary their position. The
solid material conducts the heat to the wall giving hot spots, and
the process has to be stopped in order to avoid shell perforation.
The aim of this work was the development and validation of a
computer model that describes the thermal profile of the shell of
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the furnace at different charge rates, in order to give an advise
about which should be the best charge procedure for avoiding shell
overheating. The results obtained with this model were applied to
an industrial furnace with very good results.
2. GENERAL DESCRIPTION OF THE MgO PRODUCTION PROCESS
In a general way, the MgO production process consists in an
electric arc furnace that is being charged with briquettes of
sinterized MgO. The furnace has a circular base ring (2 meters of
diameter) filled with recycled briquettes and covered with a
cylindrical shell made of steel (2 meters height, 1.80 m top
diameter, 2.10 m bottom diameter and 2.54 cm wall thickness).
There are three electrodes at 120° each one connected to its own
phase. Due to the MgO has a very high electrical resistance at
room temperature, approximately 1015 ohm-cm [3], it is necessary
to set graphite bars (2.54 cm x 2.54 cm x 12.25 cm) between the
electrodes, this arrangement has the shape of a delta. An scheme
of the shell and the electrodes arrangement is presented in Figure
1. When the electric power is connected, the graphite bars start
to heat by Joule effect until the MgO that is surrounding the bars
is smelted, in this conditions the MgO becomes a good electricity
conductor (1013 times better), thus the graphite bars become
unnecessary. When the fusion starts, the arc becomes submerged in
the semisolid MgO, the process continues by charging more
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briquettes and lifting the electrodes at the same time. Due to
that new charge is cold its conductivity is not good enough to
sustain a good electric arc until it gets hot. Normally the
current decreases until the charge is smelted, adding more charge
and continuing the cycle until the furnace is full. Generally, the
electrode current is the measured variable that permits the
control of the electrodes movement and the charge rate, high
currents means semisolid MgO, so more charge is added and the
electrodes are raised. In this furnace, the raise speed of the
electrodes could be 10 cm/hr through 20 cm/hr, while the charge
rate vary from 100 Kg/min through 280 Kg/min of MgO briquettes.
Normally the operator tries to keep the raise speed constant,
maintaining under control the current with the charge rate. The
main purpose of these controls is to prevent overheating of the
shell. The zone where temperature is high enough to smelt the MgO
starts from the end of the electrode down to the bottom of the
furnace. When the furnace is full the fusion ends, even when not
all of the material is smelted; at this point the electrodes could
be lifted without the addition of more briquettes. After the end
of the fusion the whole system is allowed to cool, the part that
was smelted becomes a solid stone of MgO, this stone is the most
important part of the process, because it is the product.
In order to avoid the shell overheat it could be convenient to (a)
insulate the steel wall; (b) use and external water jacket for
cooling the steel shell; and (c) manipulate the feeding rate of
MgO.
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The first alternative is applied practically during normal
operation because the solid MgO fed acts such as insulating layer
between the shell and the heat source; indeed thermal conductivity
of MgO is about the same (taking both pure dense and powdered MgO)
than insulating firebricks [3] and the distance between the
electrode and the shell is about 80 cm, but the overheat problem
persists.
It is important to note that plant facilities do not permit the
use of water as coolant avoiding the second alternative. Thus for
overcome the shell overheat problem the only alternative is to
manipulate the MgO feeding rate.
3. DEVELOPMENT
3.1 Process simplifications
The assumptions accepted in this model are listed below, some of
them are justified here and the rest in the experimental details
section.
- There is angular symmetry respective to the heat source, thus
the system could be reduced to two dimensions scheme, radial (r)
and height (z). Even when the shell is not a perfect cylinder,
taking this shape simplifies the solution. The most important part
is the zone where the fusion is taking place, and this part
includes just the zone between the bottom and the tip of the
electrode. Thus it is valid to take the furnace as a cylinder
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because the final position of the electrodes (that defines the
melting zone) is about 40 cm from the base ring.
- The external heat losses are due to convection, free
convection is accepted with a constant value of 30 w/m2 K. It is
accepted that the convection coefficient is a function of the
temperature of the shell, but we found that this constant
coefficient gives a good approximation of the temperature profile
on the shell. Even when the base of the furnace is not perfectly
insulated, heat transfer to the material in the base ring was
considered constant as the heat transfer to the ground below the
furnace base because this part reaches the highest temperature
almost at the beginning of the process remaining at this value
during all the test. Besides the overheat shell (hot spots), when
they appear, are present at the middle of the height. In this case
we found that thermal profile of the external shell predicted by
the model is in good agreement with the actual profile, while the
size and shape of the MgO stone obtained by the isothermal graphic
results provided by the model were also in good agreement with the
real stone. The description of the MgO stone and the measurement
procedure are presented below in the results and discussion
section. -The initial temperature of the charge is constant (room
temperature).
- The heat source has a narrow variance of power along the
process.
- The power source of the arc is being raised vertically at
constant speed.
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- The charged material is distributed uniformly inside the
furnace, so it can be considered as a continuous material with
[4]:
Once that the material is charged it remains as a packed fixed bed
until it is smelted.
3.2 Numerical method
With the above conditions and simplifications for the model, a
heat balance or control volume technique gives a description of
the system. There are several ways for obtaining the basic
equations for any geometry [5]. The general discretization
equations for cylindrical coordinates can be procured from the
extension of one dimension r (radial) in the transitory state [6];
It is true that most of the heat is being produced by Joule effect
from the graphite bars, but this stage is too short compared with
the total time required for completing the process.
3.3 Adaptation of the numerical method
For building the model it is necessary to analyze the fusion
process, taking into account the points given above and the
bed) the ofporosity - (1
k
=
kMgOe 1
∂
∂
∂
∂
∂
∂
r
T
rk
r
r
1
=
t
T
C
ρ
2
8
general discretization equation in two dimensions.
The furnace is considered a hollow cylinder with the energy source
inside, the energy distribution is uniform and concentric. This
consideration is correct at the end (tip) of the electrode that is
the place where the arc is. Even when the rest of the electrode
develops a thermal profile, it is considered that energy comes
from a single source.
Thermal characterization of the furnace proves that the
temperature profile depends of the vertical position (z) and the
radius (r), but it does not depend of the angular position in a
significative manner, thus the previous assumption of angular
symmetry is right.
In summary, the system consist in a cylinder that is being fed
with MgO, the external shell is loosing heat by convection to the
air, while there is an energy input at the tip of the electrode.
The proposed model considers that MgO bed is conductive
(regardless the graphite bar) and that the heat input is coming
from the arc that is supplying certain amount of energy (the
boundary condition is the heat flux at the tip instead of the
temperature). In other words we accepted that the heat source is
the tip of the electrode and not the dissipation of electrical
energy within the charge itself. Due to symmetry conditions, two-
dimensional discretization is performed in just half of the
furnace, along the cylinder and following one of the electrodes
axle. The discretization consists then in placing elements
following a cartesian distribution. In this particular case the
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elements over the r axle are spaced at Δr equal over all the MgO
charge.
In the z axle the discretization is uniform from the top through
the bottom of the furnace. With all the nodes placed, the lines
that conforms the mesh pass right at the middle of the distance
between two adjacent nodes.
Implicit scheme was taken for two dimensions with a heat source Q,
the discretization equations for each node are:
where:
b +
T
a
+
T
a
+
T
a
+
T
a
=
T
aS
S
N
N
O
O
E
E
P
P3
))
r
r
( + (1
r)(
z
k
=
a
0
e
e
E
Eln
δ
∆4
))
r
r
( + (1
r)(
z
k
=
a
0
e
O
O
Oln
δ
∆5
z)(
r
k
=
a
t
t
T
δ
∆6
z)(
r
k
=
a
S
S
S
δ
∆7
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The amount of elements and equations are the same in order to have
a system that can be solved at certain time. The solution of this
system is part of the program that was developed for simulating
the MgO smelting process.
3.4 Equation resolution presented as a simulation program.
The program has some sections of routines for performing the
solution of the system explained above.
In the main program the Gauss-Seidel iteration technique was
applied to get the implicit values of the temperatures in the
algebraic equations in an indirect mode [7]. Inside each iteration
the properties of the materials are calculated in a special
subroutine. For having an efficient program, regarding with the
accuracy and running time, we tried to maximize the size of the
elements and maximize the time increment. After several runs and
comparisons with the actual profile we found that the optimum
t
z r C
=
a0
P∆
∆∆
ρ
8
T
a
+z r Q = b 0
P
0
P
∆∆ 9
a
+
a
+
a
+
a
+
a
=
a0
PSTOEP 10
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amount of elements that gives mesh insensitivity are 80 elements
along the height and 42 along the radius. Measurement devices at
the plant give information each 5 minutes, so we decided to use
half of this time as the increment value.
4. Experimental details
4.1 Electrodes and power supply
The three electrodes are connected to a three phases power supply,
through a transformer of 6 MW 13700/180 V. The electrodes size is
31.2 cm diameter and 3 meters long.
4.2 The charge
The briquettes have a hazelnut shape of about 2 cm large and they
were obtained from pure MgO compacted and sinterized at more than
2000°C. MgO is a ceramic and it is considered one of the best
electric insulator, its melting point is 2800°C and it is also a
good thermal insulator. Heat conductivity and heat capacity are
given by equations (11) and (12) according to Kingery [3].
K m
J
T
0.001
+ 2.7T - 2180 =
k
2
MgO min
11
K Kg
J
T
621672915.3 - 0.1243T + 1127.78 =
C2
pMgO
12
12
4.3 Temperature measurements
After a review of the techniques for taking the temperature
measurements it was decided to use thermocouples inserted in the
steel wall at 40 cm height (the place were the hot spots usually
appear), one in front of the electrode (following the radial
coordinate), another 60° at the right of the electrode and a third
one 60° at the left of the same electrode for each electrode
(total of 6 positions over the shell).
4.4 Test description
The tests consists in, firstly fill the base ring with recycled
material (MgO briquettes that where unmelted in other previous
melting processes) and then starts the charge procedure with an
initial charge of 280 Kg, after that the charge rate is controlled
in accordance with the electrodes current, as was explained above.
Each test was 180 minutes long, taking one data each 5 minutes in
each thermocouple to get a table of temperature against time.
4.5 Test conditions for model validation
The program wrote needs the following information:
Maximum time of test (180 minutes).
Electric Power (3000 watts).
Raising speed of the electrodes (12 cm/hr).
Fraction of volume occupied by the briquettes in the bed (0.5).
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Feeding rate (variable).
In order to give make more important the charge procedure the
raise speed was fixed at a constant value along the test. The
fraction of volume occupied by the briquettes was the value
employed in the calculation of the thermal conductivity of the
MgO, separate packing tests gives a value of 0.5 for this
parameter. As explained above, the feeding rate depends on the
electrode current, therefore, the current was controlled with the
feeding rate, in the model this amount variation was taken into
account.
5. Results and discussion
5.1 Simulation adjustment
Experimental data was compared with the information given by the
model. A summary of the experimental results are presented in the
Figure 2. The curve A represents the temperatures of a
thermocouple placed at 40 cm height, in front of the electrode
(following the radial coordinate), curve B is at the same height,
but at the right of the electrode (60°), and the curve C is 60° at
the left of the same electrode. Note how close the curves are,
meaning that the two-dimension analysis was appropriate. One
important thing is the maximum temperature at the begin of the
test, where the arc is being stabilized and there are very few
material, so practically the current is passing through the
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graphite bars. This aspect was observed during the model
validation.
5.2 Validation of the computer model
Temperatures calculated with the model are shown in Figure 3.
Curve titled "Measured" corresponds to the average of the values
shown in Figure 2, while curve titled "Calculated" is plotted with
the data given by the model. It is important to notice that
temperature rises very fast at the starting of the process
decreasing when the smelting process is being conducted with the
electric arc covered by the MgO briquettes. The calculated
temperature decreases more than the measured, despite this
situation, the error is very small, maximum 13% when the furnace
is almost empty and much lower when the process has been
stabilized following the charge procedure. This error magnitude
shows that the equations and relations used in this work are
appropriate, even from an industrial point of view. Trials for
minimizing the error, supported by the operation of an empty
furnace (just with the initial charge and the electrode partially
covered by the MgO) gives a more complex model that does not have
necessarily more reliability because the arc is covered by MgO
most of the time. Other possible error source is that in the
actual process the energy is supplied at the beginning with the
help of the graphite bars that could produce higher temperatures
that the ones obtained from conduction of MgO.
One aspect taken to validate this computer program was the size
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and shape of the smelted zone that after cooling forms a solid
stone of MgO. The Figure 4 shows a scheme of the furnace,
specially the smelted zone that gives the stone product.
Temperature in the smelted zone is around melting point of MgO
because the heat of transformation and the quality of the
insulator. At the end of the fusion, the electrode is removed in
such a way that the top of the MgO stone gets plane, after few
days of cooling the steel shell is removed and the briquettes that
were not smelted are collected for a new charge. The MgO stones
are removed (there are three, one for each electrode) and they are
the product. The shape, size (about 0.2 cubic meters) and weight
(about 800 Kg) of the stone are in good agreement with those
predicted by the model. The good agreement on the temperature
profile of the shell and the shape and size of the smelted stone
provide a good degree of confidence about MgO temperature profile
predictions. The product has the shape of a cone, following the
illustration of Figure 4. Its base is about 1 meter diameter and
0.90 meters height. General information is provided by the program
while it is running. Figure 5 is the screen that the computer
shows, in this case it is just an example of the thermal profile
of the furnace after 45 minutes of processing. This figure is also
used for calculating the size of the stone, the portion that is
presented with a temperature over the MgO melting point is the
zone that at the end of the process will be the stone. Whit this
revolution body it could be deduced the size of the stone and the
weight from the MgO density. The purpose of this work was to find
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an appropriate charge scheme without hot spots over the shell, the
measurement of the stone is just an extra data for validation of
the model and thus the thermal profile. One way for calculating
the mass of the product inside the computer program is by counting
the elements that reaches temperatures above the melting point of
the MgO, these will be very useful at the moment of include the
production rate in the program. Graphic on the bottom right corner
of Figure 5 shows the temperature evolution at two different
places on the shell.
6. Conclusions
The model describes the thermal profile of the furnace, and
running different conditions allows selecting the best charge
procedure. In other words, results of the model gives the charge
procedure that permits high production rate without hot spots on
the external shell. The procedure that ensures maximum
productivity without the melting of the shell was with the
following steps:
Initial charge of 110 Kg; 110 Kg/min for 5 minutes; 220 Kg/min for
10 minutes; 160 Kg/min for 10 minutes; 50 Kg/min for 135 minutes,
and 20 minutes without feeding. These procedures were tested at
the plant and it was confirmed that it is one of the best
procedures. This procedure also maintains the raise speed
practically constant at 12 cm/hr. It was confirmed also that
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heating of the shell is due to conduction through the briquettes
of MgO bed, temperature in the smelted part is not high enough to
permit that MgO liquid of low viscosity travels through the bed
and touches the wall. This late condition is not responsible of
the hot spots on the shell. This model shows a balance between
phenomena description and observed behavior, without unnecessary
elements that makes the problem artificially more complex.
Different heat transfer coefficients on the external shell at free
convection did no change the results. Conduction to the ground
from the material in the base ring alters the results in an amount
smaller than the experimental error.
This development simplifies the description of the process and
gives a straight answer to a straight question with the capacity
for conducting a wide range of conditions, given a good advice
before the real process is conducted. Calculation of specific
energy consumption is very easy to obtain for the different charge
schemes.
7. Nomenclature
keEquivalent thermal conductivity of the bed
kMgOthermal conductivity of the MgO solid
ρdensity
Cheat capacity at constant pressure
Ttemperature
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ttime coordinate
rcoordinate r in cylindrical coordinates
ε1emissivity factor of the electric arc
ε2emissivity factor of the steel shell
σStefan-Boltzmann constant
A1area of the theoretical energy source (electric arc)
A2area of the steel shell
References
[1]Castillo A Master's Degree Thesis, Universidad Autónoma de
Nuevo León, Monterrey, N.L. México (1992)
[2]Alper A M, Mcnally R and Papa P, U.S. Patent 3,332,740 (1967)
[3]Kingery W D 1975 Introduction to Ceramics (New York: Wiley and
Sons Inc)
[4]Bogdandy L and Engell H J 1971 The Reduction of iron ores (New
York: Springer) p 576, H. Engell.-The reduction of iron ores
[5]Anderson D A, Tannehill J C and Pletcher R H Computational
fluid mechanics & heat transfer (New York: Hemisphere
Publishing Corp. (1984)
[6]Carlslaw H S and Jaeger J C 1993 Conduction of Heat in Solids
(Oxford: Clarenton Press)
[7]Patankar S V Numerical heat transfer and fluid flow (New York:
Hemisphere Publishing Corp. (1980)
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Acknowledgments
C. Esparza expresses his gratitude to CONACYT for the grant for
conducting his Science Master studies.
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Figure 1.Scheme of the shell of the furnace, and the electrodes
arrangement and graphite bars for starting the process.
21
Figure 2.Temperature of the shell (at 40 cm height from the
furnace bottom) against time in three different places around the
furnace.
22
Figure 3.Comparison between average temperature on the external
shell (at 40 cm height from the bottom of the furnace)
and the calculated temperature.
23
Figure 4.Scheme of the furnace showing the smelted zone after 160
minutes, the left side in the bottom is the center of
the furnace (the part that is between the three
electrodes).
24
Figure 5.Status of the process and thermal profile shown on the
computer's screen (black line is the charge level).
