A Blast Furnace Model to Optimize the Burden Distribution

A Blast Furnace Model to Optimize the Burden Distribution
G. Danloy (1), J. Mignon (1), R. Munnix (1), G. Dauwels (2), L. Bonte (2)
(1)
Centre for Research in Metallurgy (CRM), Liège, Belgium, www.crm-eur.com
(2)
Sidmar, Gent, Belgium, www.sidmar.be
Key Words : Blast furnace, Mathematical model, Burden distribution, Vertical probings, Gas tracing.
INTRODUCTION
Since several years, large efforts are made in the blast furnace field to increase the substitution of coke by
coal in order to meet changing economical and environmental conditions. The experience gained until now
shows that the increase of PCI rate induces important changes of gas distribution in the blast furnace which
influence the whole process, the performance and the service life. Gas flow monitoring is therefore regarded
as one of the keys to high PCI rates.
Gas distribution being the result of numerous interacting phenomena, the best approach consists in
establishing a mathematical model of the gas flow inside the blast furnace.
DESCRIPTION OF THE BLAST FURNACE MODEL
Basic principles
The blast furnace is modelled in a steady state. Therefore, it is assumed to be charged and emptied
continuously. The liquid level is considered as horizontal and fixed ; however, it is a parameter. The layered
structure is assumed to be fixed, which is allowed by the fact that the gas velocity is much higher than the
solids velocity.
Assuming an axial symmetry, the model is bi-dimensional and written in cylindrical co-ordinates. The
system of differential equations is solved by the finite differences method.
The input data are : the blast furnace geometry, the process data (blast conditioning, coal injection rate, top
pressure, etc.), the chemical and physical properties of the raw materials, the chemical composition of hot
metal and slag and the complete description of ore and coke layers (thickness and grain size distribution
along the radius).
The model simulates the burden distribution inside the whole blast furnace, the gas flow through the layered
structure, the solids flow, the liquids flow, the heat transfer between the different phases and with the walls,
the ore softening and melting in the cohesive zone as well as the main chemical reactions.
The work has been restricted to the main phenomena of the blast furnace. Some sub-models like liquids flow
and softening-melting have been simplified ; the phenomena taking place in the raceway have been limited
to a classical heat and mass balance. Attempts were made to include a char transportation and consumption
sub-model, but it was finally concluded that a research project completely devoted to this problem would be
necessary to approach a valuable solution.
The general architecture of the model is shown at
figure 1.
The modular structure makes the model more
understandable, allowing easy modifications and
further improvements. But, due to the interactions
between the blast furnace phenomena, the different
modules are integrated into a complex looping
procedure.
The results of the model consist in a complete
description of each point of the blast furnace, i.e. the
fields of temperature, pressure, velocity and chemical
composition of gas, solids and liquids, as well as the
wall thermal losses distribution.
Geometry
The model has been applied to the geometry and the
operating conditions of the blast furnace B of Sidmar.
The bottom of the calculation field corresponds to the
liquid surface which is assumed to be fixed and
horizontal. The raceway and the dead man shapes have
been fixed according to relevant literature.
The blast furnace must be divided into a great number of cells in order to obtain a correct description of the
phenomena like the gas flow through the layers of materials. A compromise between the calculation time
and the quality of the results led to a grid of 20 x 120 cells. For a blast furnace of 10.5 m in hearth diameter,
the mesh dimension is then 0.30 m x 0.23 m. On a Digital Personal Workstation 433 AU, the computation
time amounts generally to 3 hours. This time depends highly on the degree of severity imposed for
convergence detection. This model working off line, such a high computation time is not really a dramatic
drawback. Moreover, it could still be improved by using more rapid calculators. The program is written in
FORTRAN.
Burdening model
Most plants already calculate the ore and coke layers geometry at the top with their own burden distribution
model adapted to their individual situation. The modular conception of the present model allows a perfect
integration of these existing auxiliary models. In the present work, we use the Sidmar burdening model [1]
which applies to a bell-less top. This model calculates the layers thickness as well as the grain size
distribution along the blast furnace radius. It calculates also the radial distribution of the resistance to gas
flow resulting from the Ergun's law.
The Sidmar burdening model (figure 2) takes into account the trajectory of each type of material for each
position of the chute, the thickness of the material flow, the dynamic effects generated at the impact point of
the materials on the burden surface, the grain size segregation (at the hoppers discharge, on the chute and on
the burden surface) and the percolation. The results are in good agreement with the microwave profilometer
measurements [2].
The structure and the properties of the layers are then
extended from the top to the bottom of the blast furnace
on the basis of the results of the solid flow sub-model
explained below.
Gas flow
This sub-model calculates the gas velocity and pressure
at any point of the blast furnace, being given the gas flow
rate at tuyeres, the top pressure, the blast furnace
geometry and the layered structure of the burden.
In the dry zone, the voidage of each material is a
function of height and radial position. The values are
based on measurements [3] made on samples issued from
the Mannesmann furnace quenched with nitrogen in
1981. In the cohesive zone and in the dripping zone, the
voidage has been decreased to take into account the
volume occupied by the liquids.
The Ergun equation [4] which holds in a homogeneous
field, can be written in a vectorial form :
∇ P = - ( f 1 + f 2 . |G| ) G
G
P
f1
f2
gas flow vector, reported to the empty reactor section [kg/m2.s]
static pressure [Pa]
laminar flow resistance factor [s-1]
turbulent flow resistance factor [m2/kg]
The mass conservation of gas is described by :
∇. (G/M) = Cr_Gas
M
Cr_Gas
molecular weight of the gas [kg/kmol]
rate of gas creation by chemical reactions
(carbon gasification by CO2 and H2O)
[kmol/m3.s]
A preliminary study of the different resolution methods
allowed to select the Direct Differential Method
because it gives the best precision together with one of
the shortest calculation times.
Figure 3 shows the calculated gas velocity field at the
entrance of the cohesive zone. It can be seen that the
gas velocities are greater in the coke layers than in the
ore layers. Moreover, to cross the cohesive zone, the
gas tries to avoid the softening and melting ores by
flowing mainly through the coke "windows" ; the small
part of the gas which passes through the less permeable
ore layers follows a path as short as possible i.e. almost
perpendicular to the interfaces.
Solids and liquids flows
The determination of the solids flow is based on is based on a potential model taking into account the
vanishing of solids by melting and by gasification. The main hypotheses are the following :
- imposed dead man,
- uniform distribution of solids velocity at the blast furnace
top,
- the burning rate of coke in the raceway does not depend on
the radius.
The basic mass conservation equation is written as follows :
∇•(
S
ρb
Gasif
Melt
Burnt
S
) = − Gasif − Melt − Burnt
ρb
solids flow vector [kg/m2.s]
solids bulk density [kg/m3]
carbon gasification reaction rate by CO2 and H2O
[m3/m3.s]
ore melting rate [m3/m3.s]
coke burnt in the raceway [m3/m3.s]
The solution is obtained through the introduction of a potential
function Ψ [m2/s] such that :
v
∇Ψ = −
k
v
solids velocity [m/s]
k
resistance to gas flow [-]
The potential function is set at 0 on the raceway section. This
elliptic problem is solved by the over-relaxation method.
Figure 4 shows an example of results. The layer thickness
decreases progressively from the top to the tuyeres. In the upper part of the bosh, the coke layers have an
average thickness of 0.08 m at the wall which can be
compared to 0.21 m observed at the top. The inclination
angle of the layers decreases also : from 30° at the top, it
reaches about 6° in the belly. From the start of melting
line to the end of melting line, the ore layers become
thinner and thinner which reflects the melting
phenomenon.
These results fit very well with the observations made on
several dissected blast furnaces, as for example on
Hirohata n°1 BF of Nippon Steel (figure 5) [5]. This
figure highlights also a sharp inverted V shape cohesive
zone with a very low root touching the wall and the
raceway as in the model results. In the belly, the model
calculates cohesive rings of 1.7 m width which can be
compared to values ranging from 1.2 to 1.7 m on figure 5.
As concerns the liquids issued from the melting line, they
are supposed to flow vertically into the hearth.
Heat transfer
The main supplementary data required for the heat transfer description are the temperature of the gas issued
from the raceway and the standard heats of the chemical reactions. At steady state, the conservation of
energy and the thermal transfers between the solids, liquids and gas phases are described by :
For liquids
:
- ∇ . (Hl . Gl) + ∇ . (kl ∇ Tl) - Qtr, l + Σ αl, i . Ri . ∆Hr, i = 0
For gas
:
- ∇ . (Hg . Gg) + ∇. (kg ∇ Tg) - Qtr, g + Σ αg, i . Ri . ∆Hr, i = 0
For solids
:
- ∇ . (Hs . Gs) + ∇ . (ks ∇ Ts) - Qtr, s + Σ αs, i . Ri . ∆Hr, i = 0
with, for each phase,
H
G
k
T
Qtr
Ri
∆Hr, i
αi
enthalpy at temperature T [J/kg]
mass flow vector, reported to the empty reactor section [kg/m2.s]
thermal conductivity [J/m.EC]
temperature [°C]
heat transferred to the other phases and to the cooling medium by convection and radiation [W/s]
rate of reaction i [kmol/m3.s]
heat of reaction i [J/kmol]
proportion of the heat of reaction i absorbed by the considered phase [-]
The heat transferred by the liquids by conduction and radiation as well as the heat transferred by radiation by
the gas have been neglected.
The Kitaiev correlations [6] have been chosen to quantify the heat transfer coefficient between gas and
solids and to account for heat conduction inside the solid particles. However, like many authors, we have
applied a correction factor to the heat transfer coefficient at temperatures higher than 1000°C.
The heat transfer coefficients gas-liquids and solids-liquids have been determined by calibration on
industrial data in order to produce hot metal and slag at the right temperature.
The boundary conditions are expressed by the wall temperatures, themselves calculated by the following
heat transfer equation :
h p . ( T w - T wat ) = h w . ( Tg - T w )
hp
hw
Twat
Tg
Tw
global heat transfer coefficient wall-cooling water [W/m2.°C]
global convection and conduction heat transfer coefficient granular bed-wall (W/m2.°C)
cooling water temperature (°C)
gas temperature at the wall (°C)
wall surface temperature (°C)
The global heat transfer coefficient wall-cooling water has been determined in function of the height by
calibration on industrial data from BF B of Sidmar. The coefficient hw is calculated following the method set
up by Yagi and Kunii [7].
Cohesive zone sub-model
The cohesive zone starts where the solids reach 1200°C and ends where the ore is completely melted. The
ore melting degree is calculated from the available heat resulting of heat transfer. It is calculated by means
of an under-relaxation procedure which continues until convergence i.e. until the assumed and calculated
vertical positions of both isotherms don't differ more than a half mesh, which means about 0.12 m in height.
Chemical reactions sub-model
The model considers the following reactions :
FexOy + CO = FexOy-1 + CO2
(reaction 1)
CO2 + C = 2 CO
(reaction 2)
FexOy + H2 = FexOy-1 + H2O
(reaction 3)
C + H2O = CO + H2
(reaction 4)
CO + H2O = CO2 + H2
(reaction 5)
The gas composition and flow rate are known at the tuyere tip. It is supposed that in a given cell the
chemical reactions develop without any interference and that no diffusion of chemical species occur from
one cell to the others. Iron and slag are supposed to reach their final composition as soon as they are formed
in the cohesive zone.
In each cell, and for each chemical species, the continuity equation is expressed by
∇ . (Fi) = Ri
Fi
Ri
flux vector of the i species expressed on the empty section of the reactor [kmol/m2.s]
difference between generation and consumption rates of the i species [kmol/m3.s].
A single stage reduction model applied to porous spherical particles is used [8, 9]. The reactions are of first
order relative to the partial pressures of the gas components. The diffusion inside the particles is considered
but the diffusion through the boundary layer outside the particles is neglected, as it is of minor importance.
Various expressions of the reaction rate constant can be found in literature. We adopted the following value
[m/h] which is based on reduction tests performed in the 80ies in CRM laboratory :
k = 475 . exp [ - 10000 / ( 1.987 . T)]
The value was obtained from the application of the preceding equations to experimental results. The
equilibrium is calculated according to the results of Darken and Gurry [10].
For coke gasification by CO2, a gasification model applied to porous spherical particles is used [9]. The
reaction rates are of first order relative to the partial pressures of CO2 and CO. The diffusion of gas through
the external boundary layer as well as through the pores of coke is taken into account. We use the reaction
rate constant determined by Heynert [11].
The kinetics of reaction 4 is assumed proportional to the kinetics of reaction 2. Reaction 5 is assumed at
equilibrium above 850°C ; below this temperature, it is neglected.
CALIBRATION OF THE MODEL AND ILLUSTRATION OF THE RESULTS
The calibration of the model is based on experimental data obtained by vertical probings and by gas tracing
at blast furnace B of Sidmar. The results are illustrated below.
The burden consisted of 88 % sinter and 12 % pellets. The coke rate was 287 kg/thm (including 27 kg/thm
of nut coke charged together with sinter) with a coal rate of 178 kg/thm. The production level was 65
thm/m2.day or 2.7 thm/m3.day.
The measured and calculated temperature profiles are reported at figures 6 and 7. The long thermal reserve
zone observed on probes 1 to 4 is reproduced by the calculations but some tuning is still necessary to
improve the fitting. The drying of solids shown by probe 1 below 5 m needs also to be improved in the
simulation. Between 1000°C and 1300°C, area of reactions 2 and 4, the patterns of calculated temperature
profiles are similar to those measured. Results concerning probes 5 and 6 can be regarded as good.
Experimental and calculated results concerning the progress of chemical reactions are compared on a
Chaudron diagram at figures 8 and 9. On both figures, the gas path shows a similar behaviour which leads to
the conclusion that the chemical phenomena are fairly well simulated.
The calculated radial profiles of top gas
composition and temperature are also in good
agreement with the measured ones, as can be
seen at figure 10.
At figure 11, the pressure profiles calculated
along the wall compare well to the pressure
profiles measured during the vertical probings
both by the wall probe and by the wall pressure
tappings. A pressure loss of 0.300 bar has been
substracted from the pressure measured in the
hot blast main to obtain the experimental value
of the pressure at tuyere nose.
Transfer times of gas from the tuyeres to the top are measured on blast furnace B of Sidmar by gas tracing
with helium [12]. These measurements can also be used to calibrate the model. Figure 12 compares the
experimental measurements to the results of the model. Despite small differences attributed to a systematic
error in the measurement of gas transfer time through the sampling line, the profiles are almost parallel,
indicating that the gas distribution in the blast furnace is correctly simulated. This result is worth to be
highlighted, as gas distribution is the main objective of the present model.
These comparisons lead to the conclusion that the mathematical model simulates correctly the main
phenomena involved in the blast furnace process.
SIMULATION OF THE INFLUENCE OF THE BURDEN DISTRIBUTION PATTERN
The charging procedure being the most important means to influence the gas distribution, we selected by
means of the Sidmar burdening model three typical charging procedures promoting without any doubt a
central, a peripheral and an intermediate gas distribution. The layers configurations resulting from the
Sidmar burdening model appear at the top of figure 13, as well as the radial distribution of the coke volumic
fraction and of the resistance to gas flow.
With charging pattern n°1, the coke volumic fraction reaches 100 % at the blast furnace center and only
22 % at the wall ; as a consequence, the resistance to gas is very low at the center and relatively high at the
wall. With charging pattern n° 2, coke and ore are distributed in such a way to obtain a uniform distribution
of the resistance to gas flow. It is interesting to observe that the coke proportion is higher at the wall than at
the centre because it is necessary to compensate for the grain size segregation effect. Charging pattern n° 3
has been designed to create a low resistance zone at the furnace periphery ; at the wall, the coke proportion
reaches 54 %.
The operation data have been described in the preceding chapter. In order to highlight the influence of the
burden distribution, all the parameters of the model are kept constant for the three simulations.
Figure 13 shows the gas temperature map and the calculated cohesive zone in the three cases. These results
are in good agreement with industrial experience. It is also worth mentioning that the cohesive zone is much
thinner with charging pattern n° 1.
In the dry zone, the three pressure profiles are almost superposed, but they differ greatly in the cohesive and
dripping zones. The calculated pressure drops are respectively 0.99 bar, 2.19 bar and 1.38 bar for the
charging patterns n° 1, 2 and 3. Such a classification agrees well with experience.
In practice, the characteristic curve of the blower will
impose the operating conditions, so that charging
patterns n° 2 and 3 will result into lower blast and
production rates. To obtain a pressure loss of 0.99 bar in
the three cases, the model calculates that
the
productivity will be respectively 64.8, 46.1 and 52.6
thm/m2.day (i.e. 100 %, 71 % and 81 %).
At figure 14, the three radial profiles of top gas
temperature are compared. They fully agree to what
might be expected. With charging pattern n° 1, the high
temperatures observed at the centre allow to purge by the
top a significative fraction of the alkalies load, as already
reported industrially [13].
The radial profiles of top gas oxidation degree (figure15)
are coherent with the top temperature profiles. The
average value of the top gas CO2/(CO+CO2) ratio is
respectively of 0.488, 0.525 and 0.527 for the charging
types n° 1, 2 and 3.
The profiles of heat losses through the walls highlight
also the great differences between the three charging
patterns that are mainly due to the different wall
temperature profiles. As expected, the heat losses are lower with the
n°1 charging pattern. After integration on the whole wall surface, heat
losses of respectively 141 MJ/thm, 197 MJ/thm and 212 MJ/thm are
calculated for cases n° 1 to 3 (i.e. 9130 kW, 12780 kW and
13760 kW).
The main results of these calculations are summarized in table I.
The three typical charging patterns applied here above result in
extremely different blast furnace operations. But much smaller
charging modifications, more frequently encountered in the industrial
practice, can also result in appreciable modifications of the blast
furnace inner state and performance (figure 16). In this respect, the
model can certainly help the operator to choose the most appropriate
burden distribution pattern in function of the desired effect on the
blast furnace results.
Table I – Calculated results relative to the three charging types.
Unit
Pressure loss
Productivity for a pressure loss of 0.99 bar
Heat losses through the walls
Top gas CO2 / (CO + CO2)
Top gas temperature at BF centre
bar
thm/m2.24 h
%
MJ/tHM
kW
°C
Charging type
1
2
3
0.99
2.19
1.38
64.8
46.1
52.6
100
71
81
141
195
212
9130
12780
13760
0.488
0.525
0.527
818
161
46
SIMULATION OF THE INFLUENCE OF THE PRODUCTION RATE
The influence of the production rate on the blast furnace performance has been simulated for two different
charging patterns, one leading to a central operation and one leading to a uniform operation. Figures 17 and
18 illustrate the effects observed on the cohesive zone.
DISCUSSION OF THE RESULTS
The model results show that the gas flow pattern and the cohesive zone are mainly dictated by the burden
distribution.
The change of gas distribution from the lower shaft to
the upper shaft level is illustrated on figure 19 where the
gas flow rates on both sections have been related to a
normalized section divided into 10 rings of equal area.
The change of gas distribution implies that some gas is
moving from the central region towards the wall but the
phenomenon is rather limited. Considering that, in the
present simulation, the central part of the furnace is
occupied by coke only, the gas distribution in the upper
shaft appears very flat as the fraction of gas passing
through the rings varies only in the range of 13 % to
9 %. This result is totally different from the common
feeling of a very high gas flow rate at the centre, feeling
based on the usually measured top gas temperature
profiles. In conclusion, the temperature profile is mainly
related to the gas velocity profile but gives a poor
indication on the gas flow rate profile.
The validity field of the model could be enlarged by the modelling of other phenomena such as the
behaviour of unburnt coal particles, voidage modifications, grain size alteration, channelling, accretion,
scaffolding and peeling. As it includes the main phenomena involved in the blast furnace process and their
interrelations, the present model is an appropriate frame to the development of such additional modelling
work.
CONCLUSIONS
A mathematical model has been developed which simulates the main phenomena involved in the blast
furnace process at steady state. It has been calibrated with experimental data obtained by vertical probings
and by gas tracing at blast furnace B of Sidmar.
The model results show the strong influence of the burden distribution pattern on the gas distribution and on
the different operating results such as the pressure drop, the productivity, the shape and position of the
cohesive zone, the top gas temperature profile and the heat losses through the wall. As a consequence, it can
be used to simulate and to forecast the influence of the burden distribution changes which are made by the
operator. Therefore, it is a powerful tool to help him to choose the proper burden distribution pattern in
function of the desired effect on the blast furnace results.
Sidmar has decided to implement the model for an industrial use.
ACKNOWLEDGEMENTS
This research has been carried out with financial support from the Belgian Public Authorities and from the
ECSC.
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