A Blast Furnace Model to Optimize the Burden Distribution

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

=

-

(

+

.

|

G

|

)

G

f

f

1

2

G

gas flow vector, reported to the empty reactor section [kg/m

.s]

2

P  static pressure [Pa]

f

laminar flow resistance factor [s

]

-1

1

f

turbulent flow resistance factor [m

/kg]

2

2

The mass conservation of gas is described by :

.

(

G

/M) = Cr_Gas

M   molecular weight of the gas [kg/kmol]

Cr_Gas rate of gas creation by chemical reactions

(carbon gasification by CO

and H

O)

2

2

[kmol/m

.s]

3

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

(

)

=

-

Gasif

-

Melt

-

Burn

t

•

b

S

solids flow vector [kg/m

.s]

2

solids bulk density [kg/m

]

3

b

Gasif carbon gasification reaction rate by CO

and H

O

2

2

[m

/m

.s]

3

3

Melt ore melting rate [m

/m

.s]

3

3

Burnt coke burnt in the raceway [m

/m

.s]

3

3

The solution is obtained through the introduction of a potential

function

[m

/s] such that :

2

v

=

-

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  : -

. (H

.

G

) +

. (k

T

) - Q

+ S a

. R

.  H

= 0

l

l

l

l

tr, l

l, i

i

r, i

For gas  : -

. (H

.

G

) +

. (k

T

) - Q

+ S a

. R

.  H

= 0

g

g

g

g

tr, g

g, i

i

r, i

For solids  : -

. (H

.

G

) +

. (k

T

) - Q

+ S  a

. R

.  H

= 0

s

s

s

s

tr, s

s, i

i

r, i

with, for each phase,

H   enthalpy at temperature T  [J/kg]

G

mass flow vector, reported to the empty reactor section [kg/m

.s]

2

k   thermal conductivity [J/m.EC]

T temperature [°C]

Q

heat transferred to the other phases and to the cooling medium by convection and radiation [W/s]

tr

R

rate of reaction i  [kmol/m

.s]

3

i

H

heat of reaction i  [J/kmol]

r, i

a

proportion of the heat of reaction i absorbed by the considered phase [-]

i

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

.

(

-

)

=

h

.

(

-

)

T

T

T

T

p

w

wat

w

g

w

h

global heat transfer coefficient wall-cooling water [W/m

.°C]

2

p

h

global convection and conduction heat transfer coefficient granular bed-wall (W/m

.°C)

2

w

T

cooling water temperature (°C)

wat

T

gas temperature at the wall (°C)

g

T

wall surface temperature (°C)

w

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 h

is calculated following the method set

w

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 :

Fe

O

+  CO  =  Fe

O

+  CO

(reaction 1)

x

y

x

y-1

2

CO

+  C  =  2 CO

(reaction 2)

2

Fe

O

+  H

=  Fe

O

+  H

O (reaction 3)

x

y

2

x

y-1

2

C  +  H

O  =  CO  +  H

(reaction 4)

2

2

CO  +  H

O  =  CO

+  H

(reaction 5)

2

2

2

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

.

(

F

)  =  R

i

i

F

flux vector of the i species expressed on the empty section of the reactor [kmol/m

.s]

2

i

R

difference between generation and consumption rates of the i species [kmol/m

.s].

3

i

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 80

in CRM laboratory :

ies

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 CO

, a gasification model applied to porous spherical particles is used [9]. The

2

reaction rates are of first order relative to the partial pressures of CO

and CO. The diffusion of gas through

2

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/m

.day or 2.7 thm/m

.day.

2

3

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/m

.day (i.e. 100 %, 71 % and 81 %).

2

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.

Charging type

Unit

1 2 3

Pressure loss

0.99 2.19 1.38

bar

thm/m

.24 h

64.8

46.1

52.6

2

Productivity for a pressure loss of 0.99 bar

%

100

71

81

MJ/tHM

141

195

212

Heat losses through the walls

kW

9130

12780

13760

Top gas CO

/ (CO + CO

)

-

0.488 0.525 0.527

2

2

Top gas temperature at BF centre

818 161 46

°C

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.