8/3/2019 1_111-119

1/9

MATHEMATICAL MODELLING OF BLAST FURNACE

PROCESS AT SMELTING OF NON-TRADITIONAL RAW

MATERIALS

Yu.A. Chesnokov, A.N. Dmitriev

Institute of Metallurgy of Ural Branch of Russian Academy of Sciences

Ekaterinburg, Russia

ABSTRACT. The offered balance logic-statistical model of blast furnace process is

based on use of the material and thermal balances added with calculations of heat- and

mass exchange taking into account non-uniformity of gas and burden distribution on

radius of the furnace and characteristics of the basic metallurgical characteristics of

iron ore raw materials and coke on indices of blast furnace operation. For check of

applicability of model the calculations on the most critical parameters of blast furnace

process smelting of ferromanganese and iron nickel with graphic representation ofheat- and mass exchange processes, dynamics of oxides reduction on height and

radius of blast furnace have been carried out.

1. INTRODUCTION

The blast furnace process is characterized by a substantial scale, power

consumption and orientation to the expensive energy carriers. Thereupon works on its

mathematical modeling for the purpose of maintenance of possibilities of forecasting

of the furnace work indicators and optimization of the technological parameters of the

blast furnace process are executed. Because of the complexity of physical and

chemical processes the research in the given direction developed on a way of creationof private models: balance, kinetic-mathematical, dynamic, equilibrium and others.

In particular, at Institute of metallurgy of Ural Brunch of Russian Academy of

Sciences last years is widely used balance logic-statistical model of blast furnace

process [1] which is based on use of the material and thermal balances added with

statistical data and most significant regularities of heat exchange and balance

conditions of iron oxides with a gas phase.

Recently the model have added with the integral equations for calculation of the

distribution of the burden temperatures both gas on height and radius of the furnace

and differential equations for calculation of kinetic curves of iron oxides reduction

in blast furnace shaft.

2. REDUCTION OF IRON OXIDES IN THE BLAST FURNACE

For calculation of the iron oxides reduction processes in the dry part of a blast

furnace is offered to use the following modified equation [1]

( )( )

( ) 3/1 ,,,,,

3/2

,,

3/1

,,

2,,

3/1

,,

3/2

,,,,950

,,

,,

,

22

2

1,0

6

wmgOH

wmg

E

wmgwmgP

wmg

X

P

wmgwmgwmg

wmg

Xwmg

HCO

D

BdKd

BAdK

+

=

, (1)

1-111

8/3/2019 1_111-119

2/9

wherew,m,g

H,CO 2 increment of degree of reduction of hematite (g), magnetite (m)

and wustite (w) at the expense of CO 2H agreeably. Other designations are

resulted in Section 6.

Balance constants (2/) of reactions

23 24332 COOFeCOOFe +=+ , (2)3 243 COFeOCOOFe +=+ , (3)

COFeCOFeO 2+=+ (4)

are described by the equations [2]

144.2/2726lg += TKCOg , (5)

1.2/1850lg += TKCOm , (6)

9.0/688lg = TKCOw . (7)

Balance constants of iron oxides reduction reactions by hydrogen ( 22 /HOH )

are calculated on the equations

wgwmg

H

wmg KKKCO

,,,,2 = ,

(8)

where wgK balance onstant of reaction of water gas

OHCOHCO 222 +=+ . (9)

Total degrees of reduction of iron oxides are calculated in model according to

the equations

wmg

H

wmg

COi

wmgwmg ,,,,

1

,,,,

2

++=

, (10)w

CO

m

CO

g

COiCOCO +++=

724.0166.011.01 , (11)w

H

m

H

g

HiH

H 2222

2

724.0166.011.01

+++=

. (12)For check of adequacy of the accepted scheme of reduction of iron oxides

experiments on reduction of agglomerate and pellets by hydrogen in an interval 900-

1100 have been made.

In Fig.1 the experimental and settlement kinetic curves constructed with use of

the equations (1), (10-12) are resulted.

3. DISTRIBUTION OF TEMPERATURES ON BLAST FURNACE HEIGHT

The basic equations for heat exchange calculation in the differential form look

like

d)ii(dtwdtw gpmmgg ++= , (13)

mmgg dtwdtw = , (14) dttvdidtw V )( mgmhmm =+ , (15)

m

mgm

m

hmgmm)()(

w

ttv

w

ittv

d

dt VV

=

=

, (16)

1-112

8/3/2019 1_111-119

3/9

Fig. 1. The experimental (continuous) and calculating (stroke-dotted) kinetic

curves of pellets reduction () and agglomerate (b) of Kachkanarsky GOK

g

mgmg )(

w

ttv

d

dt V

=

, (17)

where mw water equivalent of burden, equals

+=

d

dtw

iww

mm

hmm 1 , (18)

gw water equivalent of gas,

=

d

dtw

iww

g

g

p

gg 1 .

(19)

1-113

8/3/2019 1_111-119

4/9

Solving in common the equations (14) and (16), at an assumptiong

M

w

wm

=

= const we receive the equations

[ ]mtttmtt

H

m

g

H

m

g

m =

1)(exp ,

(20)

[ ]m

ttmtmtt

Hm

m

Hmg

g

=

1

)(exp , (21)

)1()( mw

v

m

mV

= , (22)

where K

gt andHmt temperatures of gas and material on top (the final temperature

of gas, the reference temperature of material); gt and mt the same in the end of a

zone of heat exchange (reference temperature of gas, final temperature of material).

For the calculation of dependence of the water equivalent and water number of

the burden from temperature we shall be limited to linear functions

mmmm taw += . (23)Integrating (13) and (14) in view of (23) we shall receive

( ) ( )[ ]g

KpH

mm

g

mH

mm

g

mK

ggw

JJtt

w

tt

w

tt

++++=

22

2, (24)

whereKpJJ +

losses of heat and thermal effects of reactions at height of thefurnace limited in temperatures gt and t

g , kJ/t of pig-iron.

These equations precisely enough describe processes of heat exchange in the

blast furnace at small values of a step on temperature or time.

4. CALCULATION OF NON-UNIFORMITY OF DISTRIBUTION OF GAS ON

TOP RADIUS

As the primary information allowing to analyze the work of gas in the furnace

use usually practical data about distributions 2CO and temperatures of gas on radius

of top. Distinguish two basic types of the distribution influencing on parameters ofwork of the furnace a peripheral and axial course. In the mathematical model the

opportunity of the task of any types of distributions as on practical data, and by

expert is stipulated. The curve )r(f =2 will be transformed to non-uniformity

of distribution of streams of burden and gas, thus the blast furnace is broken intoten equal rings. Also following assumptions are accepted: ore )O( and flux )F(

are distributed on section of the furnace in regular intervals unlike coke ( )rfr = and gas.

Thus these values should be distributed on top radius so that to compensate the

accepted assumptions and to reflect such phenomena, as pinching-out oflayers ofcomponents of burden, an advancing, segregation, etc.

As a result by means of calculation heat- and mass exchange on model the setcurve is reproduced ( )rf2 = . For this purpose used the equations with help which

1-114

8/3/2019 1_111-119

5/9

the ore loading )OB( and the coke consumption (K) are put accordingly in direct

and inversely proportional dependence on )CO( 2 and quantity of gas in dependence

on the coke consumption

( )( )

2

2

CO

COOBOB rr

= , (25)

( )( )

r

rr

OB

FOK

+= , (26)

( ) ( ) ( )n

r

gir

iiiirVBAVAV

+

+++=

K

K1

K

Kln1gg , (27)

where OB and K the average ore loading and the average coke consumption; i ,

Ai , Bi , ni factors which steal up on a condition of maintenance of the greatest

possible coincidence set curve and( )rf

=2

received as a result of calculations ofheat- and mass exchange in 10 rings.

5. EXAMPLES OF PROBLEMS PRACTICAL SOLUTION OF BLAST

FURNACE SMELTING

Model possibilities are illustrated by the analysis of blast furnace process at

fusion of silikate-nickel and manganous ores.

5.1. Smelt calculation of iron nickel

The analysis of development of processes of heat exchange carried out onchange of temperatures of gas and burden in horizontal sections and on furnace height

(on periphery, on an ore crest and at a furnace wall). As initial data are set - furnace

characteristics, composition and properties iron ore raw materials, limestone, coke,

blasting parameters, factors of non-uniformity of the gas stream, coordinated with the

loading systems profile (a site of an ore crest, its height). As a result of calculation

received pig-iron and slag composition, the parametres characterising thermal and

reducing work of gas, and also technical and economic indicators of blast furnace

smelting. The basic indicators of smelting and the analysis of blast furnace process for

conditions of melt of pig-iron about 6 % Ni in a blast furnace in volume 205 3 are

resulted in tab. 1 and in fig. 2. From character of the temperature curves it is visible,

that in an ore crest heat exchange is carried out at other relation of water equivalentsof and gas, unlike the centre and periphery. Therefore this area promotes formation of

low average temperature of top gas 35 .

Table 1. The basic parameters of smelting of ferronickel in a blast furnace

Indices Value

Productivity, t/day 53

1-115

8/3/2019 1_111-119

6/9

The sinter consumption, kg/t pig-iron 6430

General contents Fe in burden, % 13,96

Coke consumption, kg/t pig-iron 1532

Flux, kg/t pig-iron 82

Blast:

natural gas consumption, m3/minute 1558

temperature, 1100

oxygen contents, % 21,0

Pig-iron, composition, %:

[Si] 1.50

[Ni] 6.39

[Cr] 1.38

Slag: quantity, kg/t pig-iron 5138

composition, %: (CaO) 28.8

(MgO) 14.9

(Al2O3) 28.8

basic capacity (CaO/SiO2) 0.60

Reduction processes of iron oxides in all cuts are developed actively enough

because of tall reductibility of sinter. The greatest activity of reduction processes of

iron oxides is observed at furnace centre. At the centre of furnace and on the rim the

reduction of iron oxides is terminated completely in the dry zone of the board, i.e.

to temperatures 950 o. In the ridge ore the rereduction processes are developed less

actively and to the emolliating zone the material is enters in which wustite it is

reduced only on 50 %. Therefore early slags in this cut will differ from slags of

central and peripheral cuts both on consumption and on properties.

5.2. Smelt calculation of ferromanganese

The smelting of manganous ferroalloys in the blast furnace is characterised by

the raised coke consumption bundled first of all with high heat consumption of the

reduction processes of the manganese oxides in the bottom of a blast furnace. In these

conditions for smelting of qualitative ferromanganese are necessary high blast

parameters: maximum heat, its deep oxygen enrichment. For the analysis it is offered

to use the combined diagramme t allowing operatively to estimate the

thermal state of furnace together with reduction processes of iron oxides depending on

the stay time of materials in the furnace. In fig. 3 the curves of heat interchange andreduction of iron oxides at smelting of 72 % of ferromanganese are presented. The

analysis shows, that in comparison with ordinary conditions of smelting the altitude of

the reserve zone on a time is much more more stretched (1-1.5 hours against 3.5-4.0

hours, accordingly), that predetermines the conclusion about usage for a

ferromanganese smelting of low-shaft furnaces.

Centre of furnace

1-116

8/3/2019 1_111-119

7/9

Ore crest

Periphery of furnace

Temperature, Reduction degree, share of units

Fig. 2. Distribution of temperatures of the burden and gas (at the left) and reduction

processes (on the right) in vertical sections (rings 1, 8, 10) of the blast furnace at

ferronickel smelting

1-117

8/3/2019 1_111-119

8/9

Fig. 3. The analysis of reduction processes and heat interchange for

ferromanganese smelting conditions

As a result of the fulfilled explorations the existing mathematical model of the

blast furnace smelting is added by a method of the taking into account kinetic

singularities of reduction process of iron oxides until temperatures of 900-950 . The

measure of the registration of irregularity of allocation of gas on shaft top radius is

developed. The calculated analysis of the critical conditions and parameters of the

combined blast has shown essential spreading of functionality and a raise of adequacy

of the model.

6. SYMBOLS

wmgHCO,,, 2

gain of the reduction degree of the hematite, magnetite and wustite at theexpense ofCO or 2H accordingly;

wmg

K,,

constants of the reduction velocities for the hematite, magnetite and

wustite;

950CO CO content at 950, %;

d diameter of the ore piece, mm;

OHCO

wmg

ED 22 ,,, )( the effective diffusivity defining the diffusive resistance of the

reduced layer for hematite, magnetite and wustite accordingly;

wmgA ,, , wmgB ,, , wmgC ,, , wmgD ,, auxiliary coefficients;

gmt , temperature of materials or gas, accordingly, ;

1-118

8/3/2019 1_111-119

9/9

V volume heat-transfer factor;

hi heat effect of the reaction, kJ/(h t);

pi warmth losses, kJ/(h t);

m the ration of water equivalents of the burden and gas;

(), (), (F) consumption of ore, coke and limestone, accordingly, kg/t pig-iron;OB ore burden;

gV top gas amount, kg/t pig-iron;

(CO2) contents of the carbon dioxide in the top gas, %.

7. CONCLUSION

Thus, the short description of a balance logic-statistical model of the blast-

furnace smelting and results of the solution of practical problems of the blast-furnace

smelting are presented.

AKNOWLEDGEMENTS

This work was executed with support from Council under Grants for Leading

Scientific Schools of Russia (School 4358.2008.3).

REFERENCES:

1. Chentsov A.V., Chesnokov Yu.A. and Shavrin S.V.: The Logic-Statistic Balance

Model of Blast Furnace Smelting. Ural Branch of Russian Academy of Sciences,

Ekaterinburg, 2003.

2. Popel S.I., Sotnikov A.I. and Boronenkov V.N.: The theory of metallurgical

processes. Moscow, Metallurgy, 1986.

3. Chentsov A.V., Chesnokov Yu.A. and Shavrin S.V.: 'Controllable parameters of

system of loading and elements of modelling of domain process'. Izvestia Vuzov,

Chernaya Mettalurgia 2006 7 22-24.

4. Belyaev I.L, Chentsov A.V., Chesnokov Yu.A. and Shavrin S.V.: 'Use of two-

dimensional model of blast furnace process at pig-iron melt about 6 % Ni'.

Izvestia Vuzov, Chernaya Mettalurgia 2006 9 18-20.

5. Kudinov D.Z., Chesnokov Yu.A. and Shavrin S.V.: Features of blast furace process

at melt of manganous alloys in the form of diagrams t . Izvestia Vuzov,

Chernaya Mettalurgia 2002 3 76-77.

1-119