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 of
heat- 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 creation
of 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]

g , m, w
CO , H 2

6 K Xg , m, w СО950  d Ag , m, w  Bg2,/m3, wС 1g/, m3 , w 
0,1d P 


K Xg , m, w d P2 B1g/, m3 , w  Вg2,/m3, w
D
g , m, w
E
СО2 , H 2 O
1-111
С 1g/, m3 , w

,
(1)
g ,m ,w
where CO
,H 2 – increment of degree of reduction of hematite (g), magnetite (m) and
wustite (w) at the expense of CO или H 2 agreeably. Other designations are resulted
in Section 6.
Balance constants (СО2/СО) of reactions
3Fe2O3  CO  2Fe3O4  CO2 ,
Fe3O4  CO  3FeO  CO2 ,
(2)
(3)
(4)
FeO  CO  Fe  CO2
are described by the equations [2]
lg K gCO  2726 / T  2.144 ,
(5)
lg K mCO  1850 / T  2.1 ,
(6)
lg K
CO
w
 688 / T  0.9 .
(7)
Balance constants of iron oxides reduction reactions by hydrogen ( H 2O / H 2 )
рассчитываются по уравнениям are calculated on the equations
K gH, m2 , w  K gCO
, m, w K wg ,
(8)
where K wg – balance сonstant of reaction of water gas
CO2  H 2  CO  H2O .
(9)
Total degrees of reduction of iron oxides are calculated in model according to
the equations
 
 
 
g , m, w
CO

H2


  
g , m, w
  
 
i 1
CO i 1
H 2 i 1
g , m, w
 CO
 Hg ,2m, w ,
(10)
g
m
w
 0.11CO
 0.166CO
 0.724CO
,
 0.11Hg  0.166Hm  0.724Hw .
2
2
2
(11)
(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 9001100 оС 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
wg dt g  wm dt m  ( i p  i g )d ,
wg dt g  wm dt m ,
(13)
(14)
wm dt m  ih d   V vm (t g  t m )d ,
(15)
dt m  V vm (t g  t m )  ih  V vm (t g  t m )


,
d
wm
wm
(16)
1-112
Fig. 1. The experimental (continuous) and calculating (stroke-dotted) kinetic
curves of pellets reduction (а) and agglomerate (b) of Kachkanarsky GOK
dt g
d

 V vm (t g  t m )
wg
,
(17)
where wm – water equivalent of burden, equals


ih
wm  wm 1 
dt m

 wm
d



,



(18)
wg – water equivalent of gas,
1-113


ip
wg  wg 1 
dt g

 wg
d



.



(19)
Solving in common the equations (14) and (16), at an assumption
wM
= const we receive the equations
m 
wg
tm 
t gк  mt mH   t gк  t mH  exp  ( )

1  m

,
(20)
t gк  mtmH  mtmк  tmH  exp  ( )
tg 
,
1  m
 v
 ( )  V m (1  m) ,
(21)
(22)
wm
where – t gK and tmH – temperatures of gas and material on top (the final temperature
of gas, the reference temperature of material); t gН and t mК – 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
wm  a m  в m t m .
Integrating (13) and (14) in view of (23) we shall receive
t g  t gK 



   J
аm
в
t m  t mH  m t m2  t mH
wg
2wg
2
p
 JK
wg
,
(23)
(24)
where J p  J K – losses of heat and thermal effects of reactions at height of the
furnace limited in temperatures t g and t Кg , 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 CO2 and temperatures of gas on radius of
top. Distinguish two basic types of the distribution influencing on parameters of work
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 СО2  f ( r ) will be transformed to non-uniformity of
distribution of streams of burden and gas, thus the blast furnace is broken into ten
equal rings. Also following assumptions are accepted: ore ( O ) and flux ( F ) are
distributed on section of the furnace in regular intervals unlike coke Кr  f r  and
gas.
1-114
Thus these values should be distributed on top radius so that to compensate the
accepted assumptions and to reflect such phenomena, as pinching-out of layers of
components of burden, an advancing, segregation, etc.
As a result by means of calculation heat- and mass exchange on model the set
curve is reproduced СО2  f r  . For this purpose used the equations with help which
the ore loading ( OB ) and the coke consumption (K) are put accordingly in direct and
inversely proportional dependence on ( CO2 ) and quantity of gas in dependence on
the coke consumption
OBr

OB  CO 2 r
CO 2
,
(25)
Kr 
O  F r ,
OB r
V 
 K

K 

  i  Ai  Vg  Ai  1   Bi ln r   1   i  V g 
K 


 Kr
g r
(26)
n

 ,

(27)
where OB and K – the average ore loading and the average coke consumption; ρi ,
Ai , Bi , ni – factors which steal up on a condition of maintenance of the greatest
possible coincidence set curve and СО2  f r  received as a result of calculations of
heat- 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 on
change 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 м3 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 equivalents
of and gas, unlike the centre and periphery. Therefore this area promotes formation of
low average temperature of top gas – 35 оС.
1-115
Table 1. The basic parameters of smelting of ferronickel in a blast furnace
Indices
Value
Productivity, t/day
The sinter consumption, kg/t pig-iron
General contents Fe in burden, %
Coke consumption, kg/t pig-iron
Flux, kg/t pig-iron
Blast:
natural gas consumption, m3/minute
temperature, оС
oxygen contents, %
Pig-iron, composition, %:
[Si]
[Ni]
[Cr]
Slag: quantity, kg/t pig-iron
composition, %: (CaO)
(MgO)
(Al2O3)
basic capacity (CaO/SiO2)
53
6430
13,96
1532
82
1558
1100
21,0
1.50
6.39
1.38
5138
28.8
14.9
28.8
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 oС. 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 “ω – t – τ” 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 and
reduction 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.
1-116
Centre of furnace
Ore crest
Periphery of furnace
Temperature, оС
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
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 оС. 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
g ,m, w
CO
, H 2 – gain of the reduction degree of the hematite, magnetite and wustite at
the expense of CO or H 2 accordingly;
K Хg ,m,w – constants of the reduction velocities for the hematite, magnetite and wustite;
CO950 – CO content at 950оС, %;
d Р – diameter of the ore piece, mm;
( DEg ,m,w ) CO2 , H 2O
– the effective diffusivity defining the diffusive resistance of the
reduced layer for hematite, magnetite and wustite accordingly;
Ag ,m , w , B g ,m , w , C g ,m, w , D g , m , w – auxiliary coefficients;
1-118
t m , g – temperature of materials or gas, accordingly, оС;
 V – volume heat-transfer factor;
ih – heat effect of the reaction, kJ/(h ∙ t);
i p – warmth losses, kJ/(h ∙ t);
m – the ration of water equivalents of the burden and gas;
(О), (К), (F) – consumption of ore, coke and limestone, accordingly, kg/t pig-iron;
OB – ore burden;
Vg  – 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 blastfurnace 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 twodimensional 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 ω – t – τ. Izvestia Vuzov,
Chernaya Mettalurgia 2002 3 76-77.
1-119