KINETICS CHARACTERISTICS OF REDUCTION WITH SOLID
CARBON OF THE WASTE DUSTS OF STEELMAKING
PRODUCTION
Rossitza Paunova, Daniela Grigorova, Dimitar Damgaliev
University of Chemical Technology and Metallurgy, Sofia, Bulgaria
Abstract. Thermodynamics of the untreated waste products reduction with solid
carbon of the steelmaking production has been carried out in temperature range
873К÷1173К and kinetics in temperature range 298К÷1273K. The correlation
between waste emissions/reducer is 1:1, 1:2 and 1:2.5. DTA analysis of the waste
products has been used for the calculation of ratio and rate of reduction in temperature
range 298К÷1273К. Experimental results have been processed mathematically. It was
created mathematical equations of the models.
INTRODUCTION
Large quantities of waste materials (dusts and slurries) are liberated after gas cleaning
installations in the extraction ferrous metallurgy (“Kremikovtzi” JSco, Sofia and
“Stomana Industry” JSCo, Pernik). The waste materials are subject of landfilling and
their accumulation cause ecological pollution. These waste dusts and slurries that are
not utilized in their greater part have considerable iron content and considerable high
content of non-ferrous metals. On the other, these waste products could be use
effectively as mineral raw materials in different branch of industry.
The waste products utilization will solve some ecological, economical and
technological problems of the firms. In other to be chosen the correct strategy of the
waste material processing, it is necessary to be investigated some thermodynamic and
kinetic characteristics of their reduction.
The mathematical processing of these characteristics enables their wide application
and use. The experimental models are received on the base of the measured data of
the entrance and exit quantities of the object.
The purpose of present work is to be received some appropriate mathematical models
for the kinetic characteristics of the waste products reduction from steelmaking
production. The received equations, deduced from real experimental data, will enable
an express mathematical calculation of kinetic characteristics of the waste products
with the same or similar composition.
EXPERIMENTS
Initial Materials
2-55
For carrying out of the investigations the waste dusts from the metallurgical plants in
Bulgaria have been used: - sample 1 - blast furnace powders; sample 2 – BOF
converter dusts; sample 3 – electric arc furnace (EAF) dusts from “Kremikovtzi”
JSco; sample 4 – EAF dusts from “Stomana Industry” JSco . Their chemical
composition is shown in Table 1.
Table 1. Chemical composition of the waste products, %
Element
FeO Fe2O3 CaO MgO SiO2 Al2O3
s,%
sample 1 9.34 45.83
9.2
0.66 9.43 2.90
sample 2 14.0 59.93
2.63 1.01 1.72 0.36
sample 3 14.2 54.82
8.62 2.90 5.66 0.65
sample
9.75 50.42
5.01 2.76 5.86 6.4
4
MnO
PbO
CuO
ZnO
1.38
5.62
7.99
2.75
2.81
1.33
0.04
1.14
0.21
2.39
0.62
2.69
5.1
5.17
-
10.6
For the experiments the following mixtures were prepared:
Mixture 1 - 88 % of waste converter output and 12 % fine cokes (Kremikovtzi JSco);
Mixture 2 - 22 % of a waste product in a blast furnace output, 68 % of waste
converter output and 9 % fine cokes (Kremikovtzi JSco);
Mixture 3 – 40% of a waste product in a blast furnace output, 40 % of waste of
converter output, 8 % of waste of EAF output and 12 % fine cokes (Kremikovtzi
JSco);
Mixture 4 – EAF output and reducing agent in correlation 1:1 (Stomana Industry
JSco);
Mixture 5 - EAF output and reducing agent in correlation 1:2 (Stomana Industry
JSco);
Mixture 6 – EAF output and reducing agent in correlation 1:2,5 (Stomana Industry
JSco);
A fine cokes with 88 % of carbon contained was used as reductive agent at pellets
formation by use of waste from „Kremikovtzi” JSco .
The quantity of the reductive agent is selected in stoichiometric ratio. The content in
mixture-3 [in %] from the three outputs is selected in such correlation taking into
account their quantities, generated in “Ktemikovtzi” JSco. Despite its different
constitution mixture-3 presents good palletization characteristics. The last could be
explained by the presence of converter slurry, which has good palletizing properties.
The waste product from the “Stomana Industry” JSco contains high percent of ZnO
and water soluble sulphur [1]. Because of that, the material was watery leached in
advance and subsequently palletized with carbon in correlation waste product
/reductive agent: 1: 1; 1: 2 and 1: 2, 5.
Experimental Apparatus
The waste products reduction was carried out with a reductive agent solid carbon at
the temperature range 298 К - 1273 К at non-isothermal conditions. The maximal
temperature for heating pellets can be up to 1423 К (1150 оC). Superficially smelting
of pellets was observed at heating over this temperature. The received results of the
gas analysis are considered as non-representative.
2-56
In thermodynamics study of the waste products reduction the following galvanic cell
was used
PtFe2O3 (waste product), C (O2,CO2ZrO2(CaO)NiO, Ni Pt
Po2
Po2
PCO2
The experimental values of lg PO2 and lg
were calculated with the following
PCO
equations as well [2]
E.20186 24406

 8,8867
T
T
PCO2
14783
lg
 1 / 2. lg PO2 
 4,57
PCO
T
The percent content was calculated at the equation in СО
lg PO2  
(1)
(2)
100
(3)
 PCO2 

1  
P
 CO 
For the kinetics investigation of the reduction of the waste metallurgical products a
thermogravimetric apparatus was being used. DТА analysis was carried out in
nonisothermal heating in the following conditions: scale sensitivity 100mg,
temperature range 293 К  1123 К. The heating rate is 10 oC/ min, sensitivity of DТА
1/5, sensitivity of DТG 1/5, errs at DTA 0. 5 oC [3,4].
The quantity of gas mixture (СОtheor. + СО2theor.) was calculated with experimental data
for CO. The result for mixture 1 was 0.16906g, for the second - 0.19884g, for the
third - 0.1878g, of fourth - 0.20097g, of fifth – 0.1364g to sixth 0.15974g as well.
%CO 
Experimental Results
Besides if in the constitution of pellets the quantity of the carbon is higher from the
stoichiometry of the reduction reactions and containing carbon addition is with weak
reducing ability, it is possible to run reduction process at roasting of pellets in neutral
atmosphere without their oxygenizing.
Mixtures 1 and 5 have a higher degree of reduction than mixture 4, that it can be
represented with the lower reduction ability at a reducing agent in these mixtures and
its well - lined spending for the reduction. The lower degree of reduction of a mix 4 is
explained with a failed reductive agent. Experimental kinetics results of the studied
mixture at non-isothermal conditions are shown in Table 2.
Kinetic investigations have been registered highest degree of reduction for EAF waste
dusts from “Stomana Industry” JSco, Pernik, in stoichiometric correlation 1:2
reducing agent (solid carbon) and waste product at temperature range 1273 К and
1423 К. The heating over this temperature is objectionable because of the pellets
smelting.
The highest degree of reduction for mixtures from metallurgical production of
“Kremikovtzi” JSco has been obtained in mix 1. In mixes 2 and 3 the degrees of
reduction are close. The EAF waste addition in mix 3 does not real influence on
degree of reduction.
By comparisons of kinetic curves of different waste mixtures for Kremikovtzi JSco
has been found the highest velocity of reduction with converter waste product while it
2-57
for the other waste products ( 2 and 3) runs comparatively slowly. The velocity of
reduction for mixture 3 is  = 5.26*10 5 kg / sec. It is due to dilution effect of the
added by the blast furnace waste great quantities of some oxides like MnO, Al2O3,
SiO2, MgO, CaO. These oxides reflect on the better contact between reductive agent
and ferrous oxides. Kinetic curves of Fe2O3 and Fe3O4 reduction with solid carbon is
reported also in [5].
Table 2. Experimental kinetics results
conditions
Mix 1
T, K m, g  *105 kg / s
α, %
613 0.015
0.00
8.87
743 0.038
6.27
22.48
773 0.045
8.27
26.62
873 0.067
7.80
39.63
973 0.082
5.32
48.50
1073 0.095
4.61
56.19
1173 0.105
3.55
62.11
1273 0.114
3.19
67.43
Mix 3
T, K m, g  *105 kg / s
α, %
693 0.017
0.00
9.05
773 0.020
1.10
10.65
873 0.032
351
17.04
973 0.045
3.80
23.96
1073 0.063
5.26
33.55
1173 0.074
3.22
39.40
1273 0.081
2.05
43.13
T, K
623
673
773
873
973
1073
1173
1273
m, g
0.019
0.021
0.036
0.053
0.073
0.090
0.101
0.107
Mix 5
 *105 kg / s
0.00
2.02
7.58
8.59
10.10
8.59
5.56
3.03
α, %
14.03
15.51
26.59
39.14
53.91
6647
74.59
79.03
of the studied mixture at non-isothermal
T, K
693
773
873
973
1073
1173
1273
m, g
0.016
0.021
0.031
0.047
0.063
0.073
0.082
T, K
573
673
723
773
873
973
1073
1173
1273
m, g
0.012
0.018
0.029
0.037
0.050
0.062
0.077
0.087
0.091
T, K
753
773
873
973
1073
1173
1273
m, g
0.011
0.012
0.021
0.032
0.042
0.048
0.054
Mix 2
 *105 kg / s
0.00
2.26
3.62
5.80
5.80
3.62
6.88
α, %
8.05
10.56
15.59
23.64
31.68
36.71
41.24
Mix 4
 *105 kg / s
0.00
2.31
7.64
5.56
4.51
4.17
5.21
3.47
1.39
Mix 6
 *105 kg / s
2.59
4.66
5.69
5.18
3.11
3.11
2.59
α, %
5.97
8.96
14.43
18.41
24.88
30.85
38.31
43.29
45.28
α, %
6.89
7.51
13.15
20.04
26.30
30.06
33.81
Mathematical Models
Kinetic characteristics of waste products reduction can be well described with
mathematical models. At the present work have been used two methods for
mathematical models inventing – regression analysis and splain-approximation.
The regression analysis is not too precise method because the curves do not pass
through every points of the model. By use of splain-approximation method curves
pass through every point. On one hand this method is more precise on the other it
2-58
does not give any information about mistake which has been received by
mathematical models inventing. Dispersion was detected with regression analysis.
The most small remainder sum of dispersion was the factor choosing appropriate
models. It was been used because the temperature was one of the indicators in
comparison of changing components. To obtain mathematical models the
experimental data were processing in the shell of Matlab.
At the present investigation was shown mathematical treatment of the third mixture. It
was chosen because it contains the waste products from the third basic metallurgical
productions (blast furnace, converter and electric arc furnace).
Splain-Approximation
Predicted value of splain-approximation of mass (m,g) dependent on temperature
(T,K) for mixture 3 is shown on Fig. 1, predicted value of splain-approximation of
velocity (v*10-5, kg/s ) dependent on temperature(T,K) is shown on Fig.2 and
predicted value of splain-approximation of degree of reduction (, % ) dependent on
temperature(T,K) is shown on Fig. 3.
6
0.09
0.08
0.07
4

0.03
0.02
0.01
600
v*10-5, kg/s

0.04

700
800
900
1000
1100
1200
1300


3


2

1
0
-1
600

700
800
900
1000
1100
1200
data
data
Fig. 2. Velocity (v*10-5, kg/s) as a
function of temperature (К)
Fig. 1. Mass (m, g) as a function of
temperature (К)
45

40


35
30

25
20

15

10
5
600
700
1300
Temperature,cubic
K spline
Temperature,
K
cubic spline
α, %
m, g
0.06
0.05

5


800
900
1000
1100
1200
1300
Temperature, K
cubic spline
Fig. 3. Degree of reduction (α,
%) as a function of
data
temperature (К)
Regression Analysis of Mathematical Models
For description of kinetic characteristic were invented regression models from first to
fifth power. Predicted value of regression model of mass (m, g) dependent on
temperature (T, K) for mixture 3 is shown on Fig. 4.
The model equation from first power is as follows Y1=b1(1)+b1(2)*x(i)
The
model
equation
from
second
power
is
as
follows
Y2=b2(1)+b2(2)*x(i)+b2(3)*x(i)^2, and it is shown on Fig. 5.
2-59
The
model
equation
from
third
power
is
as
follows
Y3=b3(1)+b3(2)*x(i)+b3(3)*x(i)^2+b3(4)*x(i)^3, and it is shown on Fig. 6.
The model equation from fourth power is as follows Y4=b4 (1)+b4 (2)*x(i)+b4
(3)*x(i)^2+b4 (4)*x(i)^3+b4 (5)*x(i)^4, and it is shown on Fig. 7.
The model equation from fifth power is as follows
Y5 = b5(1)+b5(2)*x(i)+b5(3)*x(i)^2+b5(4)*x(i)^3+b5(5)*x(i)^4+b5(6)*x(i)^5, and it is
shown on Fig. 8.
The regression coefficients and dispersion (S) from first to fifth power for a function
m  f (T ) are shown in Table 3.
Table 3. Models regression coefficients for a function m  f (T ) .
Coeffi
cients.
b(1)
Mixture 3
3 power
1 power
2 power
-7.072994
0375*10^-2
-6.00027
49482*10^-2
b(3)
1.210817
72*10^-4
-
b(4)
-
9.8303329
*10^-5
1.1611
*10^-8
-
b(5)
-
b(6)
S
0.1272
5 power
45.9778
072952*10^-2
50.283920
4065*10^-2
-77.03180
18671*10^-2
-
-1.56362
9438 *10^-3
1.740
088*10^-6
-5.86
*10^-10
-
-1.7475
39124*10^-3
2.0297
78*10^-6
-7.85
*10^-10
0.5
*10^-14
0.1565
0.0130
0.0194
5.06521
6948*10^-3
-1.2374
649*10^-5
1.4260
*10^-8
-0.8
*10^-11
0.0
0.0375
m, g
m, g
b(2)
4 power
Temperature, K
Temperature, K
Fig. 5. Model from second power for
a function m  f (T )
0.09
0.09
0.08
0.08
0.07
0.07
0.06
0.06
0.05
0.05
m, g
m, g
Fig. 4. Model from first power for
a function m  f (T )
0.04
0.04
0.03
0.03
0.02
0.02
0.01
600
700
800
900
1000
1100
1200
1300
0.01
600
700
800
900
1000
1100
1200
1300
Temperature, K
Temperature, K
Fig. 6. Model from third power for a
function m  f (T )
2-60
Fig. 7. Model from fourth power for
a function m  f (T )
0.09
0.08
0.07
m, g
0.06
0.05
0.04
0.03
0.02
0.01
600
700
800
900
1000
1100
1200
1300
Temperature, K
Fig. 8. Model from fourth power for a
function m  f (T )
Predicted value of regression analysis of velocity (  *10-5, kg/s) dependent on
temperature (T, K) for mixture 3 is shown on Fig. 9.
The model equation from first power is as follows Y1=b1 (1) +b1 (2)*x(i)
The model equation from second power is Y2=b2(1)+b2(2)*x(i)+b2(3)*x(i)^2, and it is
shown on Fig. 10.
The model equation from third power is Y3= b3(1)+b3(2) *x(i)+b3(3)*x(i)^2 +b3(4)*
x(i)^3, and it is shown on Fig. 11.
The model equation from fourth power is Y4=b4 (1)+b4 (2)*x(i)+b4 (3)*x(i)^2+b4
(4)*x(i)^3+b4 (5)*x(i)^4, and it is shown on Fig. 12.
The model equation from fifth power is
Y5 = b5(1)+b5(2)*x(i)+b5(3)*x(i)^2+b5(4)*x(i)^3+b5(5)*x(i)^4+b5(6)*x(i)^5, and it is
shown on Fig. 13.
The regression coefficients and dispersion (S) from first to fifth power for function
.10 5  f (T ) is shown in Table 4.
Table 4. Models regression coefficients for function .10 5  f (T ) .
Coeffi
cients.
b(1)
Mixture 3
3 power
1 power
2 power
b(3)
-1.512332
623509
4.322402
0443*10^-3
-
b(4)
-
-39.51494
9709620
8.501831
1552*10^-2
-4.11303
78*10^-5
-
b(5)
-
-
-7.458701
224916
-1.747744
7130*10^-2
6.546940
58*10^-5
-3.61
22*10^-8
-
b(6)
-
-
-
S
2.7898
0.4053
0.4660
b(2)
2-61
4 power
5 power
2.1874058
81394e+002
-0.009835
514725e+002
0.000015
872022e+002
-0.000000
010844e+002
0.000000000
0027e+002
-8.162337
586388e+002
0.045546
708582e+002
-0.000101
224375e+002
0.000000
111458e+002
-0.000000
000060e+002
0.0000000
0000001e+002
1.0568
0.5743
v*10-5, kg/s
v*10-5, kg/s
Temperature, K
Temperature, K
Fig. 9. Model from first power for a
function .105  f (T )
Fig. 10. Model from second power for
a function .10 5  f (T )
6
v*10-5, kg/s
v*10-5, kg/s
5
4
3
2
1
0
-1
600
700
Temperature, K
800
900
1000
1100
1200
Fig. 12. Model from fourth power for
a function .105  f (T )
Fig. 11. Model from third power for a
function .105  f (T )
6
5
v*10-5, kg/s
1300
Temperature, K
4
3
2
1
0
-1
600
700
800
900
1000
1100
1200
1300
Temperature, K
Fig. 13. Model from first power for a
function .10 5  f (T )
Predicted value of regression analysis of velocity (, %) dependent on temperature
(T, K) for mixture 3 is shown on Fig. 14.
The model equation from first power is Y1=b1 (1) +b1 (2)*x(i)
The model equation from second power is Y2=b2(1)+b2(2)*x(i)+b2(3)*x(i)^2, and it is
shown on Fig. 15.
The model equation from third power is Y3=b3(1)+b3(2)*x(i)+ b3(3)*x(i)^2+b3(4)
*x(i)^3, and it is shown on Fig. 16.
The model equation from fourth power is Y4=b4 (1)+b4 (2)*x(i)+b4 (3)*x(i)^2+b4
(4)*x(i)^3+b4 (5)*x(i)^4, and it is shown on Fig. 17.
The model equation from fifth power is Y5 =b5(1)+b5(2)*x(i)+b5(3) *x(i)^2+ b5(4)
*x(i)^3+b5(5)*x(i)^4+b5(6)*x(i)^5, and it is shown on Fig. 18.
The regression coefficients and dispersion (S) from first to fifth power for function
  f (T ) is shown in Table 5.
2-62
Table 5. Models regression coefficients for function
Mixture 3
Coeffic
1 power
2 power
3 power
ients.
b(1)
-37.66231 -31.97547 2.44734113
6439523
9639935
2462e+002
b(2)
0.06447
0.052397 -0.0083234
3168654
5669470 600094e+002
b(3)
6.15488
0.00000926
52*10^-6
3244e+002
b(4)
-0.0000000
03118e+002
b(5)
-
  f (T )
4 power
5 power
-4.226653
086562e+002
0.0276402
29407e+002
-0.0000673
10293e+002
0.000000
077415e+002
-0.000000
000042e+002
0.00000000
000001e+002
1.0697
-
-
S
3.6060
4.4385
0.3711
0.5553
α, %
-
α, %
b(6)
2.6794012
44329e+002
-0.009314
565008e+002
0.0000108
24405e+002
-0.000000
004193e+002
0.0000000
0000027e+002
-
Temperature, K
Temperature, K
Fig. 14. Model from first power for
a function   f (T )
Fig. 15. Model from second power for
a function   f (T )
45
40
35
35
30
30
α, %
40
25
20
15
10
5
600
25
20
15
10
700
800
900
1000
1100
1200
5
600
1300
Temperature, K
700
800
900
1100
1200
1300
Fig. 17. Model from fourth power for
a function   f (T )
45
40
35
30
25
20
15
10
5
600
1000
Temperature,
K
Temperature,
K
Fig. 16. Model from third power for
a function   f (T )
α, %
α, %
45
700
800
900
1000
1100
1200
1300
Temperature, K
Fig. 18. Model from fifth power for
a function   f (T )
2-63
CONCLUSION
1. The highest degree to reduction was achieved at steelmaking waste from
“Stomana Industry”JSco reduction at temperatures between 1273 К and 1423
К and reductive agent quantity twice more then stoichiometric.
2. From the investigated charges, the first one (converter slurry-88 % and a fine
coke 12 %), the highest degrees of reduction was obtained. The degrees of
reduction of charges 2 and 3 are lower and approximately equal. Adding to
electric arc steelmaking (EAF) dusts in mixture 3 doesn't influence materially
on the degree of reduction.
3. By comparison with kinetic curves for the different waste products mixtures of
“Kremikovtzi” JSco it is found out that the reducing processes of the mixture
only with converter waste run with highest velocity, while in mixtures with
wastes and from another productions (blast furnace as well EAF) the process
is quite slowly. The velocity of mixture 3 is  = 5, 26. 10-5kg/s.
4. The obtained experimental data of the mixture 3 are processed mathematically
with regression analysis. It was found out that the model of third power with
dispersion S = 0.0130 is the best for a function m  f (T ) , the model of second
power with dispersion S = 0.4053 is the best for a function .105  f (T ) and
the model of third power with dispersion S = 0.3711 is the best for a
function   f (T ) .
REFERENCES
1. Paunova R., M. Marinov, D. Grigorova: ‘Thermodynamics and Kinetics study of
the waste emission of steelmaking production of “Stomana-Factory”AD, Bulgaria’,
4th Balkan Conference on Metallurgy, Zlatibor, Serbia, 2006, p 361 – 367
2. Paunova R.: ‘Thermodynamics study of reduction of titanium magnetite
concentrate with solid carbon’, Metallurgical and Materials Transaction B, 33B, 4,
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