UDK 669.186:54-145.55 Professional article/Strokovni članek
ISSN 1580-2949 MTAEC9, 46(6)683(2012)
RELATIONSHIP BETWEEN THE CALCULATED OXYGEN ACTIVITY AND THE SULFUR PARTITION RATIO FOR CaO-Al2O3-SiO2-MgO SLAG DURING LADLE
REFINING
RAZMERJE MED IZRAČUNANO AKTIVNOSTJO KISIKA IN
DELEŽEM PORAZDELITVE ŽVEPLA V ŽLINDRI CaO-Al2O3-SiO2-MgO MED RAFINACIJO V LIVNEM LONCU
Zoran Slovic1, Karlo T. Raic2, Ljubomir Nedeljkovic2, Tatjana Volkov-Husovic2
!The Key-to-Metals, d. o. o., Zrenjaninski put 13P, 11000 Belgrade, Serbia 2University of Belgrade, Faculty of Technology and Metallurgy, Department of Metallurgical Engineering, Karnegieva 4, 11120 Belgrade, Serbia zslovicsd@gmail.com, karlo@tmf.bg.ac.rs
Prejem rokopisa — received: 2012-03-26; sprejem za objavo - accepted for publication: 2012-07-23
A slag-metal equilibrium study was carried out to investigate the effect of oxygen activity on the sulfur partition for CaO-Al2O3-SiO2-MgO slag. The sulfide capacity Cs prediction models by Sosinsky-Sommerville based on the optical basicity A and the KTH model in terms of the defined interaction coefficient of the component i to j £ 'I-ieractlon is used in this work for both a comparison and an estimation of the sulfur partition ratio between ladle-treated slag and liquid steel. From the obtained results, it was shown that the Sosinsky-Sommerville optical basicity approach gives higher values for the sulfur partition ratio (Ls) compared with the KTH model.
Keywords: sulfide capacity, sulfur partition ratio, oxygen activity, optical basicity, KTH model
Opravljena je bila raziskava učinka aktivnosti kisika na razporeditev žvepla v žlindri CaO-Al2O3-SiO2-MgO. V tem delu sta bila uporabljena model Sosinsky-Sommerville za napovedovanje kapacitete sulfida Cs, ki temelji na optični bazičnosti A, ter model KTH definiranega interakcijskega koeficienta komponent od i do j £'I-ieractlon tako za primerjavo kot tudi za določanje deleža porazdelitve žvepla med žlindro v loncu in jeklom. Iz dobljenih rezultatov izhaja, da Sosinsky-Sommervillov približek optične bazičnosti daje v primerjavi z modelom KTH višje vrednosti za delež razporeditve žvepla (Ls). Ključne besede: zmogljivost sulfida, delež porazdelitve žvepla, aktivnost kisika, optična bazičnost, model KTH
1 INTRODUCTION
Over the past few decades the sulfur level in steel has been improved enormously. Therefore, the more intensive development industries, such as automotive and pipelines for the transportation of gas and oil, require good control of the sulfur level in steel products.1 Due to these facts, close control of the sulfur level is essential for the production of good-quality steel. One of the main subjects when investigating the slag/metal interface is the behavior of the oxygen in the liquid steel.2 The state of oxidation of a bath is of vital importance in controlling the reactions between the slag and the metal in steelmaking. It influences both the metal losses in the slag and the quality of the produced steel.3 The present paper is focused on predicting the oxygen activities calculated using the sulfur equilibrium between the top slag and the steel.
1.1 Sulfide capacity models
The concept of sulfide capacity was proposed by Finchman and Richardson,4 and it was defined as:
Cs=(%S)(Po2/Ps2)1/2	(1)
The sulfide capacity is a property of the slag that is dependent only on the temperature and the slag's composition. The sulfide capacity can be used to describe the potential ability of an arbitrary homogeneous molten slag to remove sulfur and to compare the desulfurization characteristics of different slags.
The slag desulfurization capacity in the system slag-metal may be expressed as the slag sulfide capacity:5
[S] + (O2) = (S2-) + [O]	(2)
Some authors have preferred to define it with reference to the slag metal reaction, in which case the definition becomes:6
C's = (%S)[flo]/[fls]	(3)
Using Turkdogan's formulation7 the relation between Csand Cs' can be written as C's = (%S)[flo]/[fls], where Cs' can be converted to Cs using the relationship:
Cs= C's/Kos	(4)
The equilibrium constant Kos for the above equation
is:
lg Kos= - 935/T + 1.375	(5)
1.2 Calculation of the activity of oxygen in the slag
and the steel
It is well known that control of the desulfurization process is impossible if the oxygen activity is not known. When the steel is deoxidised with aluminum and silicon, the reactions deciding the oxygen content are the Al/O/AlaOs and the Si/O/SiOa equilibrium. Table 1 summarizes the chemical reactions used in this work that take part in the deoxidation of the steel melt, in the slag-melt equilibrium during ladle treatment, their mole free-energy changes in the standard state, as well as their reaction constants.
Also, the Ohta and Suito8 expressions were used to calculate the AI2O3 and the SiO2 activities in the slag, while Wagner's expressions9 in equations (6,7) were used to calculate the alumina [a]Ai and silicon [a]si activities in the steel. All the used oxides are in weight percent.
The activity coefficients of the elements in the metal are calculated by using Wagner's equation,9 as follows:
ig/i = 2 (ej [% ;])
(6)
where:
ei - interaction coefficient of j on i f - Henry's activity coefficient for the species i in the metal
From equation 6, the a activity of element i in the steel can be calculated as:
a = /i [%i ] (i = Si, Ai, S)
(7)
The interaction coefficients used in this work are as follows:
esS = (-0.153 + 233/7), esC = 0.113, esSi = 0.063, esAl = 0.035, esMn = - 0.026, ¿aia1 = (0.011+63/7), eAiC = 0.091, eAiSi = 0.056, eAiS = 0.030, esiC = 0.18, esiSi = (0.089+34.5/T), esiS = 0.056, esiAl = 0.058, and esiMn = 0.002.10-12
From the equations of the equilibrium constants given in Table 1, it was possible to derive an expression for the oxygen activity:
(8)
ag0 - RT
The sulfur partition ratio between the slag and the metal may be expressed by combining equations (4) to (9) as follows:13
lg Ls = - 935/7 + 1.375 + lg Cs+ lg /s - lg [a0] (10) where:
Cs - sulphide capacity
LS - sulfur partition between the slag and the metal,
Ls = (%S)/[%S] [ao][as] - oxygen and sulfur activity in the molten metal, [%S] - sulfur weight percent in the steel (%S) - sulfur weight percent in the slag
1.3 Optical basicity concept
The optical basicity of the molten slag can be calculated using the following relationships: 14
n
a = XA Ni
N =■
Xn 0 i
1LXš
(ii)
(12)
where:
A - optical basicity of the slag
A; - optical basicity value of the component "i"
Ni - compositional fraction
X; - mole fraction of component "i" in the slag
no; - number of oxygen atoms in the component "i"
Sosinsky and Sommerville (S-S)15 derived the following empirical correlation between the optical basicity, the temperature and the sulfide capacity of the slag at temperatures between 1400 °C and 1700 °C:
lg C s =-
22690-54640A
-+43.6A- 25.2
(13)
The values of the optical basicity for the common steelmaking oxides used in this work have been taken from the literature.16
Table 1: Thermodynamic data on chemical reactions taking place in deoxidation, and slag-metal equilibrium Tabela 1: Termodinamski podatki o kemijskih reakcijah, ki potekajo med dezoksidacijo pri ravnotežju žlindra-kovina
a
SiO
a O =
=1
a
Al i O
a O 3
Chemical reactions	Mole free energy changes, AG° (J/mol)	Constants, K = exp(-AG°/RT)
2[Al]+3[O]= (A2O3)	AG0 = -1205115 + 386.7T 13	aA2°3 3 (Eq.8) [ aAl r[ aO]
[Si]+2[O] = (SiO2)	AG S; = -581900 + 221.8T 10	r ]Sl[O2 ]2 (Eq.9) [ a Si ] [ aO ]
lg aAl2O3 = {-0.275( %CaO) + 0.167 (%MgO)}/(%SiO2)+0.033(Al2O3) - 1.560 8		
lg aSiO2 = 0.036(%MgO)+0.061(Al2O3)+0.123(%SiO2) - (%SiO2)/(%CaO) - 6.456 8		
1.4 The KTH model
2 EXPERIMENTAL
The KTH model was developed by the Department of Metallurgy in the Royal Institute of Technology (Sweden).17 According to the definition of the sulfide capacity, Cs can be expressed as:
C s = exp
-AG0 Vao2-
RT Ä fs2-
= exp
/-AG0 ^ RT
exp| RT I (14)
where ßo2- is the activity of the oxygen ions in the slag, /s2- is the activity coefficient of the sulfide ions in the slag, R is the gas constant, T is the temperature in K, and AG is the standard Gibbs energy change. In the model, the ratio of the activity of O2- to the activity coefficient of S2-, ao2-//s2- is expressed as
fs =
-= eXP
RT
(15)
In the case of unary systems, £ is a function of the temperature only. However, in a multicomponent system, £ is described as a function of both the temperature and the composition:
£ = 2(X £ + ^x)
(16)
where the subscript i denotes the component i, Xi is the mole fraction of this component, £i is expressed as a linear function of the temperature for each component in the slag in the absence of an interaction between the different species, £mix is the mutual interaction between the different species.
According to the model,17 the sulfide capacities of the six-component slags can be expressed as follows:
RT(lnCs) = 58.8157T - 118535 - {XA
157705.28 -
XCaO ■ 33099.43 + XMgO ■ 9573.07 - XMnO ■ 36626.46 +
X	168872 59} {£ Al2O3-CaO + £ A12O3-SiO2+£ A12O3-MnO
XSiO2 ' i600/2.59} - t£ Interaction +£ Interaction +£ Interaction £ CaO - SiO2 +£ MgO - SiO2 + £ MnO - SiO2 +£ CaO - FeO +£ MnO - FeO +
Interaction Interaction	Interaction	Interaction Interaction
£ FeO-SiO2 +£ A12O3 - CaO -MgO +£ A12O3 - CaO - SiO2 +£ A12O3-MgO-SiO2 +
Interaction Interaction	Interaction	Interaction
£ A12O3-MgO-MnO +£ A12O3 - MnO - SiO2 +£ CaO -MgO-SiO2 +
Interaction	Interaction	Interaction
£ CaO -MnO- SiO2 +£ CaO - MnO - SiO2 +£ MgO - MnO - SiO2 +£ A12O3 - FeO - SiO2
Interaction	Interaction	Interaction	Interaction
+£ MgO-FeO-SiO2 +£ MnO-FeO-SiO2 }	(17)
Interaction	Interaction
A1though the KTH mode1 is va1id for the atmo-sphere-s1ag interaction, in this paper it wi11 be used to compare the va1ues of Cs.
The plant data of 12 heats of low-carbon, Al-Si killed steel from the Dillinger Hütte Steel-plant in Dillingen, Germany, taken after the vacuum-degassing operation in the ladle-refining process, were used in this study. The liquid steel samples were taken using an automatic sampling system, while the slag samples were manually collected with a spoon and subjected to a chemical analysis. Because the oxygen analyses of the steel samples were not available, a logical way to estimate the oxygen levels in the steel bath was to estimate the activities of the ALO3 and SiÜ2 in the slag by thermo-dynamic calculations from the contents obtained by sampling and chemical analysis, and use them to estimate the oxygen potential in the steel bath, assuming a slag/metal equilibrium.18
3 RESULTS AND DISCUSSION
The average chemical compositions of the analyzed metal and slag phases are summarized in Table 2.
The optical basicity for all the analyzed slags was in the narrow range A = 0.77-0.79.
3.1 Comparison of the sulfide capacity results
In this work, we applied equations (3) to (7) in order to calculate the measured values of the sulfide capacity with the calculated oxygen activity [a<,] in the steel according to Eq. (8) (subsequently called Case A) and Eq. (9) (subsequently called Case B). Then the results were compared with the calculated values of the sulfide capacity by Sosinsky-Sommerville (S-S) and the KTH model. Table 3 shows the calculated values of optical basicity, the measured and calculated values of the sulfide capacity, the oxygen activities [flo] in the steel and alumina ß(Al2O3) and the silica ß(SiO2) activities in the slag for the analysed heats. As can be seen in Table 3, the calculated values for the alumina activities ß(Al2O3) are generally very low, i.e., below mass fractions w = 10 3 % and 10-4 % and sometimes even lower than w = 10-5 %. Comparatively, in the case of the calculated values of the silica activities ß(SiO2) after the VD treatment, the calculated values of the silicon activity in the slag are stable at the level of w = 10-4 % which corresponds to a SiO2 content of a few per cent. This is in accordance with the published results. 19
Table 2: Chemical composition of analysed metal and slag Tabela 2: Kemijska sestava analizirane kovine in žlindre
a
O
w/%	C	Si	Mn	S	Al	T [K]
Average	0.10	0.35	1.51	0.0004	0.027	1855
Range	0.03-0.18	0.22-0.46	1.37-1.61	0.0002-0.0005	0.011-0.037	1838-1869
w/%	CaO	SiO2	MgO	S	Al2O3	
Average	54.64	4.38	7.46	0.70	30.64	
Range	52.49-57.00	2.38-8.20	4.10-12.16	0.46-1.03	27.51-34.38	
Table 3: The calculated optical basicity, oxygen activities [ao] in steel and alumina a(Al2O3) and silica a(SiO2) activities in slag for analysed heats
Tabela 3: Izračunana optična bazičnost, aktivnosti kisika [ao] v jeklu ter aktivnosti aluminijevega oksida O(ai203) in silike a(siO2) v žlindri analiziranih talin
Heats	A	a(Al2O3)	a(SiO2)	[ao]Al,[%]	[ao]Si,[%]
1	0.78	0.000442	0.000198	2.16E-05	7.74E-05
2	0.78	0.003583	0.000247	7.34E-05	9.84E-05
3	0.77	0.000044	0.000157	9.27E-06	9.08E-05
4	0.78	0.000007	0.000175	5.68E-06	1.04E-04
5	0.78	0.000012	0.000194	5.01E-06	7.94E-05
6	0.77	0.000150	0.000220	2.03E-05	1.22E-04
7	0.78	0.000222	0.000174	1.24E-05	6.37E-05
8	0.79	0.000616	0.000151	1.92E-05	7.58E-05
9	0.78	0.000446	0.000180	3.29E-05	1.05E-04
10	0.79	0.000060	0.000148	8.77E-06	5.86E-05
11	0.78	0.000249	0.000206	1.54E-05	7.72E-05
12	0.79	0.000024	0.000127	1.25E-05	9.27E-05
Also, it can be seen from the results in Table 3 that the changes in the obtained values of the sulfide capacities at the end of ladle treatment were relatively small for the S-S model and the measured values derived by a calculation of the sulfide capacities from a prediction of the oxygen activity [«ok (Case B) and the KTH model results compared with those derived by the calculation of the sulfide capacities by a prediction of oxygen activity [fljAl (Case A). Moreover, the obtained values of the sulfide capacities of the analyzed slags are in good agreement with earlier published results.20
3.2 Comparison of the sulfur distribution ratio
The slag-metal sulfur distribution ratio Ls after desulphurization is another important parameter in the modeling of sulfur removal in steel making. In this work
Table 4: The values of sulfur partition ratio for different calculated oxygen activities [ao] and lg Cs calculated by Sosinsky-Sommerville (S-S) and KTH models
Tabela 4: Vrednosti deleža porazdelitve žvepla za različne izračunane aktivnosti kisika [ao] in lg Cs, izračunanim s Sosinsky-Sommerville (S-S) modelom in modeli KTH
Heats	j msr L S	j calc L S			
		Case A (S-S)	Case B (S-S)	Case A (KTH)	Case B (KTH)
1	3290	3940	1100	1945	543
2	2967	964	719	801	597
3	2233	8373	854	7454	760
4	1867	19479	1067	7491	410
5	1723	16515	1043	7049	445
6	1527	3463	579	1555	260
7	2060	7104	1381	3723	724
8	1984	5343	1353	3766	954
9	1520	2865	897	1813	567
10	1430	9991	1493	5356	801
11	1228	5263	1048	2066	411
12	1094	11944	1614	5167	698
the predicted values of lg Ls were calculated using equation (8), suggested by M. T. Andersson et al. 13 For the purpose of a comparison, the sulfide capacity was also calculated using the Sosinsky-Sommerville (S-S) approach based on the optical basicity concept according to he original parameters, as well as the KTH model. Then, the results were compared with the calculated values of the sulfur distribution ratio with the calculated oxygen activity [Ao]ai (Case A) and the oxygen activity [ao]Si (Case B).
The comparison of the calculation determined sulfur distribution ratio LcSalc using both cases with the measured LS" is shown in Table 4 and Figures 1 and 2.
As can be seen from Table 4 and Figures 1 and 2, both models generally exhibit higher discrepancy for the values of Ls in Case B compared with the results obtained in Case A. Also, it is evident that the correlation between the measured LmSsr and the calculated values of the sulfur distribution ratios LcSalc are more or less scattered. In contrast, it is clear that the predictions with the KTH model agree well with the measured results in Case A. The optical basicity concept, which is represented here by the Sosinsky-Sommerville (S-S) model, gives much higher predicted values. This is in good agreement with earlier published results.21
The exceptions are the results obtained when the oxygen activity data is used in the metal phase [ao]Si (Case B). It is obvious that the data points show larger scattering, but both models give better Ls prediction compared with Case A.
Based on thermodynamic calculations, it can be summarised that the equilibrium state was possibly not
Table 5: The differences between measured LI" and calculated values of sulfur partition ratio LcSalc for different calculated oxygen activities [ao] and lg Cs calculated by Sosinsky-Sommerville (S-S) and KTH models
Tabela 5: Razlike med izmerjenimi L!" in izračunanim deležem porazdelitve žvepla LcS"lc za različne izračunane aktivnosti kisika [ao] in lg Cs, izračunanim s Sosinsky-Sommerville (S-S) in modeli KTH
Heats	ALs CasesA (S_S)	ALs CasesB (S-S)	ALS Case A (KTH)	ALs CasesB (KTH)
1	-650	2190	1345	2747
2	2002	2247	2166	2370
3	-6140	1379	-5220	1473
4	-17613	800	-5624	1456
5	-14792	680	-5326	1278
6	-1936	948	-29	1267
7	-5044	679	-1663	1336
8	-3359	631	-1782	1030
9	-1345	623	-293	953
10	-8561	-63	-3926	629
11	-4035	180	-838	817
12	-10850	-520	-4073	396
Case A Case B :
rmsr _ rcalc [ao]Al " L S L S
■ jmsr _ Lcalc [ao]Si
' L S L S
Figure 1: Comparison of the relationship between measured and calculated sulfur partition ratio Ls for the different calculated values of lg Cs (S-S and KTH) and [«oJai oxygen activities Slika 1: Primerjava odvisnosti med izmerjenimi in izračunanimi vrednostmi deleža porazdelitve žvepla Ls za različne izračunane vrednosti lg Cs (S-S in KTH) in aktivnostjo kisika [aqJai
Figure 2: Comparison of the relationship between measured and calculated sulfur partition ratio Ls for the different calculated values of lg Cs (S-S and KTH) and [aQ]Si oxygen activities Slika 2: Primerjava odvisnosti med izmerjenimi in izračunanimi vrednostmi deleža porazdelitve žvepla Ls za različne izračunane vrednosti lg Cs (S-S in KTH) in aktivnostjo kisika [flota
obtained, since the vacuum degassing time for all the heats was almost the same.
Table 5 shows the differences between the measured and calculated values of the sulfur partition ratio ALS for the analysed cases. The "-" means that the calculated values of Ls are higher than the measured values.
It is clear that in Case A both models give calculated values that are higher than the measured values for almost all the analyzed heats. One possible reason for the increased deviation between the measured and calculated values of the sulfur distribution ratio Ls could be the fact that using the well-known Ohta and Suito equations8 to calculate the alumina activity might not be appropriate for the slags whose silica content was too far away from
the specified lower limit of w = 10 %. The second reason could be the relatively small number of analysed samples.
4 CONCLUSIONS
1.	The equilibrium sulfur partition ratio, calculated by considering the reaction 2[Al] + 3[O] = (A^Os) in equilibrium for the calculation of the oxygen activity in the steel during ladle treatment, was much higher compared with the reaction [Si] + 2[O] = (SiO2) with the measured sulfur partition ratio.
2.	The Sosinsky-Sommerville optical basicity model gives higher values of the sulfur partition ratio Ls compared with the KTH model.
3.	The possible reason for the increased deviation between the measured and the calculated values of sulfur partition ratio Ls was that the use of the well-known Ohta-Suito equations to calculate the alumina activity might not be appropriate for the slags whose silica content was too far away from the specified lower limit of w = 10 %.
4.	The KTH model is an applicable tool to predict the sulfur partition ratio Ls.
Acknowledgements
The authors would like to thank Dillinger Hüttenwerke AG for their permission to publish this research. The authors are particularly grateful to Prof. Dr. N. Bannenberg and Dr. H. Lachmund for valuable discussions and for their constant support.
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