1. Experimental and mathematical modeling studies on primary hot metal desulfurization February 20, Tero Vuolio Research Unit of Process Metallurgy University of Oulu

2. Tero Vuolio Doctoral Student in the Process Metallurgy Research Unit (10/2017 –)
Educational background:
M.Sc. (Tech.) in Process Engineering
Year of enrolment 2013
Graduated in 2017
Previous working history in metallurgical industry:
SSAB Europe Oy at Raahe (5/2016 – 9/2017)
Outokumpu Oy at Tornio (5/2014 – 8/2014 & 5/2015 – 8/2015)
Tero Vuolio

3. A brief introduction to HMD
Tero Vuolio

4. Hot metal desulfurization
The purpose of hot metal desulfurization is to extract sulfur from hot metal to the top-slag
Due to the fact the desulfurization demands reductive conditions, the hot metal desulfurization is most efficient to be carried out prior to converter process
Powder injection tehnique
A more or less standardized method to conduct hot metal desulfurization is a so-called powder injection tehnique
In powder injection, a typically fine-grade reagent is injected into hot metal via immersed lance
Suitable desulfurization reagents include lime*, calcium carbide, magnesium, soda ash*, limestone*
(*This study handles)
Fig. 1 – Phenomena in a hot metal ladle during the hot metal desulfurization via powder injection (Visuri et al. 2018).
Tero Vuolio

5. i) Transitory contact reaction (Reagent-metal)
The powder injection based hot metal desulfurization constitutes of two main reactions, which are:
i) Transitory contact reaction (Reagent-metal)
ii) Permanent contact reaction (Top slag-metal)
Fig. 2 – Diffusion of calcium and sulfur ions in CaS-layer (Oeters 1994).
Tero Vuolio

6. Main research topics
Experimental studies on kinetics of resulfurization (Sulfur pick- up)
The objective of work is to study the kinetics of resulfurization
The resulfurization occurs via permanent phase contact. Sulfur is transferred from slag to metal phase.
A fundamental question to be answered is that does a resulfurization of hot metal occur during the transferring of hot metal ladles?
Is the phenomenon relevant in the view point of steel manufacture?
Mathematical modeling studies on primary hot metal desulfurization
The scope of the work is to create a prediction model with an adequate prediction performance
The effect of particle size distribution on the kinetics of hot metal desulfurization is of great importance
The modeling is conducted is based on the combination of mass-transfer theory and data- driven modelling techniques
Tero Vuolio

7. Resulfurization (= Sulfur pick-up)

8. Aspects on Resulfurization
The resulfurization of hot metal can occur in various stages through permanent phase contact (= Sulfur is transferred from slag to metal phase)
The resulfurization is assumedly controlled by mass-transfer in the slag-metal interface (1st order kinetics)
The sulfur capacity of top-slag determines the sulfur distribution between slag and metal
Thus, the magnitude of the thermodynamic driving force is determined by the properties of slag
In high temperatures, the basicity of the top-slag ( 𝑩 2 ) can be considered to significantly increase the sulfur distribution
However, as the primary desulfurization operates in relatively low temperatures, the top-slag constitutes mainly of unsoluted lime particles (Not Ca 2+ ), and thus the high basicity is not realized as an increased sulfide capacity
Fig. 3 – Possible occurrence of resulfurization during the processing of hot metal.
Tero Vuolio

9. Experimental setting - The main independent variable is the Na 2 O-content of top-slag - Argon atmosphere - Constant temperature - Constant sulfur content in both phases To evaluate the generalizability to a full-scale process, the dimensional homogeneity is determined for experiments: Hot metal = g Slag = 6.78 g [S] = p-% (S) = 3.5 p-% T = ͦC
Slag
CaO (%)
Na2O (%)
SiO2 (%)
CaS (%)
CaO/SiO2
(Na2O+CaO)/SiO2
Na2O/SiO2
Exp. 1
77,00
0,00
15,10
7,87
5,10
Exp. 2
74,32
3,20
14,57
5,32
0,22
Exp. 3
71,72
6,30
14,06
5,55
0,45
Exp. 4
68,60
10,10
13,45
5,85
0,75
Tero Vuolio

10. Preparation of the slag phase
The slag phase was prepared in a chamber furnace by applying a following heating sequence:
Temperature rate of change ͦC/h
Maximum temperature ͦC/h
Holding time 2 h
Initial compounds:
CaO (> 99.9 %)
CaS (> 97 %)
Na 2 C O 3 (> 99.9 %)
SiO 2 (> 99.7 %)
Fig. 4 – Slag phase after thermal pre-treatment.
Tero Vuolio

11. Experimental setting Argon atmosphere Constant temperature
Test sequence is as follows:
Hot metal phase is melted
Temperature of the system is decreased to ͦC
Initial sample at ”t = 0”
Slag phase is set on the hot metal phase
The sampling of hot metal is conducted in every 5 minutes during the time period of 0-20 min, and in every ten minutes during the rest of the experiment
Overall duration of the experiment is 120 min
Fig. 5– A schematic illustration of the applied apparatus.
Tero Vuolio

12. - The rate constant for resulfurization is solved by means of least-squares (Crucible) - OBS! The following curves have been determined for average rate constant! - The resulfurization curve for a full-scale process is determined by applying the dimensional homogeneity - The modeling results have to be validated in industrial scale
Repetition
Test-series
k (1/s)
Sum of squares
Ls (t90)
Na2O 1 2
0,0050
0,8
151,5
3,2
0,03
137,7 3
0,0040
0,02
192,6
avg
0,0046
160,6 4
0,0027
0,05
235,4
10,1
0,0018
0,06
253,1 -
0,0022
244,3
Ladle
Crucible
Fig. 6 – Evolution of sulfur content of the metal phase.

13. A prediction model for hot metal desulfurization

14. A short description:
A scope of the work is to create a prediction model with an adequate prediction performance for end sulfur content in hot metal
The effect of particle size distribution on the kinetics of the transitory reaction is of great importance
The model has to be suitable for on-line use
A main problematique is related to complexity of certain phenomena occuring in the hot metal ladle
The uncertainties in the system identification are mainly related to interfacial area between the emulsified reagent particles and the hot metal phase
The end sulfur content is solved analytically by applying a so-called ”surface area approximation”
Surface area approximation is based on the solid surface area that is available for extraction of sulfur via the injected reagent particles
The unknown factors are identified (= ”quantified”) by solving the parameter vector by means of least-squares Eq. 5
Two numerical solution strategies combined with a cross-validation procedure are applied:
1. Genetic algorithm
2. Nelder-Mead algorithm
d S d𝑡 = − 𝑘 tot ( S − S eq ),
[1]
𝑘 𝑖, 𝑑 𝑝 = 𝛽 S 6 𝑑 𝑝 𝑚 𝑟 𝑚 Fe 𝜌 Fe 𝜌 𝑟 𝑡 res ,
[2]
𝑘 𝑡𝑜𝑡 = 𝑒 𝑏 0 𝑘 𝑡𝑜𝑡 𝑏 𝑗 ,
[3]
𝑘 𝑡𝑜𝑡 = 𝑒 𝑏 𝑑 p 𝑏 1 𝑄 𝑡𝑜𝑡 𝑏 𝑚 𝑟 𝜌 𝑟 𝑏 𝜌 Fe 𝑚 Fe 𝑏 4 𝜀.
[4]
𝐦𝐢𝐧 𝒊=𝟎 𝑴 𝐒 𝒕,𝒊 − [ [𝐒] 𝟎,𝒊 − 𝐒 𝐞𝐪 𝒆 (−(𝒆 𝒃 𝟎 𝟔 𝒅 𝒑,𝒊 𝒃 𝟏 𝑸 𝒕𝒐𝒕,𝒊 𝒃 𝟐 𝒎 𝒓,𝒊 𝝆 𝒓 𝒃 𝟑 𝝆 𝐅𝐞 𝒎 𝐅𝐞,𝐢 𝒃 𝟒 )𝒕) + 𝐒 𝐞𝐪 ] 𝟐 .
[5]
Tero Vuolio

15. Surface area approach (RRS) 0.29 0.0039 2.5
Table III. Comparison between prediction approaches for end sulfur content for the whole data (Vuolio et al. 2018).
Model R2
MAE
tres
Surface area approach (RRS)
0.29
0.0039
2.5
Surface area approach (Sauter)
0.0057
1.5
Surface area approach (RRS, Limited contact, Qtot)
0.76
0.0020 23
Linear reagent efficiency model
0.41
0.0056 -
Parameterized rate constant
0.90
0.0010
Table II. Identified modelling coefficients (Vuolio et al. 2018).
Fig. 7 – Fit (Vuolio et al. 2018).
Method
Cost-function b0 b1 b2 b3 b4 R2
MAE
SOS
MLR – Best solution
Linear
-1.40
0.52
0.70
0.97
0.63
0.90
0.0012
6.01∙10-5
GA – Best solution
Non-linear
-1.34
0.51
0.81
1.23
0.91
0.0010
5.81∙10-5
Nelder-Mead – Best solution
-2.00
0.39
0.48
0.62
1.07
0.0011
5.60∙10-5
Table IV. Results of the external validation (Vuolio et al. 2018).
Method
Cost-function R2
SOS
MAE [wt-%]
MLR – Best solution
Linear
0.89
4.2∙10-5
0.0012
GA – Best solution
Non-linear
0.91
3.7∙10-5
0.0011
Nelder-Mead – Best solution
0.83
5.9∙10-5
0.0016
Fig. 8 – Validation (Vuolio et al. 2018).
Tero Vuolio

16. Conclusions Prediction model for hot metal desulfurization:
Without an adequate measure of the particle size distribution of the applied desulfurization reagent, the prediction of the end sulfur content is not accurate, regardless of the applied type of the prediction model. A parameterized expression of the surface area approximation can be applied in prediction, if the residence time and mass transfer coefficient are substituted with a pre-exponential bias-term.
It is rather obvious that the effective surface area of the injected reagent particles is significantly smaller than the nominal surface area of the particles.
Kinetics of resulfurization:
The resulfurization of hot metal is an existing phenomenon. According to dimensional homogeneity it can be established that resulfurization is a relevant phenomenon, and its occurrence during the manufacture of hot metal has to be evaluated.
With a careful slag modification with an alkaline flux it is possible to increase the sulfide capacity of the slag phase, and thus to reduce the rate of resulfurization through the control thermodynamic driving force.
Tero Vuolio

17. Thank you! Questions?