Review Reports - Thermodynamic Guidelines for Minimizing Chromium Losses in Electric Arc Furnace Steelmaking

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

There are some remarks which are given here as commentaries in order to improve the quality of the paper.

The abstract first mentions the Fe-Cr-C-O system, and then in the next sentence it also refers to the influence of SiO2. Wouldn't it be better to mention all relevant elements right away like Fe-Cr-C-O-(Si)?
TCFE12 database which is used for calculation could be referred. By the way, the reference [22] should be completed. Sigworth, G. K., Elliott, J. F. (1974). The Thermodynamics of Liquid Dilute Iron Alloys. Metal Science, 8 (1), 298–310. doi:10.1179/msc.1974.8.1.298
I think that in equations (1) and (2) oxygen could participate in gaseous state. The number of equation (3) in the text is wrong (is given as second (2)).
Table 1. It is not explained why the values Kho [4] are ten times lower than the rest.
In Figures 1,2,5-9 the pressure units should be given.
In Figure 3 such conditions as T, P are missing. More explanations are necessary about what are std-X and y-Fe.
It is not clear how the experimental data was added to the images. The data for example [Wang2013] and [Carboni2011] are the points and not the lines; it would be interesting to compare the calculations with the experiments. The images compare calculations with calculations, which is really not meaningful.
An old database HSC8.0 8 (which also not referred) is used with the ancient method, and no comparison with the experiments is provided. The results of the calculations are not confirmed by the experimental values.

Comments for author File: Comments.pdf

Author Response

The authors are appreciative of the time and effort it took to review the paper.

There are some remarks which are given here as commentaries in order to improve the quality of the paper.

The abstract first mentions the Fe-Cr-C-O system, and then in the next sentence it also refers to the influence of SiO2. Wouldn't it be better to mention all relevant elements right away like Fe-Cr-C-O-(Si)?

Response 1: Thank you for this suggestion. We have revised the abstract to explicitly mention the influence of silicon on the system under study.

TCFE12 database which is used for calculation could be referred. By the way, the reference [22] should be completed. Sigworth, G. K., Elliott, J. F. (1974). The Thermodynamics of Liquid Dilute Iron Alloys. Metal Science, 8 (1), 298–310. doi:10.1179/msc.1974.8.1.298

Response 2: Thank you very much for the remark, we have the full reference name. We have also reffered to HSC and Thermocalc as equipment.

I think that in equations (1) and (2) oxygen could participate in gaseous state. The number of equation (3) in the text is wrong (is given as second (2)).

Response 3: We agree regarding the equation numbering inconsistency. We have re-numbered the combined reaction from (2) to (3) throughout the text. We have kept oxygen as [O] dissolved in the liquid iron for Equations (1) and (2) as this is the form that participates in the reaction at the liquid metal/gas or metal/slag interface, but we have added a clarifying sentence in Section 2 to explain this convention and its link to the overall Cr-C-O system.

Table 1. It is not explained why the values Kho [4] are ten times lower than the rest.

Response 4: The lower values reported by Kho et al. [4] are probably because their calculations were performed only for the formation of the Cr2O3 phase from elements in their standard state and CO from elements in their standard state, which differs significantly from the majority of other references that calculate the overall reaction (3) between the dissolved species.

In Figures 1,2,5-9 the pressure units should be given.

Response 5: Thank you for noting this omission. We have added the pressure (p = 1 atm) conditions to the caption of Figures 1, 2, 5, 6, 8, and 9 for clarity. For Figure 7, which explores varied pressure, we ensured the units are clearly shown in the figure legend.

In Figure 3 such conditions as T, P are missing. More explanations are necessary about what are std-X and y-Fe.

Response 6: We have added the pressure (p = 1 atm) and temperature (T = 1600 °C) conditions to the caption of Figure 3. We thank you for this comment. You are correct that the wording in the legend of Figure 3 was not the most appropriate. We have revised and supplemented the text to make it clear which method was used for the calculation of the activity coefficients.

It is not clear how the experimental data was added to the images. The data for example [Wang2013] and [Carboni2011] are the points and not the lines; it would be interesting to compare the calculations with the experiments. The images compare calculations with calculations, which is really not meaningful.

Response 7: While a direct comparison with experimental data is valuable, the focus here was to highlight method-dependent differences in the calculated Gibbs free energies and activity coefficients, which can help identify the sources of deviations and improve modeling accuracy in future work.

An old database HSC8.0 8 (which also not referred) is used with the ancient method, and no comparison with the experiments is provided. The results of the calculations are not confirmed by the experimental values.

Response 8: We used the HSC 8.0 program to obtain thermodynamic data, which were helpful for calculating the Gibbs free energies. The thermodynamic data for Gibbs free energies in HSC 8.0 are mainly obtained from I. Barin: Thermochemical Data of Pure Substances. These rarely change over time, so newer versions of the program have the same data. Unfortunately we do not own a license for newer HSC program.

Reviewer 2 Report

Comments and Suggestions for Authors

This article addresses an interesting topic, particularly in the field of steel metallurgy, and specifically the analysis of the thermodynamics of the Fe-Cr-C-O system, highlighting discrepancies in existing literature regarding Gibbs free energies, interaction parameters, and other thermodynamic data. The authors relied on 34 articles in this field; however, the introduction should have provided a more detailed description of the state of knowledge in these articles. The research methodology described here raises no major concerns. The authors analyzed the differences in the data, tabulating them and presenting them graphically. The article concludes with appropriate conclusions.

Notes:

- Chromium content – lower numbers are given first, followed by higher ones, i.e., from 0.1% to 8%.

- Page 2 – References [1-9] are given. Each of these items should be discussed; at most, two items should be listed in the same sentence, similarly to the other literature in this introduction.

- Page 2 – The authors write that numerous publications have addressed thermodynamics. However, it would be good to add a few sentences here about these differences, what they refer to – in general, and only then expand on this in subsequent chapters.

- Page 2 – Equation (2) appears twice; the second one should be marked as (3).

- The article contains many symbols. It would be a good idea to include a list of these symbols at the end of the article.

- In Table 1 – it would also be a good idea to provide the publication date.

- Fig. 1 – Some of the lines in the figure cannot be distinguished, especially those in different shades of red. The axes should be labeled descriptively.

- A statistical analysis of the obtained results should also be attempted.

Author Response

The authors are very grateful for your very constructive review, we feel it has greatly improved our paper. We have, however, had to make some changes in the conclusions due to another reviewer.

Notes:

Comment 1:

- Chromium content – lower numbers are given first, followed by higher ones, i.e., from 0.1% to 8%.

Response 1: The sentence refers to the carbon concentrations in the ferrochromium ferroalloys. The sentence has been corrected as indicated:

“Chromium is typically alloyed to the steel melt in the form of ferrochromium. Ferrochromium is available in several forms that typically vary in carbon content, from less than 0.1 wt. % up to 8 wt. %. Ferrochromium becomes more expensive as its carbon content decreases.”

Comment 2:

- Page 2 – References [1-9] are given. Each of these items should be discussed; at most, two items should be listed in the same sentence, similarly to the other literature in this introduction.

Response 2: Each reference is now discussed.

Experimental results show that CO2 injection in stainless steel smelting can significantly enhance decarburization rates and preserve chromium, potentially improving production efficiency.[1] CO2 use modeling approaches have been developed to optimize refining parameters and improve the economics of ferrosilicon (FeSi) use [2]. The control of slag composition in the EAF enables efficient optimization of Cr loss as well as minimizing MgO losess from refractory lining [3]. Computational thermodynamics helps understand the stainless steelmaking process, from slag formation to the Cr loss as well as the Cr recovery, especially during tapping [4]. High chromium content in the slag increases slag crusting, reduces reactivity, and impairs the formation of foaming slag, making slag reduction more difficult. Furthermore, stainless steel slags with high chromium oxide content cannot be easily recycled [5,6].

In VOD, carbon is selectively oxidized by blowing oxygen onto the molten steel in a vacuum, which lowers the partial pressure of carbon monoxide and favours carbon removal over chromium oxidation. While carbon contents as low as 0.001 wt-% are theoretically possible, practical limits are set by mass transfer rates [7].

In AOD, argon is used to dilute the oxygen, reducing the partial pressure of carbon monoxide and enabling preferential oxidation of carbon over chromium. Efficient reduction and recovery of chromium the slag is crucial for resource conservation and pollution prevention. Typically ferrosilicon is used to recover oxidized chromium, but its use is limited by silicon uptake in the steel [8]. Thermodynamically aluminium is a great reductant except for cost [9].

Comment 3:

Response 3: Further references discussed.

Different EAF designs and identified key process parameters that influence chro-mium yield, where spout tapping is preferred over the bottom tapping, due to better slag mixing with the reduction agent [10].

Microstructural analysis reveals two primary types of chromium oxides in slags, calcium chromites and chromite spinels. The formation of these phases depends strongly on slag chemistry and basicity. Calcium chromites form predominantly at high slag basicity, while chromite spinels can form across a wider range of basicities [11].

Experiments show that using CaC₂ achieves higher reduction rates and greater overall chromium recovery from slag compared to traditional reductants like FeSi or aluminum. CaC₂ not only efficiently reduces Cr₂O₃ to metallic chromium but also sup-ports the formation of foaming slag, which can further improve process efficiency [12].

Some Cr inevitably remains in the slag, this poses both environmental and eco-nomical issues. Some studies focus on Cr-containing slag reduction and focus on the efficiency of the reduction agents. Aluminium was proved, to be the most efficient, followed by ferrosilicon, and graphite (carbon) was the least effective [13].

Comment 4:

- Page 2 – Equation (2) appears twice; the second one should be marked as (3).

Response 4: We thank the reviewer for pointing this out. The numbering has been corrected.

Comment 5:

- The article contains many symbols. It would be a good idea to include a list of these symbols at the end of the article.

Response 5: For easier reference, we have added a table of symbols with the corresponding explanations at the end of the article.

Comment 6:

- In Table 1 – it would also be a good idea to provide the publication date.

Response 6: We have added the year of publication of the works in Table 1.

Comment 7:

- Fig. 1 – Some of the lines in the figure cannot be distinguished, especially those in different shades of red. The axes should be labeled descriptively.

Response 7: For better clarity, we have adjusted the colors of the curves in Figure 1. More detailed axis descriptions have also been added to all figures.

Comment 8:

- A statistical analysis of the obtained results should also be attempted.

Response 8: We acknowledge the value of statistical analysis, however we did not attempt it, since we do not show any results from industrial practice. Given that the core of the work is a sensitivity analysis showing the maximum extent of variation (the envelope of results) caused by literature discrepancies, a formal statistical analysis is not strictly applicable.

Reviewer 3 Report

Comments and Suggestions for Authors

Thermodynamic Guidelines for Minimizing Chromium Losses in Electric Arc Furnace Steelmaking

The aim of the work was to highlight the important points to reduce the loss of chromium in the stainless steel production process and to determine thermodynamic guidelines during the production process.

Congratulations to the authors - an interesting article, but the authors did not avoid minor errors that require correction and additional explanation.

Review

Equations (1) and (2) can be combined and written 78

as follows: 79

3[C] + Cr2O3(s) → 3CO(g) + 2[Cr] (2)

Should be equation (3)

n Table 1, calculated values based on given data from literature sources are marked 94

with 1,2,3. When calculating the Gibbs free energies, Wang et al. [15] and Ma et al. [17] took 95

add that it applies to equation (3)

When calculating the Gibbs free energy (ΔG), the reaction constant (K) must also be 108

When calculating the Gibbs free energy (ΔG), the reaction (3) constant (K) must also be 108

Where T and R represent the temperature and the gas constant, K3 is the constant of 111

Equation [3], pCO represents partial pressure of carbon monox

Equation (3)

Where, 𝑎𝑖 %, 𝑓𝑖 are the activity and the activity coefficient of element i in the iron so- 120

lution, using 1 wt. % standard state, 𝑒𝑖…

where: 𝑎𝑖%, 𝑓𝑖 are the activity and the activity coefficient of element i in the iron so- 120

lution, using 1 wt. % standard state, 𝑒𝑖

continuation of the sentence

Figure 3. Equilibrium solubility of Cr and C in liquid iron calculated according to different standard 193 states.

no legend description in the figure title

Stainless 213

steels typically contain a low concentration of carbon, necessitating intensive oxidation, 214

leading to significant chromium losses.

Does Chromium combustion involve a complex reaction of chromium with oxidizing agents, forming various chromium oxides, nitrides, or oxo-compounds depending on the reactants and conditions?

ystem, which is achieved by lowering the pressure, the direction of the reaction is fa- 254

voured towards the formation of the gaseous phase. In our case, by lowering the partial 2

reaction (3) ?, - many places in the text require clarification

Figure 10. Gibbs free energies as a function of temperature for the oxidation of alloying elements in 301 iron solution.

where do the ∆G_dis values/data presented in OY come from - is it from Table 2?

a model was created to calculate the decarburization of the 334

stainless steel melt, also partially presented in our previous work [31].

Despite this, a short description of the model would be advisable.

When reviewing literature sources, there were discrepancies in the reporting of Gibbs 383

free energies, interaction parameters, and other data in the Fe-Cr-C system. Deviations 384

occur due to different interpretations of thermodynamic reactions and states of elements 385

in the mentioned system. The data collected in the work were used to calculate the equi- 386

librium solubilities of chromium and carbon in the system. Based on thermodynamic cal- 387

culations, guidelines were determined for the management of the stainless steel melting 388

process with the aim of reducing chromium losses.

These are not conclusions and were mentioned earlier as the reason for the authors to undertake the research.

n literature sources, there are discrepancies in the citation of Gibbs free energy and 391

interaction parameters, which is the result of different interpretations of thermodynamic 392

reactions and states of elements. The parameters from the database of the HSC 8.0 pro- 393

gram and the parameters written in the work of Sigwortgh et al. [22] were used in the 394

calculations.

these are not conclusions either!

13.

Unfortunately, the conclusions are very general and do not address the interesting results obtained from thermodynamic calculations and the model used. Any conclusions that need to be improved must be related to the results of the research/modeling.

Author Response

Thermodynamic Guidelines for Minimizing Chromium Losses in Electric Arc Furnace Steelmaking

Congratulations to the authors - an interesting article, but the authors did not avoid minor errors that require correction and additional explanation.

First of all, we would like to thank the reviewer for his kind words, and an insightful review. We greatly appreciate it, as the paper is very long and we greatly appreciate the reviewer's time.

Review

Comment 1:

Equations (1) and (2) can be combined and written 78

as follows: 79

3[C] + Cr2O3(s) → 3CO(g) + 2[Cr] (2)

Should be equation (3)

Response 1: We have corrected the mistake.

Comment 2:

In Table 1, calculated values based on given data from literature sources are marked 94

with 1,2,3. When calculating the Gibbs free energies, Wang et al. [15] and Ma et al. [17] took 95

add that it applies to equation (3)

Response 2: We have added text
“In Table 1, calculated values based on given data from literature sources are marked with ^1,2,3, and were obtained using Equation (3). When calculating the Gibbs free energies, Wang et al. [15] and Ma et al. [17] took into account the energy required to dissolve solids C and Cr and considered the 1 wt. % standard state in the calculations.”

Comment 3:

When calculating the Gibbs free energy (ΔG), the reaction constant (K) must also be 108

When calculating the Gibbs free energy (ΔG), the reaction (3) constant (K) must also be 108

Response 3: Corrected

Comment 4:

Where T and R represent the temperature and the gas constant, K3 is the constant of 111

Equation [3], pCO represents partial pressure of carbon monox

Equation (3)

Response 4: Corrected

Comment 5:

Where, ?? %, ?? are the activity and the activity coefficient of element i in the iron so- 120

lution, using 1 wt. % standard state, ??…

where: ??%, ?? are the activity and the activity coefficient of element i in the iron so- 120

lution, using 1 wt. % standard state, ??

continuation of the sentence

Response 5: The explanation of the symbols has been revised for improved clarity and readability.
“In these equations, represents the activity of element i relative to the 1 wt. % standard state, and is its activity coefficient. The terms [wt. % i] and [wt. % j] refer to the weight percentages of the dissolved elements i and j, respectively. The parameter is the first-order self-interaction parameter, which quantifies the effect of the element i on its own activity. Similarly, is the first-order cross-interaction parameter, describing the effect of an alloying element j on the activity of element i in dilute liquid iron. The values for specific interaction parameters, such as , , and can vary depending on the reference source and are compiled in Table 3 [5,19,22,24–26].”

Comment 6:

Figure 3. Equilibrium solubility of Cr and C in liquid iron calculated according to different standard 193 states.

no legend description in the figure title

Response 6: We thank the reviewer for this observation. A more detailed description has been added to the legend of Figure 3.

Comment 7:

Stainless 213

steels typically contain a low concentration of carbon, necessitating intensive oxidation, 214

leading to significant chromium losses.

Does Chromium combustion involve a complex reaction of chromium with oxidizing agents, forming various chromium oxides, nitrides, or oxo-compounds depending on the reactants and conditions?

Response 7: An interesting point. There is no discussion of nitride formation in literature, nor is there any evidence for it. Furthermore, I have not encountered any chromium nitrides in my practice, but to be honest, I was never looking for them. The literature sometimes suggests CrO as an intermediary, but it complicates the calculations, and surprisingly does not yield better results.

So secondly, in the model, we considered only the oxidation of chromium to its trivalent form, i.e., Cr₂O₃. This context enhances the practical relevance of our simplified model. The model is focused on calculating the oxidation of carbon and chromium in the electric arc furnace, where the process takes place at high temperatures with open access to air, and thus to oxygen in the system.

Comment 8:

ystem, which is achieved by lowering the pressure, the direction of the reaction is fa- 254

voured towards the formation of the gaseous phase. In our case, by lowering the partial 2

reaction (3) ?, - many places in the text require clarification

Response 8: We have corrected the highlighted error in the text and carefully reviewed the manuscript. All identified mistakes have been corrected.

Comment 9:

Figure 10. Gibbs free energies as a function of temperature for the oxidation of alloying elements in 301 iron solution.

where do the ∆G_dis values/data presented in OY come from - is it from Table 2?

Response 9: We have added a statement in the text specifying the source of the data for the deoxidation reactions and the mixing Gibbs free energies presented in Figure 10.

“In addition to the interaction parameters and activity of the elements in the solution, the oxidation reactions of other elements and their Gibbs free energies should also be dis-cussed. Figure 10 shows the curves of Gibbs free energies as a function of temperature for the oxidation of various alloying elements. The data used to calculate the oxidation reac-tions were compiled from scientific literature. The standard Gibbs free energies were de-termined using the HSC 8.0 software database, while the dissolution Gibbs free energies were determined from the work of Sigworth et al. [22].”

Comment 10:

a model was created to calculate the decarburization of the 334

stainless steel melt, also partially presented in our previous work [31].

Despite this, a short description of the model would be advisable.

Response 10: A brief description of the model has been added to the text::
“Based on the thermodynamic data from the HSC 8.0 database and the parameters listed in Sigworth et al. [22], a model was created to accurately simulate the complex process of decarburization and subsequent oxidation of alloying elements in stainless steel melt, it is partially presented in our previous work [31]. The model predicts how the melt's composition changes as oxygen is blown in the melt, focusing on the simultaneous com-petition between the oxidation of carbon, chromium, and silicon. The prediction is based on the fundamental principle of minimizing the Gibbs free energy for the overall system. To account for the non-ideal behaviour of elements dissolved in the steel melt, the model rigorously incorporates the activities of all dissolved elements. These activities are calculated using established first-order interaction parameters taken from literature sources. By iteratively determining which reaction is most thermodynamically favoured at each step, the model successfully predicts the progression of oxidation and helps identify conditions that minimize undesirable chromium loss to the slag.”

Comment 11:

When reviewing literature sources, there were discrepancies in the reporting of Gibbs 383

free energies, interaction parameters, and other data in the Fe-Cr-C system. Deviations 384

occur due to different interpretations of thermodynamic reactions and states of elements 385

in the mentioned system. The data collected in the work were used to calculate the equi- 386

librium solubilities of chromium and carbon in the system. Based on thermodynamic cal- 387

culations, guidelines were determined for the management of the stainless steel melting 388

process with the aim of reducing chromium losses.

These are not conclusions and were mentioned earlier as the reason for the authors to undertake the research.

Response 11: Please see response 13

Comment 12:

n literature sources, there are discrepancies in the citation of Gibbs free energy and 391

interaction parameters, which is the result of different interpretations of thermodynamic 392

reactions and states of elements. The parameters from the database of the HSC 8.0 pro- 393

gram and the parameters written in the work of Sigwortgh et al. [22] were used in the 394

calculations.

these are not conclusions either!

Response 12: Please see response 13

Comment 13.

Response 13: We have rewritten the conclusions. However, we feel that some of the points should remain, as they are essential.

The following conclusions are drawn directly from the thermodynamic analysis and the oxidation model developed in this work:

The literature review revealed significant inconsistencies in reported Gibbs free energies (ΔG⁰) and interaction parameters, which result in highly varied predictions of Cr-C equilibrium solubility. By selecting a mean baseline using the HSC 8.0 database and Sigworth et al. [22] interaction parameters, a robust thermodynamic framework was established for subsequent process modeling.
The thermodynamic calculations demonstrate that temperature is the most powerful variable for selective decarburization. Increasing the melt temperature drastically reduces the equilibrium carbon content, thereby limiting chromium oxidation. Specifically, at 15 wt.% Cr, increasing the temperature from 1550 °C to 1800 °C lowers the equilibrium carbon concentration from 1.21 wt.% C to 0.28 wt.% C. This confirms that decarburization in the EAF should be conducted at temperatures above 1650 °C.
The oxidation model confirmed the protective role of silicon, especially at low temperatures. In a melt at 1500 °C and 20 kg of injected oxygen per ton of steel, the presence of 0.5 wt.% Si reduced the oxidized chromium from 7 kg/t to 0.3 kg/t. Silicon preferentially oxidizes first, protecting chromium and allowing carbon combustion to dominate the second phase.
The equilibrium calculations show that reducing the partial pressure of CO in subsequent processes (like VOD) is essential, as the Cr solubility increases drastically with decreasing pCO. Meaning that oxidation in the EAF should be limited.
Furthermore, while the 1 wt.% standard state is practical, calculations using the modified Henrian standard state (taking the solvent activity coefficient into account) predict a slightly higher equilibrium chromium solubility at increased carbon concentrations, providing a more accurate theoretical benchmark for non-dilute solutions.
Chromium losses during the initial low-temperature stages of the EAF phase must be minimized by limiting oxygen blowing during heating, and adding sufficient Si. Conversely, the high-temperature EAF decarburization phase must be stopped when kinetics indicate a sharp drop in CO₂ in off-gases, signifying the onset of intense chromium oxidation.

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The revised article is more readable and understandable. I have no further comments.