Physical and Mathematical Modelling of Mass Transfer in Ladles due to Bottom Gas Stirring: A Review

Round 1

Reviewer 1 Report

In general, I should reject the manuscript as a review for publication, which is with low quality.

• The author should learn about how to write Abstract and Introduction.
• The organization and logic structure of this review should be thought about and optimized.
• Sec. 1 to Sec. 3 are too short, which are not reasonable.
• The author should present future research and conclusion separately.
• The author’s affiliation is not presented in a correct way.

Author Response

I appreciate the reviewer’s criticism, their remarks of approval and specially the valuable comments and observations to improve the original version.

Reviewer 1

1. The author should learn about how to write Abstract and Introduction.

The reviewer is right about the abstract. References are never included in an abstract. Clearly with such a terrible mistake from the beginning it gives the message of the lack of experience in writing papers. The abstract was rewritten and the introduction reorganized.

2. The organization and logic structure of this review should be thought about and optimized.

The introduction was reorganized. Conclusions were separated from future research.  

3. 1 to Sec. 3 are too short, which are not reasonable.

It has been clearly stated in the beginning of the paper that this review is focused on liquid-liquid mass transfer. Why?. There are several reasons already explained in the introduction: Solid-liquid mass transfer has been reviewed extensively in the past (two reviews are mentioned) and on the other hand mass transfer in slag-liquid steel systems deserves attention. The need to include a short review on solid-liquid and gas-liquid mass transfer is to illustrate the differences in the variables involved in comparison with liquid-liquid mass transfer.

4. The author should present future research and conclusion separately.

Conclusions and future research have been separated. Small changes on future research have been added based on the contribution from the reviewers.

5. The author’s affiliation is not presented in a correct way.

The editorial office also addressed this point. The reason to keep a personal email is because my contract with my current employer is temporary and will change in the near future. Now, I have also included the official email and I hope that both can be used, however, due to the previous argument If only can be included I would prefer the personal email.

Author Response File: Author Response.docx

Reviewer 2 Report

The manuscript deals with physical and mathematical modeling of mass transfer in a complex system as ladles. I think that as review the topic can be interesting for the scientific community also for the conclusions and the future perspectives presented

Nevertheless, before the publication, I suggest this minor but important revision to make the work a little bit more clear

 

General: in-text many symbols (letters) are used to indicate quantities. I suggest providing a list of all the symbols used in the paper at the beginning of the article with the corresponding meaning

Line 27: add the reference in the text to Equation (1)

Line 33: add a comma after condition “In this condition,”

Line 60: characteristic length of the reactor (l)

Line 77: Sherwood Reynodls and Schimdt numbers abbreviation could be introduced in line 58

Line 85: add a space between (LDV)[16]

Line 172: The discussion about reference [51] is very poor if compared with the following

Table 2:  add the reference to the paper and please check that all the works cited are reported in the bibliography. (E.g. I did not find ref. for Line 30 of table 2 Li and Yin – 2009. The only work reported for these two authors is reference number 30 published in 1996)

Line 274: please specify which are the references of the sentence that starts with “In some metal/slag systems slag emulsification has been reported”

Line 323: to increase the readability please insert after “slag mtc” (k_s)

Line 335: remove the capital letter at the beginning of the third point (iii)

Line 339: After “[84]. Add It or remove the dot

Line 402: correct “Where;” with “where:” or “where”

Line 423: is reported “In the most recent mathematical models” but no references are inside the text

Author Response

please, see attachment

Author Response File: Author Response.docx

Reviewer 3 Report

General comments

The author presents a detailed review on physical and mathematical modelling of ladles due to bottom stirring. The paper focuses on the liquid-liquid and mass transfer due to bottom gas injection. This is focus is well justified given the abundance of literature on ladle metallurgy. The paper is well-written and easy to follow. Nevertheless, as review papers play an important role in the dissemination of scientific results, some additional discussion is needed to give a better overall view of the subject. Detailed comments are provided below.

Detailed comments

1. Title: please be consistent with uppercase spelling
2. Lines 10-21: It is not customary to have reference numbering in the abstract since abstract is often visible in databases which do not show the list of references.
3. Lines 26-27: The Fick´s law is relevant for many dilute systems (stationary medium approach), but it does not hold very well for concentrated systems in which convection also plays a role. The reasons why convection can often be neglected should be mentioned.
4. Line 46: The word "specie" is used to denote the plural of word "species". I think the standard way to express the plural form is "species". The only definition for the word "specie" is the following: "Specie is a technical term referring to the physical form of money, particularly coins.". Consequently, I would advise to use the word "species" for both singular and plural forms.
5. Line 69: The expression derived in Eqs. 5-10 is essentially for isothermal conditions. I think it might be worthwhile to mention this.
6. Line 142: The author states that "Stirring energy is directly proportional to the gas flow rate". Assuming the stirring energy comes from the expansion of the gas bubbles, the proportionality should be linear as shown in the books of Engh^[1] and Oeters^{[2, 3]}. This approach could be mentioned as well.
7. Lines 235-236: Aside from the experimental study of Lachmund et al.^[4], there have been numerical simulations for emulsification of slag by Sulasalmi et al.^[5] and Senguttuvan et al.^[6] I think their results might suggest an even larger interfacial area than the study of Lachmund et al.^[4].
8. Lines 256-257: The author states that "Sakaguchi and Ito [26] found a correlation of the form; ka ∝ ε⁷¹". Some observations of the effect of vacuum pressure on the mass transfer coefficient are given also in the paper of Lachmund et al.^[7]
9. Line 264-267: There are several papers discussing the conditions for emulsification, e.g.^{[5, 6, 8-11]}. Furthermore, the effect of liquid-top phase density ratio and viscosity on the fluid flow in ladles has been studied by several authors^[12-15]. It could be a good idea to extract some key points from those studies.
10. Lines 292-293: The author states that "The sulphur partition ratio (LS) is in the range from 200-500 under laboratory conditions.". This sentence should be followed by proper citations. Also, I would recommend adding some range of values for industrial conditions as well.
11. Line 350: the author writes "δ is the thickness of the boundary layer". I think it would be more specific to talk about diffusion boundary layer here.
12. Lines 353-354: the author writes "Kang et al.[85] reported that the partition ratio for sulphur should be higher than 100 to assume mass transfer control.". I assume this refers to mass-transfer control in the metal phase? Please be more specific here.
13. Lines 361-362: the author states "Notice that based on the boundary layer theory, the mtc is proportional to D to the first power; k_i ∝ D". Please consider that the thickness of the diffusion boundary layer depends on the diffusivity as well. Consequently, the proportionality of k and D depends on the mass transfer correlation employed.
14. Lines 463-465: "In one group of experiments sulphur increased the mtc but in another case its effect was null and they attributed this behaviour to different concentrations of oxygen." Please elaborate in more detail what was the expected cause? Sulphur is known to be a surface active element.
15. Table 4: Please be consistent with the abbreviations. How can the abbreviation of Large Eddy Theory be LEM and that of Small Eddy Theory SEM? Furthermore, since the main application of the kinetic descriptions is mathematical models, the authors could elaborate more on how the different kinetic descriptions perform in modelling application and give suggestions which descriptions would be best suited for different applications.
16. Lines 527: "From this list, gas emulsification has been reported to have the largest influence." Does this mean emulsification due to gas injection? It would be worthwhile to mention that calculating the kinetics of emulsions requires the knowledge their residence time, size distribution and generation rate of the droplets. Most of the mass transfer equations are not explicitly treating the kinetics of emulsion, although the rate-increasing effect of emulsification is often implicitly incorporated. Unfortunately, very few descriptions are available for the emulsification rate; one of the few examples available is that of Wei and Oeters^[8]. For the droplet size distribution there is more information available.^{[4, 5, 8, 10, 16, 17]} Nevertheless, there are relatively few mathematical models for ladle processes, which have explicitly simulated metal-slag reactions. For example, Sulasalmi et al.^[18] used the approach of Wei and Oeters^[8] for calculating the droplet generation rate and then went on to calculate the overall kinetics of the reduction stage of the CAS-OB process by summation of the rates of individual droplets.
17. Finally, it might be relevant add more discussion regarding models, which employ mass transfer between equilibrium volumes instead of mass transfer equations. Typically, the mass transfer rates between the zones are more or less arbitrary. The benefit of this approach is easy coupling with thermodynamic software. A good example of such model is the paper of van Ende and Jung^[19] already cited in the paper, but there could be more of such models.
18. The author might consider citing the model of Zhu et al.^[20], which considers powder injection in RH, but involves also a description for metal-slag reactions.

References

[1] T. A. Engh, Principles of Metal Refining, Oxford University Press, Oxford, United Kingdom, 1992, 473.

[2] F. Oeters, Metallurgie der Stahlherstellung, Verlag Stahleisen mbH, Düsseldorf, Germany, 1989, 503.

[3] F. Oeters, Metallurgy of Steelmaking, Verlag Stahleisen mbH, Düsseldorf, Germany, 1994, 512-512.

[4] H. Lachmund, Y. Xie, T. Buhles, W. Pluschkell, Steel Res. 2003, 74, 77.

[5] P. Sulasalmi, V.-V. Visuri, A. Kärnä, T. Fabritius, Steel Res. Int. 2015, 86, 212.

[6] A. Senguttuvan, G. A. Irons, ISIJ Int. 2017, 57, 1962.

[7] H. Lachmund, Y. Xie, K. Harste, Steel Res. 2001, 72, 452.

[8] T. Wei, F. Oeters, Steel Res. 1992, 63, 60.

[9] J. Mietz, S. Schneider, F. Oeters, Steel Res. 1991, 62, 10.

[10] J. Savolainen, T. Fabritius, O. Mattila, ISIJ Int. 2009, 49, 29.

[11] P. Sulasalmi, A. Kärnä, T. Fabritius, J. Savolainen, ISIJ Int. 2009, 49, 1661.

[12] L. Wu, P. Valentin, D. Sichen, Steel Res. Int. 2010, 81, 508.

[13] K. Krishnapisharody, G. A. Irons, Metall. Mater. Trans. B 2006, 37, 763.

[14] E. K. Ramasetti, V.-V. Visuri, P. Sulasalmi, P. Palovaara, A. K. Gupta, T. Fabritius, Steel Res. Int. 2019, 90, 1900088.

[15] E. K. Ramasetti, V.-V. Visuri, P. Sulasalmi, J. Savolainen, M. Li, S. Lei, T. Fabritius, Metals 2019, 9, 1048.

[16] M. G. Frohberg, F. Gerlach, G. Handschuh, Steel Res. 1990, 61, 151.

[17] T. Palovaara, V.-V. Visuri, T. Fabritius, in Proceedings of the 7th International Congress on Science and Technology of Steelmaking, Associazione Italiana di Metallurgia, Venice, Italy, 2018.

[18] P. Sulasalmi, V.-V. Visuri, A. Kärnä, M. Järvinen, S. Ollila, T. Fabritius, Metall. Mater. Trans. B 2016, 47, 3544.

[19] M.-E. van Ende, I.-H. Jung, Metall. Mater. Trans. B 2017, 48, 28.

[20] C.-Y. Zhu, P.-J. Chen, G.-Q. Li, X.-Y. Luo, W. Zheng, ISIJ Int. 2016, 56, 1368.

Author Response

please, see attachment

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

I think this version can be accepted.

Author Response

Thanks for your review.

Reviewer 3 Report

The author presents a detailed review on physical and mathematical modelling of ladles due to bottom stirring. The paper focuses on the liquid-liquid and mass transfer due to bottom gas injection. This is focus is well justified given the abundance of literature on ladle metallurgy. The paper is well-written and easy to follow, but not very insightful.

Author Response

Thanks for your review.