Particle Size Distribution Models for Metallurgical Coke Grinding Products

Round 1

Reviewer 1 Report

The coke particle size is one of the significant parameters to select metallurgical coke, which determines the fluid flow resistance, the upward gases and downwards metal liquids passing efficiency, and the iron production rate. However, the coke particle size distribution has not been studied enough. In this work, six different particle size distribution (Gates-Gaudin-Schuhmann (GGS), Rosin-Rammler (RR), Lognormal, Normal, Gamma, and Swebrec) models were implemented, and verified with experimental data at different metallurgical coke grinding conditions. Then, adjusted R² Akaike information criterion and the root mean of square error were employed as comparison criteria. It was found that the Swebrec and RR models predicted well the coke particle size distribution. Therefore, the work was suggested to be published in the journal of Metals after minor revision. In detailed, some comments are listed as follows.  

1. The Grammar must be improved.
2. The elemental and proximate analyses are incomplete, and need to be supplemented in the revised manuscript.
3. Punctuation was wrong. Please modify the punctuation.
4. Please explain the calculation steps of the least square method.
5. Please improve the quality of all figures.
6. Please supply the research progress about an effect of coke particle size on blast furnace smelting.

Author Response

R: The coke particle size is one of the significant parameters to select metallurgical coke, which determines the fluid flow resistance, the upward gases and downwards metal liquids passing efficiency, and the iron production rate. However, the coke particle size distribution has not been studied enough. In this work, six different particle size distribution (Gates-Gaudin-Schuhmann (GGS), Rosin-Rammler (RR), Lognormal, Normal, Gamma, and Swebrec) models were implemented, and verified with experimental data at different metallurgical coke grinding conditions. Then, adjusted R² Akaike information criterion and the root mean of square error were employed as comparison criteria. It was found that the Swebrec and RR models predicted well the coke particle size distribution. Therefore, the work was suggested to be published in the journal of Metals after minor revision. In detailed, some comments are listed as follows.

R: The Grammar must be improved.

A: Authors thank the reviewer for the comments; the revised version has been improved with a deep revision.

R: The elemental and proximate analyses are incomplete, and need to be supplemented in the revised manuscript.

A: Thank you for your suggestion, the complete analysis was supplied in the revised manuscript (Table 1)

R: Punctuation was wrong. Please modify the punctuation.

A: Thank you, punctuation was corrected in the revised version of the manuscript.

R: Please explain the calculation steps of the least square method.

A: Thank you for the comment; the Materials and Methods section was complemented with information about the least squared method. Additionally, an example of the custom Python script was provided in Supplementary Material.

R: Please improve the quality of all figures.

A: Thank you, the quality of the figures was improved in the revised manuscript.

R: Please supply the research progress about an effect of coke particle size on blast furnace smelting.

A: Thank you for the comment; in the Introduction section was added the following paragraph: “Various studies [14–23] have evaluated the effect of defined ranges of coke particle size in steelmaking performance as a means of process optimisation. The thickness of combustion zone, flame front, kinetic chemical reactions, and iron ores phases formation (hematite, magnetite and gangue) are broadly affected by coke PSD in sinter and blast furnace plants.”

Reviewer 2 Report

The empirical approach of relating distribution parameters to of interest.  However, the paper offers no insight as to the actual implications of the evaluation criteria. In particular, it is unclear why the maximum likelihood approach is not used for fitting the distribution parameters, and its relation to AIK. 

Also, there is a fairly liberal use of p values, i.e. “p>0.005 shows that there is no significant difference among the model based on AIC criteria”.  As far as I can tell, it seems to be an adaptation of the student T test, although there is no reason to assume normality.  The authors seem to be uninformed about the goodness of fit X2 test, or the Anderson-Darling and Komolgorov-Smirnov tests, which are commonly used to test goodness-of-fit hypotheses.

To properly compare the fitting potential of each distribution under the three listed criteria (adjusted R2, RMSE, AIK) would be to fit each of the proposed distributions so as to optimize them separately for each of the criteria;  no simply to apply a least-square procedure. For instance, optimize all of the fitting parameters in all of the distributions so as to minimize the adjusted R2 and then compare the performance; separately then optimize all of the parameters so as to optimize the RMSE, and compare them;  do the same for AIK.  The first two of these are related to the minimizing least squares (implicitly this assumes that the error around the fitted distribution follows a normal distribution, as well as the homoscedasticity condition), although I may be missing some of the details.  However, the AIK is like a "penalized" form of maximum likelihood fitting.

In the given context it doesn't seem as if the misfit of fine particles should be weighted similarly to the rest of the distribution, since there are differing operational implications.  This is not properly commented on.

Lastly there is an overwhelming quantity of grammatical errors and improper vocabulary.  The attached annotation includes 132 comments on items that should be correct.  This paper can not be published unless it undergoes thorough revision by a native English speaker.

Comments for author File: Comments.pdf

Author Response

R: The empirical approach of relating distribution parameters to of interest.  However, the paper offers no insight as to the actual implications of the evaluation criteria. In particular, it is unclear why the maximum likelihood approach is not used for fitting the distribution parameters, and its relation to AIK.

A: Thank you for the comment, a note about the implication of the evaluation criteria to clarify was added  in the Materials and Methods section. “The criteria selected are widely used in particle size models selection as well as define the better model prediction. The adjusted R² is traditional goodness of fit measurement but, its values interpretation are most considered in linear models. Additionally, to assure the model selection, RMSE and AIC were used. Both parameters are more appropriate to measure the goodness of fit in nonlinear models.”

The least squared method selection is because the authors want to compare the six distributions using the same criterion. Maximum likehood approach is used to fit parameters in statistical distribution such as Normal, Lognormal and Gamma; but RR, Schulmann and Swebrec are considered empirical models. Shangguan et al, Esmaeelnejad et al, Botula et al, Yang et al, studies used a similar approach.

References

1. Shangguan, Y. Dai, C. García-Gutiérrez, and H. Yuan, "Particle-size distribution models for the conversion of Chinese data to FAO/USDA system," Sci. World J., vol. 2014, 2014.
2. Esmaeelnejad, F. Siavashi, J. Seyedmohammadi, and M. Shabanpour, "The best mathematical models describing particle size distribution of soils," Model. Earth Syst. Environ., vol. 2, no. 4, pp. 1-11, 2016.
3. D. Botula, W. M. Cornelis, G. Baert, P. Mafuka, and E. Van Ranst, "Particle size distribution models for soils of the humid tropics," J. Soils Sediments, vol. 13, no. 4, pp. 686-698, 2013.
4. Yang, J. Lee, D. E. Barker, X. Wang, and Y. Zhang, “Comparison of six particle size distribution models on the goodness-of-fit to particulate matter sampled from animal buildings,” J. Air Waste Manag. Assoc., vol. 62, no. 6, pp. 725-735, 2012.

R: Also, there is a fairly liberal use of p values, i.e. “p>0.005 shows that there is no significant difference among the model based on AIC criteria”.  As far as I can tell, it seems to be an adaptation of the student T test, although there is no reason to assume normality.  The authors seem to be uninformed about the goodness of fit X2 test, or the Anderson-Darling and Komolgorov-Smirnov tests, which are commonly used to test goodness-of-fit hypotheses.

A: Authors thank the reviewer for the comments; the suggestion of the reviewer would improve the model selection criteria. However, the focus of this study was the PSD modelling of coke grinding product comparing the Swebrec function with other classical distributions; a different approach using descriptive statistics is presented in Results section. The table that helps to select the better models was included in the Supplementary material.

R: To properly compare the fitting potential of each distribution under the three listed criteria (adjusted R2, RMSE, AIK) would be to fit each of the proposed distributions so as to optimise them separately for each of the criteria;  no simply to apply a least-square procedure. For instance, optimise all of the fitting parameters in all of the distributions so as to minimise the adjusted R2 and then compare the performance; separately then optimise all of the parameters so as to optimise the RMSE, and compare them;  do the same for AIK.  The first two of these are related to the minimising least squares (implicitly this assumes that the error around the fitted distribution follows a normal distribution, as well as the homoscedasticity condition), although I may be missing some of the details.  However, the AIK is like a "penalised" form of maximum likelihood fitting.

In the given context it doesn't seem as if the misfit of fine particles should be weighted similarly to the rest of the distribution, since there are differing operational implications.  This is not properly commented on.

A: Authors thank the reviewer for the comments, the suggestion of the reviewer would improve the model selection. However, this type of analysis is not within the scope of this study. The criteria was to select the distribution which better describes the coke grinding product PSD. Analyses using the suggested estrategy could improve the model selection and wouls be taken in account in future research.

R: Lastly there is an overwhelming quantity of grammatical errors and improper vocabulary.  The attached annotation includes 132 comments on items that should be correct.  This paper can not be published unless it undergoes thorough revision by a native English speaker.

A: Authors really appreciate the reviewer comments and detailed correction, all suggestions were included and additional English review was performed by a native.

Reviewer 3 Report

It is recognized in the paper the importance of controlling coke particle size distributions in the steelmaking process, as presence of fines, and/or uneven particle size distributions affect the flowability of the gases and melt metal inside the furnace. More than describing coke PSD, predicting the breakage suffered by coke particles from the coke plant to the moment they are fed into the furnace is the main challenge. The sequential events suffered by those particles through several chutes, silos produce not only fines but also weaker particles due to accumulation of damage. However, the main issue with the paper is that it seems the authors aren’t aware of the vast literature regarding breakage properties and use ball mill grinding of coke as a way to study coke fragments distribution. Regarding the evaluation of the cumulative distribution functions, the procedure is well explained and document, however it presents no innovation to the knowledge on the field, as you can’t ensure that the best function found for the Boayacá coke will work on cokes from other sources that may differ in shape, chemical properties, damage level etc. Therefore, I’m cannot recommend this paper to be published.

Author Response

R: It is recognised in the paper the importance of controlling coke particle size distributions in the steelmaking process, as presence of fines, and/or uneven particle size distributions affect the flowability of the gases and melt metal inside the furnace. More than describing coke PSD, predicting the breakage suffered by coke particles from the coke plant to the moment they are fed into the furnace is the main challenge. The sequential events suffered by those particles through several chutes, silos produce not only fines but also weaker particles due to accumulation of damage. However, the main issue with the paper is that it seems the authors aren’t aware of the vast literature regarding breakage properties and use ball mill grinding of coke as a way to study coke fragments distribution.

A: Authors thank the reviewer for the comments. The objective of this paper was the PSD modelling of coke grinding product using the Swebrec function and comparing it with other classical distributions; it was not to characterise coke grinding properties, for instance, by determining breakage functions.

R: Regarding the evaluation of the cumulative distribution functions, the procedure is well explained and document, however it presents no innovation to the knowledge on the field, as you can’t ensure that the best function found for the Boayacá coke will work on cokes from other sources that may differ in shape, chemical properties, damage level etc. Therefore, I’m cannot recommend this paper to be published.

A: Authors thank the reviewer for the comment. This study aims not to establish a general rule for PSD modelling in coke, but to show a case of study. The novelty is the consideration of the Swebrec function, for there are no previous references of this function application on coke grinding modelling.

Round 2

Reviewer 1 Report

The coke particle size is one of the significant parameters to select metallurgical coke, which determines the fluid flow resistance, the upward gases and downwards metal liquids passing efficiency, and the iron production rate. However, the coke particle size distribution has not been studied enough. In this work, six different particle size distribution (Gates-Gaudin-Schuhmann (GGS), Rosin-Rammler (RR), Lognormal, Normal, Gamma, and Swebrec) models were implemented, and verified with experimental data at different metallurgical coke grinding conditions. Then, adjusted R2 Akaike information criterion and the root mean of square error were employed as comparison criteria. It was found that the Swebrec and RR models predicted well the coke particle size distribution. Therefore, the work was suggested to be published in the journal of Metals.

Author Response

R: The coke particle size is one of the significant parameters to select metallurgical coke, which determines the fluid flow resistance, the upward gases and downwards metal liquids passing efficiency, and the iron production rate. However, the coke particle size distribution has not been studied enough. In this work, six different particle size distribution (Gates-Gaudin-Schuhmann (GGS), Rosin-Rammler (RR), Lognormal, Normal, Gamma, and Swebrec) models were implemented, and verified with experimental data at different metallurgical coke grinding conditions. Then, adjusted R2 Akaike information criterion and the root mean of square error were employed as comparison criteria. It was found that the Swebrec and RR models predicted well the coke particle size distribution. Therefore, the work was suggested to be published in the journal of Metals.

A: Authors appreciate the reviewer comments that greatly helped to improved the manuscript.

Reviewer 2 Report

The paper is improved, however there are still dozens of instances of grammatical problems, and inconsistent formatting of equations and variables.

For example ,“is the as the minimisation function as Equation 4 established”  does not make sense. 

Also, the authors have now introduced “SSE” which apparently has the same meaning as “RSS” that had already been introduced.

Comments for author File: Comments.pdf

Author Response

R: The paper is improved, however there are still dozens of instances of grammatical problems, and inconsistent formatting of equations and variables.

A: Authors are really sorry for the lack of correctness; an additional and deeper review has been performed. The authors also sincerely appreciate the reviewer's constructive revision, which greatly helped improve the manuscript.

R: For example ,“is the as the minimisation function as Equation 4 established”  does not make sense.

A: Sorry because this sentence was incomplete; was corrected in the revised version of the manuscript.

R: Also, the authors have now introduced “SSE” which apparently has the same meaning as “RSS” that had already been introduced.

A: Thank you again for the thorough review, the reviewer is right, it was corrected in the revised version.

Reviewer 3 Report

Dear authors,

I appreciate the corrections you have made in the paper and the responses to my previous comments. Unfortunately, I still think the paper presents some flaws, therefore I am against its publication unless the paper is reworked.

For your assistance below are some points that needs to be addressed:

1. According to your answers the paper needs to emphasize the goals of the work which is the evaluation of Swebrec function to describe fine coke grinding product in a laboratory tumbling ball mill. This leads to the discussion presented in the document when the authors try to correlate the observations, fitting parameters to grinding conditions
2. In line 60, you say that modelling the distribution fragments of metallurgical coke allows evaluating the breakage its behaviour and mention its importance on iron and steel processes. However, this discussion is thin in the document and does not explicitly shows the need for a better PSD description of laboratory grinding of coke.
3. Additionally, a discussion should be added regarding the characteristics of the PSD curves within the size range obtained from the grinding experiments that justifies the fitting exercise performed the paper with ground coke samples.
4. The presence of GGS results in the box plots in Figure 2a makes the plots unreadable, and difficult to compare the three best functions.
5. Figure 3 would work better if all data were presented in a normalized scale.
6. Table 3 could explicitly show the experimental and calculated from RR model x50 (d50) for given ball sizes and grinding times. If the goal is showing the grinding trends along time, I recommend using time plots.
7. Phrase in line 219 should be rewritten. You mean shorter and longer grinding times? What do you mean by “conditions”? Please elaborate.
8. There is no evidence from your data and there is no discussion about acceleration of fines production. Do you mean the production rates of fines increase along grinding time? How did you measure this?
9. Line 272: Something is missing in this line: “…the metallurgical coke breakage in 4.0 cm balls presents..”
10. The claim: “...the metallurgical coke breakage in 4.0 cm balls presents significant variation with undergrinding for 0.5-1.0 min and overgrinding to grinding time from 3-10 min. 4.0 cm 274 grinding media is perhaps too large, creating voids inside the ball charge and generating less normal forces into particles. “ should be supported by data or appropriate references.
11. The grammar needs correction as some used terms are unused in comminution field: Example: Line 88: Replace “hole fraction” by “voids filling”

Author Response

R: Dear authors,

I appreciate the corrections you have made in the paper and the responses to my previous comments. Unfortunately, I still think the paper presents some flaws, therefore I am against its publication unless the paper is reworked.

For your assistance below are some points that needs to be addressed:

R: 1- According to your answers the paper needs to emphasise the goals of the work which is the evaluation of Swebrec function to describe fine coke grinding product in a laboratory tumbling ball mill. This leads to the discussion presented in the document when the authors try to correlate the observations, fitting parameters to grinding conditions

A: Thank you for the suggestion; in the introduction section was added the following paragraph: "Various studies [14–23] have evaluated the effect of defined ranges of coke particle size in steelmaking performance as a means of process optimisation. The thickness of combustion zone, flame front, chemical reaction kinetics, and iron ores phases formation (hematite, magnetite and gangue) are broadly affected by coke PSD in sinter and blast furnace plants."

R: 2-In line 60, you say that modelling the distribution fragments of metallurgical coke allows evaluating the breakage its behaviour and mention its importance on iron and steel processes. However, this discussion is thin in the document and does not explicitly shows the need for a better PSD description of laboratory grinding of coke.

A: Thank you for the comment; in the Discussion section, it was included a broad argumentation about the need for a better PSD description of laboratory grinding of coke.

R: 3-Additionally, a discussion should be added regarding the characteristics of the PSD curves within the size range obtained from the grinding experiments that justifies the fitting exercise performed the paper with ground coke samples.

A: Thank you for the comment. Again, in the Discussion section some references were added which support the PSD range implementation.

R: 4-The presence of GGS results in the box plots in Figure 2a makes the plots unreadable, and difficult to compare the three best functions.

A: Thank you for the suggestion; a Box plot excluding GGS model was included in supplementary material (Figure S1), making it more understandable.

R: 5-Figure 3 would work better if all data were presented in a normalised scale.

A: Thank you for the suggestion; it was modified in the revised version of the manuscript.

R: 6-Table 3 could explicitly show the experimental and calculated from RR model x50 (d50) for given ball sizes and grinding times. If the goal is showing the grinding trends along time, I recommend using time plots.

A: Thank you again for the suggestion; Figure 5.b was included, showing the colour map of Swebrec x₅₀ parameter.

R: 7-Phrase in line 219 should be rewritten. You mean shorter and longer grinding times? What do you mean by "conditions"? Please elaborate.

A: Sorry, it was improved in the revised version of the manuscript.

R: 8-There is no evidence from your data and there is no discussion about acceleration of fines production. Do you mean the production rates of fines increase along grinding time? How did you measure this?

A: The production of PSD with higher fines content at given times can be used to compare the fines production rate, so the interpretation of that "acceleration" can be derived form this meaning.

R:9-Line 272: Something is missing in this line: "…the metallurgical coke breakage in 4.0 cm balls presents.."

A: Sorry for the mistake, it was improved in the revised version of the manuscript

R:10-The claim: "...the metallurgical coke breakage in 4.0 cm balls presents significant variation with undergrinding for 0.5-1.0 min and overgrinding to grinding time from 3-10 min. 4.0 cm 274 grinding media is perhaps too large, creating voids inside the ball charge and generating less normal forces into particles. "should be supported by data or appropriate references.

A: Thank you, in the discussion section was added the following paragraph and references: "These results are consistent with Austin et al. [45] and Khumalo et al. [46] researches, which established the larger ball sizes break larger particles whereas small grinding media break fines particles. Additionally, Austin et al. [45] proposed that the impact force of collision involving large ball sizes gives larger quantities of fines and more catastrophic fracture behaviour."

R: 11-The grammar needs correction as some used terms are unused in the comminution field: Example: Line 88: Replace "hole fraction" by "voids filling"

A: Authors performed an additional grammar review with a different translator; please apologise. Regarding the use of "hole fraction", it is an expression usually referred in Austin's papers; however, we accepted the reviewer's suggestion and changed the expression in the paper. In any case, we consider that both expressions have the same validity.