Milling Studies in an Impact Crusher I: Kinetics Modelling Based on Population Balance Modelling

Round 1

Reviewer 1 Report

The presented article raises interesting technological issues related to the processing of mineral aggregates.
The assumed purpose of the paper seems to be logical.
I have big remarks on the quality of presented research and lack of consistency in its presentation.
A few comments on the presentation of results:
- the paper presents results for three grinding speeds and the text mentions four (142)
- very modest (or omitted) methodology of determining fraction geometry (equipment, standards, etc.)
- it would be better to use crushing time (s) than the number of cascade passes in the description of research on graphs as well as in conclusions, 
- there is no reference to the influence of subsequent stops of the mill on the process (would it be the same in the case of continuous operation e.g. equal to two passes) 
- suggests the presentation of the crushing time using seconds (s) (187), (236).
- lack of readability in the description of the "x-axis" (236), (257), (259), (296), (298), (301), (311), (313)
- very different styles in description of graphs and fonts used (Figure 3, 4, 5, 6a, ...)
- lack of complete descriptions of presented curves on graphs (Figure 7c, 8b1, 8c1, 9b),
- it is recommended to use sample coding to avoid descriptions e.g. in Figure 3.
The article requires refinement of the presentation styles of the results and completing the description of the measurement methodology.

 

Author Response

Minerals

 

Milling studies in an impact crusher I: kinetics modelling based on Population balance modelling: minerals-1171682

 

Dear Reviewer

 

RE: LIST OF CHANGES ON THE POINTS RAISED BY REVIEWER

Thank you for your useful technical comments and suggestions on our manuscript. We have modified the manuscript accordingly.

 

Detailed corrections are listed below point by point. Points raised by the reviewers are in italics and changes made or our response to those points in normal text.

 

Reviewer’s comments:

The presented article raises interesting technological issues related to the processing of mineral aggregates. The assumed purpose of the paper seems to be logical.

I have big remarks on the quality of presented research and lack of consistency in its presentation. A few comments on the presentation of results:

• Thank you.

 The paper presents results for three grinding speeds and the text mentions four (142)

• Four was mentioned in error in the text and was corrected to three.

Very modest (or omitted) methodology of determining fraction geometry (equipment, standards, etc.)

• A schematic diagram was added in Figure 1

It would be better to use crushing time (s) than the number of cascade passes in the description of research on graphs as well as in conclusions, 

• The authors have changed from the number of passes to crushing time but kept the time in minutes because of the selection function units.

There is no reference to the influence of subsequent stops of the mill on the process (would it be the same in the case of continuous operation e.g. equal to two passes) 

• The subsequent stops occur during test work and are for size analysis to obtain data needed to measure parameters for simulation of the crusher and also to investigate the effect of operational parameters on the PSD. They are similar to batch experiments using a mill where each batch is run for a given time and size analysis performed in between batches. Two passes are similar to running the mill, for a given time, then stop the mill, offload the contents and perform size analysis then return the contents and run the mill for a longer time.

Suggests the presentation of the crushing time using seconds (s) (187), (236).

• The authors maintained the time in minutes because of the units of the selection function.

 

Lack of readability in the description of the "x-axis" (236), (257), (259), (296), (298), (301), (311), (313)

• The “x-axis” are now readable

Very different styles in description of graphs and fonts used (Figure 3, 4, 5, 6a, ...)

• Styles and fonts have been unified

Lack of complete descriptions of presented curves on graphs (Figure 7c, 8b1, 8c1, 9b),

• The descriptions were improved.

The article requires refinement of the presentation styles of the results and completing the description of the measurement methodology

• The article was refined as per the reviewer’s suggestion.

The authors would like to thank the reviewer once more for the constructive comments that help to improve the quality of our work.

Kind regards,

Reviewer 2 Report

The current work studies the prediction of size distribution of ore particles in an impact crusher by implementing a well-known Population Balance Model (PBM). The experiments were performed to determine the empirical parameters of the PBM and to study the behavior of the crusher. The reviewer found the quality of the manuscript as very poor, and major corrections must be applied if the authors wish to publish this paper. The comments can be found in the attached file.

Comments for author File: Comments.pdf

Author Response

Minerals

 

Milling studies in an impact crusher I: kinetics modelling based on Population balance modelling: minerals-1171682

 

Dear Reviewer

 

RE: LIST OF CHANGES ON THE POINTS RAISED BY REVIEWER

Thank you for your useful technical comments and suggestions on our manuscript. We have modified the manuscript accordingly.

 

Detailed corrections are listed below point by point. Points raised by the reviewers are in italics and changes made or our response to those points in normal text.

 

Reviewer’s comments:

 

The English of the manuscript is very poor, and it must be edited by professional scientific language editors. The authors can't state nothing about the efficiency of the mill without providing data concerning energy that was applied to crush the particles. Please, go throughout the manuscript and correct any statement of yours regarding the efficiency of the mill.

• The corrections were done; however, the authors are of the opinion that efficiency is the eventual goal which is achieved through many steps some of which when achieved prompt the use of the word.

The PBM model is a well-known concept of predicting the size distribution of a product in any comminution process, including jet mills and pin mills. This model also has been widely investigated by many researches and many papers has been published. It should be mentioned also that the selection and breakage functions used in this work were also developed by others. The reviewer is not convinced regarding the contribution of the current work to the knowledge in the field of comminution of particles.

The authors should expand the introduction and convince the reader regarding the contribution of this work.

• The authors agree with the reviewer that PBM is a well-known model applied by many researchers to simulate different mills and that is the reason for its adoption in this work. References were also given regarding the source of the model and the authors were clear from the beginning that the model has been widely used to describe particle breakage in ball mills and cited references in which that was done. This clearly showed that the model was already established when the authors used it.

As for the contribution of the work to the body of knowledge, the reviewer has rightly pointed out that the model has been widely investigated by many researchers and many papers were published from it. It is obvious that although using the same model, those papers were investigating different comminution machines and parameters, which each making its unique contribution to the body of knowledge. The authors are thus convinced that using the model to investigate the effect of the combination of rotor speed and particle size on this particular impact crusher avails important information regarding its operation to the body of knowledge.

If the authors succeeded to predict the product size and power consumption in impact crusher with the Whiten model, what will be an effort of achieving the same results with Population Balance Model?

• Segura-Salazar et al (2017) used the Whiten model to investigate mainly the effect of rotor speed and feed rate on the PSD whereas in this work, it is the Population Balance Model used to investigate the effect of the particle size and rotor speed on the PSD.

The authors claim that the parameters µ and a depend only on mill condition. Does their values remain unchanged if you apply this model to other material?

• Every material has its own set of parameters describing its grindability. When µ and a are said to be depending only on mill conditions, it is referred to scale-up scenarios in which the parameters have to change when laboratory or pilot test results (obtained using small mills) are scaled-up to industrial conditions (using bigger mills).

Does the authors checked if the sample of 400 g is a representative sample?

• Yes it was checked after using a rotary splitter

The authors must describe in details the calculation process of the flow chart shown in Fig. 2.

 

• The description of the calculation process was added. However, it is important to note that the full calculation procedure is worth of a research paper which was cited by the authors.

“As seen in Figures 3, the breakage kinetics appear to be first order” Please explain this statement further.

• The statement was wrongly phrased. The authors wanted to say that the breakage kinetics displayed first order behaviour.

How does it possible that the both charts, Fig. 3 and Fig. 4, describe the same specific rate of breakage if the values in Fig. 4 are determined from the slopes of the function shown in Fig. 3?

In addition, please provide a title and units to the legend in the graph.

• Figure 3 presents the determination of the selection function values from the first order plots whereas Figure 4 shows variation of the selection function with particle size. In figure 4 is where the Selection function parameters a and α are determined.

The units were provided.

The word "progeny" is an improper term to use here.

In comminution of particles, we commonly use to describe the original particles as "mother particles" or "mother fraction", and describe the broken particles/fragments/product as "daughter particles". I would suggest the authors use this kind of terminology throughout the manuscript.

• The authors have changed to ‘daughter fragments’ as per the reviewer’s request. However, the word progeny has also been widely used to describe broken particles in comminution.

Please provide more information about the founding in [20] and how it is related to the current work. What was investigated there?

• The authors wanted to confirm their observations with those from the reference cited. Nevertheless, the authors resolved to remove the reference.

“As the rotor speed was increased to 2080…”

Please provide data also for 2080 RPM.

• The statement was written in error, therefore, it was removed.

The word “screen” should be replaced with "sieve". Please make the same correction throughout the manuscript.

• The word screen was replaced with sieve as per the reviewer’s suggestion

The sentence is unclear.

• The statement was corrected to improve clarity

What is the diameter of impeller and what is the distance between the impeller and the crusher base? Please provide this information in the table.

• A schematic of the crusher was included in Figure 1 providing the information

The word “flowsheet” should be changed to “flowchart”.

• The change was made as requested

The scale values of the vertical axis are missing. (Figure 3)

• The scale values were added

What are the parameters and the measurable units of the Selection Function values reported in the Table?

Please specify the units of rotor speed and the description and units of the values appear in the top row of the table.(Table 3)

• The table was deleted from the manuscript at another reviewer’s request

What is BII method? Please specify in the text

• The description of the BII method was given in the text.

Does the “size 1” represents the upper limit of the undersize cumulative distribution? Please clarify this in the text.

• “size 1” was clarified in the text

Please emphasize in the text that the horizontal axis is a normalized particle size.

Please provide more tick values in the vertical and horizontal axis.

In addition, please change the title "relative size" to "normalized particle size".

Also, instead of Average line, please plot the fitted Eq. (2) function, including the accuracy lines of the fitted function. (Figure 5)

• Data from the fitted Equation 2 function was plotted and the tick values were provided as suggested by the reviewer. The normalisability of the data was mentioned in the paragraph above Figure 5 and the relative size title can be considered standard since it is the one generally used for these plots (Austin et al 1984, Yekeler 2007, Bozkurt and Ozgur 2007 and many other researches. Thus the authors have decided to retain it.

The resizing of Figure 6-a is not proportional. Please, make a correction.

The title of the vertical axis in both the graphs should be changed to "cumulative distribution".

Please use the same format of units definition in the titles of the axis. Decide whether the units will be shown in parenthesis or not and keep it throughout the manuscript. (Figure 6)

• The proportionality issue was addressed when the figures were redrawn. The authors have decided to put the units in parenthesis and have maintained it through the manuscript.

 

Please provide the units of the values shown in the Tables. Tables 4, 5 and 6

Also, the particle size can't be 0. Please correct this value to a proper one.

• The units were provided and every zero value was replaced with a dash.

The entire paragraph is unclear. Page 8, lines 248-254

• It was clarified by providing further explanation.

Tick values of the axis and the legend text should be the same for all the three graphs in the Figure.

Change the Title of vertical axis to "cumulative distribution" in all the graphs.

There is no such units called "microns". Microns is a multiply factor for any measurable unit. Please change it to "µm". (Figure 7)

• The tick values were made similar and the legends were corrected. The units of microns were written in error, it should be “mm” and that has been corrected.

Tick values of the axis and the legend text should be the same for all the graphs in the Figure.

Change the Title of vertical axis to "cumulative distribution" in all the graphs. (Figure 8)

• Tick values of the axis and the legend were made similar and the vertical axis was renamed to cumulative distribution as suggested by the reviewer.

Change the units of horizontal axis to “µm”. (Figure 9)

The units were changed to “mm”, because “µm” was written in error.

The authors would like to thank the reviewer once more for the constructive comments that help to improve the quality of our work.

Kind regards,

 

Reviewer 3 Report

The paper is very interesting, it shows the importance of the population balance model in order to describe different types of comminution machines. However, the effect of the impact crusher variables is not deeply analyzed in the paper.

In the introduction chapter, you can include the Voegel and Peukert work, it is very important in the impactor crusher modeling:
Vogel, L., & Peukert, W. (2003). Breakage behaviour of different materials—construction of a mastercurve for the breakage probability. Powder Technology, 129(1-3), 101-110.

In the paper is expected a good agreement of the PBM predicted results with the experimental results, but the predicted results are shown only for the -13.2/11.2 mm size and 885 rpm rotor speed, then is necessary to show a comparison of the PBM predicted results for all the experimental tests conditions.

Is necessary to improve the quality of the figures and tables, comments are included in the manuscript pdf document. Many of the figure legends are illegible, the units are not included and the scales are different for all the axis then is difficult to compare the product size distributions for different operational conditions.

The reviewer recommends major changes and a better discussion of the results. Is possible to show some correlations of the selection as a function of the rotor speed, particle size, and grinding time. 

Regards

Comments for author File: Comments.pdf

Author Response

Minerals

 

Milling studies in an impact crusher I: kinetics modelling based on Population balance modelling: minerals-1171682

 

Dear Reviewer

 

RE: LIST OF CHANGES ON THE POINTS RAISED BY REVIEWER

Thank you for your useful technical comments and suggestions on our manuscript. We have modified the manuscript accordingly.

 

Detailed corrections are listed below point by point. Points raised by the reviewers are in italics and changes made or our response to those points in normal text.

 

Reviewer’s comments:

 

Please, if possible include a table with the Rolfe quarry properties as density, Young Modulus, composition, etc

• The information was provided in the first paragraph of Section 2.2

The table 3 and the Figure 4 are redundant, please choose one of them

• The authors chose Figure 4 and removed Table 3

Please if possible improve the graph using symbols with transparent filling

• The authors used symbols with transparent filling in Figures 4 and 5 as suggested by the reviewer.

Please put the graphs in the same scale and form in order to be compared and include the feed particle size distribution (Figure 6)

• The figures were put in the same scale and form as suggested by the reviewer.

This results are only population balance model predictions? Is possible you compare with experimental results? (Figure 6)

• The comparison was done as suggested by the reviewer

Please include two decimals and the units (mm) (Table 4)

• The values were presented in 2 decimal places and the units were included as suggested by the reviewer in Tables 4, 5 and 6

Put the y-axis in the same scale from 0.01 to 100 (Figure 7)

• The y-axis was put in the same scale 0.01 to 100 for all graphs in Fig. 7

Is not possible read the legend (Figure 7)

• The problem was fixed and the legend is now readable.

Please divide this Figure in 2 as you did in Figures 7 and 9 and correct the legends.

• The figures were divided as suggested but kept as Figure 8

Please correct the legend (Figure 9b)

• The legend was corrected

 

The authors would like to thank the reviewer once more for the constructive comments that help to improve the quality of our work.

Kind regards,

 

Round 2

Reviewer 1 Report

The submitted article was corrected by the authors according to the submitted comments. This work is an interesting study which, with minor corrections, can be published.
Please check and correct Figure 1 and Figure 10. I leave it to the authors to decide the legibility of the axis scale used in Figure 4, Figure 5, Figure 7 and Figure 9. The font size in Equation 1 differs significantly from the other equations. The titles of Tables 5 and 6 should at least have the statement "calculated values". In Figure 6, the reference to Figure d was left undeleted.
In general, please pay attention to the font styles used and the formatting of the data presented in the paper. 

Author Response

Minerals

 

Milling studies in an impact crusher I: kinetics modelling based on Population balance modelling: minerals-1171682

 

Dear Reviewer

 

RE: LIST OF CHANGES ON THE POINTS RAISED BY REVIEWER

Thank you for your useful technical comments and suggestions on our manuscript. We have modified the manuscript accordingly.

 

Detailed corrections are listed below point by point. Points raised by the reviewers are in italics and changes made or our response to those points in normal text.

 

Reviewer #1

The submitted article was corrected by the authors according to the submitted comments. This work is an interesting study which, with minor corrections, can be published.

Thank you

Please check and correct Figure 1 and Figure 10.

The Figures were corrected and are now displaying properly.

I leave it to the authors to decide the legibility of the axis scale used in Figure 4, Figure 5, Figure 7 and Figure 9.

The font sizes of the axis titles and scale values of the figures were increased to improve legibility.

The font size in Equation 1 differs significantly from the other equations.

The font size was increased

The titles of Tables 5 and 6 should at least have the statement "calculated values".

The values in Tables 5 and 6 were determined from the cumulative distribution plots of different crushing times, thus the authors were not sure if it is correct to refer to them as calculated values.

In Figure 6, the reference to Figure d was left undeleted.

The authors removed it.

In general, please pay attention to the font styles used and the formatting of the data presented in the paper. 

The authors have checked and unified the font styles.

The authors would like to thank the reviewer once more for the constructive comments that help to improve the quality of our work.

Kind regards,

Reviewer 2 Report

The manuscript can be published

Author Response

The manuscript can be published

Thank you

The authors would like to thank the reviewer once more for the constructive comments that help to improve the quality of our work.

Kind regards,

Reviewer 3 Report

Dear Authors,

The paper has significant improvements, however schematics in figure 1 and figure 10 are ununderstandable, you have to correct them. 

Populations balance model parameters fitting result in a good agreement experimental results description (Figure 6), you can also mention the error between the experimental and calculated PSD values. It is important to do the same comparison with the results in Figures 7, 8 and 9, in order to show the PBM good representativeness for different particle sizes. 

Regards

Comments for author File: Comments.pdf

Author Response

Milling studies in an impact crusher I: kinetics modelling based on Population balance modelling: minerals-1171682

 

Dear Reviewer

 

RE: LIST OF CHANGES ON THE POINTS RAISED BY REVIEWER

Thank you for your useful technical comments and suggestions on our manuscript. We have modified the manuscript accordingly.

 

Detailed corrections are listed below point by point. Points raised by the reviewers are in italics and changes made or our response to those points in normal text.

 

Reviewer #3

The paper has significant improvements, however schematics in figure 1 and figure 10 are ununderstandable, you have to correct them. 

Thank you. The authors have corrected the display of the figures.

Populations balance model parameters fitting result in a good agreement experimental results description (Figure 6), you can also mention the error between the experimental and calculated PSD values. It is important to do the same comparison with the results in Figures 7, 8 and 9, in order to show the PBM good representativeness for different particle sizes. 

The authors included error bars and found the graphs congested; therefore, they resolved to remove them to improve clarity. Figures 7,8 and 9 presents experimental data thus, there was no need to include simulated results since simulation is needed beyond experimentation and also the comparison has been done in figure 6.

Please correct the dimensions, is not possible to read it

The dimensions were corrected

 

Please include the modeled results in these figures

The numbers were corrected

 

The authors would like to thank the reviewer once more for the constructive comments that help to improve the quality of our work.

Kind regards,