A Comparative Analysis of Statistical Models and Mathematics in Reverse Osmosis Evaluation Processes as a Search Path to Achieve Better Efficiency

Round 1

Reviewer 1 Report

To me, review article does not need to write methodology.

However, authors need to create or produce new concept or novelty from references.

Table 1 should include the references where authors create conclusion

It is suggested create  the conclusion between statistical models and mathematic of RO in graph or figure.

It is important for readers to get understanding about this review, how is the statistical models or mathematics working?

Authors should mention which one is better or need to collaborate between statistical models and mathematic in order to produce new novelty/process.

Author Response

Reviewer 1

MPDI

Water

Of my highest consideration,

Thank you for the review and the time spent, indicating that the comments and observations made have served to substantially improve the manuscript. All observations and comments have been considered in the manuscript.

To facilitate review, the answers are detailed one by one. The manuscript is sent with track changes to facilitate the review process.

Observation 1: To me, review article does not need to write methodology.

Response O1: Thank you very much for your suggestion. The methodology described in the article tried to show the process of data collection and analysis. However, we appreciate your feedback and have changed to "review and analysis process.", Please check the line 379

Comment 1: However, authors need to create or produce new concept or novelty from references.

Response C1: Considering your observations and those of the other reviewers, the article has been improved. The detailed answers below illustrate these improvements.

Observation 2: Table 1 should include the references where authors create conclusion

Response O2: The references have been included in the table 1, thank you for your observation, please check the table 1 in the line 400

Observation 3: It is suggested create the conclusion between statistical models and mathematic of RO in graph or figure.

Response O3: Thank you for your suggestions, table 1 details the main characteristics of both models. A graph that can summarize these main characteristics is very interesting, your suggestion has been incorporated into the article, please check the line 465-469

Observation 4: It is important for readers to get understanding about this review, how is the statistical models or mathematics working?

Response O4: Thank you for this important comment, which allows a better explanation. The conclusions have been improved, being clearer and more precise, they explain better how the models work, please check lines 471-496. Considering the comments and observations of the other reviewers, lines 401-464 explain how the models work. Please also check the conclusions have been improved, lines 494-496

Observation 5: Authors should mention which one is better or need to collaborate between statistical models and mathematic in order to produce new novelty/process.

Response O5: This is an important topic, thank you for your observation. In lines 494-496 this topic is mentioned. The conclusions have been improved, they are more precise and concrete, please check lines 471-496.

Kind regards,

Esteban Manuel Villena Martínez

Universidad Católica Boliviana - Universitat Politécnica de Valencia

Author Response File: Author Response.docx

Reviewer 2 Report

Dear author,
Please consider the following comments.

1. Line 15. The article looks local. Extending the results and conclusions to other objects would be necessary, making it more attractive to readers from other countries.

2. Line 22, 492. "On the other hand". It is unclear what "the first hand."

3. Line 41, 56, 94, 110` 145, 436, 463. It is not clear what the word "this" means. It is recommended to add a noun connecting the previous and the current sentence after the word "this".

4. Line 92, 94, 433. The sentence is unclear.

5.  The equation is part of the text of the article. The equation must be followed by a punctuation mark, such as a comma or period.

6. Line 202. It is unclear what "system of equations" means. The number of equations is missing in this sentence.

7. Line 210 and others. Use the italic font for variables in the body of the article.

8. Line 210. The text "The recovery (…) is defined as the fraction (…) or also called (…)" is unclear.

9. Line 228. Avoid specifying a time period based on the time the article was written (for example, "recently", "modern", "new", "nowadays"). Indicate it absolutely (for example, "in 2000-2022"). Line 254. It is unclear what "It" means. Irreversible Thermodynamics is abbreviated as IT earlier.

10. Line 376. The sentence is unclear.

11. Line 397. The criteria for the selection do not determine. It is unclear what databases were used and so on.

12. Line 410. It is unclear what "system" has mentioned and what is elements of this system.

13. The Сonclusion is missing from this article. The results of the review are not precise.

Author Response

Reviewer 2

MPDI

Water

Of my highest consideration,

Thank you for the review and the time spent, indicating that the comments and observations made have served to substantially improve the manuscript. All observations and comments have been considered in the manuscript.

To facilitate review, the answers are detailed one by one. The manuscript is sent with track changes to facilitate the review process.

Observation 1: Line 15. The article looks local. Extending the results and conclusions to other objects would be necessary, making it more attractive to readers from other countries.

Response O1: Thank you very much for your suggestion. This work guided its contribution to the study areas, but its observation is timely and correct, so the wording was improved, making it more extensive in its application. Please check lines 15-27

Observation 2: Line 22, 492. "On the other hand". It is unclear what "the first hand."

Response O2: Thank you very much for your observation, the wording has been corrected, please Check the lines 20-21 and 487

Observation 3: Line 41, 56, 94, 110` 145, 436, 463. It is not clear what the word "this" means. It is recommended to add a noun connecting the previous and the current sentence after the word "this".

Response O3: Your observation is correct, thank you very much for pointing it out. the wordings on each marked line have been improved. please check the lines 40-41, 56, 94, 110-112, 145, 431 and 458-459

Observation 4: Line 92, 94, 433. The sentence is unclear.

Response O4: Indeed, it is not clear, thank you for your observation. Improved wording, please check the lines 92-94 and 428-431.

Observation 5:  The equation is part of the text of the article. The equation must be followed by a punctuation mark, such as a comma or period.

Response O5: The punctuations corresponding to the equations have been placed, thank you for your observation, Please Check lines 171-172, 203, 210, 214 and 217.

Observation 6: Line 202. It is unclear what "system of equations" means. The number of equations is missing in this sentence.

Response O6: Thank you for your observation, the sentence has been improved, the number of the equations was included, Please check lines 201

Observation 7: Line 210 and others. Use the italic font for variables in the body of the article.

Response O7: Thank you for your contribution to improve the article. All the variables of the article have been placed in italics, please check the lines 206, 92, 98-99, 104-105, 124, 175-183, 185, 206.

Observation 8: Line 210. The text "The recovery (…) is defined as the fraction (…) or also called (…)" is unclear.

Response O8: Thank you for your observation. has been corrected. Please check the line 207-208

Observation 9: Line 228. Avoid specifying a time period based on the time the article was written (for example, "recently", "modern", "new", "nowadays"). Indicate it absolutely (for example, "in 2000-2022"). Line 254. It is unclear what "It" means. Irreversible Thermodynamics is abbreviated as IT earlier.

Response O9: That's right, thank you very much, your recommendation has been considered. Please check the line 197, 222

Observation 10: Line 376. The sentence is unclear.

Response O10: The wording has been improved, Thank you for your observation, please check the lines 374-376

Observation 11: Line 397. The criteria for the selection do not determine. It is unclear what databases were used and so on.

Response O11: Indeed, these important data were not placed. Thanks for your observation. This information has been completed in the methodology, section 3, please check the lines 392-395

Observation 12: Line 410. It is unclear what "system" has mentioned and what is elements of this system.

Response O12: The explanation has been improved, please check the lines 404-406, thanks for your comment.

 Observation 13: The Сonclusion is missing from this article. The results of the review are not precise.

Response O13: The conclusions have been improved making them clearer and more precise. Thank you for your important comment. please check the lines 471-496

Kind regards,

Esteban Manuel Villena Martínez

Universidad Católica Boliviana - Universitat Politécnica de Valencia

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

This manuscript entitled A comparative analysis between statistical models vs. mathe- matics in reverse osmosis evaluation processes as a search path to achieve better efficiency

This is a review paper, however, it is important to produce a new novelty (could be method, model, etc.) of all reviews articles read. So far, I couldn't see this.

Author Response

Reviewer 1

MPDI

Water

Of my highest consideration,

Thanks again for the review and the time spent, your comments and observations have allowed us to substantially improve the manuscript. All observations and comments have been considered in the manuscript.

To facilitate review, the answers are detailed one by one. The manuscript is sent with track changes to facilitate the review process.

Observation 1: This is a review paper, however, it is important to produce a new novelty (could be method, model, etc.) of all reviews articles read. So far, I couldn't see this.

Response O1: Thank you very much for your important observation and comment. The manuscript has been improved by incorporating a better explanation of the novelty and proposed methodology

Lines 70-72 and 374-378 indicate the importance and objective of the study. In the Summary, Introduction, Results and Conclusions section, the wording was improved detailing the novelty and proposal, please check the lines:

• In the abstract: Line 27-28: A comparative method is proposed to establish advantages and selection criteria to apply the different models in IO
• In the introduction: Line 73-75: The study constitutes a novel methodology to identify the most efficient model in the evaluation of the operation of the IO, this, based on the advantages and characteristics of each model
• In the goals: 381-382: A methodology is proposed to identify and choose the most appropriate model.
• In the results: Line 474-478: The scheme details a methodology for choosing a mathematical or statistical model based on its main features and uses. To plan the operation and control from a series of operating data of the RO system, the approach suggests a statistical model. If we need greater energy efficiency in industrial scaling based on the physical behavior of the membrane, mathematical models are applied.
• In the conclusions: 506-508: A methodology is proposed to identify and choose an evaluation model for RO systems based on the review of different mathematical and statistical models, what are their main characteristics and uses

Kind regards,

Esteban Manuel Villena Martínez

Universidad Católica Boliviana - Universitat Politécnica de Valencia

Author Response File: Author Response.docx

Reviewer 2 Report

Dear author,
Thank you for improving the manuscript.

Author Response

Reviewer 2

MPDI

Water

Of my highest consideration,

Thanks again for the review and the time spent, your comments and observations have allowed us to substantially improve the manuscript.  

Kind regards,

Esteban Manuel Villena Martínez

Universidad Católica Boliviana - Universitat Politécnica de Valencia

Author Response File: Author Response.docx

Round 3

Reviewer 1 Report

thanks for the answer.

I found the manuscript is well improved, however, it would be very nice if authors could provide mechanism of both model. It is important to show which one is the best to apply

Author Response

Response to Reviewer 1 Comments

Reviewer 1

MPDI

Water

Of my highest consideration,

Thanks again for the review and the time spent, your comments and observations have allowed us to substantially improve the manuscript. All observations and comments have been considered in the manuscript.

To facilitate review, the answers are detailed one by one. The manuscript is sent with track changes to facilitate the review process.

Observation 1: I found the manuscript is well improved, however, it would be very nice if authors could provide mechanism of both model. It is important to show which one is the best to apply

Response O1: Thank you very much for your important observation and comment. The manuscript has been improved by incorporating a better explanation of the novelty and proposed methodology. A subsection 4.1 was placed detailing the procedure and mechanism proposed to choose the most suitable model, based on the main characteristics of each model, its uses and applications. Please check line 469-487 and 515-517.

4.1. Mechanism for the identification and application of the model

The diagram in Figure 7 summarizes the mechanism to identify the ideal model to be implemented, based on the main characteristics and applications of both models.

Figure 7. Schematic procedure to define the ideal model

The scheme details a mechanism to choose a suitable model based on the main characteristics and uses of the RO system.

The first step is to define the context and the limitations of the place where you want to implement the RO. The second step is to know and the main characteristics of each model. The third step is to define the information available and the objective of the analysis. To plan operation and control from a set of RO system operational data, the approach suggests a statistical model, this is a suitable model at the scale you want to improve your planning and operation. If we need greater energy efficiency in industrial scale-up based on the physical behavior of the membrane, this model is suitable for new scale-ups that require lower energy consumption.

A mathematical model may be more suitable for new scale-ups and for countries with economic limitations.

Kind regards,

Esteban Manuel Villena Martínez

Universidad Católica Boliviana - Universitat Politécnica de Valencia

Author Response File: Author Response.docx