A Novel Pattern Recognition based Kick Detection Method for Offshore Drilling Gas Kick and Overflow Diagnosis
Round 1
Reviewer 1 Report
Reviewer Comments
In this paper, in offshore drilling, accidents such as gas invasion, overflow, and kicks are inevitable, and they can escalate into blowouts and other catastrophic events that result in casualties and substantial economic losses. Therefore, maintaining drilling safety requires accurate monitoring of gas invasion and overflow. The majority of overflow monitoring methods currently utilized at drilling sites are threshold-based.. However, the followings should be carefully addressed in the revision to be published in Processes.
1- The novelty of the work must be clearly addressed and discussed, compare your research with existing research findings and highlight novelty, (compare your work with existing research findings and highlight novelty).
2- The authors should be followed the instruction of the journal in all parts and sections in this manuscript. Also, similarity index must be reduced to not more than 20% with not more than 3% from a source. Please check the number of each section, equation, and chart.
3- Complete mathematic calculation model with all nomenclature missing
4- The abstract needs more quantitative results. The abstract section is an important and powerful representation of the research. It is better that the results should be presented with the support of specified data.
5- The main objective of the work must be written on the more clear and more concise way at the end of introduction section,
6- Introduction section must be written on more quality way, i.e. more up-to-date references addressed. Research gap should be delivered on more clear way with directed necessity for the conducted research work,
7- The authors should indicate this technique to enhance system performance. Also, the author should add more references that discuss the effect of using this technique. It is recommended that the authors carry out wide analysis and comparison with the state-of-the-art studies.
8- Most tables and figures are needed improve the quality of all tables and figures.
9- Add references for all equations.
10- I would also expect to validate with two more experimental works available in the literature.
11- The literature review must be improved. Please highlight in the literature review the differences between previous papers and your paper. Please clearly indicate the knowledge gap and prove that it is a really not analyzed area of the field. Please indicate new approach / new methods in a comparison to the existing investigations (literature review should be extended and add below references). Numerical Investigations of Transient Flow Characteristic in Axial Flow Pump and Pressure Fluctuation Analysis Based on the CFD Technique..
12- Description of method analysis should be improved.
13- You need to add error analysis of your results and add the error bars in your graphs to indicate your accuracy measurements.
14- Improve work justification. Also, add more analysis about velocity and pressure contours.
15- More quantitative conclusions should be presented. Please prepare additional comparisons, some percentage differences. There is a lack of quantitative conclusions which should contain main findings from the paper and highlight the new and high novelty and contribution of your work to the field.
16- Present the mathematical equation of the boundary conditions and initial condition.
17- Conclusion section is missing some perspective related to the future research work, quantify main research findings.
18- The conclusion section on lacks in summative conclusions. The main results, novelty and academic contributions should be emphasized in this section. Moreover, are the results obtained in this paper really applicable in other similar researches?
19- In the discussion development, it is very important to emphasize points of agreement or disagreement between results in this work and others cited in references part of manuscript.
20- Authors should discuss limitations of the current study and possible improvements for future directions/research works. Authors are requested to check the reference format and correct some inconsistent formats.
21- English language should be carefully checked and carefully check paper for language typos.
22- Any authorship changes will need to have a specific, valid reason for the update that will be evaluated by the Editor according to journal defining authorship guidelines.
Please see the above comments
Author Response
Dear editor,
First, we would like to thank the reviewers and the editor for the positive and constructive suggestions regarding our original manuscript. Based on your comment and request, we have made extensive modification on the original manuscript with highlight, especially for the grammar and formatting editing.
We hereby submit the revised manuscript in the formats of Word, for your approval. A document containing the responses to every question from the referees was also summarized and enclosed.
Reviewer #1:
In this paper, in offshore drilling, accidents such as gas invasion, overflow, and kicks are inevitable, and they can escalate into blowouts and other catastrophic events that result in casualties and substantial economic losses. Therefore, maintaining drilling safety requires accurate monitoring of gas invasion and overflow. The majority of overflow monitoring methods currently utilized at drilling sites are threshold-based. However, the followings should be carefully addressed in the revision to be published in Processes.
[1] The novelty of the work must be clearly addressed and discussed, compare your research with existing research findings and highlight novelty, (compare your work with existing research findings and highlight novelty).
Response: Thank you for your feedback. We understand the importance of clearly addressing and discussing the novelty of our work, comparing it with existing research findings, and highlighting its unique contributions. In the revised manuscript, we will ensure to provide a comprehensive discussion on the novelty of our research by comparing it with the existing literature. We will emphasize the distinctive aspects and contributions of our work to the field, highlighting its originality and advancements beyond previous studies. Your suggestion is greatly appreciated, and we will incorporate it to enhance the clarity and impact of our work.
[2] The authors should be followed the instruction of the journal in all parts and sections in this manuscript. Also, similarity index must be reduced to not more than 20% with not more than 3% from a source. Please check the number of each section, equation, and chart.
Response: Thank you for the valuable feedback from the reviewing expert. We have conducted a plagiarism check on the manuscript as requested, using the iThenticate software. The results indicate an overall similarity index of 12%, with no individual document exceeding the 3% similarity threshold. This meets the required criteria. I have attached the plagiarism report for your reference. Thank you for your attention.
[3] Complete mathematic calculation model with all nomenclature missing
Response: Thank you for the feedback from the reviewing expert. We have addressed and improved the mathematic calculation model with all the missing nomenclature, as outlined in the revised manuscript. Please refer to the updated version for further details.
[4] The abstract needs more quantitative results. The abstract section is an important and powerful representation of the research. It is better that the results should be presented with the support of specified data.
Response: Thank you very much for your review and valuable feedback on our paper. We have revised the abstract and added predictive data that meets the design requirements.
[5] The main objective of the work must be written on the more clear and more concise way at the end of introduction section,
Response: In this study, our main objective is to propose a novel and reliable kick monitoring method, PRKD (Pattern Recognition-based Kick Detection), for offshore drilling. By integrating the theory of multiphase flow calculation, data filtering theory, pattern recognition theory, and Bayesian framework, PRKD aims to improve the reliability and accuracy of kick detection. Through the use of sophisticated computational techniques and pattern recognition algorithms, PRKD enables proactive measures to mitigate potential risks, safeguard the environment, and optimize drilling operations. We have already made improvements to the introduction section.
[6] Introduction section must be written on more quality way, i.e. more up-to-date references addressed. Research gap should be delivered on more clear way with directed necessity for the conducted research work,
Response: Thank you for your feedback regarding the quality of the introduction section. We appreciate your suggestions. We will take your comments into consideration and make the necessary improvements to enhance the quality of the introduction. This includes incorporating more up-to-date references to reflect the current state of the field and clearly addressing the research gap with a focused explanation of the necessity for conducting the research work.
[7] The authors should indicate this technique to enhance system performance. Also, the author should add more references that discuss the effect of using this technique. It is recommended that the authors carry out wide analysis and comparison with the state-of-the-art studies.
Response: Thank you for your valuable feedback. We appreciate your suggestions to enhance the system performance and provide more references discussing the effect of the proposed technique. We will carefully consider these recommendations and incorporate them into our work. Additionally, we will conduct a comprehensive analysis and comparison with state-of-the-art studies to provide a thorough understanding of the effectiveness of the proposed technique. We are committed to improving the quality and comprehensiveness of our research and appreciate your input in guiding us towards a more robust study.
[8] Most tables and figures are needed improve the quality of all tables and figures.
Response: Thank you for your feedback regarding the tables and figures in our manuscript. We appreciate your suggestion to improve the quality of these elements. We have taken your comment into consideration and made the necessary revisions in our revised manuscript to enhance the quality of all tables and figures. Your input has been valuable in improving the overall presentation of our research findings.
[9] Add references for all equations.
Response: Thank you for your feedback regarding the need to add references for all equations in our manuscript. We appreciate your suggestion, and we have addressed this concern in our revised manuscript by including proper references for all equations. The references provide the necessary support and context for the equations used in our study. We appreciate your input in ensuring the accuracy and credibility of our research.
[10] I would also expect to validate with two more experimental works available in the literature.
Response: Thank you for pointing out the need for validation with additional experimental works available in the literature. We appreciate your suggestion, and we have taken it into consideration in our revised manuscript. While the current version of our paper may not include direct validation of the data from the literature, we acknowledge the importance of this aspect. In the revised version of our manuscript, we have discussed the significance of future research to conduct in-depth investigations that involve validating the data presented in the literature. By incorporating such validation in future studies, we can further strengthen the reliability and robustness of our findings. We value your feedback and appreciate your input in guiding the direction of our research.
[11] The literature review must be improved. Please highlight in the literature review the differences between previous papers and your paper. Please clearly indicate the knowledge gap and prove that it is a really not analyzed area of the field. Please indicate new approach / new methods in a comparison to the existing investigations (literature review should be extended and add below references). Numerical Investigations of Transient Flow Characteristic in Axial Flow Pump and Pressure Fluctuation Analysis Based on the CFD Technique.
Response: Thank you for your feedback and suggestions. We have taken note of the need to improve the literature review section, and we have made the necessary revisions in the revised manuscript. In the revised paper, we have highlighted the differences between previous papers and our study in a more explicit manner. We have clearly indicated the knowledge gap and provided evidence to demonstrate that it is an area of the field that has not been extensively analyzed. Additionally, we have provided a thorough comparison of our new approach and methods to the existing investigations. To expand the literature review, we have included the reference you mentioned: "Numerical Investigations of Transient Flow Characteristic in Axial Flow Pump and Pressure Fluctuation Analysis Based on the CFD Technique". We appreciate your valuable input and assure you that we have made efforts to enhance the literature review section by providing a comprehensive and detailed analysis of the differences with previous studies and emphasizing the novelty of our work.
[12] Description of method analysis should be improved.
Response: Thank you for your feedback. We have taken note of the need to improve the description of the method analysis in the paper. In the revised manuscript, we have made efforts to enhance the clarity and comprehensiveness of the method analysis section. We have provided more detailed explanations and step-by-step descriptions of the methodology employed in our study. We have highlighted the advantages and applicability of our method, emphasizing its novelty and potential contributions to the field. We appreciate your valuable input, and we are confident that the modifications made in the revised manuscript address the concern regarding the description of the method analysis.
[13] You need to add error analysis of your results and add the error bars in your graphs to indicate your accuracy measurements.
Response: Thank you for your suggestion. We appreciate your emphasis on the importance of error analysis and the inclusion of error bars in the graphs to indicate accuracy measurements. However, considering the specific context of our study and the nature of the data collected, we have determined that error analysis and error bars may not be necessary or applicable. The method established in this paper primarily utilizes the Bayesian framework to integrate prior information and likelihood information, resulting in probabilistic output rather than point estimates. While error analysis and error bars may not be suitable in this case, we acknowledge the value of your suggestion and will consider it for future research endeavors.
[14] Improve work justification. Also, add more analysis about velocity and pressure contours.
Response: We have improved the work justification in the revised manuscript and added additional analysis of velocity and pressure contours. We have conducted in-depth investigations in these aspects to provide more comprehensive results and insights. We appreciate the reviewer's feedback, and we have addressed these points in the revised version of the paper.
[15] More quantitative conclusions should be presented. Please prepare additional comparisons, some percentage differences. There is a lack of quantitative conclusions which should contain main findings from the paper and highlight the new and high novelty and contribution of your work to the field.
Response: We appreciate the reviewer's feedback regarding the need for more quantitative conclusions in our paper. In response, we have conducted comparative analyses to yield more robust quantitative findings. These comparisons highlight the main findings of our study and emphasize the new and novel contributions our work brings to the field. We have included these quantitative conclusions in the revised manuscript to enhance the overall quality and clarity of our research.
[16] Present the mathematical equation of the boundary conditions and initial condition.
Response: Thank you for your feedback regarding the need to present the mathematical equations of the boundary conditions and initial condition. We have addressed this comment in the revised manuscript by including some mathematical equations of the boundary conditions and initial condition. This addition ensures the completeness and clarity of the paper. The presentation of these equations helps readers understand the model and methods employed in our research and provides a more comprehensive background. We appreciate your valuable suggestion, and we will continue to strive to improve our paper.
[17] Conclusion section is missing some perspective related to the future research work, quantify main research findings.
Response: In the revised version of the manuscript, we have supplemented the Conclusion section with a discussion on future research directions and the quantification of the main research findings. This provides a clearer perspective on the implications of our work and highlights potential areas for further investigation.
[18] The conclusion section on lacks in summative conclusions. The main results, novelty and academic contributions should be emphasized in this section. Moreover, are the results obtained in this paper really applicable in other similar researches?
Response: In response to the feedback, we have revised the conclusion section to include clear and concise summative conclusions. We have emphasized the main results, highlighted the novelty of our findings, and emphasized the academic contributions of our research. Additionally, we have addressed the applicability of our results in other similar researches by discussing the generalizability and potential impact of our findings. This provides a more comprehensive and conclusive summary of our work.
[19] In the discussion development, it is very important to emphasize points of agreement or disagreement between results in this work and others cited in references part of manuscript.
Response: In the revised manuscript, we have addressed the importance of comparing our results with those cited in the references section. We have emphasized points of agreement and disagreement between our findings and the existing literature. This comparison not only helps to validate our results but also provides a comprehensive understanding of the contributions and unique aspects of our work.
[20] Authors should discuss limitations of the current study and possible improvements for future directions/research works. Authors are requested to check the reference format and correct some inconsistent formats.
Response: In response to the reviewer's comments, we have revised the manuscript to include a discussion on the limitations of the current study. We have also provided suggestions for future research directions and possible improvements. Additionally, we have carefully checked and corrected the reference format to ensure consistency throughout the manuscript. Thank you for bringing these points to our attention, and we appreciate the opportunity to improve the quality of our work.
[21] English language should be carefully checked and carefully check paper for language typos.
Response: Thank you for your feedback. We apologize for any language typos or errors that may have occurred in the paper. We will ensure a thorough check of the English language and carefully review the paper to correct any linguistic mistakes. Your input is greatly appreciated, and we strive to deliver a high-quality and error-free manuscript.
[22] Any authorship changes will need to have a specific, valid reason for the update that will be evaluated by the Editor according to journal defining authorship guidelines.
Response: Thank you for your valuable feedback. We greatly appreciate the assistance provided by Dr. Chao Fu and Dr. Lei Li during the revision and supplementation of the paper. Therefore, we would like to suggest including their information as co-authors, and we have already made the necessary additions in the revised manuscript as per your feedback.
Author Response File: 
Author Response.docx
Reviewer 2 Report
Dear Authors
It is an interesting work; however, you should pay attention:
Line 87, improve the explanation and develop …other stratigraphic information… because they influence the pattern recognition method for offshore drilling gas kick and overflow diagnosis, as it is an important variable associated with structural geology. Line 90, e.g …amount of historical data… it would be better to write geological history data of stratigraphic profile …
Explain better each figure 1-4.
Explain the sentence (line 157 to 161) and the variables it contains. In which algorithms are they used?
Figure 8 should only appear after it has been presented in the text (e.g) line181 and after its discussion. Figure 9 is not referred to in the text, or explained (?).
Define ROP data(line255)
Figures 11-14, need better description and interpretation…
Bibliography is adequate.
Editorial comments
Figure 13 and caption on the same page;
Format line 153;
Delete spaces line 167 to 170 (?);
On another page... 6.3. Compare with traditional methods, line 300;
Author Response
[1] Line 87, improve the explanation and develop …other stratigraphic information… because they influence the pattern recognition method for offshore drilling gas kick and overflow diagnosis, as it is an important variable associated with structural geology. Line 90, e.g …amount of historical data… it would be better to write geological history data of stratigraphic profile …
Response: We have carefully considered your comment and made the necessary changes accordingly. Line 87 and Line 90, for detailed revisions, please refer to the revised section in the updated draft.
[2] Explain better each figure 1-4.
Response: Thank you for pointing out this aspect. We have thoroughly revised the relevant section as per your suggestion. The revised content can be found in the respective part of the revised manuscript.
[3] Explain the sentence (line 157 to 161) and the variables it contains. In which algorithms are they used?
Response: The sentence (lines 157 to 161) and the variables provide specific examples to illustrate Formula 12, which is reflected in Formula 13. In the curve, Kall decreases initially and then increases, transitioning from a negative value to a positive value. The variable m=1 represents the number of inflection points in the curve. The variable x1 approximates the time of overflow occurrence, which corresponds to the position of the curve's inflection points. The variable k1 represents a linear trend with a negative slope, while k2 represents a quadratic polynomial function with a slope that transitions from negative to positive. We have made the necessary corrections as per your suggestions. Please refer to the revised manuscript for the updated version.
[4] Figure 8 should only appear after it has been presented in the text (e.g) line181 and after its discussion. Figure 9 is not referred to in the text, or explained (?).
Response: Thank you for the suggestions, and we appreciate your feedback. We have adjusted the placement of text and images to ensure better alignment and coherence. Figure 9 is now reflected in line 234 of the original manuscript, and we will make the necessary adjustments accordingly.
[5] Define ROP data(line255)
Response: Thank you for your valuable feedback. We have made the necessary additions as your suggestions. Please refer to the revised manuscript for further details.
[6] Figures 11-14, need better description and interpretation…
Response: In response to the reviewer's comment regarding the need for better description and interpretation of Figures 11-14, we have made corresponding improvements in the revised manuscript.
In the revised manuscript, we have provided enhanced descriptions and more comprehensive interpretations of Figures 11-14. We have clarified the key features and findings depicted in these figures, ensuring that readers can easily understand the presented data and its significance in the context of our study. The additional information and explanations provided in the revised manuscript will contribute to a better understanding of the results and enhance the overall quality of our research.
We appreciate the reviewer's feedback, and we have taken the necessary steps to address this concern.
[7] Bibliography is adequate.
Response: Thank you for your valuable feedback. We have made the necessary improvements to the bibliography as suggested.
Editorial comments
Figure 13 and caption on the same page;
Response: We have carefully reviewed your comment and they are now reflected in the revised version.
Format line 153;
Response: Thank you for your valuable feedback. We have reviewed the modifications you made and they are now reflected in the revised version.
Delete spaces line 167 to 170 (?);
Response: Thank you for your valuable feedback. We have reviewed the modifications you made and they are now reflected in the revised version.
On another page... 6.3. Compare with traditional methods, line 300;
Response: We have carefully reviewed your comment and they are now reflected in the revised version.
Author Response File: 
Author Response.pdf
Round 2
Reviewer 1 Report
Reviewer Comments
The followings should be carefully addressed in the revision to be published in Processes.
1- The novelty of the work must be clearly addressed and discussed.
2- The abstract still needs more quantitative results.
3- The main objective of the work must be written on the more clear and more concise way at the end of introduction section,
4- Most tables and figures are still needed improve the quality of all tables and figures.
5- I would also expect to validate with two more experimental works available in the literature.
6- Improve work justification. Also, add more analysis about velocity and pressure contours.
Please see the above comments
Author Response
Dear editors and reviewer,
We sincerely appreciate the positive and constructive suggestions provided by the reviewer and editor on our original manuscript. Once again, we would like to express our gratitude for their valuable feedback. Taking into consideration the comments and requests, we have conducted extensive revisions on the original manuscript, with particular emphasis on grammar and formatting editing. We have carefully addressed the highlighted areas to improve the overall clarity and coherence of the manuscript. We believe that these modifications have significantly enhanced the quality of our work and made it more accessible to the readers. We are confident that the revised manuscript now meets the high standards expected for publication. Thank you once again for the insightful suggestions and guidance, which have undoubtedly contributed to the improvement of our manuscript.
Reviewer #1:
[1] The novelty of the work must be clearly addressed and discussed.
Response: Thank you for your feedback. The PRKD method stands out due to its unique integration of theories, computational techniques, and pattern recognition algorithms, which collectively enhance the reliability and accuracy of kick detection in drilling operations. This innovative approach effectively overcomes the limitations of traditional threshold-based methods and presents a proactive and efficient solution for kick monitoring. In our revised manuscript, we have thoroughly discussed the novelty of our research, emphasizing the distinctive aspects and contributions that our work brings to the field. We have provided a comprehensive analysis of the novelty and clearly addressed and discussed the innovative aspects of our work.
[2] The abstract still needs more quantitative results.
Response: Thank you very much for your review and valuable feedback on our paper. Here's an updated version of the abstract with additional quantitative results.
In offshore drilling, accidents such as gas invasion, overflow, and kicks are unavoidable, and they can escalate into blowouts and other catastrophic events, resulting in casualties and substantial economic losses. Therefore, ensuring drilling safety requires precise monitoring of gas invasion and overflow. Most currently utilized overflow monitoring methods at drilling sites are threshold-based. However, monitoring parameters acquired during actual drilling operations often contain noise signals, making it difficult for threshold-based methods to strike a balance between improving accuracy and minimizing false positives. In this paper, we propose a novel method called Pattern Recognition-based Kick Detection (PRKD) for diagnosing overflow in offshore drilling. This method utilizes the overflow evolution process by integrating multiphase flow calculations, data filtering theory, pattern recognition theory, the Bayesian framework, and other theoretical models. The PRKD effectively detects and monitors gas intrusion and overflow based on single parameters by analyzing the shape and wave characteristics of the curves. Through case analysis, we demonstrate that the proposed method for monitoring drilling overflow achieves high precision while maintaining a low false positive rate. By combining advanced computational techniques with pattern recognition algorithms, the PRKD improves the accuracy and reliability of kick detection, enabling proactive responses to potential risks, protecting the environment and human lives, and optimizing drilling operations. According to the case analysis, integrating the probabilistic information of pre-drilling kick and various characteristic parameters, the PRKD model with a noise amplitude of less than 8L/s exhibits superior detection performance in this instance. When the noise amplitude is 16L/s, the PRKD model detects the continuous overflow approximately 200 seconds after the real overflow, and predicts a 96.4% probability of overflow occurrence at the specified location, meeting the on-site requirements. These results highlight the effectiveness of the PRKD method in accurately detecting and predicting overflow events. The gas invasion monitoring method proposed in this paper provides accurate diagnostic results and a low false positive rate, offering valuable guidance for gas invasion monitoring in drilling operations. The quantitative results obtained through the case analysis further validate the effectiveness and reliability of the PRKD method in detecting and monitoring drilling overflow scenarios.
[3] The main objective of the work must be written on the more clear and more concise way at the end of introduction section
Response: Thank you for your feedback regarding the quality of the introduction section. We will take your comments into consideration and make the necessary improvements to enhance the quality of the introduction. In this study, our main objective is to propose a novel and reliable kick monitoring method, called Pattern Recognition-based Kick Detection (PRKD), specifically designed for offshore drilling. The PRKD method integrates the theory of multiphase flow calculation, data filtering theory, pattern recognition theory, and Bayesian framework to enhance the reliability and accuracy of kick detection. By combining advanced computational techniques with pattern recognition algorithms, PRKD enables proactive measures to mitigate potential risks, protect the environment, and optimize drilling operations. The significance and innovation of this research lie in its ability to address the limitations of existing kick monitoring methods by providing a more robust and precise approach. This novel method, PRKD, clearly outlines its research significance and innovation, making it a valuable contribution to the field of offshore drilling safety.
[4] Most tables and figures are still needed improve the quality of all tables and figures.
Response: Thank you for your feedback regarding the tables and figures in our manuscript. We have taken your comment into consideration and made the necessary revisions in our revised manuscript to enhance the quality of all tables and figures.
[5] I would also expect to validate with two more experimental works available in the literature.
Response: Thank you for pointing out the need for validation with additional experimental works available in the literature. We appreciate your suggestion, and we have taken it into consideration in our revised manuscript. However, due to the constraints of this study, it was not feasible to include validation with the specific experimental works mentioned. Nevertheless, we acknowledge the importance of validation and recognize that it is an essential aspect of research. In future studies, we intend to conduct more in-depth investigations that involve validating the data presented in the literature. By incorporating such validation in future research, we can further strengthen the reliability and robustness of our findings. We value your feedback and appreciate your input in guiding the direction of our research.
[6] Improve work justification. Also, add more analysis about velocity and pressure contours.
Response: Thank you for your feedback. We will further enhance the justification of our work and provide more analysis regarding velocity and pressure contours. Firstly, we will reinforce the rationale and significance of our study. By proposing a novel Pattern Recognition-based Kick Detection (PRKD) method, we aim to address the challenges associated with kick event monitoring in offshore drilling operations. Kick events can lead to severe accidents and losses, highlighting the criticality of accurate monitoring and prediction. Our research fills the existing gaps and offers a more reliable and precise approach to enhance kick event detection and prediction. Furthermore, we will delve into a more comprehensive analysis of parameters such as velocity and pressure distributions. By conducting a detailed investigation and analysis of these parameters, we can gain deeper insights into the evolution and relevant physical characteristics of kick events. This will aid in better understanding the mechanisms behind kick events and provide more accurate foundations for subsequent prediction and control measures. We will perform quantitative analysis on the contours of velocity and pressure parameters, offering more comprehensive and detailed research outcomes. We will strengthen the justification of our work and provide more in-depth analysis of velocity and pressure distributions to offer a more comprehensive study and results. Thank you for your suggestion, and we are committed to further improving our research.
Author Response File: Author Response.pdf
