Simulation Research on the Dual-Electrode Current Excitation Method for Distance Measurements While Drilling

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper presents a dual-electrode current excitation method aimed at real-time measurement of wellbore trajectory and distances to adjacent wells, enhancing safety and efficiency in drilling operations. Through theoretical analysis and simulations, the authors derive equations for current amplitude attenuation and magnetic field distribution, offering a cost-effective solution for relief well interconnection. The numerical analysis validates key factors. The study is relevant and falls within the scope of the Applied Sciences journal. I recommend its publication, provided the authors satisfactorily address the following minor comments:

1.        There is a type in the manuscript title “Reasearch”; please correct it.

2.        The abstract could be shortened by removing some introductory sentences. Please refer to the journal’s guidelines for abstract length.

3.        The keyword “simulation” is too broad. Consider replacing it with a more specific term.

4.        While the Introduction reads well, the significance of the study across different disciplines should be emphasized. Additionally, the literature review requires significant expansion (currently only 8 references are cited). I strongly recommend adding more literature to provide a broader perspective for readers less familiar with drilling engineering. You may wish to highlight the importance of optimizing various drilling parameters and consider citing the following relevant works:

·        Farahani et al., 2021, October. A Dynamic Model for Non-Newtonian Drilling Fluid’s Filtration in Casing Drilling Technology. In 82nd EAGE Annual Conference & Exhibition (Vol. 2021, No. 1, pp. 1-5). European Association of Geoscientists & Engineers.

·        Farahani et al., 2018, June. A robust modeling approach for predicting the rheological behavior of thixotropic fluids. In 80th EAGE Conference and Exhibition 2018 (Vol. 2018, No. 1, pp. 1-5). European Association of Geoscientists & Engineers.

5.        It would also be beneficial to include more references from *Applied Sciences* to underline the study’s relevance to the journal.

6.        Please discuss the limitations or disadvantages of current MWD (Measurement While Drilling) devices used in the oil and gas industry.

7.        Define all abbreviations (e.g., MGT, RMRS, SWG) upon first use to ensure clarity.

8.        Figure 1: The caption should be expanded to better describe the visualized parameters. Currently, it provides limited information, making it hard to interpret even with reference to the text.

9.        In the phrase “uniform formation and regular borehole comparison,” the meaning of "uniform formation" and "regular borehole" is unclear. Please provide more detailed explanations.

10.   In Equation (3), you mention that the range of kc values is [0,1]. Could you clarify why this is the case?

11.   For Equation (6), I recommend adding an appendix with the derivation.

12.   In Section 6, it is unclear if the input parameters are arbitrary. For example, could the authors clarify the specific formations and drilling fluids that exhibit resistivity values of 10 and 1 Ohm.m?

Author Response

Reviewer 1

Comments1.There is a type in the manuscript title "Reasearch"； please correct it.

Response1:Your comments are very valuable and the author has revised them.

Comments2.The abstract could be shortened by removing some introductory sentences. Please refer to the journals guidelines for abstract length.

Response2:Thanks very much to the expert's advice, the author has removed the first sentence of the abstract as requested.

Comments3.The keyword "simulation" is too broad. Consider replacing it with a more specific term.

Response3:Thanks very much for the expert's advice, the keyword  "simulation"  has been changed to "Matlab simulation".

Comments4. While the Introduction reads well, the significance of the study across different disciplines should be emphasized. Additionally, the literature review requires significant expansion (currently only 8 references are cited). I strongly recommend adding more literature to provide a broader perspective for readers less familiar with drilling engineering. You may wish to highlight the importance of optimizing various drilling parameters and consider citing the following relevant works:

• Farahani et al., 2021, October. A Dynamic Model for Non-Newtonian Drilling Fluids Filtration in Casing Drilling Technology. In 82nd EAGE Annual Conference & Exhibition (Vol. 2021, No. 1, pp. 1-5). European Association of Geoscientists & Engineers.
• Farahani et al., 2018, June. A robust modeling approach for predicting the rheological behavior of thixotropic fluids. In 80th EAGE Conference and Exhibition 2018 (Vol. 2018, No. 1, pp. 1-5). European Association of Geoscientists & Engineers.

Response4:Your suggestion is very important, and the author has re-added the literature and modified it as required.

Comments5.It would also be beneficial to include more references from *Applied Sciences* to underline the studys relevance to the journal.

Response5:Your suggestion is very important, and the author has re-added the literature and modified it as required.

Comments6.Please discuss the limitations or disadvantages of current MWD (Measurement While Drilling) devices used in the oil and gas industry.

Response6:Experts' suggestions are very important. The author has expanded the number of references in the introduction to 14, and analyzed the references suggested by experts.

Comments7.Define all abbreviations (e.g., MGT, RMRS, SWG) upon first use to ensure clarity.

Response7:Thanks very much for the expert's advice, the author has revised the text in lines 47-48.

Comments8.Figure 1: The caption should be expanded to better describe the visualized parameters. Currently, it provides limited information, making it hard to interpret even with reference to the text.

Response8:Thanks very much for the valuable advice of experts, Figure 1 has been adjusted. The reason for this processing is that the content of the two figures is merged into one figure due to the limited requirement of the journal on the chart of the paper.

Comments9.In the phrase “uniform formation and regular borehole comparison,” the meaning of "uniform formation" and "regular borehole" is unclear. Please provide more detailed explanations.

Response9:The expert advice is very good, Uniform formation means that the electrical conductivity of a single geological structure is unchanged. Regular borehole comparison refer to horizontal or vertical casing wellheads so that casing resistance is relatively easy to calculate.

Comments10. Equation (3), you mention that the range of kc values is [0,1]. Could you clarify why this is the case?

Response10:Thank you very much for the expert advice. ,the numerator in formula 3 is the parallel of two resistors, and the denominator is equivalent to the numerator plus a constant, so it can be seen that the numerator is less than the denominator, so the result k_c is greater than 0 and less than 1.

Comments11.For Equation (6), I recommend adding an appendix with the derivation.

Response11:Thank you very much for the advice of the experts. The specific formula is derived as follows.By substituting Formula (4) into Formula (5), the axial equivalent current density of the casing can be calculated using the following Equation:

 

（6）

Comments12. In Section 6, it is unclear if the input parameters are arbitrary. For example, could the authors clarify the specific formations and drilling fluids that exhibit resistivity values of 10 and 1 Ohm.m?

Response12:The section 6 is the principle of parameter setting and selection, which mainly comes from reference15 and 16, so as to ensure the continuity of the research. In addition, the choice of 10 Ohm.m and 1 Ohm.m mentioned by experts is a parameter selected by relevant literature and actual situation.

Reviewer 2 Report

Comments and Suggestions for Authors

Lack of Novelty in the Proposed Work: The article introduces a dual-electrode current excitation method for distance measurement while drilling, positioning it as a novel advancement. However, the method is an incremental modification of existing electromagnetic ranging techniques, such as the single-electrode excitation method mentioned in the manuscript (Section 1, page 2). The proposed dual-electrode setup merely changes the configuration of electrodes without addressing more fundamental limitations of existing methods, such as the inability to achieve real-time measurements in certain conditions or the need for non-invasive measurement tools. Furthermore, similar concepts have been explored in existing literature, such as using dual or multiple electrodes to improve measurement accuracy (e.g., the "magnetic positioning detection system" mentioned on page 2). The lack of a clear differentiation or innovative leap over these prior studies undermines the claim of novelty.

 

Limited Impact on the Industry: The manuscript suggests that the proposed method can enhance safety and reduce costs in drilling operations (Abstract, page 1), but fails to provide convincing evidence or detailed analysis to support these claims. The benefits are stated in general terms without specific examples of how much time, cost, or risk is actually reduced compared to current methods like the single-pole excitation method or other existing tools like the Wellspot system. Moreover, the impact on the industry is likely limited, as the technique is primarily validated through idealized simulations rather than diverse real-world scenarios. For example, the manuscript mentions that the method is "particularly suitable for rescue well connectivity operations at offshore platforms" (Abstract, page 1), but it does not provide any case studies, field trials, or empirical data to substantiate these claims, which makes it difficult to evaluate the practical relevance of the research.

 

Questionable Reliability and Applicability of Research: The reliability of the proposed method is questionable due to its reliance on theoretical models and simulations without sufficient real-world testing. The simulations presented in the manuscript are based on several idealized assumptions, such as uniform formation resistivity and consistent electrode placement (Section 6.1, page 14). These assumptions do not account for the complexities and variabilities encountered in actual drilling environments, such as heterogeneous geological formations, fluctuating mud properties, or irregular well orientations. The absence of empirical validation or field tests means that the applicability of the proposed method in real-world scenarios remains uncertain. For instance, the manuscript suggests using the method in offshore rescue operations (Abstract, page 1), yet it does not address how the method would perform in challenging conditions like high-pressure zones, varying temperatures, or in the presence of multiple well paths.

 

Insufficient Validation Studies: The manuscript lacks rigorous validation against real-world data or existing industry standards. The authors rely almost exclusively on numerical simulations to validate their method (Sections 6.1–6.6, pages 14–18). While these simulations provide some initial insights, they are insufficient to establish the effectiveness or reliability of a method intended for complex drilling operations. For example, the simulation results showing the "current amplitude gathered on the target casing" (Section 6.1, page 14) and "magnetic induction intensity distribution" (Section 6.2, page 15) are based on ideal conditions and do not include any real-world experimental data or field tests. Without such validation, the study cannot adequately demonstrate that the proposed method will perform as expected under various operational conditions, such as different geological settings or during unforeseen drilling incidents.

 

Limited Diversity of Data Used for Validation: The article does not employ a diverse range of data to validate the proposed method, instead relying solely on idealized simulated datasets (Sections 6.1–6.6, pages 14–18). The simulations assume a uniform formation resistivity and consistent electrode placement, which do not reflect the wide range of conditions encountered in actual drilling operations. For instance, there is no consideration of varying geological formations, such as different rock types, varying formation porosity levels, or the presence of faults and fractures. The lack of diverse data raises concerns about the generalizability of the results. To establish broader applicability, the authors should have included validation across multiple scenarios or conditions, ideally supported by real-world field tests.

 

Absence of a Comprehensive Limitations Section: The manuscript lacks a detailed discussion of the limitations of the proposed method. There is no evaluation of potential challenges in implementing the dual-electrode method in real-world settings, such as the impact of environmental conditions, limitations in equipment compatibility, or the constraints of deploying the method in offshore or remote locations. For instance, the paper does not address potential issues related to the complexity of installing and maintaining dual electrodes in deep-water drilling environments or how the method might be affected by electromagnetic interference from nearby wells or other equipment. A comprehensive limitations section is essential for providing a balanced perspective and would significantly enhance the manuscript's credibility.

 

Poor Writing Style and Clarity: The manuscript suffers from several writing issues that detract from its clarity and readability. Many sections are overly dense and filled with technical jargon, making it difficult for readers to follow the key arguments and findings. For example, the descriptions of the mathematical models and equations (Section 3, page 6) are complex and lack clear explanations or diagrams to illustrate the concepts for non-specialist readers. Additionally, there are numerous grammatical errors and awkward sentence structures throughout the text, such as in the abstract where the phrasing is convoluted ("particularly suitable for target well ranging operations with safety risks"). The writing would benefit from substantial editing to improve clarity, flow, and accessibility.

 

Inadequate Presentation of Results: The presentation of key findings and their implications is insufficient. The simulation results are not clearly explained or contextualized within the broader field. For example, while the manuscript provides data on "magnetic induction intensity" and "casing current distribution" (Sections 6.2–6.4, pages 15–17), it does not clearly explain how these findings compare with existing methods or why they are significant. Moreover, the figures and tables lack sufficient captions and are not always referenced effectively in the text, making it difficult to interpret their relevance to the study's objectives.

Overemphasis on Simulation Results: There is an over-reliance on simulation data without complementary empirical data to support the findings. While the manuscript provides extensive numerical results (Sections 6.1–6.6, pages 14–18), these are all based on idealized models and fail to account for the uncertainties and variabilities that would be encountered in real-world applications. For instance, the discussion on the "impact of different electrode distances on the induced magnetic field intensity" (Section 6.4.2, page 17) is purely theoretical and lacks empirical validation. This emphasis on simulated data gives the impression that the research is still in the preliminary stages and not yet ready for practical application.

Comments on the Quality of English Language

Poor Writing Style and Clarity: The manuscript suffers from several writing issues that detract from its clarity and readability. Many sections are overly dense and filled with technical jargon, making it difficult for readers to follow the key arguments and findings. For example, the descriptions of the mathematical models and equations (Section 3, page 6) are complex and lack clear explanations or diagrams to illustrate the concepts for non-specialist readers. Additionally, there are numerous grammatical errors and awkward sentence structures throughout the text, such as in the abstract where the phrasing is convoluted ("particularly suitable for target well ranging operations with safety risks"). The writing would benefit from substantial editing to improve clarity, flow, and accessibility.

Author Response

Comments1.Lack of Novelty in the Proposed Work: The article introduces a dual-electrode current excitation method for distance measurement while drilling, positioning it as a novel advancement. However, the method is an incremental modification of existing electromagnetic ranging techniques, such as the single-electrode excitation method mentioned in the manuscript (Section 1, page 2). The proposed dual-electrode setup merely changes the configuration of electrodes without addressing more fundamental limitations of existing methods, such as the inability to achieve real-time measurements in certain conditions or the need for non-invasive measurement tools. Furthermore, similar concepts have been explored in existing literature, such as using dual or multiple electrodes to improve measurement accuracy (e.g., the "magnetic positioning detection system" mentioned on page 2). The lack of a clear differentiation or innovative leap over these prior studies undermines the claim of novelty.

Response1: I sincerely appreciate the expert's inquiry. The author has thoroughly considered the expert advice in his interpretation. The 'magnetic positioning detection system' proposed by experts bears resemblance to that presented in this paper and lacks distinct novelty. In this study, both the dual electrode excitation scheme and 'the magnetic positioning detection system' are products of the same research team, indicating a heritage relationship between them. However, it is not merely an addition of electrodes. The 'magnetic positioning detection system' represents research conducted many years ago, with its core ranging formula as follows, it involves two variables—d and θ. When θ cannot be determined, multi-point measurements must be performed; through various (d, θ) combinations to assess magnetic induction intensity values, one can derive the B-d corresponding curve and subsequently ascertain the magnitude of d based on this curve.In addition, this scheme does not give the angle θ measurement method. Compared with the proposed two-electrode excitation ranging scheme, we not only derive the single point ranging formula(Formula(15)) and the adjacent well angle formula(Formula(18)), but also realize the measurement while drilling and save the ranging time.

 

Comments2.Limited Impact on the Industry: The manuscript suggests that the proposed method can enhance safety and reduce costs in drilling operations (Abstract, page 1), but fails to provide convincing evidence or detailed analysis to support these claims. The benefits are stated in general terms without specific examples of how much time, cost, or risk is actually reduced compared to current methods like the single-pole excitation method or other existing tools like the Wellspot system. Moreover, the impact on the industry is likely limited, as the technique is primarily validated through idealized simulations rather than diverse real-world scenarios. For example, the manuscript mentions that the method is "particularly suitable for rescue well connectivity operations at offshore platforms" (Abstract, page 1), but it does not provide any case studies, field trials, or empirical data to substantiate these claims, which makes it difficult to evaluate the practical relevance of the research.

Response2:Firstly, it is widely recognized within the industry that Measurement While Drilling (MWD) technology can accurately measure the distance between adjacent wells in real time as drilling progresses, making it the most effective solution for anti-collision detection among neighboring wells. In contrast, alternative detection methods necessitate tripping-out , which not only disrupts normal drilling operations but also introduces uncertain safety risks to personnel on the drilling platform. Therefore, the advantages of MWD systems are self-evident and do not require further elaboration; additionally, the approach proposed in this manuscript represents an enhancement of existing MWD technologies and thus does not warrant special explanation.
   Secondly, at present, this manuscript remains in a theoretical research phase. We have initiated preparations for laboratory simulation experiments; however, field validation is constrained by limited research funding. The rationale behind selecting this scheme for offshore drilling platforms lies in their restricted operational space where frequent tripping-out is impractical. Consequently, employing MWD technology proves more advantageous under these conditions—allowing us to infer its applicability effectively. In response to inquiries raised by experts, clarifications have been provided in the discussion section of the manuscript.

Comments3.Questionable Reliability and Applicability of Research: The reliability of the proposed method is questionable due to its reliance on theoretical models and simulations without sufficient real-world testing. The simulations presented in the manuscript are based on several idealized assumptions, such as uniform formation resistivity and consistent electrode placement (Section 6.1, page 14). These assumptions do not account for the complexities and variabilities encountered in actual drilling environments, such as heterogeneous geological formations, fluctuating mud properties, or irregular well orientations. The absence of empirical validation or field tests means that the applicability of the proposed method in real-world scenarios remains uncertain. For instance, the manuscript suggests using the method in offshore rescue operations (Abstract, page 1), yet it does not address how the method would perform in challenging conditions like high-pressure zones, varying temperatures, or in the presence of multiple well paths.

Response3:We sincerely appreciate the insights provided by the experts, which have significantly illuminated our future scientific research directions. As is well known, field experiments in oil drilling represent a critical undertaking that cannot be supported by our current research funding and experimental capabilities. We have thoroughly addressed the experts' recommendations in the discussion section, and we hope they find our responses satisfactory.

Comments4.Insufficient Validation Studies: The manuscript lacks rigorous validation against real-world data or existing industry standards. The authors rely almost exclusively on numerical simulations to validate their method (Sections 6.1–6.6, pages 14–18). While these simulations provide some initial insights, they are insufficient to establish the effectiveness or reliability of a method intended for complex drilling operations. For example, the simulation results showing the "current amplitude gathered on the target casing" (Section 6.1, page 14) and "magnetic induction intensity distribution" (Section 6.2, page 15) are based on ideal conditions and do not include any real-world experimental data or field tests. Without such validation, the study cannot adequately demonstrate that the proposed method will perform as expected under various operational conditions, such as different geological settings or during unforeseen drilling incidents.

Response4:In view of the inability to carry out field experiments, we proposed to change the title of the manuscript to "Simulation Research", which is more consistent with the content of the paper, in order to gain understanding from experts. 

Comments5.Limited Diversity of Data Used for Validation: The article does not employ a diverse range of data to validate the proposed method, instead relying solely on idealized simulated datasets (Sections 6.1–6.6, pages 14–18). The simulations assume a uniform formation resistivity and consistent electrode placement, which do not reflect the wide range of conditions encountered in actual drilling operations. For instance, there is no consideration of varying geological formations, such as different rock types, varying formation porosity levels, or the presence of faults and fractures. The lack of diverse data raises concerns about the generalizability of the results. To establish broader applicability, the authors should have included validation across multiple scenarios or conditions, ideally supported by real-world field tests.

Response5:Thanks very much to the expert's suggestion, the manuscript adopts idealized data to conduct simulation experiments in order to obtain regular conclusions. We have revised the suggestions made by the experts in the discussion section.

Comments6.Absence of a Comprehensive Limitations Section: The manuscript lacks a detailed discussion of the limitations of the proposed method. There is no evaluation of potential challenges in implementing the dual-electrode method in real-world settings, such as the impact of environmental conditions, limitations in equipment compatibility, or the constraints of deploying the method in offshore or remote locations. For instance, the paper does not address potential issues related to the complexity of installing and maintaining dual electrodes in deep-water drilling environments or how the method might be affected by electromagnetic interference from nearby wells or other equipment. A comprehensive limitations section is essential for providing a balanced perspective and would significantly enhance the manuscript's credibility.

Response6:The opinions raised by the experts are very important, and the author has revised them accordingly in the discussion section.

Comments7.Poor Writing Style and Clarity: The manuscript suffers from several writing issues that detract from its clarity and readability. Many sections are overly dense and filled with technical jargon, making it difficult for readers to follow the key arguments and findings. For example, the descriptions of the mathematical models and equations (Section 3, page 6) are complex and lack clear explanations or diagrams to illustrate the concepts for non-specialist readers. Additionally, there are numerous grammatical errors and awkward sentence structures throughout the text, such as in the abstract where the phrasing is convoluted ("particularly suitable for target well ranging operations with safety risks"). The writing would benefit from substantial editing to improve clarity, flow, and accessibility.

Response7:Thank you very much for the expert's advice, and the language has been revised and improved by the polishing agency. In addition, the author also adds an appendix to deduce the formula and label the variables.

Comments8.Inadequate Presentation of Results: The presentation of key findings and their implications is insufficient. The simulation results are not clearly explained or contextualized within the broader field. For example, while the manuscript provides data on "magnetic induction intensity" and "casing current distribution" (Sections 6.2–6.4, pages 15–17), it does not clearly explain how these findings compare with existing methods or why they are significant. Moreover, the figures and tables lack sufficient captions and are not always referenced effectively in the text, making it difficult to interpret their relevance to the study's objectives.

Response8:Thank you very much for the expert advice. The manuscript is only the design of the program, the regular results of the main research program. The expert said that the comparative experiment is not within the scope of our research, and can only compare regular results. Only when field experiments are carried out can the data content needed by experts be obtained.

Comments9.Overemphasis on Simulation Results: There is an over-reliance on simulation data without complementary empirical data to support the findings. While the manuscript provides extensive numerical results (Sections 6.1–6.6, pages 14–18), these are all based on idealized models and fail to account for the uncertainties and variabilities that would be encountered in real-world applications. For instance, the discussion on the "impact of different electrode distances on the induced magnetic field intensity" (Section 6.4.2, page 17) is purely theoretical and lacks empirical validation. This emphasis on simulated data gives the impression that the research is still in the preliminary stages and not yet ready for practical application.

Response9:The opinions of experts are very pertinent. Our research work is only to propose a new scheme, then establish a mathematical model, verify the feasibility of the model through data simulation, and obtain regular conclusions.

Comments10.Poor Writing Style and Clarity: The manuscript suffers from several writing issues that detract from its clarity and readability. Many sections are overly dense and filled with technical jargon, making it difficult for readers to follow the key arguments and findings. For example, the descriptions of the mathematical models and equations (Section 3, page 6) are complex and lack clear explanations or diagrams to illustrate the concepts for non-specialist readers. Additionally, there are numerous grammatical errors and awkward sentence structures throughout the text, such as in the abstract where the phrasing is convoluted ("particularly suitable for target well ranging operations with safety risks"). The writing would benefit from substantial editing to improve clarity, flow, and accessibility.

Response10:Thank you very much for the expert's advice, and the language has been revised and improved by the polishing agency. In addition, the author also adds an appendix to deduce the formula and label the variables.

Reviewer 3 Report

Comments and Suggestions for Authors

1- The introduction could be more concise and focused on clearly stating the research gap and the specific problem being addressed. More context and motivation for the proposed "dual-electrode current excitation" method should be provided.

2- The literature review section covers existing ranging methods quite comprehensively, which is good. However, it could benefit from a more critical analysis of the limitations and shortcomings of existing methods, to better highlight the need for the proposed approach.

3- The mathematical modeling and derivations seem rigorous and comprehensive. However, some explanations and justifications for the assumptions and simplifications made could be provided for better clarity. The notation and variable definitions could be made more consistent and user-friendly.

4- The paper lacks a dedicated section for presenting and discussing the results of numerical calculations, simulations, or experimental validations. This section is crucial to demonstrate the effectiveness, accuracy, and advantages of the proposed method over existing approaches. Comparative analyses with existing methods, parametric studies, and sensitivity analyses could be included to strengthen the claims made in the paper.

Author Response

Reviewer 3

Comments1.The introduction could be more concise and focused on clearly stating the research gap and the specific problem being addressed. More context and motivation for the proposed "dual-electrode current excitation" method should be provided.

Response1:Thank you very much for the advice of experts. The author has revised and improved this part of the content considering the comprehensive opinions of many experts. In hazardous drilling incidents, such as blowouts, the safety risks near the wellhead of the accident well are significant. Therefore, it is necessary to run a ranging excitation device and measuring tool into the relief well. Currently, the primary ranging system used for communication between the relief well and the accident well is the Wellspot tool developed by VM company. This tool adopts drilling well current unipole incentive that requires cable ranging and drilling intersection operation. In order to achieve synchronous operation of ranging and drilling, as well as improve ranging range and measuring accuracy, this paper proposes a new method for MWD based on dual-electrode current excitation. The research results provide a theoretical basis for developing and optimizing parameters of distance MWD systems for relief well.

Comments2.The literature review section covers existing ranging methods quite comprehensively, which is good. However, it could benefit from a more critical analysis of the limitations and shortcomings of existing methods, to better highlight the need for the proposed approach.

Response2:Thanks very much for the expert's advice. Due to the foreign technology monopoly and technology blockade, the author can only make relevant technical analysis through relatively few literatures, and make corresponding modifications, in order to meet the expectations and requirements of the experts.

3.The mathematical modeling and derivations seem rigorous and comprehensive. However, some explanations and justifications for the assumptions and simplifications made could be provided for better clarity. The notation and variable definitions could be made more consistent and user-friendly.

Response3:Thank you very much for the expert's advice, the author to modify the related content, and increase the appendix for the variables in the manuscript.

Variable	Implication
d	The distance between the drilling well and the target well.
θ	The angle between the central axis of the casing and BHA.
Hu and Hd	The upper/lower frequency magnetic field detectors.
du and dd	The vertical distance between the upper/lower low-frequency magnetic field detector and the casing.
L	The distance between the upper current electrodes and the lower current electrodes.
Lch and Lcl	The distance between the measuring point of the casing M and the casing wellhead and well bottom.
Φ1 and Φ2	The drilling well axis and the target well casing axis.
Ref	The formation equivalent resistance.
Rem	The resistance in the outer annulus of drilling tool.
Rec	The target well casing loop equivalent resistance.
Rf	The formation resistivity.
Rm	The mud resistivity.
σc	The conductivity of the casing.
rd	The borehole radius of drilling well.
rt	The radius of the drilling well ranging tool.
rc	The casing radius of the target well.
hc	The casing wall thickness.
kc	The current attenuation factor.
Is	The excitation current intensity.
Ic	The casing axial current.
Jc	The current density .
lu	The effective length of the upper electrode.
ld	The effective length of the lower electrode.
Puc	The correction coefficient for the formation equivalent resistance from upper electrode to the casing.
Pdc	The correction coefficient for formation equivalent resistance from lower electrode to the casing.
kcc	The corrected current attenuation coefficient.
Icc	The corrected axial current.
B	The magnetic field intensity.
G	The gravity
βu	The angle between the gravity high side of the upper-low frequency magnetic field measurement sub and the direction of the target well.
βd	The angle between the gravity high side of the lower-low frequency magnetic field measurement sub and the direction of the target well.

Comments4.The paper lacks a dedicated section for presenting and discussing the results of numerical calculations, simulations, or experimental validations. This section is crucial to demonstrate the effectiveness, accuracy, and advantages of the proposed method over existing approaches. Comparative analyses with existing methods, parametric studies, and sensitivity analyses could be included to strengthen the claims made in the paper.

Response4:Thanks very much for the expert advice, the author has added a "discussion section" to the manuscript.

Reviewer 4 Report

Comments and Suggestions for Authors

This paper content is well written, and the research is novel. I think my suggestions will further enhance the quality of the paper.

Please correct the drilling spelling in Line 7.

The abstract provides a concise summary of the research, including the problem addressed and the proposed method but it could benefit from a clearer statement of the research`s novelty. Please add very clear statement about the novelty in the last 1-2 lines.

The methodology is described in detail and particularly, the explanation of different current loop modes and how they contribute to the overall measurement process is in detail. I really liked it.

The results are well-explained and seem to support the proposed method`s effectiveness. However, it would be beneficial to see comparisons with existing methods in the market to demonstrate the practical advantages. Basically, if you can present comparative analysis between your novel approach and existing technique effectiveness.

Author Response

Reviewer 4

This paper content is well written, and the research is novel. I think my suggestions will further enhance the quality of the paper.

Comments1.Please correct the drilling spelling in Line 7.

Response1:Thanks very much for the expert opinion, the author has made revisions in the manuscript.

Comments2.The abstract provides a concise summary of the research, including the problem addressed and the proposed method but it could benefit from a clearer statement of the research`s novelty. Please add very clear statement about the novelty in the last 1-2 lines.

Response2:Thanks very much to the expert's opinion, the author has revised the abstract as requested.

Based on a comprehensive analysis of existing methods for measuring adjacent well distances along with their advantages and disadvantages, this study employs theoretical analysis, simulation experiments, and other comprehensive research methods to investigate a distance measurement method based on current excitation. In response to the need for measuring and controlling the connection of relief wells, a method utilizing double electrode current excitation during drilling is proposed. This approach facilitates synchronous excitation measurement while drilling, significantly reducing both time and costs while ensuring safety and efficiency, making it particularly suitable for the connection operations of relief wells that involve safety risks. Firstly, the paper establishes a drilling-with-measurement model corresponding to the excitation mode, which derives calculation formulas for target casing current amplitude attenuation as well as induced magnetic field distribution within the formation. Additionally, it provides calculation methods for determining target well distance and azimuth direction. Lastly, the impact levels of various key factors are verified through numerical calculations and simulation analyses, which confirm the correctness and effectiveness of this distance measurement method. The findings from this research establish both a core theoretical foundation and a technological basis for real-time measurement of adjacent well distances during rescue operations.

Comments3.The methodology is described in detail and particularly, the explanation of different current loop modes and how they contribute to the overall measurement process is in detail. I really liked it.

Response3:Thank you very much, experts, I will continue to work hard in the future.

Comments4.The results are well-explained and seem to support the proposed method`s effectiveness. However, it would be beneficial to see comparisons with existing methods in the market to demonstrate the practical advantages. Basically, if you can present comparative analysis between your novel approach and existing technique effectiveness.

Response4:Thank you very much for the expert advice, your suggestions have been refined by the author in the "Discussion" and " Conclusions" sections.

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

I am happy with the authors' responses to my feedback and their revisions. This revised version of the manuscript is now ready for publication.

Comments on the Quality of English Language

I am happy with the authors' responses to my feedback and their revisions. This revised version of the manuscript is now ready for publication.

Reviewer 3 Report

Comments and Suggestions for Authors

Accepted!