Characterization of Pore Heterogeneity in Lacustrine Shale Based on MIP, LTNA, NMR, and Multifractal Characteristics: A Case Study of the Jurassic Dongyuemiao Member, China

Round 1

Reviewer 1 Report (Previous Reviewer 1)

Comments and Suggestions for Authors

All the comments have been amended and revised to be considered for publication.

Author Response

Thank you very much for agreeing to review our manuscript, We sincerely appreciate your time and expertise in evaluating our work.

Reviewer 2 Report (Previous Reviewer 2)

Comments and Suggestions for Authors

Author has responded well to each comment.

Author Response

Thank you very much for agreeing to review our manuscript, We sincerely appreciate your time and expertise in evaluating our work.

Reviewer 3 Report (Previous Reviewer 5)

Comments and Suggestions for Authors

please see attached review

Comments for author File: Comments.pdf

Comments on the Quality of English Language

This third revised version shows significant improvements in the scientific presentation and English writing compared to the previous ones. 

Author Response

1. Final editing is required to ensure proper formatting (e.g., copying and pasting from a PDF should not remove spaces between words).

Response: Thank you for taking the time out of your busy schedule to provide me with valuable feedback. I sincerely appreciate your thorough review of the space and formatting issues in the article, and have made revisions accordingly.

2. Errors in formulas persist, particularly in 12, 13, and 19. Please correct them (see detailed review and [2])

Response: According to your request, the above three formulas have been further modified.

Author Response File: Author Response.doc

Reviewer 4 Report (New Reviewer)

Comments and Suggestions for Authors

The authors' article is devoted to the definition of Characterization of Pore Heterogeneity in Lacustrine Shale 2 Based on MIP, LTNA, NMR, and Multifractal Characteristics: A 3 Case Study of Jurassic Dongyuemiao Member, China.

Indeed, the pore structure plays a critical role in evaluating shale “sweet spots”. To determine the the micropore structures and heterogeneity of different lithofacies in the Jurassic Dongyuemiao Member lacustrine shale the authors used methods such as mercury intrusion porosimetry (MIP), field emission scanning electron microscopy (FE-SEM), nuclear magnetic resonance (NMR), and X-ray diffraction (XRD) and also described the experiment in sufficient detail.

However, there are a number of questions and comments regarding the results presented in the authors’ work:

1. The results obtained by the authors during the study are applicable only to the area considered in the work from which the samples for the study were taken. It would be good if the authors took samples from different areas to see the patterns of pore structures and fractal features of formations.
2. The article lacks uniformity of measurement units. For example, in section 3.2.2. there are units of temperature measurement in °C and in K. It is necessary to convert the temperature values ​​to a single unit of measurement.
3. Lines 266-267. There is an extra inscription in brackets where references are given. The inscription: "Error! Reference source not found."

Author Response

1. The results obtained by the authors during the study are applicable only to the area considered in the work from which the samples for the study were taken. It would be good if the authors took samples from different areas to see the patterns of pore structures and fractal features of formations

Response: Thank you for your thoughtful suggestion regarding the analysis of pore structure patterns and fractal characteristics across different regions. We agree that such comparative studies could provide valuable insights into geological heterogeneity.

However, after careful consideration, we find it challenging to implement this suggestion in the current study due to the limited availability of representative core samples from other geological regions. This study mainly focuses on the continental shale in the Dongyuemiao section of the Fuling areaThe substantial additional work required would exceed the scope of this manuscript.

We sincerely appreciate this constructive suggestion and will certainly consider it in our ongoing research project investigating. Thank you again for your valuable input that has helped improve our manuscript.

2. The article lacks uniformity of measurement units. For example, in section 3.2.2. there are units of temperature measurement in °C and in K. It is necessary to convert the temperature values to a single unit of measurement.

Response: Based on your suggestion, the temperature unit in the article has been uniformly changed to Celsius degrees.

3. Lines 266-267. There is an extra inscription in brackets where references are given. The inscription: "Error! Reference source not found.

Response: The cross citation of reference 56 has been modified. Thank you again for your suggestion.

Author Response File: Author Response.doc

Reviewer 5 Report (New Reviewer)

Comments and Suggestions for Authors

I have studied your work with care and have come to the conclusion that:

- Provide details for all chemicals and apparatus used including city and country.

- The parameters used during characterization are missing (voltage, current, atmosphere, XRD parameters,..).

- XRD analysis: XRD patterns of the samples are missing.

- Measurement errors are missing.

- The resolution of figures must be improved.

- The scale of SEM images is not clear.

- A comparison with the existing published literature and discussion of the results are missing.

- Avoid numbering the conclusions.

Author Response

1.Provide details for all chemicals and apparatus used including city and country.

Response: Thanks for your suggestions on this article! Based on your suggestion, the detailed information of the experimental equipment used in this study, including the city, has been added to the article. Separately in line 148-149、line 155、line 160、line 162、line 190、line 214、line 223-224.

2. The parameters used during characterization are missing (voltage, current, atmosphere, XRD parameters,..).

Response: According to your suggestion, the experimental instrument parameter information for whole rock diffraction has been added in line 155-158.

3.- XRD analysis: XRD patterns of the samples are missing.

Response: Based on your suggestion, we have selected samples representing various lithofacies to supplement XRD patterns, as shown in Figure 3

4.- Measurement errors are missing.

Response: The measurement errors of TOC, clay minerals, and quartz content have been added to the main text in line 321-323.

5. The resolution of figures must be improved.

Response: Based on your suggestion, we have carefully checked the resolution issues of each image and have replaced Figure 4 and Figure 6 with clearer versions.

6. The scale of SEM images is not clear.

Response: Corresponding scales have been added to the upper right corner of each photo in Figure 4.

7. A comparison with the existing published literature and discussion of the results are missing.

Response: Based on the feedback you provided, we have supplemented and compared the previously published results in Articles 5.1 and 5.2 regarding the heterogeneity control factors and characterization of porosity and permeability heterogeneity in line 517-520、547-550.

8. Avoid numbering the conclusions.

Response: The article has been renumbered according to your suggestion.

Author Response File: Author Response.doc

Round 2

Reviewer 5 Report (New Reviewer)

Comments and Suggestions for Authors

Thanks for your work in revising your manuscript according to the indicated comments and suggestions.

So, the revised paper is well improved. 

 

Good luck!

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript "Characterization of pore heterogeneity in lacustrine shale based on MIP, LTNA, NMR, and multifractal characteristics: a case study of Jurassic Dongyuemiao Member, China" by Xu Wu, Yifan Gu, Yuqiang Jiang, Zhanlei Wang, Yonghong Fu is acceptable. The manuscript has been written and discussed well. Hence, it deserves to be published after some minor corrections.

 

Comments:

1. Introduction: Please include the research gap and highlight the issue the author aims to resolve.

2. Methods:

(i) An incorrect citation number for the formula was detected (Lines 208, 213, 217, & 219). Please check again.

(ii) How was the sample analyzed using NMR? Was it liquid or solid NMR? If liquid, please specify the type of deuterated solvent used.

(iii) Please provide the frequency of the NMR instrument.

3. Results: Please ensure to include an appropriate reference that supports the data, providing proper citation to enhance the reliability and accuracy of the information presented.

4. Conclusion: Please revise the conclusion part and summarize the main research findings.

Author Response

Reviewer 1

The manuscript "Characterization of pore heterogeneity in lacustrine shale based on MIP, LTNA, NMR, and multifractal characteristics: a case study of Jurassic Dongyuemiao Member, China" by Xu Wu, Yifan Gu, Yuqiang Jiang, Zhanlei Wang, Yonghong Fu is acceptable. The manuscript has been written and discussed well. Hence, it deserves to be published after some minor corrections.

Comments:

1. Introduction: Please include the research gap and highlight the issue the author aims to resolve.

Response: Thank for your suggestions on this article!

Increase the methods and shortcomings of previous research on pore structure, and point out the research highlights of this article, which are the addition of multifractal methods to further study pore structure and heterogeneity on lines 110-117.

2. Methods:

(i) An incorrect citation number for the formula was detected (Lines 208, 213, 217, & 219). Please check again.

Response: Based on your suggestions, I carefully checked the citation format of the formula and made corresponding modifications on line 226、231 and 235.

 

(ii) How was the sample analyzed using NMR? Was it liquid or solid NMR? If liquid, please specify the type of deuterated solvent used.

Response: The sample for this study saturated fluid for 12 hours before obtaining the NMR T₂ signals, related content supplement has been added to line 245.

 

(iii) Please provide the frequency of the NMR instrument.

Response: The main frequency of the NMR instrument is 12MHz, related content supplement has been added to line 211.

 

3. Results: Please ensure to include an appropriate reference that supports the data, providing proper citation to enhance the reliability and accuracy of the information presented.

 

Response: Verify the accuracy of the experimental results by citing references to experimental methods such as nuclear magnetic resonance, high-pressure mercury intrusion, and nitrogen adsorption in the experimental results ,corresponding references have been added to the results section.

 

4. Conclusion: Please revise the conclusion part and summarize the main research findings.

Response: Simplify to obtain clearer conclusions while ensuring complete and detailed conclusions.

Reviewer 2 Report

Comments and Suggestions for Authors

1. Some sentences in the article are too long, which may affect the fluency of reading. For example: “Based on experiments such as mercury intrusion porosimetry (MIP), field emission scanning electron microscopy (FE-SEM), nuclear magnetic resonance (NMR), and X-ray diffraction (XRD), the micro pore structures and heterogeneity of different lithofacies in the lacustrine shale from the Jurassic Dongyuemiao Member were determined.”

2. Although the research background covers the importance of lacustrine shale pore heterogeneity, the uniqueness and scientific issues of the Dongyuemiao section are not clearly highlighted. It is recommended to add in the introduction.

3. Although the descriptions of the techniques are complete, the logical flow of the experiments does not seem clear. For example: First, how to sample and ensure the representativeness of experimental samples. Next, how to select the analytical scale and specific objectives for each characterization method (e.g., MIP for mesopores and macropores, LTNA for micropores). Finally, how to integrate experimental data into the multifractal analysis.

4. In Table 2, the author proposed three types of pore sizes. What is the basis for the author's classification? Can you provide relevant references?

5. The current study is based only on the Dongyuemiao section and lacks comparison with other lacustrine shales. It is recommended to supplement or cite other research data from Horizontal for comparison.

6. The author has done a lot of work in multifractal theory, but the physical meaning of each parameter in the article is too simple. For readers who are not familiar with multifractal theory, it is difficult to understand the application of this theory to rock pore heterogeneity.

7. The current discussion focuses on the lack of explanation of experimental results and their connection with broader theory.

Author Response

Reviewer 2

1. Some sentences in the article are too long, which may affect the fluency of reading. For example: “Based on experiments such as mercury intrusion porosimetry (MIP), field emission scanning electron microscopy (FE-SEM), nuclear magnetic resonance (NMR), and X-ray diffraction (XRD), the micro pore structures and heterogeneity of different lithofacies in the lacustrine shale from the Jurassic Dongyuemiao Member were determined.”

Response: Thank for your suggestions on this article!

The sentences in the entire text have been carefully revised to avoid affecting the fluency of reading, The sentence you gave as an example has been revised on lines 113-116.

2. Although the research background covers the importance of lacustrine shale pore heterogeneity, the uniqueness and scientific issues of the Dongyuemiao section are not clearly highlighted. It is recommended to add in the introduction.

Response: Based on your suggestion, more detailed information on the shale of Dongyuemiao section has been added and the characteristics of Dongyuemiao section have been further clarified on line 88-94.

 

3. Although the descriptions of the techniques are complete, the logical flow of the experiments does not seem clear. For example: First, how to sample and ensure the representativeness of experimental samples. Next, how to select the analytical scale and specific objectives for each characterization method (e.g., MIP for mesopores and macropores, LTNA for micropores). Finally, how to integrate experimental data into the multifractal analysis.

Response: For the selection of experimental samples, we sampled all 1-4 layers of the Dongyuemiao section, which can effectively and comprehensively characterize the Dongyuemiao section, Lines 139,364,394 add the required content; This article mainly conducts multifractal analysis through nuclear magnetic resonance parameters. High pressure mercury intrusion and nuclear magnetic resonance are methods for exploring pore structure and have not been involved in multifractal analysis.

 

4. In Table 2, the author proposed three types of pore sizes. What is the basis for the author's classification? Can you provide relevant references?

Response: This article mainly classifies three types of pore sizes: micropores with pore sizes less than 2nm, mesopores with pore sizes between 2-50nm, and macropores with pore sizes bigger than 50nm.Corresponding references have been added in line 435-437 and add the reference.

 

5. The current study is based only on the Dongyuemiao section and lacks comparison with other lacustrine shales. It is recommended to supplement or cite other research data from Horizontal for comparison.

Response: Added the characteristics of lacustrine shale in different study areas and layer series, as well as the differences from lacustrine shale in this study section and compared them horizontally with the study area on line 94-97.

 

6. The author has done a lot of work in multifractal theory, but the physical meaning of each parameter in the article is too simple. For readers who are not familiar with multifractal theory, it is difficult to understand the application of this theory to rock pore heterogeneity.

Response: Based on your suggestion, we provide more detailed supplements to multifractal parameters and formulas to help readers have a clearer understanding of multifractal in method in line 259-264.

 

7. The current discussion focuses on the lack of explanation of experimental results and their connection with broader theory.

Response: In response to the feedback you provided, we have combined the results of the discussion section with some practical theories through literature review. Therefore, the discussion section is more persuasive, relevant literature and theoretical explanation foundations have been added in line 519-524.

Reviewer 3 Report

Comments and Suggestions for Authors

Comments are presented in pdf

Comments for author File: Comments.pdf

Comments on the Quality of English Language

English is good small changes are needed

Author Response

Reviewer 3

The manuscript focuses on characterization of pore heterogeneity in lacustrine shale. The

research group's coherently detailed analysis of their results along with correct English writing.

There are few recommendations for more complete and better outcome.

1. The introduction part is too small and narrow. Pore structure characterization must

include also other type of rocks e.g., coal, granite etc, that have used same techniques

such as SEM, Mercury Intrusion, Nitrogen adsorption, NMR etc. The below references

can help you:

[1] Han, W., Zhou, G., Gao, D., Zhang, Z., Wei, Z., Wang, H. and Yang, H., 2020.

Experimental analysis of the pore structure and fractal characteristics of different

metamorphic coal based on mercury intrusion-nitrogen adsorption porosimetry. Powder

Technology, 362, pp.386-398.

[2] Cai, Y., Li, Q., Liu, D., Zhou, Y. and Lv, D., 2018. Insights into matrix compressibility

of coals by mercury intrusion porosimetry and N2 adsorption. International Journal of

Coal Geology, 200, pp.199-212.

[3] Longinos, S.N. and Hazlett, R., 2024. Cryogenic fracturing using liquid nitrogen on

granite at elevated temperatures: a case study for enhanced geothermal systems in

Kazakhstan. Scientific Reports, 14(1), p.160.

[4] Longinos, S.N., Tuleugaliyev, M. and Hazlett, R., 2024. Influence of subsurface

temperature on cryogenic fracturing efficacy of granite rocks from

Kazakhstan. Geothermics, 118, p.102919.

[5] Zhao, X., Yang, Z., Lin, W., Xiong, S., Luo, Y., Wang, Z., Chen, T., Xia, D. and Wu,

Z., 2019. Study on pore structures of tight sandstone reservoirs based on nitrogen

adsorption, high-pressure mercury intrusion, and rate-controlled mercury

intrusion. Journal of Energy Resources Technology, 141(11), p.112903.

[6] Al-Mahrooqi, S.H., Grattoni, C.A., Moss, A.K. and Jing, X.D., 2003. An investigation

of the effect of wettability on NMR characteristics of sandstone rock and fluid

systems. Journal of Petroleum Science and Engineering, 39(3-4), pp.389-398.

Response: Thanks for your suggestions on this article!

We will further supplement the introduction section and add information about the pore structure characteristics of coal. Add the required content to lines 79-82 based on the provided references and added references

 

2. The citation did not fully explain the necessity and innovation of this study. It is

recommended that more literature be referred to and that the necessity of this study be

analyzed in detail.

Response: We further introduced the basic data of the Dongyuemiao section shale and emphasized its uniqueness. We also briefly explained the development space of multifractal theory to clarify the uniqueness and necessity of this study, the added content is on lines 88-99.

 

3. There is no information about coal’s porosity, permeability, etc.

Response: The pore structure characteristics of coal have been added to 79-82 line

 

4. Figures have different fonds. Correct and keep same size

Response: Based on your suggestion, we carefully checked the size of the characters in the picture and made corresponding modifications, the Figures in the picture uses the same font size.

 

5. In nitrogen adsorption experiments the graphs are not presented correct. You should

mention the low- and high-pressure area along with hysteresis loop. Why there is no

estimation of fractal dimension D1 and D2 and combination with adsorption results?

Response: The curve characteristics of nitrogen adsorption curve in high pressure and low pressure area have been added in line 395-397, and the hysteresis loop morphology will be mentioned in the subsequent introduction;

The multifractal analysis used in this article mainly relies on nuclear magnetic resonance data for research, while nitrogen adsorption and high-pressure mercury injection data are mainly used for singlet fractal analysis

 

6. In Mercury intrusion results again, you do not show the augmentation in hysteresis loop.

Response: Thank you for the reviewer's suggestion to the Mercury intrusion hysteresis loop .This study mainly characterized the connectivity of the pore structure of the experimental sample through the mercury removal efficiency for high-pressure mercury injection experiments, and did not consider the description of hysteresis loops. Currently, the explanation of hysteresis loops for high-pressure mercury injection is not comprehensive, so hysteresis loops were not used to represent the experimental results. Thank you again for the valuable feedback from the reviewer.

 

7. Make a comparative analysis of nitrogen adsorption and mercury intrusion capacities

showing Nmax and Mmax values.

Response: Nmax and Mmax values can be obtained from the experimental results of high-pressure mercury injection and nitrogen adsorption. By comparing the two horizontally, it can be concluded that nitrogen adsorption and mercury intrusion capacities. These two types of data have been added in Table 2

 

8. Fix a graph showing cumulative pore volume changes (e.g adsorption pores, seepage

pores, total pores etc).

Response: Figure 7 shows the cumulative pore volume changes. In this study, we mainly used nitrogen adsorption and high-pressure mercury injection to jointly characterize the pore volume changes and distinguish the pore structure characteristics of different lithofacies. The pore volume change of one of the two is not significant between different lithofacies, so this article did not involve the other two types of volume changes

 

9. The discussion lacks a good explanation and comparison with similar works. For a more

complete analysis, your outcomes must be compared with previous works, and the

reasons for similarities and differences must be explained.

Response: By reviewing relevant research literature, we found that the previous results on the impact of TOC on heterogeneity differed from the views presented in this paper. We clarified the previous explanations for these results, and subsequently provided a comprehensive explanation for the results of our study to achieve comprehensiveness on line 506-509.

10. Conclusions need to be rewritten highlighting the most important results.

Response: The conclusion section has been simplified while ensuring the completeness of the conclusion, as the multifractal method itself is an abstract tool. Therefore, the conclusion section can only use multifractal parameters to build a bridge with geological parameters and clarify the controlling factors of lacustrine shale heterogeneity.

Reviewer 4 Report

Comments and Suggestions for Authors

Dear Authors,

 

Thank you for your interesting submission. The paper suggests a combination of experimental techniques, including mercury intrusion porosimetry (MIP), low-temperature nitrogen adsorption (LTNA), nuclear magnetic resonance (NMR), and multifractal theory, to investigate pore heterogeneity in lacustrine shale.

The manuscript should be revised according to the following remarks:

-        The study handles advanced techniques. It would be interesting to discuss the limitations of these methods (for instance, MIP and NMR) which might affect pore size characterization.

-        The study is focused on the Jurassic Dongyuemiao Member. For completeness, is it possible to consider other regions (or geological settings) ?

-        To enrich your results, a detailed statistical analysis of the different parameters (quartz content, clay minerals, TOC, pore heterogeneity and multifractal results) should be carried out to highlight the possible correlations.

-        The paper should highlight the benefit of the study for reservoir characterization.

-        Minor proofreading and language revision is needed.

 

Author Response

Reviewer 4

 

Thank you for your interesting submission. The paper suggests a combination of experimental techniques, including mercury intrusion porosimetry (MIP), low-temperature nitrogen adsorption (LTNA), nuclear magnetic resonance (NMR), and multifractal theory, to investigate pore heterogeneity in lacustrine shale.

The manuscript should be revised according to the following remarks:

 

1.The study handles advanced techniques. It would be interesting to discuss the limitations of these methods (for instance, MIP and NMR) which might affect pore size characterization.

Response: Thanks for your suggestions on this article!

Each method for quantitatively measuring pore structure has its own shortcomings, and the most obvious difference among the methods mentioned in this article is that nitrogen adsorption and high-pressure mercury injection have significant differences in measuring pore size in different intervals. Nitrogen adsorption mainly measures microporous mesoporous pore structure, while high-pressure mercury injection mainly measures the pore volume of macropores. The limitations of methods for characterizing pore structure through nitrogen adsorption and high-pressure mercury intrusion have been added in line 363、393

 

2.The study is focused on the Jurassic Dongyuemiao Member. For completeness, is it possible to consider other regions (or geological settings) ?

Response: Based on your suggestion, we have included the lacustrine shale of the Lianggaoshan Formation in the Sichuan Basin in the article and compared it with the shale of the Dongyuemiao section Additional explanations were provided in the introduction regarding lacustrine shale from other regions in line 94-97.

 

3.To enrich your results, a detailed statistical analysis of the different parameters (quartz content, clay minerals, TOC, pore heterogeneity and multifractal results) should be carried out to highlight the possible correlations.

Response: The left vertical axis of Figure 10 represents TOC, and the right vertical axis represents the content of quartz and clay minerals, which shows the relationship between TOC, clay mineral and quartz content, and multifractal parameters.

 

4.The paper should highlight the benefit of the study for reservoir characterization.

Response: By studying the heterogeneity of pore structure in shale reservoirs, a more comprehensive understanding of the basic characteristics of the reservoir can be obtained, and theoretical support can be provided for future effective reservoir exploitation and sweet spot prediction . It has been elaborated in the introduction section in line 118-120.

5.Minor proofreading and language revision is needed.

Response: Detailed modifications have been made to the sentences in this article to improve readers' reading fluency.

Reviewer 5 Report

Comments and Suggestions for Authors

Please kindly see the attachment.

Comments for author File: Comments.pdf

Comments on the Quality of English Language

English writing should be extensively reviewed, some formulas must be corrected and edited.

Author Response

Reviewer 5

1.Most references cited are from national sources, with a notable absence of works by Mandelbrot, whose pioneering contributions to fractal theory have profoundly advanced the understanding of porosity and permeability relationships. Some additional referees have been suggested (see detailed review);

Response: Thank you for your suggestions on this article!

Based on the detailed suggestions you provided, I have selected several references you provided to introduce multifractal theory to readers more clearly.

2. Some formulas are incorrectly reproduced (e.g.: Eq.(9), (10), (12), etc.) and should be checked for consistency, along with a comprehensive review of all notations to ensure uniformity. Additionally, the theoretical section lacks proper references. After each formulas, used notations should be defined that is not done systematically (see Eqs. (10), (13), (14), (15), etc.).

Response: Based on your suggestions and derivation of the formula, formula 11 has been replaced and formulas 9, 10, and 12 have been modified. Further explain the parameters in the formula according to your suggestions 

3. Uncertainty and precision (± σ) of measurements or estimated values should be indicated (e.g., table 1, 2, 3). If available, it should be beneficial to include the atomic H/C and O/C ratios as additional columns in table 1 in order to try to characterize multifractals parameters with organic matter maturation.

Response: High pressure mercury intrusion precision (± σ) of measurements has been added to Table 2; Uncertainty and precision between nitrogen adsorption and nuclear magnetic resonance did not appear in the experiment, so there is no data to support it; Meanwhile, this study mainly characterized the basic characteristics of shale reservoirs through TOC measurement, clay mineral analysis, and pore structure, and did not involve data such as H/C and O/C ratio.

4. Previous works sustaining the interpretation of ΔD, D curves, Δα, and f(α) should be cited, for instance [2] together with the extensive literature on soil and rock porosity.

Response: We have added some detailed explanations about multifractal parameters below the formula based on your suggestion for readers to understand.

5.Principal component analysis (PCA) is a valuable technique for extracting and condensing essential information from a multivariable datasets. It is recommended to apply this analysis to a table containing multifractal parameters, depth, facies types, mineralogical composition, TOC, H/C, O/C, porosity, and permeability, on order to better understand potential

Response: Thank you for the reviewer's suggestion to use PCA to further explore the relationships between variables. Considering that this article has already analyzed the relationship between multifractal parameters and shale lithology through the intersection method TOC、 The correlation between mineral composition and pore permeability has been fully revealed, and the main controlling factors of heterogeneity have been fully revealed, so PCA may not significantly add new conclusions. However, I am willing to briefly mention the potential applications of PCA in the discussion section or use it as a future research direction. Thank you again for the valuable feedback from the reviewer.

6.The precision of R2 values with four decimal places is unnecessary given the number of samples. Use two decimal places instead and correct the figures accordingly (e.g., R2=0.9327 should be adjusted to R2=0.93). Update figures 10 to 12 accordingly.

Response: R² in Figure 10-12 has been modified to two decimal places, and R² values that are too small are still written to four decimal places

7. The English written needs some revisions.

Response: The English writing has been extensively revised based on your suggestions.

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

The authors did not follow and did not correct the suggestions. Hence their work does not meet the criteria to be published in Fractal and Fractional Journal.

Comments for author File: Comments.docx

Comments on the Quality of English Language

Must be improved

Author Response

Reviewer 3

The manuscript focuses on characterization of pore heterogeneity in lacustrine shale. The

research group's coherently detailed analysis of their results along with correct English writing.

There are few recommendations for more complete and better outcome.

1. The introduction part is too small and narrow. Pore structure characterization must

include also other type of rocks e.g., coal, granite etc, that have used same techniques

such as SEM, Mercury Intrusion, Nitrogen adsorption, NMR etc. The below references

can help you:

[1] Han, W., Zhou, G., Gao, D., Zhang, Z., Wei, Z., Wang, H. and Yang, H., 2020.

Experimental analysis of the pore structure and fractal characteristics of different

metamorphic coal based on mercury intrusion-nitrogen adsorption porosimetry. Powder

Technology, 362, pp.386-398.

[2] Cai, Y., Li, Q., Liu, D., Zhou, Y. and Lv, D., 2018. Insights into matrix compressibility

of coals by mercury intrusion porosimetry and N2 adsorption. International Journal of

Coal Geology, 200, pp.199-212.

[3] Longinos, S.N. and Hazlett, R., 2024. Cryogenic fracturing using liquid nitrogen on

granite at elevated temperatures: a case study for enhanced geothermal systems in

Kazakhstan. Scientific Reports, 14(1), p.160.

[4] Longinos, S.N., Tuleugaliyev, M. and Hazlett, R., 2024. Influence of subsurface

temperature on cryogenic fracturing efficacy of granite rocks from

Kazakhstan. Geothermics, 118, p.102919.

[5] Zhao, X., Yang, Z., Lin, W., Xiong, S., Luo, Y., Wang, Z., Chen, T., Xia, D. and Wu,

Z., 2019. Study on pore structures of tight sandstone reservoirs based on nitrogen

adsorption, high-pressure mercury intrusion, and rate-controlled mercury

intrusion. Journal of Energy Resources Technology, 141(11), p.112903.

[6] Al-Mahrooqi, S.H., Grattoni, C.A., Moss, A.K. and Jing, X.D., 2003. An investigation

of the effect of wettability on NMR characteristics of sandstone rock and fluid

systems. Journal of Petroleum Science and Engineering, 39(3-4), pp.389-398.

Response: Thanks for your suggestions on this article!

In response to your suggestions and references, relevant studies on coal, granite, and sandstone using the same characterization method for pore structure have been added in line 82-95

2. The citation did not fully explain the necessity and innovation of this study. It is

recommended that more literature be referred to and that the necessity of this study be

analyzed in detail.

Response: We further introduced the basic data of the Dongyuemiao section shale and emphasized its uniqueness. We also briefly explained the development space of multifractal theory to clarify the uniqueness and necessity of this study, the added content is on lines 102-108、116-121.

 

3. There is no information about coal’s porosity, permeability, etc.

Response: In response to your suggestion, basic information and measurement methods for coal porosity and permeability have been added in line 77-82

 

4. Figures have different fonds. Correct and keep same size

Response: Based on your suggestion, we carefully checked the size of the characters in the picture and made corresponding modifications, the font sizes in Figure 5-8 have been standardized

5. In nitrogen adsorption experiments the graphs are not presented correct. You should

mention the low- and high-pressure area along with hysteresis loop. Why there is no

estimation of fractal dimension D1 and D2 and combination with adsorption results?

Response: The curve characteristics of nitrogen adsorption curve in high pressure and low pressure area have been added in line 409-411, and the hysteresis loop morphology will be mentioned in the subsequent introduction;

This study focuses on the heterogeneity of microscopic pores in shale. The complexity and developmental degree of pore interiors are not the primary research objectives of this paper. Therefore, we utilized only nuclear magnetic resonance (NMR) T2 spectra for multifractal analysis. However, the study of univariate fractal dimensions using nitrogen adsorption and high-pressure mercury intrusion data is also an important research endeavor. I will briefly address the application of univariate fractal analysis in the discussion section or consider it as a potential direction for future research. Once again, I sincerely appreciate the reviewer's valuable feedback.

6. In Mercury intrusion results again, you do not show the augmentation in hysteresis loop.

Response: Thanks for the reviewer's suggestion to the Mercury intrusion hysteresis loop. This study mainly characterized the connectivity of the pore structure of the experimental sample through the mercury removal efficiency for high-pressure mercury injection experiments, while the augmentation in hysteresis loop indicates an increase in the pressure of mercury injection. At higher pressures, mercury enters smaller pores. Therefore, a greater amount of mercury intrusion at high pressures reflects more developed microporosity. This is described in detail on line 382-388.

7. Make a comparative analysis of nitrogen adsorption and mercury intrusion capacities

showing Nmax and Mmax values.

Response: Nmax and Mmax values can be obtained from the experimental results of high-pressure mercury injection and nitrogen adsorption. By comparing the two horizontally, it can be concluded that nitrogen adsorption and mercury intrusion capacities. These two types of data have been added in Table 2

 

8. Fix a graph showing cumulative pore volume changes (e.g adsorption pores, seepage

pores, total pores etc).

Response: Figure 7 shows the cumulative pore volume changes. In this study, we mainly used nitrogen adsorption and high-pressure mercury injection to jointly characterize the pore volume changes and distinguish the pore structure characteristics of different lithofacies. The pore volume change of one of the two is not significant between different lithofacies, so this article did not involve the other two types of volume changes

 

9. The discussion lacks a good explanation and comparison with similar works. For a more

complete analysis, your outcomes must be compared with previous works, and the

reasons for similarities and differences must be explained.

Response: By reviewing relevant research literature, we found that the previous results on the impact of TOC on heterogeneity differed from the views presented in this paper and characterization of porosity and permeability using multifractal dimensions. We clarified the previous explanations for these results, and subsequently provided a comprehensive explanation for the results of our study to achieve comprehensiveness on line 511-513、523-525、540-541.

 

10. Conclusions need to be rewritten highlighting the most important results.

Response: The conclusion section has been simplified while ensuring the completeness of the conclusion, as the multifractal method itself is an abstract tool. Therefore, the conclusion section can only use multifractal parameters to build a bridge with geological parameters and clarify the controlling factors of lacustrine shale heterogeneity.

Reviewer 4 Report

Comments and Suggestions for Authors

Dear Authors,

Thanks your for your efforts. The paper is publishable now.

Author Response

Comment: Thanks your for your efforts. The paper is publishable now.

Response: Thank you for agreeing to publish the revised version. Thank you for your approval of the revised content.

Reviewer 5 Report

Comments and Suggestions for Authors

2nd Review of the paper entitled
Characterization of Pore Heterogeneity in Lacustrine Shale Based on MIP, LTNA, NMR, and Multifractal Characteristics: A Case Study of Jurassic Dongyuemiao Member, China
By Xu Wu1,2, Yifan Gu1,2,*, Yuqiang Jiang1,2, Zhanlei Wang1,2 and Yonghong Fu1
This revised version shows significant improvement in English writing compared to the previous one. However, further editing is required before the paper is ready for publication. Some misprints and issues identified in the previous review remain uncorrected and have been noted the detailed review below. 
The following errors need to be addressed:
    Extensive editing is required before final submission (ensure that copying and pasting from a PDF does not remove spaces between words).
    Errors in formulas persist (see detailed review).
    References should be carefully checked.
Major scientific concerns from the first review have been addressed. I have provided a detailed review below, including improvements to the English writing in paragraphs that were added or rewritten after the previous review. No evidence of plagiarism was found. 
Once these corrections are made, the paper will be suitable for publication.
See attached detailed PDF review
Detailed comments
WARNING: When copying and pasting from the PDF-reviewed document, words may not be properly separated by spaces. Please carefully check and proofread your final document before submission. 

 

Comments for author File: Comments.pdf

Comments on the Quality of English Language

English writing needs extensive revision.

Author Response

Reviewer 5

1.Extensive editing is required before final submission (ensure that copying and pasting from a PDF does not remove spaces between words).

Thanks you for providing valuable suggestions again

Response: The formatting issues in the article have been thoroughly revised

2.Errors in formulas persist (see detailed review).

Response: Formulas 12, 13, 19 and mercury removal efficiency formula in the article have been modified accordingly

3.References should be carefully checked.

Response: The references have been extensively revised

4. Comments: Previous works sustaining the interpretation of ΔD, D curves, Δα, and f(α) should be cited in this §, for instance, reference [2] (my ref.) and the extensive literature on soil and rock porosity would provide valuable context and justification for these interpretations.

Response: Previous studies have been added to this section based on the literature you provided

5. In table 1, the uncertainty and precision (± σ) of the mineralogical compositions should be indicated. It should be beneficial to include the atomic H/C and O/C ratios as additional columns in table 1

Response: The uncertainty and accuracy (± σ) of mineral composition have been added to Table 1, but the atomic H/C and O/C ratios were not specifically considered in this experiment. Your suggestion will be applied in future research. Thanks again for your suggestion.