The Impact of Elastoplastic Deformation Behavior on the Apparent Gas Permeability of Deep Fractal Shale Rocks
Round 1
Reviewer 1 Report
Comments and Suggestions for Authors
Referee Report
The authors presents a novel model to characterize the stress-dependent apparent gas permeability in deep shale gas reservoirs, accounting for the contributions of viscous flow, Knudsen diffusion, surface diffusion, real gas effects, and slip effects of gas based on the fractal theory and thick-walled cylinder model. They outcomes are validated against experimental data that demonstrates the model’s high accuracy and strong consistency with existing literature. In general, the paper presents some intriguing findings. However, the authors should answer to the following questions before the publication in the journal Fractal Fract.
- The authors outcomes are validated against experimental data that demonstrates the model’s high accuracy and strong consistency with existing literature without comparing their results with those in the literature.
- Equations in the manuscript are written without any punctuation.
- Some places within text equations are referred to as (#) whereas other places they are referred to as Eq. (#). Please, used the same notation in the whole manuscript.
- Why the effects of multi-layer adsorption of shale gas were not considered in the present study?
- Why references 3, 9, 16 and 36 are written in capital letters?
Author Response
Response to Reviewers
Dear Editors and Reviewers:
Thank you very much for giving us the opportunity to submit a revised draft of the manuscript “The impact of elastoplastic deformation behavior on the apparent gas permeability of deep fractal shale rocks” for publication in the Fractal and Fractional. We deeply appreciate the time and effort that you and the reviewers dedicated to providing feedback on our manuscript and are grateful for the insightful comments on and valuable improvements to our paper. We have incorporated the suggestions made by the reviewers. Those changes are highlighted within the manuscript. Please see below, in blue, for a point-by-point response to the reviewers’ comments and concerns. All page numbers refer to the revised manuscript file with tracked changes. We sincerely hope to meet with your approval and hope that the revised manuscript is suitable for publication.
We highlighted all revisions in red colour.
Reviewer #1:
Comments 1: The authors outcomes are validated against experimental data that demonstrates the model’s high accuracy and strong consistency with existing literature without comparing their results with those in the literature.
Response 1: Thank you for your careful and professional review, next, I will respond to the questions regarding the result of the fractal mathematical model is validated against experimental data that demonstrates the model’s high accuracy and strong consistency with existing literature without comparing their results with those in the literature. This study includes two validations of the proposed mathematical model. The first validation, using experimental data from prior studies, examined the permeability–stress relationship during shale's elastic deformation. The second validation used experimental data from this study to analyze the same relationship under elastoplastic deformation in deep shale gas reservoirs. Together, these validations not only demonstrate the model’s general applicability but also its ability to capture both elastic and elastoplastic deformation behaviors of shale gas rock.
Comments2: Equations in the manuscript are written without any punctuation.
Response 2: We appreciate your diligence and professionalism review and in response, before submission, we thoroughly reviewed the journal’s formatting template, which offers two equation styles—one with punctuation and one without. We adopted the latter.
Comments3: Some places within text equations are referred to as (#) whereas other places they are referred to as Eq. (#). Please, used the same notation in the whole manuscript.
Response 3: Thank you for your careful and professional review, next, the following section provides a detailed explanation. In this paper, various explanatory statements are used to introduce the complete formula in different sections, we present this formula for the first time in the paper, that some places within text equations are referred to as (#) is used to further elaborate on the content of the paper. The formula is cited, emphasized, and applied again in the text as Eq. (#).
Comments 4: Why the effects of multi-layer adsorption of shale gas were not considered in the present study?
Response 4: Thank you for your careful and professional review. This study primarily focuses on the influence of rock elastoplastic deformation on the apparent gas permeability of fractal porous media in deep shale gas reservoirs, rather than on the effects of multilayer adsorption on shale gas flow. However, multilayer adsorption is addressed in the research conclusions, future work will incorporate a multilayer adsorption model to evaluate its effect on apparent gas permeability in deep shale gas reservoirs.
Comments 5: Why references 3, 9, 16 and 36 are written in capital letters?
Response 5: We appreciate the comment regarding the reference citation format. The issue has been addressed, and revisions have been made throughout the manuscript.
Best wishes,
Sincerely thanks for all the help!
Zhaoqin Huang
State Key Laboratory of Deep Oil and Gas and School of Petroleum Engineering
China University of Petroleum (East China)
E-mail: huangzhqin@upc.edu.cn
Reviewer 2 Report
Comments and Suggestions for Authors
The manuscript titled "The impact of elastoplastic deformation behavior on the apparent gas permeability of deep fractal shale rocks" is well written and interesting. It contains a large number of equations, which can be difficult to understand, but are necessary to explain the methodology used. I belive that this work can be published after correct some details.
- Introduce the figures in the text before presenting them.
- Figure 1 presents "Force on three-dimensional single..." and p are pressures and not forces. Correct this in the list of symbols, in the figures, and along the text.
- Check the sentence on line 144: "Under the Tresca yield criterion. ρ is the ratio..."
- It is not clear if the stress is in the direction of L0 or perpendicular to it.
- Must define what LT is.
- There are some citations in the wrong format. (lines 292, 361. Check along the text).
- What is Amin in the legend of Figure 4?
- Line 367: "Under varying effective stresses, the three-color square-dotted curves represent..." I don't see any square-dotted curves in Figure 4. Check this in all the figures and their descriptions.
- You must decide whether to use r or λ to represent the pore radius. In some parts of the text, one symbol is used and in others another.
- For rock sample 1, Young’s modulus, Poisson’s ratio, and porosity are 15.67GPa, 0.281, and 0.055, respectively are used Young’s modulus of 15 GPa, a Poisson’s ratio of 0.22, and a porosity
of 0.055 are used, values similar to those obtained experimentally. For the rock sample 2, these parameters are 15.77 GPa, 0.237, and 0.052 experimentally, and a Young’s modulus of 10 GPa, a Poisson’s ratio of 0.2, and a porosity of 0.052. Why is only the porosity similar, and the other properties quite different?
- It is not clear what the percentage is in Figures 11, 13, 15, and 17.
- Figures 10, 12, 14, and 16 would have to have the same amplitude to be able to purchase each of the effects analyzed.
- Lines 466 to 472, the values presented in the text don't coincide with those presented in Figure 11b. Check the information about this study.
- Variations of less than 3% between Elasticity and Eastoplasticity compensate for this implementation? Errors less than 1% are representative and found in the experimental problems?
- The results present a model calibration and then a robust (quite excessive) sensitivity analysis, but there is no model verification. Furthermore, the calibration utilizes parameters that do not accurately represent the material properties measured experimentally.
Author Response
Response to Reviewers
Dear Editors and Reviewers:
Thank you very much for giving us the opportunity to submit a revised draft of the manuscript “The impact of elastoplastic deformation behavior on the apparent gas permeability of deep fractal shale rocks” for publication in the Fractal and Fractional. We deeply appreciate the time and effort that you and the reviewers dedicated to providing feedback on our manuscript and are grateful for the insightful comments on and valuable improvements to our paper. We have incorporated the suggestions made by the reviewers. Those changes are highlighted within the manuscript. Please see below, in blue, for a point-by-point response to the reviewers’ comments and concerns. All page numbers refer to the revised manuscript file with tracked changes. We sincerely hope to meet with your approval and hope that the revised manuscript is suitable for publication.
We highlighted all revisions in red colour.
Reviewer #2:
Comments 1: Introduce the figures in the text before presenting them.
Response 1: Thank you for your careful and professional review. We are very sorry for this mistake, it caused difficulties for you and the readers in understanding this paper and related papers. We have adjusted the layout of some figures in the manuscript to make the overall layout structure of the paper more reasonable.
Comments 2: Figure 1 presents "Force on three-dimensional single..." and p are pressures and not forces.
Response 2: Thank you for your careful and professional review, we have checked the manuscript thoroughly again and corrected this mistake. See Line 189.
Comments 3: Check the sentence on line 144: "Under the Tresca yield criterion. ρ is the ratio...".
Response 3: Thanks for pointing out the problem, we have checked the sentence on line 144 and corrected the corresponding sentence writing problem. And we have checked the manuscript thoroughly again to Ensure that such problem do not occur again.
Comments 4: It is not clear if the stress is in the direction of L0 or perpendicular to it.
Response 4: Thank you for your careful and professional review, next, the following section provides a detailed explanation. In this paper, stress variations induce changes in capillary diameter, thereby affecting capillary tortuosity and further altering capillary length, which in turn modifies the gas apparent permeability of shale gas. So, the stress is perpendicular to the direction of L0. For details, refer to Equation 7 and Figure 1.
Comments 5: Must define what LT is.
Response 5: Thank you for your suggestion. We apologize for any confusion caused by our inaccurate description. The term refers to the length of the capillary bundle, denoted as "Lp" in the paper. We have thoroughly reviewed the manuscript and revised the relevant sections accordingly.
Comments 6: There are some citations in the wrong format. (lines 292, 361. Check along the text).
Response 6: Thank you for your suggestion. We have checked the entire manuscript and revised the format of references.
Comments 7: What is Amin in the legend of Figure 4?
Response 7: Thank you for your careful and professional review. We have made revisions at the corresponding sections in the manuscript. See line 367.
Comments 8: Line 367: "Under varying effective stresses, the three-color square-dotted curves represent..." I don't see any square-dotted curves in Figure 4. Check this in all the figures and their descriptions.
Response 8: Thank you for your careful and professional review, we apologize for the incorrect description of Figure 4, which has misled you. We have revised the description of Figure 4 and reviewed all figures in the manuscript along with their descriptions. See line 365-367.
Comments 9: You must decide whether to use r or λ to represent the pore radius. In some parts of the text, one symbol is used and in others another
Response 9: Thanks for the heads up. We are very sorry for that mistake in the manuscript, we have examined it closely, and made corresponding modifications in the manuscript. See line 452-470.
Comments 10: For rock sample 1, Young’s modulus, Poisson’s ratio, and porosity are 15.67GPa, 0.281, and 0.055, respectively are used Young’s modulus of 15 GPa, a Poisson’s ratio of 0.22, and a porosity of 0.055 are used, values similar to those obtained experimentally. For the rock sample 2, these parameters are 15.77 GPa, 0.237, and 0.052 experimentally, and a Young’s modulus of 10 GPa, a Poisson’s ratio of 0.2, and a porosity of 0.052. Why is only the porosity similar, and the other properties quite different?
Response 10: We appreciate the reviewer’s insightful comment. The mechanical properties of single capillary such as Young’s modulus and Poisson’s ratio which we used in model to represent the mechanic properties of whole rock sample. So, the porosity values were matched closely between simulation and experiment, and the mechanical properties parameters are quite different. Despite the deviation, the selected values are still within a reasonable range and maintain the essential mechanical response of the rock. We have added an explanation of this choice in the revised manuscript.
Comments 11: It is not clear what the percentage is in Figures 11, 13, 15, and 17.
Response 11: We appreciate the reviewer’s valuable comment. The percentage values shown in Figures 11, 13, 15, and 17 indicate t proportion of pore volumes corresponding to different flow mechanisms to the total pore volume of the shale porous media. Refer to Equation 52-53 for details.
Comments 12: Figures 10, 12, 14, and 16 would have to have the same amplitude to be able to purchase each of the effects analyzed.
Response 12: We appreciate the reviewer’s suggestion regarding the amplitude (scale) of Figures 10, 12, 14, and 16. However, each figure highlights different physical conditions and ranges of interest. Unifying the amplitude across all figures may obscure important local variations that are critical to the analysis. We kindly ask the reviewer to understand the reasons for our approach.
Comments 13: Lines 466 to 472, the values presented in the text don't coincide with those presented in Figure 11b. Check the information about this study.
Response 13: We appreciate the reviewer’s careful observation. We have thoroughly rechecked the values presented in Lines 466 to 472 and compared them with those shown in Figure 11b. We identified an inconsistency between the textual description and the figure. The manuscript has now been revised accordingly to ensure consistency and accuracy.
Comments 14: Variations of less than 3% between Elasticity and Elastoplasticity compensate for this implementation? Errors less than 1% are representative and found in the experimental problems?
Response 14: We thank the reviewer for this insightful question. The variation of less than 3% between the elastic and elastoplastic models indicates a relatively small difference in proportion of pore volume in different flow mechanisms. This suggests that, for the specific case studied, considering the introduction of elastoplasticity in deep shale gas reservoirs, it does not alter the inherent microscopic flow mechanisms of the shale. We have not yet observed that errors less than 1% are representative and found in the experimental problems in experiments. We agree with the reviewer's comments and plan to use nuclear magnetic resonance (NMR) equipment to carry out relevant experiments in the next stage of research.
Comments 15: The results present a model calibration and then a robust (quite excessive) sensitivity analysis, but there is no model verification. Furthermore, the calibration utilizes parameters that do not accurately represent the material properties measured experimentally.
Response 15: We sincerely thank the reviewer for this constructive comment. We conducted two validations of the model based on experimental data. The first was an elastic validation, and the second was an elastoplastic validation. Both validations demonstrated high accuracy. For the second validation, all the data used were measured in our laboratory. As for why there is a deviation, it is because we used the mechanical properties of a single capillary to replace the overall mechanical properties of the rock sample. I hope this response can resolve the reviewer's confusion.
Best wishes,
Sincerely thanks for all the help!
Zhaoqin Huang
State Key Laboratory of Deep Oil and Gas and School of Petroleum Engineering
China University of Petroleum (East China)
E-mail: huangzhqin@upc.edu.cn
Round 2
Reviewer 2 Report
Comments and Suggestions for Authors
The manuscript has been improved with the corrections done
Author Response
Response to Reviewers
Dear Editors and Reviewers:
We would like to express our gratitude to the reviewers for their evaluation of our manuscript and for their recognition of the revised version.
Best wishes,
Sincerely thanks for all the help!
Zhaoqin Huang
State Key Laboratory of Deep Oil and Gas and School of Petroleum Engineering
China University of Petroleum (East China)
E-mail: huangzhqin@upc.edu.cn
