the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 16 Oct 2024
Elastic anisotropy differentiation of thin shale beds and fractures using a novel hybrid rock physics model
Abstract. Elastic anisotropy is frequently used to characterize fracture distribution. However, sets of parallel fractures and thin shale beds in tight sand both can cause elastic anisotropy. Here, we are not referring to shale layers on the logging scale but rather to very thin shale beds, a few centimeters thick, within tight sand. To accurately differentiate the anisotropy caused by fractures or thin shale beds, we propose a hybrid rock physics model. This new model combines the Hudson model and the shale compacting Orientation Distribution Function (ODF) model, based on the anisotropic Self-Consistent Approximation and Differential Effective Medium (SCA&DEM) theory. The new model’s reliability is demonstrated by comparing to the well logs. The proposed model can characterize the elastic properties of both thin shale beds and fractures. Based on this model, the rock physical analysis reveals that thin shale beds and fractures exhibit distinct elastic anisotropy characteristics. Furthermore, we analyse the seismic response differences between fractures and thin shale beds using the anisotropic Ruger’s approximation formula. The analysis indicates that tight sand containing thin shale beds interfere with the identification of some fractured tight sand. On the other hand, there are identifiable differences between the fractured tight sand that can form fractured reservoirs and the tight sand containing thin shale beds. Based on this difference, we develop a new seismic attribute to characterize the fracture distribution. These difference-based attributes can effectively eliminate the interference from thin shale beds, making the distribution of fractures more apparent.
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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RC1: 'Comment on egusphere-2024-2483', Anonymous Referee #1, 17 Nov 2024
This is a deeply flawed manuscript. The primary means to differentiate thins beds from fractures is through their different orientations, which is imbedded here but not emphasized. No elaborate rock physics model, containing many strong assumptions, is required.
Even deeper, the authors have not mastered the prior literature, for example they have misunderstood and mischaracterized Hill (1952), Brown and Korringa (1975), Hudson (1980), Thomsen 2023) among others.
Physically, their first error occurs at equation (2) (which does not appear in Hudson, 1980). In an aggregate like that considered, the compliances of the members are additive, not their stiffnesses (see e.g., Schoenberg and Sayers, Geophysics, 60, 204-211, 1995). As a result of this basic error, all that follows is in error. The error is covered over by the numerous model assumptions and calibrations which follow.
It may be possible for the authors to recover from this fundamental error while retaining their modeling effort. If so, any revised manuscript should focus on differentiating fractures from shales via their orientations. But this manuscript is so flawed that it should be rejected by the editor.
Citation: https://doi.org/10.5194/egusphere-2024-2483-RC1 -
AC1: 'Reply on RC1', Li Haoyuan, 20 Nov 2024
Thank you for your thoughtful review and detailed critique.
The Equation (2) in our manuscript is derived from the Handbook of Rock Physics authored by the SRB group, published by Cambridge University Press in 2020. Specifically, it is summarized in Section 4.1.3 as Equation (4.13.1). This formula fully corresponds to Hudson’s summary in Chapter 2 of his 1981 work, which builds upon his original 1980 formulations. Moreover, the application of Brown and Korringa (BK) and Thomsen's equations follows the methodology provided in the latest Handbook of Rock Physics. This modeling process has been widely applied in other studies, and therefore, we do not consider the stiffness calculation within the Hudson model to be inappropriate.
It is possible that our description was not sufficiently detailed, as this modeling workflow was not the primary focus of our manuscript. We will provide a more comprehensive explanation in the revised version.
Our manuscript considers the orientations of sandstones and shales in two parts: one using the Hudson model and the other utilizing a mudrock compaction model. In our study area, the thin interbedded shale layers are much smaller than the resolution of well logs. Therefore, we believe it is crucial to incorporate the anisotropy of both formations comprehensively within the rock physics model.
For additional context, here is a relevant reference that describes and applies the Hudson model:
Mavko, G., Mukerji, T., and Dvorkin, J.: The rock physics handbook, Cambridge university press,2020.
de Figueiredo, J. J. S. j. g. c., Chiba, B. F. F., do Nascimento, M. J., da Silva, C. B., and Santos, L. K.: Can Hudson-Crampin effective model be applied in cracked medium in which the background is weakly anisotropic, Journal of Applied Geophysics, Vol.161, 255-260, 10.1016/j.jappgeo.2018.12.007, 2019.
Huang, X., Huang, X., Xu, Y., Li, H., Zhang, Z., and Xu, W.: Anisotropic Rock Model-Guided Post-Stack Attribute Analysis With Pore Type and Production Data for a Carbonate Gas Reservoir, Frontiers in Earth Science, Vol.9, 10.3389/feart.2021.641705, 2021.
Hudson, J. A.: Overall properties of a cracked solid, Mathematical Proceedings of the Cambridge Philosophical Society, Vol.88, 371-384, 10.1017/s0305004100057674, 1980.
Hudson, J. A.: Wave speeds and attenuation of elastic waves in material containing cracks, Geophysical Journal International,
Vol.64, 133-150, 10.1111/j.1365-246X.1981.tb02662.x, 1981.Yue, C. and Yue, X.: Simulation of acoustic wave propagation in a borehole surrounded by cracked media using a finite difference method based on Hudson's approach, Journal of Geophysics and Engineering, Vol.14, 633-640, 10.1088/1742-2140/aa5af8, 2017.
Zhang, X., Yang, Z., Tang, B., Wang, R., and Wei, X.: Distinguishing oil and water layers in a cracked porous medium using pulsed neutron logging data based on Hudson's crack theory, Geophysical Journal International, Vol.213, 1345-1359, 10.1093/gji/ggy065, 2018.
Thank you once again for your valuable comments, which will help us improve the clarity and rigor of our work.
Citation: https://doi.org/10.5194/egusphere-2024-2483-AC1 -
RC2: 'Reply on AC1', Anonymous Referee #1, 22 Nov 2024
Reviewer’s response to AC1
Elastic anisotropy differentiation of thin shale beds and fractures
using a novel hybrid rock physics model
by Haoyuan Li, et al
The references cited in AC1, by Hudson (1981) and by Mavko et al (2020) both state explicitly that these formulae are for small perturbations only. They are first order Taylor approximations of the correct formula, which is given by Schoenberg and Sayers (1995).
The other misunderstandings are:
- Hill (1952): The Voigt and Reuss “limits” discussed by Hill are only valid for mixtures of isotropic minerals, whereas all of the minerals included in this ms are anisotropic.
- Brown and Korringa (1975): In the present ms, equation (3) has two errors:
- In the second term on the right, the compliance elements with superscript “sand” should instead have superscript “dsand”; this may be just a typo.
- In the same term, the compliance elements s with superscript “sand0” should instead have superscript “sandM”, and the stiffness element K with subscript “sand0” should instead have subscript “sandM”. This notation more closely follows that of Brown and Korringa. Many authors since 1975 (including Mavko et al) have considered M to represent the solid Mineral of the porous rock, but as explained by Thomsen (2023), a better interpretation of M is Mean.
- Thomsen (2023): This paper revises the treatment of fluids within porous rocks in a fundamental way, not consistent with Mavko et al (2020).
- Hudson (1980,1981): These papers consider only cracks in non-porous rock, like granite. If the rock also has non-crack porosity, hydraulically connected to the cracks (e., if they are typical sedimentary rocks), the authors should instead cite Hudson et al, Geophys. J. Int. (1996) 124, 105-112.
More fundamentally, however: All that is needed to differentiate cracks from thin-bedded shales is to recognize that the shales have VTI symmetry, and the cracks do not. No elaborate modelling is required.
Citation: https://doi.org/10.5194/egusphere-2024-2483-RC2 -
AC3: 'Reply on RC2', Li Haoyuan, 27 Nov 2024
Thank you for your valuable suggestions regarding our methodology. We deeply appreciate your insightful comments and will address them in our revised manuscript.
Fracture Model Formula Description
We acknowledge the need to improve the description of the equations in our fracture model to better align with professional standards. This will be updated in the next version.Hudson Model Limitation
You are correct that the Hudson model is unsuitable for representing the elastic properties of rocks with high fracture densities. As you mentioned, the limitation occurs around a fracture density of 0.1, and this is also influenced by the fracture aspect ratio. Beyond this threshold, the elastic parameters of rocks increase with fracture density, which is inconsistent with physical expectations. We have ensured that the fracture density in our model does not exceed this limit. In the revised version, we will provide further clarification and analysis of this threshold in a single part.Shale and Fracture Anisotropy
We agree that shale is characterized by VTI anisotropy, while fractures exhibit HTI anisotropy. In our study, we consider the complex tight sands as a unified skeleton containing both thin shale beds and fractures. Because the thickness of individual shale layers is too small to serve as a separate skeleton compare with tight sand in the area; instead, they are treated as part of the tight sand skeleton. This is mean the model is need consider the comprehensive anisotropic characterise of them. And we analyzed the anisotropic characteristics of this unified framework under varying proportions of shale layers and fractures. We believe this approach is meaningful and has yielded promising results in applications.Thank you once again for your constructive feedback, which has helped us refine and improve our work. We look forward to incorporating these updates and enhancing the clarity and robustness of our research.
Citation: https://doi.org/10.5194/egusphere-2024-2483-AC3 -
RC3: 'Reply on AC3', Anonymous Referee #1, 01 Dec 2024
Reviewer’s response to AC2
Elastic anisotropy differentiation of thin shale beds and fractures
using a novel hybrid rock physics model
by Haoyuan Li, et al
The authors have misunderstood the important aspect of Hudson, et al (1996). The issue is not larger crack density, it is the presence of equant porosity. The pores are much less compliant than the cracks, and if fluid flows between cracks and pores, that changes the effect of the fluid on the elasticity of the rocks.
The authors have also employed an unnecessarily restrictive model for fractures, one that assumes “penny-shaped” cracks. That makes for HTI, if embedded in an otherwise isotropic matrix (not if imbedded in shales, or in thin-beds). If, for example, the fractures are “ribbon-shaped”, i.e. if they are joints, the HTI model is not accurate. HTI is a special case of azimuthal anisotropy, probably never occurring in nature. A more general model for cracks embedded in shales or thin-beds is given by Sayers, C. M., 2022, Elastic properties of fractures in transversely isotropic media: Journal of Applied Geophysics, 197.
More fundamentally, however: All that is needed to differentiate cracks from thin-bedded shales is to recognize that the shales have VTI symmetry, and the cracks do not. No elaborate modelling is required.
Citation: https://doi.org/10.5194/egusphere-2024-2483-RC3 -
AC4: 'Reply on RC3', Li Haoyuan, 10 Dec 2024
We fully agree that the fracture compliance is an important parameter for describing the elastic characteristics of fractures. We will pay more attention to the fracture compliance in our future research.
However, the focus of this paper is on the structure of tight sands in the Sichuan Basin of China, which simultaneously exhibit both fault fractures (horizontal shear fracture) and thin shale beds. These tight sand contain horizontal and short fractures, which are significantly different from typical fractures. Therefore, despite the limitations of the Hudson fracture model, the calibration results in this paper clearly demonstrate its applicability to this type of fracture.
On the other hand, the thin shale beds, which are considered as part of the rock skeleton, are particularly thin, making it essential to adopt a comprehensive modeling approach. It is worth noting that both of these structures can lead to similar VTI anisotropy. For these reasons, we believe that it is necessary to combine them for modeling.
Citation: https://doi.org/10.5194/egusphere-2024-2483-AC4
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AC4: 'Reply on RC3', Li Haoyuan, 10 Dec 2024
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RC3: 'Reply on AC3', Anonymous Referee #1, 01 Dec 2024
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RC2: 'Reply on AC1', Anonymous Referee #1, 22 Nov 2024
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AC2: 'Reply on RC1', Li Haoyuan, 20 Nov 2024
Thank you for your thoughtful review and detailed critique.
The Equation (2) in our manuscript is derived from the Handbook of Rock Physics authored by the SRB group, published by Cambridge University Press in 2020. Specifically, it is summarized in Section 4.1.3 as Equation (4.13.1). This formula fully corresponds to Hudson’s summary in Chapter 2 of his 1981 work, which builds upon his original 1980 formulations. Moreover, the application of Brown and Korringa (BK) and Thomsen's equations follows the methodology provided in the latest Handbook of Rock Physics. This modeling process has been widely applied in other studies, and therefore, we do not consider the stiffness calculation within the Hudson model to be inappropriate.
It is possible that our description was not sufficiently detailed, as this modeling workflow was not the primary focus of our manuscript. We will provide a more comprehensive explanation in the revised version.
Our manuscript considers the orientations of sandstones and shales in two parts: one using the Hudson model and the other utilizing a mudrock compaction model. In our study area, the thin interbedded shale layers are much smaller than the resolution of well logs. Therefore, we believe it is crucial to incorporate the anisotropy of both formations comprehensively within the rock physics model.
For additional context, here is a relevant reference that describes and applies the Hudson model:
Mavko, G., Mukerji, T., and Dvorkin, J.: The rock physics handbook, Cambridge university press,2020.
de Figueiredo, J. J. S. j. g. c., Chiba, B. F. F., do Nascimento, M. J., da Silva, C. B., and Santos, L. K.: Can Hudson-Crampin effective model be applied in cracked medium in which the background is weakly anisotropic, Journal of Applied Geophysics, Vol.161, 255-260, 10.1016/j.jappgeo.2018.12.007, 2019.
Huang, X., Huang, X., Xu, Y., Li, H., Zhang, Z., and Xu, W.: Anisotropic Rock Model-Guided Post-Stack Attribute Analysis With Pore Type and Production Data for a Carbonate Gas Reservoir, Frontiers in Earth Science, Vol.9, 10.3389/feart.2021.641705, 2021.
Hudson, J. A.: Overall properties of a cracked solid, Mathematical Proceedings of the Cambridge Philosophical Society, Vol.88, 371-384, 10.1017/s0305004100057674, 1980.
Hudson, J. A.: Wave speeds and attenuation of elastic waves in material containing cracks, Geophysical Journal International,
Vol.64, 133-150, 10.1111/j.1365-246X.1981.tb02662.x, 1981.Yue, C. and Yue, X.: Simulation of acoustic wave propagation in a borehole surrounded by cracked media using a finite difference method based on Hudson's approach, Journal of Geophysics and Engineering, Vol.14, 633-640, 10.1088/1742-2140/aa5af8, 2017.
Zhang, X., Yang, Z., Tang, B., Wang, R., and Wei, X.: Distinguishing oil and water layers in a cracked porous medium using pulsed neutron logging data based on Hudson's crack theory, Geophysical Journal International, Vol.213, 1345-1359, 10.1093/gji/ggy065, 2018.
Thank you once again for your valuable comments, which will help us improve the clarity and rigor of our work.
Citation: https://doi.org/10.5194/egusphere-2024-2483-AC2 -
RC4: 'Reply on AC2', Anonymous Referee #1, 12 Dec 2024
Please provide a reference which shows the field occurrence of horizontal fractures with VTI symmetry.
Citation: https://doi.org/10.5194/egusphere-2024-2483-RC4 -
AC5: 'Reply on RC4', Li Haoyuan, 12 Dec 2024
We have uploaded images of outcrops, cores, imaging logs, and digital cores that demonstrate the horizontal fractures in this area. These images are sourced from studies conducted by other Chinese scholars, and the references are listed below.
Specifically:
Huang (2022) provides a detailed discussion on sweet spots related to horizontal fractures.
Han (2022) introduces the application of the VTI equivalent model inversion in this area.
Zhao (2020) gives an overview of the fractures across the region.
Additionally, references such as Yue et al. (2018), Zhao et al. (2021), Li et al. (2019), and Zhang et al. (2021) cover various aspects of the reservoir quality, petrophysical properties, tectonic fractures, and stress anisotropy in the Xujiahe Formation, Sichuan Basin.
References:
Yue D, Wu S, Xu Z, et al. Reservoir quality, natural fractures, and gas productivity of upper Triassic Xujiahe tight gas sandstones in western Sichuan Basin, China. Marine and Petroleum Geology. 2018. DOI: 10.1016/j.marpetgeo.2017.10.007.
Zhao H, Shang X, Li M, et al. Investigation on petrophysical properties of fractured tight gas sandstones: a case study of Jurassic Xujiahe Formation in Sichuan Basin, Southwest China. Arabian Journal of Geosciences. 2021;14(2):1-8. DOI: 10.1007/s12517-021-06454-3.
Li H, Tang H, Qin Q, et al. Characteristics, formation periods, and genetic mechanisms of tectonic fractures in the tight gas sandstones reservoir: A case study of Xujiahe Formation in YB area, Sichuan Basin, China. Journal of Petroleum Science and Engineering. 2019;178:723-735. DOI: 10.1016/j.petrol.2019.04.007.
Huang Y, Wang A, Xiao K, et al. Types and genesis of sweet spots in the tight sandstone gas reservoirs: Insights from the Xujiahe Formation, northern Sichuan Basin, China. Energy Geoscience. 2022;3(3):270-281. DOI: 10.1016/j.engeos.2022.03.007.
Han L, Liu J, Yang R, et al. Application of pre-stack elastic impedance inversion method based on VTI medium: A case of tight sandstone fractured reservoir in Xujiahe Formation, Western Sichuan Depression. Petroleum Reservoir Evaluation and Development. 2022;12(2):313-319. DOI: 10.13809/j.cnki.cn32-1825/te.2022.02.006.
Zhang J, Fan X, Huang Z, et al. Evaluation method of anisotropic in-situ stress in the Xujiahe Formation, Sichuan Basin. Oil & Gas Geology. 2021. DOI: 10.11743/ogg20210416.
If you are interested in more details from these studies, you can refer to the articles. Should you have any further questions, please feel free to contact us. Once again, thank you for your feedback and suggestions.
Citation: https://doi.org/10.5194/egusphere-2024-2483-AC5 -
RC5: 'Reply on AC5', Anonymous Referee #1, 15 Dec 2024
Reviewer’s response to AC5
Elastic anisotropy differentiation of thin shale beds and fractures
using a novel hybrid rock physics model
by Haoyuan Li, et al
This reviewer changes his recommendation from REJECT to MAJOR REVISION. The revision should encompass the following points:
- The paper must emphasize that the subject fractures are bed-parallel fractures with assumed VTI symmetry. The more common tectonic fractures may be differentiated from thin beds via their orientation alone, with no modelling required.
- The field occurrence of subsurface bed-parallel fractures must be amply demonstrated with cited references and discussion. Outcrops are not acceptable proof, since the near-surface has low vertical stress.
- The bed-parallel fractures may or may not have VTI symmetry since their orientation alone is not sufficient to establish that (as it is with the bedding). Logs establish orientation, but not symmetry. The shear slip on these fractures may or may not destroy the VTI symmetry. So, VTI symmetry of the fractures must be explicitly assumed.
- The modeling and discussion must respect the criticisms stated earlier.
Citation: https://doi.org/10.5194/egusphere-2024-2483-RC5 -
AC7: 'Reply on RC5', Li Haoyuan, 15 Dec 2024
Thank you for your valuable and professional suggestions regarding our manuscript. We will carefully organize all your comments and incorporate them into our revisions to improve the quality and clarity of the manuscript.
Thank you again for your insightful suggestions.
Citation: https://doi.org/10.5194/egusphere-2024-2483-AC7
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RC5: 'Reply on AC5', Anonymous Referee #1, 15 Dec 2024
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AC6: 'Reply on RC4', Li Haoyuan, 12 Dec 2024
We have uploaded images of outcrops, cores, imaging logs, and digital cores that demonstrate the horizontal fractures in this area. These images are sourced from studies conducted by other Chinese scholars, and the references are listed below.
Specifically:
Huang (2022) provides a detailed discussion on sweet spots related to horizontal fractures.
Han (2022) introduces the application of the VTI equivalent model inversion in this area.
Zhao (2020) gives an overview of the fractures across the region.
Additionally, references such as Yue et al. (2018), Zhao et al. (2021), Li et al. (2019), and Zhang et al. (2021) cover various aspects of the reservoir quality, petrophysical properties, tectonic fractures, and stress anisotropy in the Xujiahe Formation, Sichuan Basin.
References:
Yue D, Wu S, Xu Z, et al. Reservoir quality, natural fractures, and gas productivity of upper Triassic Xujiahe tight gas sandstones in western Sichuan Basin, China. Marine and Petroleum Geology. 2018. DOI: 10.1016/j.marpetgeo.2017.10.007.
Zhao H, Shang X, Li M, et al. Investigation on petrophysical properties of fractured tight gas sandstones: a case study of Jurassic Xujiahe Formation in Sichuan Basin, Southwest China. Arabian Journal of Geosciences. 2021;14(2):1-8. DOI: 10.1007/s12517-021-06454-3.
Li H, Tang H, Qin Q, et al. Characteristics, formation periods, and genetic mechanisms of tectonic fractures in the tight gas sandstones reservoir: A case study of Xujiahe Formation in YB area, Sichuan Basin, China. Journal of Petroleum Science and Engineering. 2019;178:723-735. DOI: 10.1016/j.petrol.2019.04.007.
Huang Y, Wang A, Xiao K, et al. Types and genesis of sweet spots in the tight sandstone gas reservoirs: Insights from the Xujiahe Formation, northern Sichuan Basin, China. Energy Geoscience. 2022;3(3):270-281. DOI: 10.1016/j.engeos.2022.03.007.
Han L, Liu J, Yang R, et al. Application of pre-stack elastic impedance inversion method based on VTI medium: A case of tight sandstone fractured reservoir in Xujiahe Formation, Western Sichuan Depression. Petroleum Reservoir Evaluation and Development. 2022;12(2):313-319. DOI: 10.13809/j.cnki.cn32-1825/te.2022.02.006.
Zhang J, Fan X, Huang Z, et al. Evaluation method of anisotropic in-situ stress in the Xujiahe Formation, Sichuan Basin. Oil & Gas Geology. 2021. DOI: 10.11743/ogg20210416.
If you are interested in more details from these studies, you can refer to the articles. Should you have any further questions, please feel free to contact us. Once again, thank you for your feedback and suggestions.
Citation: https://doi.org/10.5194/egusphere-2024-2483-AC6
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AC5: 'Reply on RC4', Li Haoyuan, 12 Dec 2024
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RC4: 'Reply on AC2', Anonymous Referee #1, 12 Dec 2024
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AC1: 'Reply on RC1', Li Haoyuan, 20 Nov 2024
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RC6: 'Comment on egusphere-2024-2483', Anonymous Referee #2, 17 Dec 2024
The paper proposed the hybrid rock physics model to describe the elastic and anisotropic characteristics of sandstones due to thin shale layers and bedding-parallel fractures. Then, the elastic and anisotropic characteristics and associated seismic responses were analyzed. Finally, a novel seismic attribute was proposed to detect the development of horizontal fractures. Overall, the paper provides an interesting investigation of the elastic and seismic responses of bedding-parallel fractures and the applicable method for detecting these fractures using the seismic method.
It is recommended for publication after addressing the following minor issues:
1. Please check the number of the table in the context.
2. In Fig. 1, the Hudson model was applied to calculate the characteristics of sandstones with fractures. Please discuss how this method considers the matrix porosity or clarify the assumption in the modeling.
3. Please explain the meaning of “shale domain” in Fig. 1.
4. In Fig. 4, please clarify the meaning of porosity. Does it refer to fracture porosity specifically?
5. In Fig. 8, please consider the reasonability of using the term “anisotropic aspect ratio”. For example, why call it “anisotropic”? Meanwhile, “aspect ratio” is usually used to describe pore or fracture geometry.
6. Please provide more geological descriptions of the bedding-parallel fractures in the studied area.
Citation: https://doi.org/10.5194/egusphere-2024-2483-RC6 -
AC8: 'Reply on RC6', Li Haoyuan, 17 Dec 2024
We sincerely appreciate your valuable comments and constructive suggestions, which have significantly improved the quality of our manuscript. Below, we address each of the raised issues in detail:
1 Table Numbers: We will carefully check and revise the numbering of all tables to ensure consistency and accuracy throughout the manuscript.
2 Hudson Model in Fig. 1: We will clarify the assumption in our modeling and provide a detailed explanation of how the sand model incorporates the effect of matrix porosity.
3 “Shale Domain” in Fig. 1: The definition of the "shale domain" was introduced by Bandyopadhyay (2008). We will supplement the manuscript with a clear explanation of this term and update the relevant citation.
4 Porosity in Fig. 4: We will clarify the meaning of “porosity” in Fig. 4, explicitly distinguishing between total porosity and fracture porosity where applicable.
5 "Anisotropic Aspect Ratio" in Fig. 8: We agree with your suggestion and will revise the terminology accordingly.
6 Geological Description of Bedding-Parallel Fractures: We will add more geological background and references to describe the formation, characteristics, and relevance of bedding-parallel fractures in the studied area.
Once again, we thank you for your insightful comments and suggestions, which we have addressed comprehensively. These revisions will ensure the manuscript is both accurate and more informative.References
Bandyopadhyay K. Seismic anisotropy: Geological causes and its implications to reservoir geophysics [J]. Dissertations & Theses - Gradworks,2009. DOI: http://dx.doi.org/.
Citation: https://doi.org/10.5194/egusphere-2024-2483-AC8
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AC8: 'Reply on RC6', Li Haoyuan, 17 Dec 2024
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2024-2483', Anonymous Referee #1, 17 Nov 2024
This is a deeply flawed manuscript. The primary means to differentiate thins beds from fractures is through their different orientations, which is imbedded here but not emphasized. No elaborate rock physics model, containing many strong assumptions, is required.
Even deeper, the authors have not mastered the prior literature, for example they have misunderstood and mischaracterized Hill (1952), Brown and Korringa (1975), Hudson (1980), Thomsen 2023) among others.
Physically, their first error occurs at equation (2) (which does not appear in Hudson, 1980). In an aggregate like that considered, the compliances of the members are additive, not their stiffnesses (see e.g., Schoenberg and Sayers, Geophysics, 60, 204-211, 1995). As a result of this basic error, all that follows is in error. The error is covered over by the numerous model assumptions and calibrations which follow.
It may be possible for the authors to recover from this fundamental error while retaining their modeling effort. If so, any revised manuscript should focus on differentiating fractures from shales via their orientations. But this manuscript is so flawed that it should be rejected by the editor.
Citation: https://doi.org/10.5194/egusphere-2024-2483-RC1 -
AC1: 'Reply on RC1', Li Haoyuan, 20 Nov 2024
Thank you for your thoughtful review and detailed critique.
The Equation (2) in our manuscript is derived from the Handbook of Rock Physics authored by the SRB group, published by Cambridge University Press in 2020. Specifically, it is summarized in Section 4.1.3 as Equation (4.13.1). This formula fully corresponds to Hudson’s summary in Chapter 2 of his 1981 work, which builds upon his original 1980 formulations. Moreover, the application of Brown and Korringa (BK) and Thomsen's equations follows the methodology provided in the latest Handbook of Rock Physics. This modeling process has been widely applied in other studies, and therefore, we do not consider the stiffness calculation within the Hudson model to be inappropriate.
It is possible that our description was not sufficiently detailed, as this modeling workflow was not the primary focus of our manuscript. We will provide a more comprehensive explanation in the revised version.
Our manuscript considers the orientations of sandstones and shales in two parts: one using the Hudson model and the other utilizing a mudrock compaction model. In our study area, the thin interbedded shale layers are much smaller than the resolution of well logs. Therefore, we believe it is crucial to incorporate the anisotropy of both formations comprehensively within the rock physics model.
For additional context, here is a relevant reference that describes and applies the Hudson model:
Mavko, G., Mukerji, T., and Dvorkin, J.: The rock physics handbook, Cambridge university press,2020.
de Figueiredo, J. J. S. j. g. c., Chiba, B. F. F., do Nascimento, M. J., da Silva, C. B., and Santos, L. K.: Can Hudson-Crampin effective model be applied in cracked medium in which the background is weakly anisotropic, Journal of Applied Geophysics, Vol.161, 255-260, 10.1016/j.jappgeo.2018.12.007, 2019.
Huang, X., Huang, X., Xu, Y., Li, H., Zhang, Z., and Xu, W.: Anisotropic Rock Model-Guided Post-Stack Attribute Analysis With Pore Type and Production Data for a Carbonate Gas Reservoir, Frontiers in Earth Science, Vol.9, 10.3389/feart.2021.641705, 2021.
Hudson, J. A.: Overall properties of a cracked solid, Mathematical Proceedings of the Cambridge Philosophical Society, Vol.88, 371-384, 10.1017/s0305004100057674, 1980.
Hudson, J. A.: Wave speeds and attenuation of elastic waves in material containing cracks, Geophysical Journal International,
Vol.64, 133-150, 10.1111/j.1365-246X.1981.tb02662.x, 1981.Yue, C. and Yue, X.: Simulation of acoustic wave propagation in a borehole surrounded by cracked media using a finite difference method based on Hudson's approach, Journal of Geophysics and Engineering, Vol.14, 633-640, 10.1088/1742-2140/aa5af8, 2017.
Zhang, X., Yang, Z., Tang, B., Wang, R., and Wei, X.: Distinguishing oil and water layers in a cracked porous medium using pulsed neutron logging data based on Hudson's crack theory, Geophysical Journal International, Vol.213, 1345-1359, 10.1093/gji/ggy065, 2018.
Thank you once again for your valuable comments, which will help us improve the clarity and rigor of our work.
Citation: https://doi.org/10.5194/egusphere-2024-2483-AC1 -
RC2: 'Reply on AC1', Anonymous Referee #1, 22 Nov 2024
Reviewer’s response to AC1
Elastic anisotropy differentiation of thin shale beds and fractures
using a novel hybrid rock physics model
by Haoyuan Li, et al
The references cited in AC1, by Hudson (1981) and by Mavko et al (2020) both state explicitly that these formulae are for small perturbations only. They are first order Taylor approximations of the correct formula, which is given by Schoenberg and Sayers (1995).
The other misunderstandings are:
- Hill (1952): The Voigt and Reuss “limits” discussed by Hill are only valid for mixtures of isotropic minerals, whereas all of the minerals included in this ms are anisotropic.
- Brown and Korringa (1975): In the present ms, equation (3) has two errors:
- In the second term on the right, the compliance elements with superscript “sand” should instead have superscript “dsand”; this may be just a typo.
- In the same term, the compliance elements s with superscript “sand0” should instead have superscript “sandM”, and the stiffness element K with subscript “sand0” should instead have subscript “sandM”. This notation more closely follows that of Brown and Korringa. Many authors since 1975 (including Mavko et al) have considered M to represent the solid Mineral of the porous rock, but as explained by Thomsen (2023), a better interpretation of M is Mean.
- Thomsen (2023): This paper revises the treatment of fluids within porous rocks in a fundamental way, not consistent with Mavko et al (2020).
- Hudson (1980,1981): These papers consider only cracks in non-porous rock, like granite. If the rock also has non-crack porosity, hydraulically connected to the cracks (e., if they are typical sedimentary rocks), the authors should instead cite Hudson et al, Geophys. J. Int. (1996) 124, 105-112.
More fundamentally, however: All that is needed to differentiate cracks from thin-bedded shales is to recognize that the shales have VTI symmetry, and the cracks do not. No elaborate modelling is required.
Citation: https://doi.org/10.5194/egusphere-2024-2483-RC2 -
AC3: 'Reply on RC2', Li Haoyuan, 27 Nov 2024
Thank you for your valuable suggestions regarding our methodology. We deeply appreciate your insightful comments and will address them in our revised manuscript.
Fracture Model Formula Description
We acknowledge the need to improve the description of the equations in our fracture model to better align with professional standards. This will be updated in the next version.Hudson Model Limitation
You are correct that the Hudson model is unsuitable for representing the elastic properties of rocks with high fracture densities. As you mentioned, the limitation occurs around a fracture density of 0.1, and this is also influenced by the fracture aspect ratio. Beyond this threshold, the elastic parameters of rocks increase with fracture density, which is inconsistent with physical expectations. We have ensured that the fracture density in our model does not exceed this limit. In the revised version, we will provide further clarification and analysis of this threshold in a single part.Shale and Fracture Anisotropy
We agree that shale is characterized by VTI anisotropy, while fractures exhibit HTI anisotropy. In our study, we consider the complex tight sands as a unified skeleton containing both thin shale beds and fractures. Because the thickness of individual shale layers is too small to serve as a separate skeleton compare with tight sand in the area; instead, they are treated as part of the tight sand skeleton. This is mean the model is need consider the comprehensive anisotropic characterise of them. And we analyzed the anisotropic characteristics of this unified framework under varying proportions of shale layers and fractures. We believe this approach is meaningful and has yielded promising results in applications.Thank you once again for your constructive feedback, which has helped us refine and improve our work. We look forward to incorporating these updates and enhancing the clarity and robustness of our research.
Citation: https://doi.org/10.5194/egusphere-2024-2483-AC3 -
RC3: 'Reply on AC3', Anonymous Referee #1, 01 Dec 2024
Reviewer’s response to AC2
Elastic anisotropy differentiation of thin shale beds and fractures
using a novel hybrid rock physics model
by Haoyuan Li, et al
The authors have misunderstood the important aspect of Hudson, et al (1996). The issue is not larger crack density, it is the presence of equant porosity. The pores are much less compliant than the cracks, and if fluid flows between cracks and pores, that changes the effect of the fluid on the elasticity of the rocks.
The authors have also employed an unnecessarily restrictive model for fractures, one that assumes “penny-shaped” cracks. That makes for HTI, if embedded in an otherwise isotropic matrix (not if imbedded in shales, or in thin-beds). If, for example, the fractures are “ribbon-shaped”, i.e. if they are joints, the HTI model is not accurate. HTI is a special case of azimuthal anisotropy, probably never occurring in nature. A more general model for cracks embedded in shales or thin-beds is given by Sayers, C. M., 2022, Elastic properties of fractures in transversely isotropic media: Journal of Applied Geophysics, 197.
More fundamentally, however: All that is needed to differentiate cracks from thin-bedded shales is to recognize that the shales have VTI symmetry, and the cracks do not. No elaborate modelling is required.
Citation: https://doi.org/10.5194/egusphere-2024-2483-RC3 -
AC4: 'Reply on RC3', Li Haoyuan, 10 Dec 2024
We fully agree that the fracture compliance is an important parameter for describing the elastic characteristics of fractures. We will pay more attention to the fracture compliance in our future research.
However, the focus of this paper is on the structure of tight sands in the Sichuan Basin of China, which simultaneously exhibit both fault fractures (horizontal shear fracture) and thin shale beds. These tight sand contain horizontal and short fractures, which are significantly different from typical fractures. Therefore, despite the limitations of the Hudson fracture model, the calibration results in this paper clearly demonstrate its applicability to this type of fracture.
On the other hand, the thin shale beds, which are considered as part of the rock skeleton, are particularly thin, making it essential to adopt a comprehensive modeling approach. It is worth noting that both of these structures can lead to similar VTI anisotropy. For these reasons, we believe that it is necessary to combine them for modeling.
Citation: https://doi.org/10.5194/egusphere-2024-2483-AC4
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AC4: 'Reply on RC3', Li Haoyuan, 10 Dec 2024
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RC3: 'Reply on AC3', Anonymous Referee #1, 01 Dec 2024
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RC2: 'Reply on AC1', Anonymous Referee #1, 22 Nov 2024
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AC2: 'Reply on RC1', Li Haoyuan, 20 Nov 2024
Thank you for your thoughtful review and detailed critique.
The Equation (2) in our manuscript is derived from the Handbook of Rock Physics authored by the SRB group, published by Cambridge University Press in 2020. Specifically, it is summarized in Section 4.1.3 as Equation (4.13.1). This formula fully corresponds to Hudson’s summary in Chapter 2 of his 1981 work, which builds upon his original 1980 formulations. Moreover, the application of Brown and Korringa (BK) and Thomsen's equations follows the methodology provided in the latest Handbook of Rock Physics. This modeling process has been widely applied in other studies, and therefore, we do not consider the stiffness calculation within the Hudson model to be inappropriate.
It is possible that our description was not sufficiently detailed, as this modeling workflow was not the primary focus of our manuscript. We will provide a more comprehensive explanation in the revised version.
Our manuscript considers the orientations of sandstones and shales in two parts: one using the Hudson model and the other utilizing a mudrock compaction model. In our study area, the thin interbedded shale layers are much smaller than the resolution of well logs. Therefore, we believe it is crucial to incorporate the anisotropy of both formations comprehensively within the rock physics model.
For additional context, here is a relevant reference that describes and applies the Hudson model:
Mavko, G., Mukerji, T., and Dvorkin, J.: The rock physics handbook, Cambridge university press,2020.
de Figueiredo, J. J. S. j. g. c., Chiba, B. F. F., do Nascimento, M. J., da Silva, C. B., and Santos, L. K.: Can Hudson-Crampin effective model be applied in cracked medium in which the background is weakly anisotropic, Journal of Applied Geophysics, Vol.161, 255-260, 10.1016/j.jappgeo.2018.12.007, 2019.
Huang, X., Huang, X., Xu, Y., Li, H., Zhang, Z., and Xu, W.: Anisotropic Rock Model-Guided Post-Stack Attribute Analysis With Pore Type and Production Data for a Carbonate Gas Reservoir, Frontiers in Earth Science, Vol.9, 10.3389/feart.2021.641705, 2021.
Hudson, J. A.: Overall properties of a cracked solid, Mathematical Proceedings of the Cambridge Philosophical Society, Vol.88, 371-384, 10.1017/s0305004100057674, 1980.
Hudson, J. A.: Wave speeds and attenuation of elastic waves in material containing cracks, Geophysical Journal International,
Vol.64, 133-150, 10.1111/j.1365-246X.1981.tb02662.x, 1981.Yue, C. and Yue, X.: Simulation of acoustic wave propagation in a borehole surrounded by cracked media using a finite difference method based on Hudson's approach, Journal of Geophysics and Engineering, Vol.14, 633-640, 10.1088/1742-2140/aa5af8, 2017.
Zhang, X., Yang, Z., Tang, B., Wang, R., and Wei, X.: Distinguishing oil and water layers in a cracked porous medium using pulsed neutron logging data based on Hudson's crack theory, Geophysical Journal International, Vol.213, 1345-1359, 10.1093/gji/ggy065, 2018.
Thank you once again for your valuable comments, which will help us improve the clarity and rigor of our work.
Citation: https://doi.org/10.5194/egusphere-2024-2483-AC2 -
RC4: 'Reply on AC2', Anonymous Referee #1, 12 Dec 2024
Please provide a reference which shows the field occurrence of horizontal fractures with VTI symmetry.
Citation: https://doi.org/10.5194/egusphere-2024-2483-RC4 -
AC5: 'Reply on RC4', Li Haoyuan, 12 Dec 2024
We have uploaded images of outcrops, cores, imaging logs, and digital cores that demonstrate the horizontal fractures in this area. These images are sourced from studies conducted by other Chinese scholars, and the references are listed below.
Specifically:
Huang (2022) provides a detailed discussion on sweet spots related to horizontal fractures.
Han (2022) introduces the application of the VTI equivalent model inversion in this area.
Zhao (2020) gives an overview of the fractures across the region.
Additionally, references such as Yue et al. (2018), Zhao et al. (2021), Li et al. (2019), and Zhang et al. (2021) cover various aspects of the reservoir quality, petrophysical properties, tectonic fractures, and stress anisotropy in the Xujiahe Formation, Sichuan Basin.
References:
Yue D, Wu S, Xu Z, et al. Reservoir quality, natural fractures, and gas productivity of upper Triassic Xujiahe tight gas sandstones in western Sichuan Basin, China. Marine and Petroleum Geology. 2018. DOI: 10.1016/j.marpetgeo.2017.10.007.
Zhao H, Shang X, Li M, et al. Investigation on petrophysical properties of fractured tight gas sandstones: a case study of Jurassic Xujiahe Formation in Sichuan Basin, Southwest China. Arabian Journal of Geosciences. 2021;14(2):1-8. DOI: 10.1007/s12517-021-06454-3.
Li H, Tang H, Qin Q, et al. Characteristics, formation periods, and genetic mechanisms of tectonic fractures in the tight gas sandstones reservoir: A case study of Xujiahe Formation in YB area, Sichuan Basin, China. Journal of Petroleum Science and Engineering. 2019;178:723-735. DOI: 10.1016/j.petrol.2019.04.007.
Huang Y, Wang A, Xiao K, et al. Types and genesis of sweet spots in the tight sandstone gas reservoirs: Insights from the Xujiahe Formation, northern Sichuan Basin, China. Energy Geoscience. 2022;3(3):270-281. DOI: 10.1016/j.engeos.2022.03.007.
Han L, Liu J, Yang R, et al. Application of pre-stack elastic impedance inversion method based on VTI medium: A case of tight sandstone fractured reservoir in Xujiahe Formation, Western Sichuan Depression. Petroleum Reservoir Evaluation and Development. 2022;12(2):313-319. DOI: 10.13809/j.cnki.cn32-1825/te.2022.02.006.
Zhang J, Fan X, Huang Z, et al. Evaluation method of anisotropic in-situ stress in the Xujiahe Formation, Sichuan Basin. Oil & Gas Geology. 2021. DOI: 10.11743/ogg20210416.
If you are interested in more details from these studies, you can refer to the articles. Should you have any further questions, please feel free to contact us. Once again, thank you for your feedback and suggestions.
Citation: https://doi.org/10.5194/egusphere-2024-2483-AC5 -
RC5: 'Reply on AC5', Anonymous Referee #1, 15 Dec 2024
Reviewer’s response to AC5
Elastic anisotropy differentiation of thin shale beds and fractures
using a novel hybrid rock physics model
by Haoyuan Li, et al
This reviewer changes his recommendation from REJECT to MAJOR REVISION. The revision should encompass the following points:
- The paper must emphasize that the subject fractures are bed-parallel fractures with assumed VTI symmetry. The more common tectonic fractures may be differentiated from thin beds via their orientation alone, with no modelling required.
- The field occurrence of subsurface bed-parallel fractures must be amply demonstrated with cited references and discussion. Outcrops are not acceptable proof, since the near-surface has low vertical stress.
- The bed-parallel fractures may or may not have VTI symmetry since their orientation alone is not sufficient to establish that (as it is with the bedding). Logs establish orientation, but not symmetry. The shear slip on these fractures may or may not destroy the VTI symmetry. So, VTI symmetry of the fractures must be explicitly assumed.
- The modeling and discussion must respect the criticisms stated earlier.
Citation: https://doi.org/10.5194/egusphere-2024-2483-RC5 -
AC7: 'Reply on RC5', Li Haoyuan, 15 Dec 2024
Thank you for your valuable and professional suggestions regarding our manuscript. We will carefully organize all your comments and incorporate them into our revisions to improve the quality and clarity of the manuscript.
Thank you again for your insightful suggestions.
Citation: https://doi.org/10.5194/egusphere-2024-2483-AC7
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RC5: 'Reply on AC5', Anonymous Referee #1, 15 Dec 2024
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AC6: 'Reply on RC4', Li Haoyuan, 12 Dec 2024
We have uploaded images of outcrops, cores, imaging logs, and digital cores that demonstrate the horizontal fractures in this area. These images are sourced from studies conducted by other Chinese scholars, and the references are listed below.
Specifically:
Huang (2022) provides a detailed discussion on sweet spots related to horizontal fractures.
Han (2022) introduces the application of the VTI equivalent model inversion in this area.
Zhao (2020) gives an overview of the fractures across the region.
Additionally, references such as Yue et al. (2018), Zhao et al. (2021), Li et al. (2019), and Zhang et al. (2021) cover various aspects of the reservoir quality, petrophysical properties, tectonic fractures, and stress anisotropy in the Xujiahe Formation, Sichuan Basin.
References:
Yue D, Wu S, Xu Z, et al. Reservoir quality, natural fractures, and gas productivity of upper Triassic Xujiahe tight gas sandstones in western Sichuan Basin, China. Marine and Petroleum Geology. 2018. DOI: 10.1016/j.marpetgeo.2017.10.007.
Zhao H, Shang X, Li M, et al. Investigation on petrophysical properties of fractured tight gas sandstones: a case study of Jurassic Xujiahe Formation in Sichuan Basin, Southwest China. Arabian Journal of Geosciences. 2021;14(2):1-8. DOI: 10.1007/s12517-021-06454-3.
Li H, Tang H, Qin Q, et al. Characteristics, formation periods, and genetic mechanisms of tectonic fractures in the tight gas sandstones reservoir: A case study of Xujiahe Formation in YB area, Sichuan Basin, China. Journal of Petroleum Science and Engineering. 2019;178:723-735. DOI: 10.1016/j.petrol.2019.04.007.
Huang Y, Wang A, Xiao K, et al. Types and genesis of sweet spots in the tight sandstone gas reservoirs: Insights from the Xujiahe Formation, northern Sichuan Basin, China. Energy Geoscience. 2022;3(3):270-281. DOI: 10.1016/j.engeos.2022.03.007.
Han L, Liu J, Yang R, et al. Application of pre-stack elastic impedance inversion method based on VTI medium: A case of tight sandstone fractured reservoir in Xujiahe Formation, Western Sichuan Depression. Petroleum Reservoir Evaluation and Development. 2022;12(2):313-319. DOI: 10.13809/j.cnki.cn32-1825/te.2022.02.006.
Zhang J, Fan X, Huang Z, et al. Evaluation method of anisotropic in-situ stress in the Xujiahe Formation, Sichuan Basin. Oil & Gas Geology. 2021. DOI: 10.11743/ogg20210416.
If you are interested in more details from these studies, you can refer to the articles. Should you have any further questions, please feel free to contact us. Once again, thank you for your feedback and suggestions.
Citation: https://doi.org/10.5194/egusphere-2024-2483-AC6
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AC5: 'Reply on RC4', Li Haoyuan, 12 Dec 2024
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RC4: 'Reply on AC2', Anonymous Referee #1, 12 Dec 2024
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AC1: 'Reply on RC1', Li Haoyuan, 20 Nov 2024
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RC6: 'Comment on egusphere-2024-2483', Anonymous Referee #2, 17 Dec 2024
The paper proposed the hybrid rock physics model to describe the elastic and anisotropic characteristics of sandstones due to thin shale layers and bedding-parallel fractures. Then, the elastic and anisotropic characteristics and associated seismic responses were analyzed. Finally, a novel seismic attribute was proposed to detect the development of horizontal fractures. Overall, the paper provides an interesting investigation of the elastic and seismic responses of bedding-parallel fractures and the applicable method for detecting these fractures using the seismic method.
It is recommended for publication after addressing the following minor issues:
1. Please check the number of the table in the context.
2. In Fig. 1, the Hudson model was applied to calculate the characteristics of sandstones with fractures. Please discuss how this method considers the matrix porosity or clarify the assumption in the modeling.
3. Please explain the meaning of “shale domain” in Fig. 1.
4. In Fig. 4, please clarify the meaning of porosity. Does it refer to fracture porosity specifically?
5. In Fig. 8, please consider the reasonability of using the term “anisotropic aspect ratio”. For example, why call it “anisotropic”? Meanwhile, “aspect ratio” is usually used to describe pore or fracture geometry.
6. Please provide more geological descriptions of the bedding-parallel fractures in the studied area.
Citation: https://doi.org/10.5194/egusphere-2024-2483-RC6 -
AC8: 'Reply on RC6', Li Haoyuan, 17 Dec 2024
We sincerely appreciate your valuable comments and constructive suggestions, which have significantly improved the quality of our manuscript. Below, we address each of the raised issues in detail:
1 Table Numbers: We will carefully check and revise the numbering of all tables to ensure consistency and accuracy throughout the manuscript.
2 Hudson Model in Fig. 1: We will clarify the assumption in our modeling and provide a detailed explanation of how the sand model incorporates the effect of matrix porosity.
3 “Shale Domain” in Fig. 1: The definition of the "shale domain" was introduced by Bandyopadhyay (2008). We will supplement the manuscript with a clear explanation of this term and update the relevant citation.
4 Porosity in Fig. 4: We will clarify the meaning of “porosity” in Fig. 4, explicitly distinguishing between total porosity and fracture porosity where applicable.
5 "Anisotropic Aspect Ratio" in Fig. 8: We agree with your suggestion and will revise the terminology accordingly.
6 Geological Description of Bedding-Parallel Fractures: We will add more geological background and references to describe the formation, characteristics, and relevance of bedding-parallel fractures in the studied area.
Once again, we thank you for your insightful comments and suggestions, which we have addressed comprehensively. These revisions will ensure the manuscript is both accurate and more informative.References
Bandyopadhyay K. Seismic anisotropy: Geological causes and its implications to reservoir geophysics [J]. Dissertations & Theses - Gradworks,2009. DOI: http://dx.doi.org/.
Citation: https://doi.org/10.5194/egusphere-2024-2483-AC8
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AC8: 'Reply on RC6', Li Haoyuan, 17 Dec 2024
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Haoyuan Li
Xuri Huang
Limin Sa
Lei Li
Fang Li
Tiansheng Chen
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