Modeling Method to Characterize the Pore Structure of Fractured Tight Reservoirs

Round 1

Reviewer 1 Report

Reviewer Comments

Paper title: Methodology to improve anisotropic rock physics model for deep-buried tight sandstone reservoir

The present manuscript describes the Methodology to improve the anisotropic rock physics model for deep-buried tight sandstone reservoirs by combining a dual-connected pore model and linear slip model. A manuscript has a practical application and also provide important theoretical for the next studies.

The paper is well structured and can be accepted for publication after providing the corrections mentioned below.

Point 1. Abstract section sounds as description section. The abstract should follow the MDPI style of structured abstracts:

- Background (place the question addressed in a broad context and highlight the purpose of the study);

- Methods (describe briefly the main methods);

- Results (summarize the article's main findings);

- Conclusion (indicate the main conclusions or interpretations).

Point 2. In the Introduction section, an enhanced literature review is required. For this study, the authors have used only 37 literature sources (only 25 in the Introduction section). It seems insufficient for such type of research. It will be great if the authors show some description in context – Why it is important to conduct this study?

Point 3. The aim and the tasks must be highlighted at the end of the Introduction section.

Point 4. It is suggested to use common section title according to IMRaD “Materials and Methods” instead of “Experimental samples and modeling methods”.

Point 5. Figure 1 must be redrawn and presented in colour as the Applied Sciences journal strives to publish high-quality materials.

Point 6. Figure 2 and Figure 3 – the scales of sand samples are necessary.

Point 7. Why the Section 3 is titled as Application?

Point 8. Please add a full description of Y-axys at Figure 6, Figure 7a, and Figure 8.

Point 9. Please consider the suggested research in your paper when enhancing the literature review:

Olovyannyy, A., & Chantsev, V. (2019). Numerical experiments concerning long-term deformation of rock samples. Mining of Mineral Deposits, 13(4), 18-27. https://doi.org/10.33271/mining13.04.018

Skipochka, S., Krukovskyi, O., Palamarchuk, T., & Prokhorets, L. (2020). On the methodology for considering scale effect of rock strength. Mining of Mineral Deposits, 14(4), 24-30. https://doi.org/10.33271/mining14.04.024

Point 10. In general, I must admit that a very good study was performed.

Author Response

Response to Reviewer 1 Comments

 

Point 1: Abstract section sounds as description section. The abstract should follow the MDPI style of structured abstracts:

-Background (place the question addressed in a broad context and highlight the purpose of the study);

- Methods (describe briefly the main methods);

- Results (summarize the article's main findings);

- Conclusion (indicate the main conclusions or interpretations).

 

Response 1: Thank you for your valuable comments. Following your suggestion, we have made changes to the abstract as detailed below:

Background: The study of unconventional reservoirs has been paid more and more attention with the deep-ening of exploration and development, especially deep-buried tight sandstone reservoirs. We could not obtain the accurate elastic parameters of reservoirs using the conventional rock phys-ics model, since the tight sandstone reservoirs have the characteristics of strong heterogeneity, complex lithology and storage space.

Methods: In order to better describe the tight sandstone reservoirs, we improve the traditional tight sand-stone rock physics model by combining dual-connected pore model and linear slip model. Since the combined modeling process subtly considers four characteristics including the diversity of tight sandstone matrix minerals, the irregularities of pores structure, the connectivity between pores, and the anisotropy caused by fractures, multiple reservoir characteristic parameters can be derived from the limited logging information by the improved model.

Results: These reservoir characteristic parameters could account for the difference of diagenesis, which are useful to distinguish different pore types and eliminate ineffective reservoirs.

Conclusion: The practical application shows that the improved model can extract microscopic reservoir information hidden in logging data more effectively than the traditional model. It provides a reliable tool for identifying effective reservoirs of tight sandstone.

 

Point 2: In the Introduction section, an enhanced literature review is required. For this study, the authors have used only 37 literature sources (only 25 in the Introduction section). It seems insufficient for such type of research. It will be great if the authors show some description in context – Why it is important to conduct this study?

 

Response 2: Thank you for mentioning this problem. Although the text in the introduction section is not altered a lot, proper references have been included where necessary. Meanwhile we have added some descriptions in context based on your suggestion.

 

Point 3: The aim and the tasks must be highlighted at the end of the Introduction section.

 

Response 3: Thank you for pointing out this problem. Based on your suggestion, we have highlighted the purpose and significance of this study at the end of the introductory section.

 

Point 4. It is suggested to use common section title according to IMRaD “Materials and Methods” instead of “Experimental samples and modeling methods”.

 

Response 4: Thank you for this suggestion. We have changed the title of Section 2 as “Materials and Methods”.

 

Point 5. Figure 1 must be redrawn and presented in colour as the Applied Sciences journal strives to publish high-quality materials.

 

Response 5: Thank you for mentioning this problem. According to your suggestion, we have redrawn the Figure 1.

 

Point 6. Figure 2 and Figure 3 – the scales of sand samples are necessary.

 

Response 6: Thank you for this suggestion. We have added the scale information for sandstone samples in Figure 2 and Figure 3.

 

Point 7. Why the Section 3 is titled as Application?

 

Response 7: Thank you for pointing this out. We have changed the title of Section 3 as “Results” following the Applied Sciences journal template.

 

Point 8. Please add a full description of Y-axys at Figure 6, Figure 7a, and Figure 8.

 

Response 8: Thank you for this suggestion. We have added a full description of Y-axys at Figure 6, Figure 7a, and Figure 8.

 

Point 9. Please consider the suggested research in your paper when enhancing the literature review:

Olovyannyy, A., & Chantsev, V. (2019). Numerical experiments concerning long-term deformation of rock samples. Mining of Mineral Deposits, 13(4), 18-27. https://doi.org/10.33271/mining13.04.018

Skipochka, S., Krukovskyi, O., Palamarchuk, T., & Prokhorets, L. (2020). On the methodology for considering scale effect of rock strength. Mining of Mineral Deposits, 14(4), 24-30. https://doi.org/10.33271/mining14.04.024

 

Response 9: We have thoroughly read the literature you recommended and have benefited greatly. So we added them to the reference list of our paper, the two articles are in ref. 27 and ref. 51 respectively.

 

Point 10. In general, I must admit that a very good study was performed.

 

Response 10: Thank you for your compliment on our research. We hope you are satisfied with all these revisions to this article.

Author Response File: Author Response.docx

Reviewer 2 Report

Please see attached file

Comments for author File: Comments.docx

Author Response

Response to Reviewer 2 Comments

 

Point 1: The Abstract should contain answers to the following questions: What problem was studied and why is it important? What methods were used? What are the important results?

 

Response 1: Thank you for your valuable comments. Following your suggestion, we have made changes to the abstract as detailed below:

Background: The study of unconventional reservoirs has been paid more and more attention with the deep-ening of exploration and development, especially deep-buried tight sandstone reservoirs. We could not obtain the accurate elastic parameters of reservoirs using the conventional rock phys-ics model, since the tight sandstone reservoirs have the characteristics of strong heterogeneity, complex lithology and storage space.

Methods: In order to better describe the tight sandstone reservoirs, we improve the traditional tight sand-stone rock physics model by combining dual-connected pore model and linear slip model. Since the combined modeling process subtly considers four characteristics including the diversity of tight sandstone matrix minerals, the irregularities of pores structure, the connectivity between pores, and the anisotropy caused by fractures, multiple reservoir characteristic parameters can be derived from the limited logging information by the improved model.

Results: These reservoir characteristic parameters could account for the difference of diagenesis, which are useful to distinguish different pore types and eliminate ineffective reservoirs.

Conclusion: The practical application shows that the improved model can extract microscopic reservoir information hidden in logging data more effectively than the traditional model. It provides a reliable tool for identifying effective reservoirs of tight sandstone.

 

Point 2: What sets your work apart from the other publications in this area?

 

Response 2: The improved anisotropic rock physics modeling method considers the effects of connectivity between different shapes pores and the anisotropy caused by fractures. Our approach can estimate shear-wave velocity, pore aspect ratio and fracture density more accurately from the conventional well logging data comparing with the traditional rock physics model.

It provides the key parameters to other workflows, such as logging evaluation, seismic anisotropy inversion and fracturing development of tight sandstones. In addition, our modeling workflow has achieved good results in the application of the fine characterization for the deep-buried tight sandstone reservoirs with strong heterogeneity.

 

Point 3: To make the literature of “introduction” more informative, the below references are highly recommended:

- Energy Reports, Volume 7, November 2021, Pages 5239-5247

-Journal of Energy Storage, Volume 37, May 2021, 102464

-Heat Transfer - Asian Research, 2019, 48(7), pp. 3278–3294

-https://doi.org/10.1080/01430750.2020.1824942

-https://doi.org/10.1016/j.csite.2018.07.003

-https://doi.org/10.1007/s42452-021-04731-0

-International Journal of Ambient, 2021, 42(16), pp. 1815–1822

 

Response 3: Thank you for the literature you recommend. We have thoroughly read the literature you recommended and have benefited greatly.

 

Point 4. Please improve the chapter 5 “result” with discussing some physical reason for per result.

 

Response 4: Thank you for mentioning this problem. According to your suggestion, we have explained the physical reasons for per result in the Discussion section.

 

Point 5. “Conclusion” is too long. It should be maximum a half page.

 

Response 5: Thank you for this suggestion. We have revised the Conclusion section to within half a page.

 

Point 6. To improve the “conclusion” please add some suggestions for future works in this area to the end of this section.

 

Response 6: Thank you for this suggestion. We have added some suggestions for future works as follows “Anyway, the theoretical model cannot fully explain the elastic properties of real tight sandstones underground because the simplified pore and fracture geometry models using effective theory are still far away from the structure of actual rock. Furthermore, a potentially significant over-simplification is that the pressure dependence of the poros-ity is ignored in our modeling process, and more work is required to develop a proper ef-fective model in the future”.

 

Point 7. There are some typo errors at the length of the article that should be corrected.

 

Response 7: Thank you for pointing out this problem. We have corrected the typo errors at the length of the article.

 

Point 8. Choose a better title for the article.

 

Response 8: Thank you for this suggestion. We have changed the article title as “Modeling method to characterize the pore structure of fractured tight reservoirs”.

 

 

Author Response File: Author Response.docx

Reviewer 3 Report

Dear Authors

Scientific comments

It is an interesting work about methodology to improve anisotropic rock physics model for deep-buried tight sandstone reservoir.

In introduction it should be noted that the heterogeneity of rock masses is dependent on the scale of observation, therefore the scale of application of the model and the difficulty of introducing other variables such as the liquid that fills the voids and its viscosity (surface stresses).

It should not refer to fractures, it should be replaced by the term discontinuities. It would be important to know the orientation of the stress field, the pre-existing fracture, and the orientation (dip, dip direction) of the discontinuities. The structural geology of the potential reservoir site is very important. According to Fig.4 b) you have 3 families of discontinuities (its important explain the discontinuities in terms of families). Line 388 and 454 “… fracture density…” is not correct, you must describe the distribution of the poles in the stereographic projection of the planes, it is more correct in the spatial interpretation of the 4 families.

In Fig.1 the structural map needs to explain the definition of attributes to individualize those zones. Structural zones presented are more geotechnical zones because you define “… tight sandstone reservoir characterized by low (line 110) porosity, low permeability, and strong microscopic heterogeneity, belongs to the braided…” . Geological structural maps need information, e.g., families of discontinuities, orientation of the stress field. If you do not want to change the map, change the legend, as it is not a structural geology map.

Explain the stiffness matrix (8) and (9) how it is constituted, e.g., if it is of the general element, if it is in terms of global coordinates and how did you change from local coordinates to global coordinates.

In Fig.10, in x-axis, Azimuth of direction of dip? Or direction of plane?

Line 128, standard deviation is necessary In Fig 7. b) define Aspect ratio in yy-axis;

Fig.8, in x-axis put every number of samples, e.g.,2 – 3 – 4 – 5 …;

Line 503, define neutron values of rock skeleton;

The bibliography is adequate.

Editorial comments

The text has portions that are marked in yellow;

Table 1 – in same page;

Fig. 7 b) – see legend;

Author Response

Response to Reviewer 3 Comments

 

Point 1: In introduction it should be noted that the heterogeneity of rock masses is dependent on the scale of observation, therefore the scale of application of the model and the difficulty of introducing other variables such as the liquid that fills the voids and its viscosity (surface stresses).

 

Response 1: Thank you for this suggestion. We have added a discussion of the issue of observation scale in our paper.

 

Point 2: It should not refer to fractures, it should be replaced by the term discontinuities. It would be important to know the orientation of the stress field, the pre-existing fracture, and the orientation (dip, dip direction) of the discontinuities. The structural geology of the potential reservoir site is very important. According to Fig.4 b) you have 3 families of discontinuities (its important explain the discontinuities in terms of families). Line 388 and 454 “… fracture density…” is not correct, you must describe the distribution of the poles in the stereographic projection of the planes, it is more correct in the spatial interpretation of the 4 families.

 

Response 2: Thank you for mentioning this problem. According to your suggestion, we have corrected some expression errors in our paper.

 

Point 3: In Fig.1 the structural map needs to explain the definition of attributes to individualize those zones. Structural zones presented are more geotechnical zones because you define “… tight sandstone reservoir characterized by low (line 110) porosity, low permeability, and strong microscopic heterogeneity, belongs to the braided…” . Geological structural maps need information, e.g., families of discontinuities, orientation of the stress field. If you do not want to change the map, change the legend, as it is not a structural geology map.

 

Response 3: Thank you for pointing out this problem. According to your suggestion, we have redrawn the Figure 1.

 

Point 4. Explain the stiffness matrix (8) and (9) how it is constituted, e.g., if it is of the general element, if it is in terms of global coordinates and how did you change from local coordinates to global coordinates.

 

Response 4: Hooke’s law for a general anisotropic, linear, elastic solid states that the stress   is linearly proportional to the strain  , as expressed by

in which summation is implied over the repeated subscripts  and  . The elastic stiffness tensor, with elements  , is a fourth-rank tensor obeying the laws of tensor transformation and has a total of 81 components. However, not all 81 components are independent. The symmetry of stresses and strains implies that

reducing the number of independent constants to 36. In addition, the existence of a unique strain energy potential requires that

further reducing the number of independent constants to 21. This is the maximum number of independent elastic constants that any homogeneous linear elastic medium can have. Additional restrictions imposed by symmetry considerations reduce the number much further. Isotropic, linear elastic materials, which have maximum symmetry, are completely characterized by two independent constants, whereas materials with triclinic symmetry (the minimum symmetry) require all 21 constants.

Alternatively, the strains may be expressed as a linear combination of the stresses by the following expression:

In this case  are elements of the elastic compliance tensor which has the same symmetry as the corresponding stiffness tensor. The compliance and stiffness are tensor inverses, denoted by

The stiffness and compliance tensors must always be positive definite. One way to express this requirement is that all of the eigenvalues of the elasticity tensor (described below) must be positive.

It is a standard practice in elasticity to use an abbreviated Voigt notation for the stresses, strains, and stiffness and compliance tensors, for doing so simplifies some of the key equations (Auld, 1990). In this abbreviated notation, the stresses and strains are written as six-element column vectors rather than as nine-element square matrices:

   

Note the factor of 2 in the definitions of strains, but not in the definition of stresses.

With the Voigt notation, four subscripts of the stiffness and compliance tensors are reduced to two. Each pair of indices ij(kl) is replaced by one index I(J) using the following convention:

The relation, therefore, is  and N, where

Note how the definition of  differs from that of  . This results from the factors of 2 introduced in the definition of strains in the abbreviated notation. Hence the Voigt matrix representation of the elastic stiffness is

and similarly, the Voigt matrix representation of the elastic compliance is

The Voigt stiffness and compliance matrices are symmetric. The upper triangle contains 21 constants, enough to contain the maximum number of independent constants that would be required for the least symmetric linear elastic material.

Using the Voigt notation, we can write Hooke’s law as

It is very important to note that the stress (strain) vector and stiffness (compliance) matrix in Voigt notation are not tensors.

The nonzero components of the more symmetric anisotropy classes commonly used in modeling rock properties are given below in Voigt notation.

The structure of the Voigt elastic stiffness matrix for an isotropic linear elastic material has the following form:

The relations between the elements c and Lame´’s parameters  and  of isotropic linear elasticity are

The HTI medium can be considered as a simple combination of fractures and isotropic background rocks. The isotropic background rocks are characterized by the Lamé parameter   and shear modulus, while the imbedded fractures are characterized by the dimensionless normal and tangen-tial fracture weakness parameters  and  , respectively. By using these four parameters, expressions for the stiffness matrix of fractured dry-rock can be written as

where the normal and tangential weaknesses parameters  and  can be calculated from the normal and tangential fracture compliances of the fractured rocks. The P-wave modulus .

References:

Mavko G.; Mukerji T.; Dvorkin J. The Rock Physics Handbook Tools for Seismic Analysis of Porous Media, 2nd ed.; Cam-bridge University Press: New York, USA, 2009.

Schoenberg, M. Elastic wave behavior across linear slip interfaces. J. Acoust. Soc. Am. 1980, 68, 1516. http://dx.doi.org//10.1121/1.385077

Sil, S. Fracture parameter estimation from well-log data. Geophysics. 2013, 78, D129-D134. http://dx.doi.org//10.1190/GEO2012-0407.1

Bakulin, A.; Grechka, V.; Tsvankin, I. Estimation of fracture parameters from reflection seismic data—Part I: HTI model due to a single fracture set. Geophysics. 2000, 65: 1788-1802. http://dx.doi.org//10.1190/1.1444863

Backus, G.E. Long-wave anisotropy produced by horizontal layering. J. Geophys. Res. 1965, 66, 4427-4440. http://dx.doi.org//10.1029/JZ067i011p04427

 

Point 5. In Fig.10, in x-axis, Azimuth of direction of dip? Or direction of plane?

 

Response 5: The x-axis is defined as the Azimuth of direction of plane.

 

Point 6. Line 128, standard deviation is necessary In Fig 7. b) define Aspect ratio in yy-axis;

 

Response 6: Thank you for pointing this out. According to your suggestion, we have added the standard deviation of aspect ratio in our paper. The text description is as follows ” It can be calculated that the pore aspect ratio distribution range of rock samples is 0.01-0.65, with an average of 0.21 and a standard deviation of 0.16”.

 

Point 7. Fig.8, in x-axis put every number of samples, e.g.,2 – 3 – 4 – 5 …;

 

Response 7: Thank you for this suggestion. According to your suggestion, we have redrawn the Figure 8.

 

Point 8. Line 503, define neutron values of rock skeleton;

 

Response 8: Thank you for this suggestion. We refer to other literature to define the neutron value of rock skeleton as 16.5.

References:

Zhang, C.; Shan, W.; Wang, X. Quantitative evaluation of organic porosity and inorganic porosity in shale gas reservoirs using logging data. Energy Sources Part A-Recovery Util. Environ. Eff. 2019, 41, 811-828. http://dx.doi.org//10.1080/15567036.2018.1520361

 

Point 9. The bibliography is adequate.

 

Response 9: Thank you for reminding.

 

Point 10. The text has portions that are marked in yellow; Table 1 – in same page; Fig. 7 b) – see legend;

 

Response 10: Thank you for mentioning this problem. Following your suggestion, we have corrected the editorial errors in this article.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Dear authors,

I am more than satisfied with the corrections provided by you.

This study is an important contribution to the field of reservoir engineering.

Congratulations to the authors.

Dr. V. Lozynskyi