An Investigation into the Effects of Weak Interfaces on Fracture Height Containment in Hydraulic Fracturing

Round 1

Reviewer 1 Report

Reviewer’s comments for the submitted manuscript
“An investigation about the effect of weak interfaces on fracture height containment in hydraulic fracturing” by Yongxiang Zheng, Jianjun Liu and Bohu Zhang

Summary: The submitted manuscript suggests an computational approach for fracture propagation with pre-existing joints. The topic seems interesting and meaningful, as it would suggest important features of induced fracture geometry and its propagation behavior.

Recommendation: Based on the close review of the submitted manuscript, I recommend that the manuscript needs major revision, of both (A) content and (B) format, prior to possible acceptance.

(A) Comments on content

Although the authors provided a certificate, the manuscript still contains a lot of grammatical errors. I strongly recommend that the manuscript is thoroughly reviewed by native English speakers. The poor English hides the interesting observations and analyses. In addition, it is very hard for me to understand what the authors imply, and I believe the readers would have same difficulties when the manuscript is accepted and published. I try to mention some of the errors. But please keep in mind that there are more.

 

In line 54, the authors indicate that the stress contrast is one of the most important mechanisms for the fracture containment phenomenon. Please briefly explain what the stress contrast is.

 

In line 58, ‘less’ should be ‘lower’.

 

The sentence in line 66, ‘The experiment looked at~~~’ is hard to understand. Please re-write.

 

In line 74, the sentence, ‘Weng and Chuprakov~~~’, needs to be re-written.

 

In line 92, do you mean the shape or geometry of the crack tip?

 

In line 123, what do you mean by ‘close contact’? Do you mean the complete contact? Or do you assume there is a small distance?

 

In line 142, do you mean the fluid flow only occurs within the fracture? Then, I think the ‘fracture surface’ should be the ‘fracture surfaces’. Otherwise, please elaborate.

 

It seems like ‘The block’ should be ‘The blocks’ in the second sentence in 158.

 

 

In line 182, what parameters do the authors indicate?

 

In line 184, please indicate the value of the maximum principal stress as the minimum principal stress is specified right after the statement.

 

Seems like the model in Figure 3 does not contain any pore space. Since the manuscript aims at hydraulic fracturing process in formations, the limitation of the model should be specified.

 

In line 201, the sentence, ‘The geometries of~~~’ is confusing. Please re-write.

 

In figure 4 (a-d), the injection pressure should be separately displayed. This is because i) it is very important emphasize the pressure response and ii) it is very confusing as it overlays the aperture values that are at a certain time.

 

In line 208, I think it would be meaningful to add explanation about why the vibration occurs although the rate is constant.

 

What do Figure 5 a and b indicate? One of the horizontal joints?

 

Please make the terminologies consistent. Throughout the entire manuscript, joints and fractures are mixed. Do you mean that the joints are the pre-existing natural fractures?

 

In line 251, what do you mean by the stress on them is also similar?

 

In line 302-304, please specify what the variables indicate, i.e. Z_I, A, etc.

 

Please re-write the sentence in line 423 ‘For stress field reconstruction~~~’

 

(B) Comments on format

 

In line 179, pi/2 should be 90°, as the other parts of the paper use ‘degree’ for angles.

 

Are ‘a’ in line 299, ‘a’ in equation 18 and a in line 309 different? Those seem different (as one of them is italic, and one is bold and the other is not).

 

Author Response

Dear Reviewer 1,

 

Thank you for the comments concerning our manuscript entitled “An investigation into the effects of weak interfaces on fracture height containment in hydraulic fracturing” (energies-548551).

Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our research. We have studied comments carefully and have made correction which we hope meet with approval. We have revised each one according to your comments. In addition, with the help of MDPI editing service, the paper was further polished. Revised portions in the revised manuscript are marked by the ‘track change’. The main corrections in the paper and the responds to the reviewer’s comments are with a table.  Please see the attachmen for details.

 

No.	Comment(s)	Answer to the comment(s)
Q1	In line 54, the authors   indicate that the stress contrast is one of the most important mechanisms for   the fracture containment phenomenon. Please briefly explain what the stress   contrast is.	A brief explanation   about the stress contrast is added in line 54. The details is as follow: The stress   contrast means that the differences in in-situ stress between adjacent   layers.
Q2	In line 58, ‘less’ should   be ‘lower’.	We have revised it. And   we checked other words in the manuscript.
Q3	The sentence in line 66,   ‘The experiment looked at~~~’ is hard to understand. Please re-write.	We have re-write it as   follow: There are four types of   fracture geometries: containment, height growth, T-shaped growth, and the   combination of height and T-shaped growth with different interface fracture   toughness.
Q4	In line 74, the sentence,   ‘Weng and Chuprakov~~~’, needs to be re-written.	We have re-write it as   follow: Weng [4] and Chuprakov [1]   developed the FracT model to examine shear slippage along the bedding   interface. This model considered the strength and frictional properties, and   the effective vertical stress at the frictional and cohesive interface.
Q5	In line 92, do you mean   the shape or geometry of the crack tip?	It means the shape of   crack tip. The shape is shown in fig.5 b. We have revised it in the   manuscript.
Q6	In line 123, what do you   mean by ‘close contact’? Do you mean the complete contact? Or do you assume   there is a small distance?	It should be ‘closed contact’. The contact is closed   (or not open) at initial time. It has some strength for tensile and shear. We have changed the word   ‘close’ to ‘closed’.
Q7	In line 142, do you mean   the fluid flow only occurs within the fracture? Then, I think the ‘fracture   surface’ should be the ‘fracture surfaces’. Otherwise, please elaborate.	Yes. We only considered   the fluid flow within the fracture. Thanks for your advices, we have revised   it.
Q8	It seems like ‘The block’   should be ‘The blocks’ in the second sentence in 158.	Thanks you very much. The   word is corrected in the manuscript.
Q9	In line 182, what parameters do the authors indicate?	It is the parameters used   in the simulation. It is revised in the manuscript.
Q10	In line 184, please   indicate the value of the maximum principal stress as the minimum principal   stress is specified right after the statement.	The minimum principal   stress is 61.21 MPa. It is 0.8 times the vertical stress.
Q11	Seems like the model in   Figure 3 does not contain any pore space. Since the manuscript aims at   hydraulic fracturing process in formations, the limitation of the model   should be specified.	Yes. Thanks for your   advice. We added the limitation of the model in the manuscript.as follow: Besides, the model in this   study only consider the fluid flow in fractures. The flow in formation is not   considered for the low permeability of real shale.
Q12	In line 201, the   sentence, ‘The geometries of~~~’ is confusing. Please re-write.	We have re-write it as   follow: The geometries of   fluid-driven cracks were obtained with the same stress and rock properties.   That means that there is no difference in the in-situ stress and rock   properties.
Q13	In figure 4 (a-d), the   injection pressure should be separately displayed. This is because i) it is   very important emphasize the pressure response and ii) it is very confusing   as it overlays the aperture values that are at a certain time.	Thank you for your   suggestion. It is very useful. However, the pressure curve is nested in the   picture. I have to say how difficult it is to adjust the picture. Besides, the pressure is   not the main topic of this study. And the aperture value in the figure is at   the maximum time of the horizontal coordinate. Their time is the same.
Q14	In line 208, I think it   would be meaningful to add explanation about why the vibration occurs   although the rate is constant.	In our opinion, we think   that it is because volume ratio of the new open fractures to the existing   fractures. The details are as follow. In the early stage of   fracturing, the fracture volume is small and the ratio of new extended   fracture volume to existing fracture volume is large. In this case, the flow   of fluid to the new fracture will lead to obvious pressure drop. On the   contrary, when the existing fracture volume is large, the newly generated   fracture volume has little influence on the pressure inside the fracture.   Therefore, the injection pressure fluctuates greatly in the initial fracturing   period. As injection time increases, fracture volume increases. As a result,   the pressure fluctuations in the later stages of fracturing gradually   decrease. We add a brief explanation in the manuscript..
Q15	What do Figure 5 a and b   indicate? One of the horizontal joints?	Yes, it is. As shown in   Figure 4e,f, the displacements of the two horizontal joints are similar and   the model is symmetrical. Therefore, the stress on them is also similar. Then we choose one of the   horizontal joints. We added a brief   description in the manuscript.
Q16	Please make the   terminologies consistent. Throughout the entire manuscript, joints and   fractures are mixed. Do you mean that the joints are the pre-existing natural   fractures?	Yes. We set the joint as   the pre-existing natural fractures. The fractures always mean the open   joints.
Q17	In line 251, what do you   mean by the stress on them is also similar?	It means that there is no   much difference between figure 4e and f.
	Fig.4 e and f
Q18	In line 302-304, please   specify what the variables indicate, i.e. ZI, A, etc.	We have add the   description about related variables.
Q19	Please re-write the   sentence in line 423 ‘For stress field reconstruction~~~’	we have revised it as   follow: For stress field   reconstruction, if the crack is expected to cross the interface, the normal   stress needs to be increased and the shear stress need to be reduced.
Q20	In line 179, pi/2   should be 90°, as the other parts of the paper use ‘degree’ for angles.	We have revised it in the   manuscript.
Q21	Are ‘a’ in line 299,   ‘a’ in equation 18 and a in line 309 different? Those seem different (as one   of them is italic, and one is bold and the other is not).	They are the same. We   revised the style in equation (18) and (A6).

 

Author Response File: Author Response.pdf

Reviewer 2 Report

This paper has been modified based on reviewer’s comments. The English has also been edited by native speaker. Only minor revision need.

1. The arrow between Figure 11(b) and (c) should be removed. It is redundant.

Author Response

:Thanks for your advice. We have removed the arrow in fig.11.

Reviewer 3 Report

This paper addresses an interesting topic: the impact of weak interface on the fracture height growth. The authors conduct numerical experiments to investigate the issue and bring some insights into it. my comments on this manuscript are as below:

in line 123, the authors adopt Goodman's assumption. How good is this assumption? The authors should validate it by presenting some comparison with either commercial software or analytical solution for plain strain problems. Is there a reference for Equation 9? The terms n s F in Equation 10 are undefined. Especially, the integral needs some physical explanation. In chapter 2.2, what is the grid system used in udec? How large is each element? How is the simulation set up in details? This section should be enriched otherwise it is impossible for readers to reproduce the results.

Author Response

Q1: In line 123, the authors adopt Goodman's assumption. How good is this assumption? The authors should validate it by presenting some comparison with either commercial software or analytical solution for plain strain problems.

 

A: We added some proofs with relevant literatures to prove that the Goodman element is an effective method for describing discontinuous medium. The details are as follow:  

 

(Line 119) The Goodman element is one of the most commonly interface elements to describe the interface characteristics of discontinuous medium such as faults or joints [23]. And the Goodman elements method is employed in some numerical software such as RFPA [24] or 3DEC [25]. The detail about Goodman element method can be found in [26].

 

References:

Zhang Z, Chen F, Li N, et al. Influence of Fault on the Surrounding Rock Stability for a Mining Tunnel: Distance and Tectonic Stress[J]. Advances in Civil Engineering, 2019, 2019. Zhu J B, Liao Z Y, Tang C A. Numerical SHPB tests of rocks under combined static and dynamic loading conditions with application to dynamic behavior of rocks under in situ stresses[J]. Rock mechanics and rock engineering, 2016, 49(10): 3935-3946. Zheng Y, Liu J, Lei Y. The Propagation Behavior of Hydraulic Fracture in Rock Mass with Cemented Joints[J]. Geofluids, 2019, 2019.

  26: Goodman RE, Taylor RL, Brekke TL (1968) A model for the mechanics            of  jointed rock. J Soil Mech Found Div 94(3):637–660

 

 

Q2:.Is there a reference for Equation 9?

A:Yes, it is. Both equation 8 and 9 are based on the literature [25]. We have add the reference in the manuscript.

 

Q3:.The terms n s F in Equation 10 are undefined. Especially, the integral needs some physical explanation.

 

A: We added the explanation about the terms and integral in the equation 10. The details are as follow.

(line 167) where s is the outside surface, m is the mass on the grid point, g_i is the acceleration of gravity, and F_i is the result of an external force applied to a node. n_j is the unit normal vector pointing to the outside. The integral represents the sum of forces on the surface.

 

Q4. In chapter 2.2, what is the grid system used in 3dec? How large is each element? How is the simulation set up in details? This section should be enriched otherwise it is impossible for readers to reproduce the results.

A: The geometric dimensions and mesh generation of the model are introduced in line 188. A model diagram with blocks is added in figure 3b.

 

The model is 20m cube. The two horizontal joints are 2m away from the injection point. The edge of the grid is 0.5.

 

 

Round 2

Reviewer 1 Report

Thanks for the revision made and effort.

I think the manuscript looks ok and ready to be accepted. 

Author Response

Thank you for your comments on our manuscript. I would like to express my sincere gratitude for your work.

Reviewer 2 Report

This manuscript can be accepted. 

Author Response

Thank you for your comments on our manuscript. I would like to express my sincere gratitude for your work.

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

Round 1

Reviewer 1 Report

The paper discusses fracture height containment due to the presence of discontinuities such as joints. It is a numerical investigation performed by 3DEC, a 3D numerical code for geotechnical analysis of soil, by Itasca.

For the following major issues, I do not recommend the publication of this paper in this journal, in its current form:

1) The paper has serious issues regarding English language usage. There are several grammatical and language usage errors, from the abstract all the way to the discussions. Even in some instances, the meaning of the sentence cannot be understood. I put some examples here:

·         Line 23-25:  The results show that the fracture height is still limited by the weak interface in the formation without the difference of in-situ stress and rock properties.

·         Line 169-170: The model including two horizon joints and one vertical joint.

·         Line 190-191: Therefore, the all different colors, but not blue, could display the geometry of fracture in every figure.

·         Line 215: The aperture curves along vertical line passing through center point of vertical joint for four steps with time increasing are plotted in figure 5 (c).

2) There are several equations mentioned in the manuscript which are used in this numerical modeling. However, most of them do not have any references.

 

3) The result section is very limited. Only 2 plots are shown and even the description of the figures are very simplistic.

 

4) Some of the citations in the text are not referred properly. For example: reference No. 18 is referred to as Ivan, but this reference at the end does not have such name. or reference No. 19 is referred to as Zhang, while there are 2 authors.

 

5) The discussion and analysis part is totally irrelevant to the result. It is talking about LEFM equations that can be readily found in any textbook. The discussion part can be brought to introduction of the paper, even the equations are redundant.

 

6) many sketches lack proper referencing.

 

 

Reviewer 2 Report

Reviewer’s comments for the submitted manuscript
“An investigation about the effect of weak interfaces on fracture height containment in hydraulic fracturing” by Yongxiang Zheng, Jianjun Liu and Bohu Zhang

Summary: The submitted manuscript suggests an computational approach for fracture propagation with pre-existing joints. The topic seems interesting and meaningful, as it would suggest important features of induced fracture geometry and its propagation behavior.

Recommendation: Based on the close review of the submitted manuscript, I recommend that the manuscript needs major revision, of both (A) content and (B) format, prior to possible acceptance.

(A) Comments on content

The manuscript needs to be written in plain English. The reviewer highly recommends that the authors ask a native English speaker to double check on grammars, structures, vocabularies, etc. In addition, it seems that a lot of sentences could have been simply translated without delivering insights, which would make the readers quite confused. For example, in line 21, ‘the blunting at crack tip’ should be ‘the blunt crack tip’ or ‘the blunted crack tip’. And the sentences in line 37-39, ‘The crack~~~ pay zone’ should be stated in a sentence or two. And there are a lot more through the entire manuscript.

 

In line 58, what stress do the authors indicate? The far-field stress or the effective stress? or something else? Please specify.

 

The 3rd paragraph in page 2 (line 53-62), It seems like the paragraph is mainly dealing with the fracture containment at first, but it ends with the containment phenomenon solely in sandstone. Since the manuscript deals with the containment in shale as well, more description about the phenomenon in shale layers also needs to be specified.

 

Brief outcomes from Wang et al [16] in line 69 should be stated.

 

Is Equation (1) correct?

 

In line 118, c is not force, but strength.

 

Brief information about the contact friction joint model needs to be added in Ch. 2.1.2.

 

In line 121, what do the authors mean with ‘positive pressure’? In definition, stress and pressure are not same.

 

Equations in Ch. 2.1.4 are not readable. Please revise.

 

In Ch. 2.2, why do the authors use the model with two horizon joints and one vertical joint? Is this a general case? Or are there any other insights that the authors have in mind?

 

In table 1, what is the ‘initial vertical stress’? Do the author mean the in-situ far-field stress? Is the vertical stress changing by time? And please specify what are h, ρ and g for the readers.

 

How did you determine the stress and rock properties in Table 1? If referred to data from an available literature, please specify. If general numbers are used, please elaborate on the authors’ assumptions, insight, etc. Since the basic model dominates the results, how to determine the parameters for the model is also very important.

 

What is 3DEC in line 179? Since the term was not mentioned in the manuscript, more information needs to be specified. And there is no logical explanation why 3DEC is relevant for the purpose of the study.

 

In Ch. 3, more explanation for Figure 4 is required. It is very hard to figure out what the axes mean. Where is the axis for the pressure? Why the displacement in x-y plane is only shown although the 3D simulation was performed?

 

Please revise Figure 4. Most of the letters and numbers are too small. And some of them are not readable.

 

The title of Figure 4 needs to be elaborated. What does each figure (a-h) mean?

 

In line 196, the author stated as ‘This is consistent with the trend of actual monitoring data on site, which means that the simulation results are suitable for research’. Please provide references that show that the results are consistent with the field scale data.

 

In line 209, what do the authors mean by the statement, ‘Therefore, the interface was selected as our object’?

 

In Figure 5, there are only stresses on a single joint, although there are two horizontal joints in the analysis. Are the stress distributions identical to both joints?

 

The first paragraph in page 7 (line 209-214) should contain more analysis, such as reasons, and implications as it only has observations.

 

(B) Comments on format

Please make the Figure title format consistent. Some are in bold, some are not.

 

 Please keep the letters for the variables consistent. For example, Ksn and Kns in line 113 should be ‘K_sn’ and ‘K_ns’.

 

In 343-345, the degree symbols are underlined. Is it intended?

 

In 358, did you mean According ‘to’ Equation (2)?

Comments for author File: Comments.docx

Reviewer 3 Report

Hydraulic fracture technique has been usually used to enhance oil/gas produce and carbon storage. The effect of weak joint on fracture containment is an important issue for hydraulic fracture. The manuscript can be considered to accept if clarify the following major comments.    

 

1. Table 1 shows the input parameters used in this study for numerical mode construction. What kind of rock and fluid is simulated? Please explain it.

2. Line 196: you mention that the analysis result is consist of actual monitoring data on site. Please give evidence or related reference.

3. The sentence in Line 343(the coefficient decreases at range 0⁰-30⁰ and increases at range 30⁰-90⁰) is not clear. The description phenomenon cannot be found in figure 11.

4. Line 353-355: you said that when cracks were required to propagate in pay zone, the cracks should perpendicular to the interface, and when cracks were required to connect multilayers, the cracks should be 30º to the interfaces. Why? How about 15⁰ angle? Please show the analysis results in figure associated with Line 353-355.

5. In this study, interface parameter was set constant. However, in Line 399-401, the influence of interface property on fracture mechanism was discussed. Please show the analysis results to prove it.

6. Line 404-410: the effect of fluid viscosity on fracture mechanism was discussed. Please also show the evidences.