Analytical Model of Hydraulic Fracturing for Low Permeability Hot Dry Rock Reservoirs and DEM Simulation Base on Fluid-Solid Coupling

Round 1

Reviewer 1 Report

The research is focused on the hot dry rock reservoir. A simplified DEM model by PFC software, which divide the reservoir into two parts rock and fracture. The hydraulic fracturing micro-fracture based on particle contact connection model was established.

The manuscript is well organized, fits the scope of the journal and the topic is important, but the novelty should be better expressed. The following issues might be reconsidered and revised.

1.       The introduction on Chinese national background may be revised from a world perspective since this is world wide journal. The descriptions on domestic should all be deleted and revised.

2.       The recent research status not only Chinese researchers should be given for the introduction part. The novelty of this study should be given. References of recent years and high quality journals might be referred.

3.       The English in the second paragraph of introduction should be revised.

4.       A nomenclature of all symbols is recommended.

5.       The authors should supply 1 reference where this software PFC is presented/validated.

6.       Show the full name of abbreviations when it appears first time, for example DEM

Author Response

The manuscript is well organized, fits the scope of the journal and the topic is important, but the novelty should be better expressed. The following issues might be reconsidered and revised.

1. The introduction on Chinese national background may be revised from a world perspective since this is world wide journal. The descriptions on domestic should all be deleted and revised.

We have changed the introduction according to the reviewer’s suggest. we deleted the words about the introduction on Chinese national background.

2. The recent research status not only Chinese researchers should be given for the introduction part. The novelty of this study should be given. References of recent years and high quality journals might be referred.

Thanks for the reviewer’s comment. We have inserted some latest research results at home and abroad. The innovation of this paper is to establish hydraulic fracturing micro fractures based on the parallel connection model, and study the expansion process.

3. The English in the second paragraph of introduction should be revised.

Thanks for the reviewer’s comment. We have revised it in the revised paper.

4. A nomenclature of all symbols is recommended.

Thanks for the reviewer’s comment. We have revised it in the revised paper. We convert the formula(1)and (2) expressed by tensor into differential expression in Cartesian coordinate system

5. The authors should supply 1 reference where this software PFC is presented/validated.

Thanks for the reviewer’s comment. We added a citation of master's thesis in the text to emphasize the application of PFC software。

24.Yang Fangchuan. Stability analysis of sandy soil tunnel end based on PFC fluid structure coupling. 2018. Changsha University of Technology.

6. Show the full name of abbreviations when it appears first time, for example DEM

Thanks for the reviewer’s comment. We have revised it in the revised paper. DEM representatives Discrete Element Method

Author Response File: Author Response.docx

Reviewer 2 Report

In this paper, the particle flow method of micro-mechanical discrete element theory is introduced to simulate mechanical behavior of hydraulic fracturing for HDR low permeability reservoir. I think authors have done a solid work and this paper can be considered for publication in Processes. Some questions and suggestions are listed as follows.

1. Authors can add more introduction and background about particle flow method.

2. How to validate the reliability of the new method? Do authors compare it with production data or other models?

3. How does this model deal with intersected fractures? Does it calculate efficiency?

4. The English can be improved.

Author Response

In this paper, the particle flow method of micro-mechanical discrete element theory is introduced to simulate mechanical behavior of hydraulic fracturing for HDR low permeability reservoir. I think authors have done a solid work and this paper can be considered for publication in Processes. Some questions and suggestions are listed as follows.

1. Authors can add more introduction and background about particle flow method.

Thanks for the reviewer’s comment. We added the following introduction between the second paragraph and the third paragraph of Introduction:

“Particle flow method is based on molecular dynamics to study the mechanical properties and behaviors of media. Boundary walls are used to constrain the basic elements. Particle flow method only needs to define the micro mechanical parameters for particles and bonds, and does not need to define the constitutive relationship and corresponding parameters of materials, which can reflect the macro problems. PFC software is the particle flow numerical simulation software developed by Itasca Company of the United States. PFC follows the discontinuous medium theory, and the movement between its basic units does not need to meet the constraint of the deformation compatibility equation, but only needs to meet the balance equation. The contact force and relative displacement between particles are controlled through the built-in physical equation, and the physical equation will show linear or nonlinear laws due to the distribution between particles and the change of contact force, so that the movement between units is constrained.”

2. How to validate the reliability of the new method? Do authors compare it with production data or other models?

Thanks for the reviewer’s comment. The method used in this paper applies force on particles according to formula (10). The programming process is relatively simple and there are not many difficulties. The most critical step affecting the accuracy of this method is how to find the particles around the hydraulic fracturing fracture. In the programming, the author selects the most conservative traversal search method for particle search. The traversal method has been very mature in mathematical applications. At the same time, the reliability of the algorithm has been guaranteed through repeated tests. Therefore, the accuracy of the method in this paper can be guaranteed. Due to the calculation example in this paper, the author obtained the trend and spacing of natural fractures based on the field geological data, so it is difficult to find a hydraulic fracturing well with the same geological conditions as this case for field data comparison.

3. How does this model deal with intersected fractures? Does it calculate efficiency?

Thanks for the reviewer’s comment. The discrete element can consider natural cracks, and the treatment method is to set the cohesive force between adjacent particles to zero, with only extrusion force and friction,and the entire fracture area is set as a fluid area. This calculation method, depending on the total number of particles, is relatively inefficient in a large range of calculations.

4. The English can be improved.

Thanks for the reviewer’s comment. We have revised it in the revised paper.

Author Response File: Author Response.docx

Reviewer 3 Report

This paper is focused on analytical model for hydraulic fracturing in low permebaility model. I suggest the following major revisions before a possible publication:

(1) Typo: please revise analysis model to analytical model.

(2) Pleae add the explanation of q in the description for Equation 6.

(3) For low-permeability rock, usually we use apparent permeability. It is OK if the author did not use apparent permeability. But please give a brief introduction section. The following papers can be references:

On the flow regime model for fast estimation of tight sandstone gas apparent permeability in high-pressure reservoirs

Nanoscale free gas transport in shale rocks: a hard-sphere based model

(4) Figure 4: what is the maximum fracturing pressure? Is 65 MPa reasonable?

(5) Figure 9a: there is intersection between green line and red line. How do you explain the physics behind it?

(6) How does the temperature affect the permeability and porosity? How did you consider it in the study? If you ignore it, please give the assumption.

Author Response

This paper is focused on analytical model for hydraulic fracturing in low permebaility model. I suggest the following major revisions before a possible publication:

• Typo: please revise analysis model to analytical model.

Thanks for the reviewer’s comment. We have revised it in the revised paper.

• Pleae add the explanation of q in the description for Equation 6.

Thanks for the reviewer’s comment. q is the flow rate, We have explaned it in the paper.

(3) For low-permeability rock, usually we use apparent permeability. It is OK if the author did not use apparent permeability. But please give a brief introduction section. The following papers can be references:

On the flow regime model for fast estimation of tight sandstone gas apparent permeability in high-pressure reservoirs

Nanoscale free gas transport in shale rocks: a hard-sphere based model

Thanks for the reviewer’s comment. We have carefully considered your suggestions and have taken appropriate action to address them. In response to your comment, we have added a brief introduction section to explain the method we used in low-permeability rock, even though we did not use apparent permeability. Additionally, we have included the papers you recommended as references to enhance the content of our paper.

(4) Figure 4: what is the maximum fracturing pressure? Is 65 MPa reasonable?

Thanks for the reviewer’s comment. The maximum fracture pressure is the fracturing fluid pressure when the fracture opens. Figure 4 shows the relationship curve between injection pressure and number of fractures. As a scientific study, it is possible to study more laws under several working conditions. According to the existing development environment, the 65MPa data is high, but if the development of deep dry hot rock is carried out later, the pressure is still acceptable. Therefore, the authors of this paper agree that the analysis of this pressure is reasonable.

 (5) Figure 9a: there is intersection between green line and red line. How do you explain the physics behind it?

Thanks for the reviewer’s comment. The author personally believes that there will be multiple fracturing fractures, and the figure 9 only shows the maximum fracture length, Since there is no information about other remaining fractures. The authors believe that this kind of crossing may be caused by the extension of the remaining non main fractures and the extension of the restricted main fractures.

(6) How does the temperature affect the permeability and porosity? How did you consider it in the study? If you ignore it, please give the assumption.

Thanks for the reviewer’s comment.

Through literature research and experiments, the authors found that temperature will reduce the permeability and porosity of rocks, because the thermal expansion of rock matrix materials will reduce the pore throat and effective volume in the matrix, thus reducing the permeability and porosity. The theoretical part of this paper does not involve the influence of temperature, so the numerical simulation part of this paper also fails to consider this content. For the influence of temperature field, this paper deals with it indirectly from the micro-parameters of HDR rock particles. And we give the assumption in the part of discussion as following:

“By literature research,The temperature will reduce the permeability and porosity of rocks, because the thermal expansion of rock matrix materials will reduce the pore throat and effective volume in the matrix, thus reducing the permeability and porosity. But this paper simply reflects the temperature effect on the difference of micro-parameters of HDR rock particles(see Table 3) and analyzes the influence of injection pressure, horizontal minimum principal stress, and reservoir permeability on the change of fracturing.”

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

This manuscript can be accepted.

Reviewer 3 Report

Good to go now.