Numerical Investigation of Fracture Morphology Characteristics in Heterogeneous Reservoirs

Round 1

Reviewer 1 Report

This paper presents a comprehensive study on hydraulic fracture propagating in heterogeneous media. The topic is very interesting and the results are reasonable. I think the paper can be accepted with minor revisions.
1. How are the governing equations of fractures propagation model solved numerically? Fully implicit?
2. What are the main advantages of the proposed model over some other models?
3. What shape functions are used to discretize the displacement field?

Author Response

Reviewers' comments:

This paper presents a comprehensive study on hydraulic fracture propagating in heterogeneous media. The topic is very interesting and the results are reasonable. I think the paper can be accepted with minor revisions.

 

1. How are the governing equations of fractures propagation model solved numerically? Fully implicit?

Response: Thank you very much for your helpful comments. The governing equations for fractures propagation model in this paper are solved by fully implicit. The manuscript was revised accordingly.

 

2. What are the main advantages of the proposed model over some other models?

Response: Thank you very much for your helpful comments. At present, many numerical models have been developed and used to simulate the fracture propagation, such as the finite element model [1], the extended finite element model [2] and the displacement discontinuity model [3]. The cohesive elements can simulate the propagation of hydraulic fractures in heterogeneous reservoirs, but the propagation direction is limited to predefined paths. The extended finite element model does not require mesh reconstruction and can simulate hydraulic fractures propagate along arbitrary paths on a fixed mesh. However, the convergence of the model is very poor especially for three-dimensional problems. Displacement discontinuity model could simulate crack propagation in high accuracy, but it fails in dealing with the anisotropy and heterogeneity of material. The phase field model [4] used in this paper can simulate anisotropic formations, and handle complex intersection behaviors such as hydraulic fracture bifurcation and coalescence. We have added the discussions in the introduction section of the revised manuscript accordingly.

 

Reference:

1. Chen, Z. Finite element modelling of viscosity-dominated hydraulic fractures. J Pet Sci Eng. 2012, 88-89, 136-144.
2. Ren, Q., Dong, Y., Yu, T. Numerical modeling of concrete hydraulic fracturing with extended finite element method. Sci China Ser E Technol Sci. 2009, 52(3), 559-565.
3. Dong, C, Y., de, Pater, C, J. Numerical implementation of displacement discontinuity method and its application in hydraulic fracturing. Comput Methods Appl Mech Eng. 2001, 191(8-10), 745-760.
4. Ni, L., Zhang, X., Zou, L., Huang, J. Phase-field modeling of hydraulic fracture network propagation in poroelastic rocks. Comput Geosci. 2020, 24, 1767–1782.

 

3. What shape functions are used to discretize the displacement field?

Response: Thank you very much for your helpful comments. Linear shape functions are used to discretize the displacement field. The manuscript was revised accordingly.

Author Response File: Author Response.docx

Reviewer 2 Report

The author intends to morph the fracture characteristic in shale reservoirs with heterogenous, using randomly distributed gravels and weak interfaces by phase field method. The topic is interesting, while some problems have still existed.

 

1. I have the sense that another round of revision by an English-native professional editor could help to improve the readability of the manuscript.

 

2. In the part 4, the model construction part, for shale reservoirs, the gravel and the weak interface are not distributed like this. If this is the traditional oil and gas reservoirs, like the sandstone, it is useful, while the model is not correct!

 

3. What is the innovation of the manuscript proposed model based on phase field method compared with previous research? The manuscript did not explain clearly. At the same time, some constitutive equations, boundary conditions, fluid flow, etc. in the mathematical model are based on the previous research results. I'm curious about the innovation of your model and the credibility of the model. Clearly indicating the novelty and significance of your manuscript. Developing your manuscript further by providing more in-depth and critical interpretations of the recent literature, especially from the recommended journals that you wish to choose. This is IMPORTANT!

 

4. Improving Abstract by adding a clear problem statement, underlying research question, methodology used, the novelty of the study and adding some of your key results and findings. This will help the editors, reviewers, and readers understand the paper's scope.

 

5. This model is based on the numerical method, but the verification uses the analytical solution. Whether the results obtained are reliable? This is a big question. I suggest that you can verify the models established in this paper according to the more classical models established by a series of numerical simulation methods, such as finite element method, extended finite element method, boundary element method, etc., so as to highlight the advantages of your models.

 

6. As shown in Fig. 3-5 and Fig. 7-14, since the gravel is crossed by hydraulic fractures, the gravel should be broken rather than in a complete state. This will lead the fracture to a new routine.

 

7. For figure 11, the number of sub-figure(e) is wrong.

Author Response

Reviewers' comments:

The author intends to morph the fracture characteristic in shale reservoirs with heterogenous, using randomly distributed gravels and weak interfaces by phase field method. The topic is interesting, while some problems have still existed.

 

1. I have the sense that another round of revision by an English-native professional editor could help to improve the readability of the manuscript.

Response: Thank you very much for your helpful comments and suggestions. The manuscript has been carefully reviewed and revised by an English-native professional scholar.

 

2. In the part 4, the model construction part, for shale reservoirs, the gravel and the weak interface are not distributed like this. If this is the traditional oil and gas reservoirs, like the sandstone, it is useful, while the model is not correct!

Response: Thank you very much for your helpful comments. The proposed model was constructed based on the properties of glutenite reservoirs. Glutenite reservoirs are characterized by deep burial, low permeability and low porosity. The gravels in an irregular shape are randomly distributed within the reservoir. Some parameters in the model, such as the gravel size and properties of rock matrix, are set by referring to the previous literatures [1,2]. The manuscript was revised accordingly.

 

Reference:

1      Tang, J., Liu, B., Zhang, G. Investigation on the Propagation Mechanisms of a Hydraulic Fracture in Glutenite Reservoirs Using DEM. Energies. 2022, 15(20), 7709.

2      Rui, Z.; Guo, T.; Feng, Q.; Qu, Z.; Qi, N, Gong, F. Influence of gravel on the propagation pattern of hydraulic fracture in the glutenite reservoir. J Pet Sci Eng. 2018, 165, 627-639.

 

3. What is the innovation of the manuscript proposed model based on phase field method compared with previous research? The manuscript did not explain clearly. At the same time, some constitutive equations, boundary conditions, fluid flow, etc. in the mathematical model are based on the previous research results. I'm curious about the innovation of your model and the credibility of the model. Clearly indicating the novelty and significance of your manuscript. Developing your manuscript further by providing more in-depth and critical interpretations of the recent literature, especially from the recommended journals that you wish to choose. This is IMPORTANT!

Response: Thank you very much for your helpful comments. There are some studies on the propagation characteristics of hydraulic fractures in heterogeneous reservoirs [1,2]. Li et al. proposed a numerical method for constructing glutenite heterogeneity by embedding digital image technology (DIP) into a numerically coded rock failure process analysis to study the effect of gravel on hydraulic fracture propagation [3]. Tang et al. established a two-dimensional numerical model based on the discrete element method to study the effects of permeability, gravel strength and stress difference on hydraulic fracture propagation in glutenite reservoirs [4]. In addition, some studies focus on the influence of single heterogeneous particles and discrete heterogeneous particles on the evolution of hydraulic fractures in heterogeneous formations based on the finite-discrete element method [5]. Based on the above studies, it is found that the previous studies neglect the weak interfaces of the gravel. Therefore, this paper considers the weak interface between gravel and rock matrix, and studies the influence of gravel with weak interface on the morphology of hydraulic fractures. It is found that hydraulic fractures are more likely to deflect and bifurcate in the reservoirs where weak interfaces were considered, and at the same time, the fluid pressure within the fractures is reduced. This provides guidance on hydraulic fracturing design in practical engineering. We have added the discussions in the introduction section of the revised manuscript accordingly.

 

Reference:

1      Liu, L., Li, L., Elsworth, D., Zhi, S., Yu, Y. The Impact of Oriented Perforations on Fracture Propagation and Complexity in Hydraulic Fracturing. Processes. 2018, 6(11), 213.

2      Shi, S., Zhuo, R., Cheng, L., Xiang, Y., Ma, X., Wang, T. Fracture Characteristics and Distribution in Slant Core from Conglomerate Hydraulic Fracturing Test Site (CHFTS) in Junggar Basin, Northwest China. Processes. 2022, 10(8), 1646.

3      Li, Z., Li, L., Zhang, Z., Li, M., Zhang, L., Huang, B., Tang, C. The Fracturing Behavior of Tight Glutenites Subjected to Hydraulic Pressure. Processes. 2018, 6(7), 96.

4      Tang, J., Liu, B., Zhang, G. Investigation on the Propagation Mechanisms of a Hydraulic Fracture in Glutenite Reservoirs Using DEM. Energies. 2022, 15(20), 7709.

5      Wu, M.; Wang, W.; Song, Z.; Liu, B.; Feng, C. Exploring the influence of heterogeneity on hydraulic fracturing based on the combined finite–discrete method. Eng Fract Mech. 2021, 252, 107835.

 

4. Improving Abstract by adding a clear problem statement, underlying research question, methodology used, the novelty of the study and adding some of your key results and findings. This will help the editors, reviewers, and readers understand the paper's scope.

Response: Thank you very much for your helpful comments and suggestions. We have added a clear problem statement, underlying research questions, methodology used, novelty of the study, key results and findings to the abstract section accordingly. Here is the revised abstract.

Highly heterogeneous glutenite reservoirs with large amounts of gravels and weak interfaces pose a great challenge to predict the trajectory of hydraulic fractures during the fracturing process. Based on the phase field method, a fully coupled numerical model of hydraulic fracturing is established. This paper is devoted to investigating the variation of the overall expansion pattern of hydraulic fractures in reservoirs considering randomly distributed gravels and weak interfaces. The numerical results demonstrate that the existence of gravel and weak interface could alter the extending paths of the hydraulic fractures as well as the value of critical bifurcation injection rate. As the fracture energy of the weak interface is large enough, the hydraulic fracture tends to cross the gravel and the weak interface between the rock matrix and the gravel, forming a planar fracture. Deflection and branching of hydraulic fractures are more likely to occur in reservoirs containing larger size gravels. The presented results extend the understandings of fractures propagating in heterogeneous reservoirs.

The manuscript was revised accordingly.

 

 

5. This model is based on the numerical method, but the verification uses the analytical solution. Whether the results obtained are reliable? This is a big question. I suggest that you can verify the models established in this paper according to the more classical models established by a series of numerical simulation methods, such as finite element method, extended finite element method, boundary element method, etc., so as to highlight the advantages of your models.

Response: Thank you very much for your helpful comments and suggestions. In this paper, we adopt a toughness-dominated asymptotic solution of the KGD model proposed by Santillan et al. [1] for verification. Analytical solutions of hydraulic fracture have been adopted to verify the numerical models based on the extended finite element method and the displacement discontinuity method [2,3,4]. The minor difference between the analytical results and numerical predictions implies that our numerical model achieves the same order of accuracy with the classical models. Hydraulic fractures propagation in heterogenous formation usually leads to complex trajectories based on cohesive zone method and discrete element method [5,6], which is coincident with our simulation results. Moreover, since we consider the weak interfaces of the gravel in the model, more complex extending paths such as branching as well as intersections with many weak interfaces are observed in the numerical results. The manuscript was revised accordingly.

 

Reference:

1. Santillán, D., Juanes, R., Cueto-Felgueroso, L. Phase field model of fluid-driven fracture in elastic media: Immersed-fracture formulation and validation with analytical solutions: PHASE FIELD MODEL FLUID-DRIVEN FRACTURE. J Geophys Res Solid Earth. 2017, 122(4), 2565-2589.Tang, J., Liu, B., Zhang, G. Investigation on the Propagation Mechanisms of a Hydraulic Fracture in Glutenite Reservoirs Using DEM. Energies. 2022, 15(20), 7709.
2. Gutierrez, Escobar, R., Mejia, Sanchez, E.C., Roehl, D., Romanel, C. Xfem modeling of stress shadowing in multiple hydraulic fractures in multi-layered formations. J Nat Gas Sci Eng. 2019, 70, 102950.
3. Luo, Z., Xie, Y., Zhao, L., Cheng, L., Wen, G., Wang, C., Gao, Y., Wang, N. A Random‐XFEM technique modeling of hydraulic fracture interaction with natural void. Energy Sci Eng. 2022, 10(8), 2637-2660.
4. Fan, H., Li, S., Feng, X, T., Zhu, X. A high-efficiency 3D boundary element method for estimating the stress/displacement field induced by complex fracture networks. J Pet Sci Eng. 2020, 187, 106815.
5. Tang, J., Liu, B., Zhang, G. Investigation on the Propagation Mechanisms of a Hydraulic Fracture in Glutenite Reservoirs Using DEM. Energies. 2022, 15(20), 7709.
6. Rui, Z.; Guo, T.; Feng, Q.; Qu, Z.; Qi, N, Gong, F. Influence of gravel on the propagation pattern of hydraulic fracture in the glutenite reservoir. J Pet Sci Eng. 2018, 165, 627-639.

 

6. As shown in Fig. 3-5 and Fig. 7-14, since the gravel is crossed by hydraulic fractures, the gravel should be broken rather than in a complete state. This will lead the fracture to a new routine.

Response: Thank you very much for your helpful comments. When the gravel intersects the hydraulic fracture, the broken of the gravel mainly depends on the strength of the gravel and the interface, and the simulations in this paper show that the gravel could be split into two separate parts by the hydraulic fracture (the blue line denotes the fracture as shown in Fig.9(a) and Fig.10(c)). More complex cases such as the heterogeneity and anisotropy of the gravel are not considered, which needs further work. The manuscript was revised accordingly.

 

7. For figure 11, the number of sub-figure(e) is wrong.

Response: Thank you very much for the helpful comment. For Figure 11, the number of sub-figure(e) has been modified to (d). We have revised the mistake in the manuscript accordingly.

Author Response File: Author Response.docx