The Investigation of Two-Phase Fluid Flow Structure Within Rock Fracture Evolution in Terms of Flow Velocity: The Role of Fracture Surface Roughness and Shear Displacement

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper focused on conducting a series of numerical simulation to investigate the role of 1- fracture aperture, 2- surface roughness and 3- shear displacement in the transition of two-phase fluid flow.

Though the topic in interesting for the related rock engineers, yet the following notes were recorded:

1-  Based on the iThenticate report report there is 31% matching with other papers. This percentage is very high and MUST be reduced.  

2- Provide validate equations 1 and 2 ( More details to be provided here to validate these equations for the authors model )

3- In lines 208 and 209 the authors are claiming ( In this study, the density and viscosity of the fluid at 20°C were chosen, the dissolution of the gas in water was neglected, ) is this true for real underground case ? validate this point.

4- I would require to see part of the MATLAB written program by the authors.

5- Figures 7 , 8 and 9 are not clear

 

Author Response

This paper focused on conducting a series of numerical simulation to investigate the role of 1- fracture aperture, 2- surface roughness and 3- shear displacement in the transition of two-phase fluid flow. Though the topic in interesting for the related rock engineers, yet the following notes were recorded:

Response: Thanks a lot for your time reviewing our paper and helping us improve this work! We appreciate it very much!

Comment 1:   "Based on the iThenticate report report there is 31% matching with other papers. This percentage is very high and MUST be reduced."

Response: Thanks a lot for your comment! To ensure that the article meets the basic requirements of the journal, we have downscaled the revised manuscript.

Comment 2:   "Provide validate equations 1 and 2 ( More details to be provided here to validate these equations for the authors model )"

Response: Thanks a lot for your comment! In the model validation of this study, the simulations used the same geometric model and boundary conditions as the experiments, and in order to further clarify the conditions used in the model validation process, we added information about the inlet flow rate of the two-phase fluid in the simulations and experiments to Fig. 2 of the revised manuscript.

 

Comment 3:   "In lines 208 and 209 the authors are claiming ( In this study, the density and viscosity of the fluid at 20°C were chosen, the dissolution of the gas in water was neglected, ) is this true for real underground case ? validate this point."

Response: Thanks a lot for your suggestion! The dissolution of natural gas in the liquid phase was not considered in this study, as the focus was on the influence of surface morphology and flow dynamics on two-phase flow. Neglecting gas dissolution may lead to slight deviations in saturation distribution, but its impact is limited under the given pressure and temperature conditions, this hypothesis was confirmed to be valid in the study by many researchers [29,33].

References

29. Wang, Y.; Zhang, Z.; Ranjith, P.G.; Han, X. Flow structure transition and identification of two-phase fluid flow through rough rock fractures. Eur Phys J Plus 2023, 138, doi: 10.1140/epjp/s13360-023-03977-4.
30. Liu, D.; Pu, H.; Xue, K.; Ni, H. Numerical Simulation of Gas–Water Two-Phase Flow Patterns in Fracture: Implica-tion for Enhancing Natural Gas Production. Water 2024, 16, 2860. https://doi.org/10.3390/w16192860.

Comment 4:   "I would require to see part of the MATLAB written program by the authors. "

Response: Thanks a lot for your comment! The following MATLAB code is used to generate 1D rough cleavage curves in this study:

clear;

x_min = 0; x_max = 10;     

min_jingdu = 0.2            ;       

chazhicishu = ceil(log(x_max / min_jingdu) / log(2));

x = linspace(x_min, x_max, 2^chazhicishu + 1);

sigm0 = 0.5; H = 0.27;        

A = normrnd(0, sigm0^2 / 2, 1, 2);

sigm = sigm0^2 * (1 - 4^(H - 1)) ./ (4.^(H * (1:chazhicishu)));

roughness_params = zeros(chazhicishu, 4);

labels = {'Iteration', 'RMS', 'Peak-to-Valley', 'Tortuosity', 'JRC'};

for chazhi = 1:chazhicishu

    A = reshape([A; zeros(size(A))], 1, []);

    A(2:2:end-1) = (A(1:2:end-2) + A(3:2:end)) / 2;

    A = A + normrnd(0, sigm(chazhi) / 2, size(A));

    x = linspace(x_min, x_max, length(A)); 

    meanHeight = mean(A);

    RMS = sqrt(mean((A - meanHeight).^2));

    PeakToValley = max(A) - min(A);     

    L = sum(sqrt(diff(x).^2 + diff(A).^2));

    L_proj = x_max - x_min;              

    Tortuosity = L / L_proj;            

    Z2 = sqrt(sum(diff(A).^2) / ((length(A) - 1) * (x(2) - x(1))^2)); %Z2

    JRC = 32.2 + 32.47 * log10(Z2);   

    roughness_params(chazhi, :) = [RMS, PeakToValley, Tortuosity, JRC];

end

Comment 5:   "Figures 7 , 8 and 9 are not clear."

Response: Thanks for your comment! We apologize for uploading unclear images due to our carelessness, we have replaced Figs 7-9 with high-resolution images in the revised manuscript.

Reviewer 2 Report

Comments and Suggestions for Authors

The paper presents a numerical study on the two-phase flow in rock fractures. The use of level set function for the mesh deformation has been known for years, and the two-phase flow has also been studied well. Hence, there is no significant contribution in methodology. The use of Matlab code to generate random roughness have made the study mathematical and, possibly, unrealistic. This adds burden to my biggest concern that the study has not been verified. The two-phase flow rate from 0.3 to 0.9 m/s in a fracture of 0.4mm requires some justification.

If the authors don't verify the results of study, the paper has no contribution.

Here are some minor comments:

• Plunger flow is not defined in the initial list (line 74-75). As there is no definition, it is hard to follow. To my understanding this is slug flow. If that, authors should unify the terms.
• Source for Equation (3)? The number is on the next line.
• Check the format. For example, 2 must be subcript in line 174 and line 186. Equations in line 159 and176 are inaccurately numbered. Line 178: h must be explained. Random typos are found throughout.
• Line 201: delta is used before explained.
• Figure 4: Sw is used without explanation. This figure must be scrutinised. Why saturation of the flow with U_g=0.9 m/s and U_w = 0.9 m/s is higher than the saturation of the flow with U_g = 0.3 m/s and U_w =0.3?
• Figure 10 deserves a better discussion. I am not convinced with the argument about saturation.

Author Response

The paper presents a numerical study on the two-phase flow in rock fractures. The use of level set function for the mesh deformation has been known for years, and the two-phase flow has also been studied well. Hence, there is no significant contribution in methodology. The use of Matlab code to generate random roughness have made the study mathematical and, possibly, unrealistic. This adds burden to my biggest concern that the study has not been verified. The two-phase flow rate from 0.3 to 0.9 m/s in a fracture of 0.4mm requires some justification. If the authors don't verify the results of study, the paper has no contribution. Here are some minor comments:

Response: Thanks a lot for your time reviewing our paper and helping us improve this work! We appreciate it very much!

Comment 1:   "Plunger flow is not defined in the initial list (line 74-75). As there is no definition, it is hard to follow. To my understanding this is slug flow. If that, authors should unify the terms."

Response: Thanks a lot for your comment! We apologize for the inconsistency in terminology caused by our irregular expression. In fact, plunger flow and slug flow in the text refer to the same kind of flow structure, and we have unified plunger flow into slug flow in the revised manuscript.

Comment 2:   "Source for Equation (3)? The number is on the next line."

Response: Thanks a lot for your comment! We added a source on surface tension modeling in line 137 of the revised manuscript, the literature is : “35.Brackbill, J. U, D. B. Kothe, C. Zemach. A continuum method for modeling surface tension. Journal of Computa-tional Physics 1992, 100, 2:335-354.”

 

Comment 3:   "Check the format. For example, 2 must be subcript in line 174 and line 186. Equations in line 159 and176 are inaccurately numbered. Line 178: h must be explained. Random typos are found throughout."

Response: Thanks a lot for your suggestion! We have corrected related formatting issues in the revised manuscript. In addition, h stands for lag distance, and the description of h in the text was not clearly visible due to formatting issues, for which we have corrected the formatting of h in the text.”

 

Comment 4:   "Line 201: delta is used before explained."

Response: Thanks a lot for your comment! The delta in the text represents the shear displacement of the fracture, in order to ensure the logical rigor of the article, we have standardized the delta in the revised manuscript to δ and added the relevant description at the first mention of δ.

Comment 5:   "Figure 4: Sw is used without explanation. This figure must be scrutinised. Why saturation of the flow with Ug=0.9 m/s and Uw = 0.9 m/s is higher than the saturation of the flow with Ug = 0.3 m/s and Uw =0.3?"

Response: Thanks for your comment! To obtain the saturation of each phase, we are based on the definition of the level set function for the volume fraction, 0.5 is the phase interface of the two-phase fluid, and the integral method is used to calculate the area in the fracture where the level set function is less than 0.5 divided by the total area of the fracture as the saturation of the water phase. At low flow rates, since the water phase inlet stands at 25% above and below the fracture inlet, and the gas phase inlet is 50% in the middle, which makes the water phase in the fracture more likely to receive the shear influence of the gas phase, and thus exists in the fracture in the form of a discrete phase, so it is difficult for the water phase in the fracture to form a continuous flow channel at low flow rates, which results in a low degree of water saturation in the fracture. When the velocity of gas phase and water phase are both at a high level, the gas phase and water phase can exist in the form of continuous phase in the fracture, which is conducive to the transportation of two-phase fluids in the fracture, and at high flow rates, the water phase continuous channels on both sides of the fracture can compress the gas channel in the middle, which makes the water saturation in the fracture increase.

Comment 6:   "Figure 10 deserves a better discussion. I am not convinced with the argument about saturation."

Response: Thanks for your comment! In order to more accurately describe the water saturation evolution in Figure 10, we have optimized this part of the discussion to better show the physical laws behind it: “To further analyze the impact of dislocation (δ) on the flow area of two-phase fluid in fractures, Figure 10 presents the evolution patterns of water saturation at different flow structure stages in fractures 1 and 2 under varying ? values. The water saturation patterns differ significantly between the two fractures.

In Fracture 1, water saturation increases notably with rising ? during the slug flow and slug-annular flow stages, while it remains relatively unchanged in the laminar flow stage. This suggests that larger dislocations expand the aqueous phase flow area, primarily affecting discontinuous flow structures within the fracture.

In Fracture 2, water saturation initially increases and then decreases as ? grows, indicating that the influence of fracture roughness on the two-phase flow area intensifies with greater dislocation. Combined with previous observations on flow structure evolution, it is evident that high-roughness fractures exhibit a more pronounced response to dislocation. The interplay between roughness and dislocation leads to irregular flow structure variations, resulting in complex changes in the two-phase flow area within the fracture channel.”.

Reviewer 3 Report

Comments and Suggestions for Authors

The topic is interesting for various applications related to fractured rock (contaminants, energies, mineral resources, tunnelling), and studies of various effects on different regimes of two-phase flow in narrow channels (fractures) can bring more insight into the complex phenomena. 
However, the contribution of this particular paper is not very well specified against the existing results in the literature, and the obtained observations on limited choice of input data are yet far from a general understanding of the two-phase flow regimes depending on parameters.
I have several specific comments to the paper text and calculation methodology.

(1)
literature review

The first part of the Introduction (until about line 88 / ref.27) follows a style where generic statements are referred to the literature of rather narrow focus. I understand a need for every incoming idea to be somehow supported by literature, but this goes to an extreme where things I believe widely accepted are "supported" by works, whose results are something else but (I guess) use similar sentences in their own introductions. Few review papers of textbooks would serve better for a reader. In many cases the reference is factually inappropriate: 18 is referred in the context of environment remediation but its application context is gas reservoirs,  21 is used for introduction of two-phase flow regime, but the report is about 3D printing not specifically aimed to the listed four regimes, 25,26 are referred as application examples, but seem to be more theoretical, 27 is referred for experiments but its topic is modelling (maybe they referred some experiments, which could be cited instead).
Contrary, it would be much useful if the current work modelling methods/results were compared to other modelling results, to focus the novelty better. Paragraphs 113-122 discuss the motivation for modelling, but only one reference is used. Many of the previous cited works also used numerical simulations for similar or related problems, but altogether they were not evaluated as state of the art . E.g. which of the parameter sensitivity was already tested and which is for the first time (velocity, aperture, roughness, viscosity, wetting angle), or which others use the same equation and numerical formulation with the level set method or what are other approaches (e.g. there was the lattice Boltzmann method in one of the papers). Other issue could be a dimension (present work considers 1D fracture, ref.24 uses 2D fracture). Ref.23 has much denser diagram of various regimes than authors figs 2b and 4b.

ref 11 seems incomplete (likely a book?, so publisher, pages), while the title is duplicated

ref 16 and 20 are the same

ref 22 typing X-FEM
 

(2) mathematical model
some factual inaccuracies or typing errors

- F terms in eqn (2) should be of unit N/m3, not just N 
- line 141 symbol A instead of phi
- line 139 check the validity/context of the Dirac formula, it looks strange how Dirac could be obtained from continuous function phi
- level set function introduced after its used on line 139
- equation numbering (8), (9)
- eqn (10) isn't there extra "r" in the Z argument on the right-hand side? (otherwise the terms with Z appear both the same, and considering (11))
- line 213 pressure symbol should be lower case to be consistent

- Tab2 unit "Pa.s"
- how the input values U_w and U_g fit to the governing equation where only one function "u" is used for both fluids with continuous transition?

I am missing more details for the inlet boundary condition (line 218). If the velocities of liquid and gas (Uw and Ug used in the paper) are independent input parameters, I would suppose the formulation somehow require to input the ratio of liquid and gas at the input profile. In other words, a boundary condition for the level set function, the PDE on line 159. Considering mass-balance, this ratio would be then preserved in the whole fracture length, so the postprocessed saturation (Sw in the presented results) would be fixed. So I suppose, the phase distribution on the inlet was specified somehow adaptively, maybe referring to pressure and phase-specific flow resistance (commented with the results).  

The solution in Comsol is described very coarsely. It focuses to the algebraic solver but not at all to the differential equations. Is any of the Comsol's physics module used, or is it input as a custom equation (e.g. "general form PDE")?  

Mesh could be specified in more details - how to understand the range 0.2-10, which are the areas with finer and coarser meshes, was any check of mesh dependence on results made?

(3) results
The model is by its nature transient, so some explanation would be expected how a single time was chosen for presentation and evaluation of results.

Several parts of text just routinely read a content of graphical material without giving additional interpretation, e.g. lines 324-330. 

Figs 3,5,... Color scale or a reminder what is the liquid and gas phase would be useful.

Fig 2b and 4b, I find these plots not an efficient form of presentation. It is more like qualitative information. Could be added as labels to 2a and 4a.  

(4) typing and language 
Terms "slug flow" and "plunger flow" likely denoting the same should be unified.

Several times fogotten subscripts/superscripts at symbols in the text

Tab.3 I do not find it meaningful to present a table with two identical rows.

Repeated text
lines 85 and 73
lines 290-293
lines 382-386

SRA used line 116 before definition line 168

section 3.2, repeated long term "two-phase fluid flow rate" I would suggest to used the expanded form once at the beginning (or where specifically important) and shorten to "flow rate" elsewhere. Also once is enough in the section title.

3.1 "validation of validity .." seems duplicate

 

Author Response

The topic is interesting for various applications related to fractured rock (contaminants, energies, mineral resources, tunnelling), and studies of various effects on different regimes of two-phase flow in narrow channels (fractures) can bring more insight into the complex phenomena. However, the contribution of this particular paper is not very well specified against the existing results in the literature, and the obtained observations on limited choice of input data are yet far from a general understanding of the two-phase flow regimes depending on parameters. I have several specific comments to the paper text and calculation methodology.

Response: Thanks a lot for your time reviewing our paper and helping us improve this work! We appreciate it very much!

Comment 1:   "The first part of the Introduction (until about line 88 / ref.27) follows a style where generic statements are referred to the literature of rather narrow focus. I understand a need for every incoming idea to be somehow supported by literature, but this goes to an extreme where things I believe widely accepted are "supported" by works, whose results are something else but (I guess) use similar sentences in their own introductions. Few review papers of textbooks would serve better for a reader. In many cases the reference is factually inappropriate: 18 is referred in the context of environment remediation but its application context is gas reservoirs, 21 is used for introduction of two-phase flow regime, but the report is about 3D printing not specifically aimed to the listed four regimes, 25,26 are referred as application examples, but seem to be more theoretical, 27 is referred for experiments but its topic is modelling (maybe they referred some experiments, which could be cited instead).Contrary, it would be much useful if the current work modelling methods/results were compared to other modelling results, to focus the novelty better. Paragraphs 113-122 discuss the motivation for modelling, but only one reference is used. Many of the previous cited works also used numerical simulations for similar or related problems, but altogether they were not evaluated as state of the art . E.g. which of the parameter sensitivity was already tested and which is for the first time (velocity, aperture, roughness, viscosity, wetting angle), or which others use the same equation and numerical formulation with the level set method or what are other approaches (e.g. there was the lattice Boltzmann method in one of the papers). Other issue could be a dimension (present work considers 1D fracture, ref.24 uses 2D fracture). Ref.23 has much denser diagram of various regimes than authors figs 2b and 4b, ref 11 seems incomplete (likely a book?, so publisher, pages), while the title is duplicated, ref 16 and 20 are the same, ref 22 typing X-FEM"

Response: Thanks a lot for your comment! We apologize that we used an inappropriate presentation in the introduction. Following your suggestions, we have made appropriate modifications to the introduction section of the article, the main modifications are as follows:

• Since reference 1 did not serve well as a general introduction to the entire article, we changed reference 1 and chose more authoritative articles in the field to introduce the topic of the article: We changed the reference 1 in revised manuscript from “ Sur, A.; Yang, L.; Liu, D. Experimental and numerical investigation of two-phase patterns in a cross-junction mi-crofluidic chip. PROCEEDINGS OF THE 8TH INTERNATIONAL CONFERENCE ON NANOCHANNELS, MI-CROCHANNELS AND MINICHANNELS, 2010, PTS A AND B 2011, doi: 10.1115/fedsm-icnmm2010-31267.” to “1. Brian Berkowitz, Characterizing flow and transport in fractured geological media: A review, Adv Water Resour 2002, 25(8-12), 861-884, https://doi.org/10.1016/S0309-1708(02)00042-8.”
• In order to enhance the coherence and rationality of the logic of the introduction, we have removed some redundant references in the revised manuscript, such as references 7-9,11-13.
• We have changed the word in revised manuscript lines 52-55 from “Single fracture as the fundamental element of the fracture network, which serves as the basic knowledge for understanding the multiphase fluid flow through rock fracture [11-13]. Analyzing the multiphase fluid flow characteristics within individual fractures is essential for studying the multiphase fluid flow through fractured rock.” to “Single fracture as the fundamental element of the fracture network, it is essential to analyze the multiphase fluid flow characteristics within individual fractures is in order to investigate the multiphase fluid flow in fractured rocks”.
• We have changed the word in revised manuscript lines 61-66 from “Consequently, accurate and effective modeling of multiphase fluid flow within a single rock fracture holds immense theoretical importance and significant practical and strategic value for applications of multiphase flow structures to enhance underground oil and gas recovery, optimize extraction processes, evaluate the impact of fracture net-works on water storage and transport, resource extraction, groundwater management, and environmental protection.” to “Consequently, accurate and effective modeling of multiphase fluid flow within a single rock fracture holds immense theoretical importance and significant practical and strategic value for applications of multiphase flow structures to enhance underground oil and gas recovery, optimize extraction processes, evaluate the impact of fracture networks on water storage and transport.”
• We have changed the words in revised manuscript lines 66-67 from “The study of two-phase fluid flow migration patterns in fracture media, thereby providing a foundation for environmental remediation” to “The study of two-phase fluid flow migration patterns in fracture media, thereby providing a foundation for oil and gas extraction”.
• We have changed the reference 21(15 in revised manuscript) from “Taira, K.; Sun, Y.; Canuto, D. 3d printing of fluid flow structures. arXiv (Cornell University) 2017, doi: 10.48550/arxiv.1701.07560.” to “Cheng L., Xia G., Flow patterns and flow pattern maps for adiabatic and diabatic gas liquid two phase flow in microchannels: fundamentals, mechanisms and applications, Experimental Thermal and Fluid Science 2023, 148, 110988, https://doi.org/10.1016/j.expthermflusci.2023.110988.”
• We have added the introduction about the numerical investigation about two-phase flow in fractures in revised manuscript lines 101-117: “Current numerical simulation methods for modeling two-phase fluid flow in rock fractures primarily include the Volume of Fluid (VOF) method, the Lattice Boltzmann Method (LBM), and the Level Set Method [29-32]. Wang et al. [29] examined the effects of fluid flow rate and wettability on two-phase flow structures in 1D fractures. Guiltinan et al. [30] explored how heterogeneous wetting properties in 2D fractures influence the displacement of water by supercritical carbon dioxide using the LBM method. Zhao et al. [31] investigated the impact of wettability heterogeneity on the relative permeability of two-phase flow in porous media through a multi-ple-relaxation-time colored gradient LBM model. Huang et al. [32] employed the VOF method to analyze gas-phase flow characteristics in different fluids at the microscopic scale within 1D fractures, as well as the influence of fluid parameters on flow patterns. Liu et al. [33] utilized the Level Set Method to simulate the evolution of plug structures under varying flow ratios, fracture surface wettability, and fracture tortuosity in 1D fractures.These studies have laid a solid foundation for understanding the evolution of two-phase fluid flow structures in fractures. However, the influence of two-phase fluid velocity, surface roughness, and shear displacement on the evolution of these structures remains insufficiently explored, highlighting the need for further investigation.”
• We have reordered the revised references in the revised manuscript.

Comment 2:   " some factual inaccuracies or typing errors, F terms in eqn (2) should be of unit N/m3, not just N, line 141 symbol A instead of phi, line 139 check the validity/context of the Dirac formula, it looks strange how Dirac could be obtained from continuous function phi, level set function introduced after its used on line 139, equation numbering (8), (9), eqn (10) isn't there extra "r" in the Z argument on the right-hand side? (otherwise the terms with Z appear both the same, and considering (11)), line 213 pressure symbol should be lower case to be consistent, Tab2 unit "Pa.s", how the input values U_w and U_g fit to the governing equation where only one function "u" is used for both fluids with continuous transition?

Response: Thank you for your valuable suggestions, we have corrected the wrong units, formulas and symbols in the text according to your suggestions, for U_w and U_g refer to the entrance velocity at the entrance of the two-phase fluid in the fracture, which both satisfy the ns equation during the two-phase fluid flow process, and maintain the conservation of energy and momentum during the flow process.

 

Comment 3:   "I am missing more details for the inlet boundary condition (line 218). If the velocities of liquid and gas (Uw and Ug used in the paper) are independent input parameters, I would suppose the formulation somehow require to input the ratio of liquid and gas at the input profile. In other words, a boundary condition for the level set function, the PDE on line 159. Considering mass-balance, this ratio would be then preserved in the whole fracture length, so the postprocessed saturation (Sw in the presented results) would be fixed. So I suppose, the phase distribution on the inlet was specified somehow adaptively, maybe referring to pressure and phase-specific flow resistance (commented with the results)."

Response: Thanks a lot for your rigorous comment! In fact, due to the hydrophilicity of the fissure wall and the consideration about the two-phase fluid flow state in the actual engineering, this paper sets up the two-phase fluid inlet conditions in a segmented way, and divides the fissure inlet into three parts, with the upper 25% and lower 25% as the water-phase inlet, and the middle 50% as the gas-phase inlet.

 

Comment 4:   "The solution in Comsol is described very coarsely. It focuses to the algebraic solver but not at all to the differential equations. Is any of the Comsol's physics module used, or is it input as a custom equation (e.g. "general form PDE")?"

Response: Thanks a lot for your comment! In this paper, the coupled computation of the laminar flow module in COMSOL and the level set module in multiphase flow module is used to simulate the gas-water two-phase fluid flow in the fissure, where the laminar flow module is used to solve the N-S equations in the laminar flow state, and the level set module is adopted to realize the accurate tracking of the gas-water flow interface, while the surface tension model is used to realize the surface tension setting. We did not use the PDE module for the simulation. In order to show more clearly the physical modules used for the solution, we have added the following description in the revised manuscript lines 221-226: “In this study, the coupled computation of the laminar flow module and the level set module in the multiphase flow module of COMSOL Multiphysics is employed to simulate gas-water two-phase flow in a fracture. The laminar flow module solves the Navier-Stokes (N-S) equations for laminar flow, while the level set module enables precise tracking of the gas-water interface.”

Comment 5:   "Mesh could be specified in more details, how to understand the range 0.2-10, which are the areas with finer and coarser meshes, was any check of mesh dependence on results made?""

Response: Thanks for your comment! In order to ensure the accuracy of the simulation results, we control the mesh size while optimizing the mesh with local encryption, the purpose of doing so is to adapt to the meandering characteristics of the fissure wall, so that the level-set method can effectively simulate the actual flow state of the fluid flowing through the vicinity of the meandering wall, and thus to ensure the accuracy of the results, and at the same time, we carried out the independence test of the mesh size, and finally choose the mesh with a total number of 60,000 to 70,000 meshes. We have added a relevant statement about computational meshes in the revised manuscript lines 235-240 : “In order to ensure the accuracy of the simulation results, local encryption optimization of the mesh was carried out in this study, which was done to adapt to the meandering characteristics of the fissure wall, so that the level set method can effectively simulate the actual flow state of the fluid flowing through the vicinity of the meandering wall, and at the same time, the mesh size was checked independently, and the total number of meshes was finally selected to be 60,000 to 70,000 meshes.”

Comment 6:   "The model is by its nature transient, so some explanation would be expected how a single time was chosen for presentation and evaluation of results."

Response: Thanks for your comment! In order to ensure that the simulation results are not affected by time, we extend the simulation time to ensure that the fluid can completely flow through the fracture, and after the two-phase fluid flow structure in the crack is stabilized, we select the calculation results at the stabilization time to be processed and exported.

Comment 7:   "Several parts of text just routinely read a content of graphical material without giving additional interpretation, e.g. lines 324-330."

Response: Thanks for your rigorous comment. We have revised in the revised manuscript lines 335-342 from “when Uw= 0.3 m/s, the water saturation in fracture 1 is between 0.3 and 0.4, and that in fracture 2 is between 0.4 and 0.5; when Uw= 0.6 m/s, the water saturation in fracture 1 is between 0.45 and 0.6, and that in fracture 2 is between 0.5 and 0.7; when Uw= 0.9 m/s, the water saturation in fracture 1 is between 0.5 and 0.7; when Uw= 0.9 m/s, the water saturation in fracture 2 is between 0.5 and 0.7; and when Uw= 0.9 m/s, the water saturation in fracture 1 is between 0.4 and 0.5. When Uw= 0.9 m/s, the water saturation in fracture 1 is between 0.6 and 0.75, and the water saturation in fracture 2 is between 0.6 and 0.8.” to “A comparison of water saturation evolution in Fracture 1 and Fracture 2 under different water-phase flow rates reveals that when U? = 0.3 m/s, water saturation in Fracture 1 ranges from 0.3 to 0.4, while in Fracture 2, it is 0.4 to 0.5, and as the gas flow rate increases from 0.3 m/s to 0.9 m/s, water saturation in Fracture 2 decreases by 22%. When Uw= 0.6 m/s, water saturation in Fracture 1 is 0.45 to 0.6, while in Fracture 2, it is 0.5 to 0.7, and water saturation in Fracture 2 decreases by 26% as the gas flow rate rises from 0.3 m/s to 0.9 m/s., when Uw= 0.9 m/s, water saturation in Fracture 1 is 0.6 to 0.75, while in Fracture 2, it is 0.6 to 0.8, and water saturation in Fracture 2 decreases by 22% as the gas flow rate increases from 0.3 m/s to 0.9 m/s.”

Comment 8:   "Figs 3,5,... Color scale or a reminder what is the liquid and gas phase would be useful."

Response: Thanks for your rigorous comment! We have added the color scale in the revised manuscript Fig. 3, 5.

Comment 9:   "Fig 2b and 4b, I find these plots not an efficient form of presentation. It is more like qualitative information. Could be added as labels to 2a and 4a."

Response: Thanks for your rigorous comment! We have revised the in Fig. 2 and 4 in the revised manuscript.

Comment 10: "Terms "slug flow" and "plunger flow" likely denoting the same should be unified."

Response: Thanks for your rigorous comment! We have unified the slug and plunger flow to “slug flow” in the revised manuscript.

Comment 11: "Several times fogotten subscripts/superscripts at symbols in the text."

Response: Thanks for your rigorous comment! We have revised the symbols in the revised manuscript.

Comment 12: "Tab.3 I do not find it meaningful to present a table with two identical rows."

Response: Thanks for your rigorous comment! We optimized the presentation in Table 4 of the revised manuscript and placed the same parameters in one row.

Comment 13: "Repeated text, lines 85 and 73, lines 290-293, lines 382-386"

Response: Thanks for your rigorous comment! We have reduced the repeated text in the revised manuscript.

Comment 14: "SRA used line 116 before definition line 168"

Response: Thanks for your rigorous comment! We have added the full name of the SRA in lines 119-120 of the revised manuscript.

Comment 15: "section 3.2, repeated long term "two-phase fluid flow rate" I would suggest to used the expanded form once at the beginning (or where specifically important) and shorten to "flow rate" elsewhere. Also once is enough in the section title."

Response: Thanks for your rigorous comment! We have shorten the “two-phase fluid flow rate” to "flow rate" in section 3.2. We have also changed the name of section 3.2 in the revised manuscript from “Effect of two-phase fluid flow rate on the structure of two-phase fluid flow” to “Effect of flow rate on the structure of two-phase fluid flow”.

Comment 16: "3.1 "validation of validity .." seems duplicate"

Response: Thanks for your rigorous comment! We have changed the name of section 3.1 in the revised manuscript from “Validation of the validity of numerical simulation methods” to “Validation of numerical simulation methods”.

 

 

Reviewer 4 Report

Comments and Suggestions for Authors

(1) Natural gas will dissolve into liquids such as water or oil, thereby affecting the flow patterns of two-phase flow. Moreover, temperature and pressure can seriously affect the dissolution of natural gas in the liquid phase. We can see from the basic theory in the second part of the manuscript that the dissolution of natural gas in the liquid phase has not been taken into account. What impact does this have on the simulation results obtained from the research conducted in this article? Moreover, from equation (1), it can be observed that the liquid phase does not separate into gas and liquid phases. How can the saturation levels of each phase be obtained in subsequent simulations?
(2) The manuscript provides some basic theories related to porous media seepage and fracture seepage, which is very helpful for understanding the mechanism of fracture flow simulation results. However, the geometric model used for simulation research was not explicitly provided. If we consider Figure 1 as the geometric model used for simulation research in the manuscript, does such a small model have obvious boundary effects? After all, it is impossible for mass transfer to occur between the fracture wall and the porous medium.
(3) From Table 2, we note that the author's assumption in the study is that the gas phase in the porous medium is nitrogen, rather than natural gas or other gases. Although nitrogen accounts for the vast majority of gases in the atmosphere, it is not the main component in underground porous media. In this case, what is the rationale or basis for assuming that the gas phase in porous media is nitrogen? Moreover, any gas is extremely sensitive to temperature and pressure. But Table 2 considers these data as constants, isn't that appropriate?
(4) Understanding the structural evolution of two-phase fluid flow in fractured rock masses is of great significance for the study of related issues such as underground oil and gas extraction. Therefore, the statements in lines 66-70 need to be reinforced with the following pa-pers to enhance persuasiveness: The Crack Propagation Behaviour of CO2 Fracturing Fluid in Unconventional Low Permeability Reservoirs: Factor Analysis and Mechanism Revelation; Wellhead Stability during Development Process of Hydrate Reservoir in the Northern South China Sea: Evolution and Mechanism.
(5) The applicability of research methodology has been studied by comparing simulation results with experimental results, which is a commonly used approach. In this study, the author compared the simulation results with the experimental results of previous research. However, the manuscript did not provide a validation model or experimental (or simulation conditions), only a comparison between experimental and simulation results. This is difficult to persuade. In addition, the simulation provides the basic theory of fracture flow, while the verification experiment shows obvious pipe flow. Are the two based on the same basic theory?
(6) There are some minor issues that need to be addressed by the authors to improve the quality of the manuscript. In Figure 2, what are the physical meanings represented by each color block in the simulation results? Other nephogram also have the same problem.; The conclusion is not a repetition or extension of the results in the abstract, and the conclusion needs to be appropriately modified.
(7) In almost all experimental results, all curves were plotted based on three data points. In terms of academic rigor, this is not rigorous because using three points cannot accurately describe the patterns obtained from research.

Author Response

Response: Thanks a lot for your time reviewing our paper and helping us improve this work! We appreciate it very much!

Comment 1:   "Natural gas will dissolve into liquids such as water or oil, thereby affecting the flow patterns of two-phase flow. Moreover, temperature and pressure can seriously affect the dissolution of natural gas in the liquid phase. We can see from the basic theory in the second part of the manuscript that the dissolution of natural gas in the liquid phase has not been taken into account. What impact does this have on the simulation results obtained from the research conducted in this article? Moreover, from equation (1), it can be observed that the liquid phase does not separate into gas and liquid phases. How can the saturation levels of each phase be obtained in subsequent simulations?"

Response: Thanks a lot for your comment! The dissolution of natural gas in the liquid phase was not considered in this study, as the focus was on the influence of surface morphology and flow dynamics on two-phase flow. Neglecting gas dissolution may lead to slight deviations in saturation distribution, but its impact is limited under the given pressure and temperature conditions. Regarding Equation (1), the liquid phase is treated as a single continuum, and phase saturations are obtained based on mass conservation and phase equilibrium assumptions. To obtain the saturation of each phase, we are based on the definition of the level set function for the volume fraction, 0.5 is the phase interface of the two-phase fluid, and the integral method is used to calculate the area in the fracture where the level set function is less than 0.5 divided by the total area of the fracture as the saturation of the water phase. Future work could incorporate gas dissolution effects for a more comprehensive analysis.

Comment 2:   "The manuscript provides some basic theories related to porous media seepage and fracture seepage, which is very helpful for understanding the mechanism of fracture flow simulation results. However, the geometric model used for simulation research was not explicitly provided. If we consider Figure 1 as the geometric model used for simulation research in the manuscript, does such a small model have obvious boundary effects? After all, it is impossible for mass transfer to occur between the fracture wall and the porous medium."

Response: Thanks a lot for your comment! In order to facilitate the viewing of the geometric model used in this paper, we have optimized the representation of Figure 1. Given that mass transfer between the fracture wall and the porous medium is not considered, the primary focus is on the internal flow dynamics within the fracture. In order not to affect the accuracy of the results of the case, this paper by reducing the length of the model to reduce the amount of calculations, due to the crack opening in this paper are 0.1 mm, and the length of the crack is 10 mm, the difference between the two is large, the impact of the boundary effect in this scale is still relatively small compared to the overall flow, so the boundary effect can be ignored in this case.

 

Comment 3:   "From Table 2, we note that the author's assumption in the study is that the gas phase in the porous medium is nitrogen, rather than natural gas or other gases. Although nitrogen accounts for the vast majority of gases in the atmosphere, it is not the main component in underground porous media. In this case, what is the rationale or basis for assuming that the gas phase in porous media is nitrogen? Moreover, any gas is extremely sensitive to temperature and pressure. But Table 2 considers these data as constants, isn't that appropriate?"

Response: Thanks a lot for your suggestion! Since desorption adsorption and dissolution of gases were not considered in this study, in which case the variability between the gases is reduced, in order to perform the calculations without affecting the results, the simulation using the inert gas nitrogen can facilitate the calculations. In this paper, the initial temperature is set to room temperature 20°C. The compressibility of the gas is taken into account in the process of two-phase fluid flow, and the density of the gas is iterated by the ideal gas equation of state for real-time calculations, which leads to the flow of the compressible gas.”

 

Comment 4:   "Understanding the structural evolution of two-phase fluid flow in fractured rock masses is of great significance for the study of related issues such as underground oil and gas extraction. Therefore, the statements in lines 66-70 need to be reinforced with the following pa-pers to enhance persuasiveness: The Crack Propagation Behaviour of CO2 Fracturing Fluid in Unconventional Low Permeability Reservoirs: Factor Analysis and Mechanism Revelation; Wellhead Stability during Development Process of Hydrate Reservoir in the Northern South China Sea: Evolution and Mechanism."

Response: Thanks a lot for your comment! To enhance the persuasiveness of the statements in lines 66–70, it is essential to reinforce the discussion with relevant literature on the structural evolution of two-phase fluid flow in fractured rock masses, particularly in the context of underground oil and gas extraction. The studies "The Crack Propagation Behavior of CO₂ Fracturing Fluid in Unconventional Low Permeability Reservoirs: Factor Analysis and Mechanism Revelation" and "Wellhead Stability during Development Process of Hydrate Reservoir in the Northern South China Sea: Evolution and Mechanism" provide critical insights into fracture dynamics and reservoir stability. We have added these two references in revised manuscript’s reference No.12 and 13. Integrating these references will strengthen the theoretical foundation, highlighting the broader implications of fracture flow research in subsurface resource development.

Comment 5:   "The applicability of research methodology has been studied by comparing simulation results with experimental results, which is a commonly used approach. In this study, the author compared the simulation results with the experimental results of previous research. However, the manuscript did not provide a validation model or experimental (or simulation conditions), only a comparison between experimental and simulation results. This is difficult to persuade. In addition, the simulation provides the basic theory of fracture flow, while the verification experiment shows obvious pipe flow. Are the two based on the same basic theory?"

Response: Thanks for your comment! The validation in this study was conducted by comparing simulation results with experimental data from previous research, a widely used approach for assessing methodological applicability. However, we acknowledge the concern regarding the absence of a detailed validation model and experimental (or simulation) conditions in the manuscript. To enhance the credibility of the comparison, we will provide additional details on the experimental setup, boundary conditions, and key parameters used in the referenced study.

Comment 6:   "There are some minor issues that need to be addressed by the authors to improve the quality of the manuscript. In Figure 2, what are the physical meanings represented by each color block in the simulation results? Other nephogram also have the same problem.; The conclusion is not a repetition or extension of the results in the abstract, and the conclusion needs to be appropriately modified."

Response: Thanks for your comment! In order to show the physical meaning of each color in the cloud map more clearly, we added color bars in Figs. 2, 3, and 5 in revised manuscript to explain the physical meaning and parameter values represented by different colors. We have modified the conclusion in revised manuscript as follows:

In this study, the effects of two-phase fluid flow rate, surface roughness, and dis-location on gas-water flow structures in rock fractures were investigated using the level set method. The key findings are as follows:

(1)Impact of Two-Phase Fluid Flow Rate

The flow structure within the fracture evolves from slug flow to slug-annular flow and ultimately to annular flow as the water and gas flow rates increase. A stable an-nular flow structure forms only when the water-phase flow rate surpasses a critical threshold. At a constant water-phase flow rate, increasing the gas-to-water flow rate ratio reduces water saturation within the fracture.

(2)Effect of Surface Roughness

Surface roughness disrupts the formation of stable, continuous gas-phase flow channels. Higher roughness increases flow irregularity and hinders annular flow for-mation at low water-phase flow rates. Under identical flow conditions, greater roughness leads to higher water saturation within the fracture.

(3)Effect of Dislocation

Dislocation significantly alters the two-phase flow structure. As dislocation in-creases, the number of slugs in slug flow decreases, slug length increases, and the flow structure becomes more irregular. The slug-annular flow gradually transitions to an-nular flow with increased irregularity. Additionally, the influence of roughness on flow structure intensifies with greater dislocation. Under identical flow conditions, water saturation increases with dislocation in low-roughness fractures, whereas in high-roughness fractures, it initially rises and then declines as dislocation increases.

These findings provide valuable insights into the interplay between flow rates, surface roughness, and dislocation, enhancing the understanding of two-phase fluid flow behavior in fractured rock.

Based on the existing research results, the numerical simulation of fracture gas-water flow can be further extended to the three-dimensional fracture and fracture network, and combined with the machine learning method to predict the fluid flow behavior, which can effectively guide the engineering applications.

Comment 7:   "In almost all experimental results, all curves were plotted based on three data points. In terms of academic rigor, this is not rigorous because using three points cannot accurately describe the patterns obtained from research."

Response: Thanks for your comment! The results in this study were plotted using three data points for each curve. While this provides a basic representation of trends, it may not fully capture the underlying patterns with high accuracy. From an academic rigor standpoint, a greater number of data points would enhance the reliability and statistical robustness of the findings. Future studies should consider increasing the data density to ensure a more comprehensive and precise characterization of the observed flow behaviors.

Reviewer 5 Report

Comments and Suggestions for Authors

This paper presents an interesting numerical study on two-phase fluid flow in fractured rocks, considering the effects of fracture surface roughness and shear displacement. However, there are some points or comments that I would like to ask from authors: 

- The abstract mentions some key findings, but the results section needs to provide a more detailed and quantitative analysis of the simulation results. 

- The introduction effectively highlights the importance of understanding two-phase fluid flow in fractured rock for various applications. However, it could benefit from a clearer articulation of the specific knowledge gap that this study aims to address. 

- The literature review provides a good overview of previous studies on two-phase flow in fractures. However, it could be strengthened by including a more critical analysis of the limitations of existing research and how the current study builds upon or departs from these previous works. Mentioning author contributions would be interesting. 

- The governing equations are clearly presented. However, providing a brief justification for why these specific equations were chosen and how they are applicable to the specific problem being studied would be beneficial.

-The description of the SRA method for generating rough fracture surfaces is adequate, but more details regarding the choice of parameters used in the algorithm would be helpful. 

- The conclusion effectively summarizes the key findings, but it could be enhanced by suggesting specific directions for future research that could further advance the understanding of two-phase flow in fractured rocks. 

Author Response

This paper presents an interesting numerical study on two-phase fluid flow in fractured rocks, considering the effects of fracture surface roughness and shear displacement. However, there are some points or comments that I would like to ask from authors: Response: Thanks a lot for your time reviewing our paper and helping us improve this work! We appreciate it very much!

Comment 1:   "The abstract mentions some key findings, but the results section needs to provide a more detailed and quantitative analysis of the simulation results."

Response: Thanks a lot for your comment! In order to improve the clarity and rigor of the results section, we have performed a more detailed quantitative analysis of the simulation results. This will include specific numerical, statistical comparisons. The quantitative description of the degree of change in water saturation in the fractures is enhanced by the inclusion of quantitative metrics.

Comment 2:   "The introduction effectively highlights the importance of understanding two-phase fluid flow in fractured rock for various applications. However, it could benefit from a clearer articulation of the specific knowledge gap that this study aims to address."

Response: Thanks a lot for your comment! In order to be able to articulate more clearly the specific knowledge gaps that this study aims to address, we have added a literature survey on numerical simulation and summarized and analyzed the methodology and research interests of simulation, among others, in the introduction section in revised manuscript lines 101-117, as follows: “The numerical simulation methods currently used to simulate two-phase fluid flow in rock fractures mainly include the Volume Of Fluid (VOF) method, the lattice Boltzmann (LBM) method, and the level set method [29-32]. Wang et al. [29] investigated the effects of fluid flow rate and wettability on the flow structure of two-phase fluids in 1-d fractures. Guiltinan et al. [30] investigated the effect of heterogeneous wetting proper-ties of 2-d fractures on supercritical carbon dioxide displacement of water based on LBM method. Zhao et al. [31] investigated the effect of wettability heterogeneity on the relative permeability of two-phase flow in porous media using a multiple relaxation time colored gradient LBM model. Huang et al. [32] used the VOF method to analyze the flow characteristics of the gas phase in different fluids at the microscopic scale in a 1D fracture as well as the effect of fluid parameters on the flow pattern. Liu et al. [33] used the level set method to simulate the evolution of the plug structure under the effect of different flow ratios, fracture surface wettability and fracture tortuosity in 1-D fracture. These studies have provided a solid foundation for understanding the evolution of two-phase fluid flow structures in fractures. However, the influence of two-phase fluid flow velocity, surface roughness, and shear displacement on the evolution of two-phase fluid flow structures remains unclear.”

 

Comment 3:   "The literature review provides a good overview of previous studies on two-phase flow in fractures. However, it could be strengthened by including a more critical analysis of the limitations of existing research and how the current study builds upon or departs from these previous works. Mentioning author contributions would be interesting."

Response: Thanks a lot for your suggestion! In order to enhance the completeness of the literature review, we have analyzed the limitations of previous studies in greater detail, highlighting the shortcomings of existing research on two-phase flow in fractures. This includes a discussion of the methodology, findings, and unresolved challenges from previous experimental and numerical simulation work.

 

Comment 4:   "The governing equations are clearly presented. However, providing a brief justification for why these specific equations were chosen and how they are applicable to the specific problem being studied would be beneficial."

Response: Thanks a lot for your comment! To illustrate the rationale for the physical model used in the numerical simulations in this paper, we have added a detailed description of the physical model in lines 221-226 of the revised manuscript.

Comment 5:   "The description of the SRA method for generating rough fracture surfaces is adequate, but more details regarding the choice of parameters used in the algorithm would be helpful."

Response: Thanks for your comment! In order to explain the parameter descriptions in the SRA algorithm in more detail, we have added descriptions the values of Z₂ and Hurst index H in Table 1 of the revised manuscript.

Comment 6:   "The conclusion effectively summarizes the key findings, but it could be enhanced by suggesting specific directions for future research that could further advance the understanding of two-phase flow in fractured rocks."

Response: Thanks for your comment! We have included an outlook on future research directions in lines 486-489 of the revised manuscript as follows: “Based on the existing research results, the numerical simulation of fracture gas-water flow can be further extended to the three-dimensional fracture and fracture network, and combined with the machine learning method to predict the fluid flow behavior, which can effectively guide the engineering applications.”

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The authors have provided some responses on the minor concerns, but not the major concern. I still don't think that the model has been verified properly. Nevertheless, it seems that a proper verification is out of reach at this stage. I will let the editor decide.

Regarding the response to comment 5, I think the author miss the fact that air is compressible. At high speed, i.e. high pressure, air will be compressed and, therefore, the saturation will increase. 

 

Author Response

Author Responses:

Response: Thanks a lot for your time reviewing our paper and helping us improve this work! We appreciate it very much!

Comment 1: &nbsp"The authors have provided some responses on the minor concerns, but not the major concern. I still don't think that the model has been verified properly. Nevertheless, it seems that a proper verification is out of reach at this stage. I will let the editor decide."

Response: Thanks a lot for your comment! We sincerely appreciate the reviewer’s continued time and effort in evaluating our manuscript. We fully understand and respect the reviewer’s concern regarding the verification of the model. In our previous responses and the revised manuscript, we have attempted to address this issue by Optimization of the picture representation as well as the addition of a table of parameter settings for model validation (Table 3 in revised manuscript), we have added a detailed controlled validation of the experimental procedure with Sur et al. [41]. However, as the reviewer rightly pointed out, conducting a more comprehensive or large-scale verification is currently beyond the scope of our available data and resources. Despite these limitations, we believe the current level of verification provides reasonable confidence in the model's capability to simulate the two-phase flow in fractures. Once again, we thank the reviewer for their valuable feedback and leave it to the editor's judgment regarding the suitability of our work for publication.

Reference:

41. Sur, A.; Yang, L.; Liu, D. Experimental and numerical investigation of two-phase patterns in a cross-junction microfluidic chip. PROCEEDINGS OF THE 8TH INTERNATIONAL CONFERENCE ON NANOCHANNELS, MI-CROCHANNELS AND MINICHANNELS, 2010, PTS A AND B 2011, doi: 10.1115/fedsm-icnmm2010-31267

Comment 2: &nbsp"Regarding the response to comment 5, I think the author miss the fact that air is compressible. At high speed, i.e. high pressure, air will be compressed and, therefore, the saturation will increase."

Response: Thank you for your insightful comment! We acknowledge the fact that air is compressible and that its compression at high speed (or high pressure) can lead to an increase in saturation. We also recognize that our previous response may not have explicitly clarified this aspect. In our current model, we have taken into account the compressibility of the air in our simulations. However, under the simulation conditions of this study, the fluid was not under significant high velocity or high pressure where the air was significantly compressed, and the compressibility of the air did not have a significant effect on the water content saturation, which has been proved by Wang et al. [29]. In response to the valuable comments made by the reviewer, we will add two-phase flow simulation under high-speed and high-pressure conditions to our future research to further study the effect of air compressibility on water saturation.

Reference:

29. Wang, Y.; Zhang, Z.; Ranjith, P.G.; Han, X. Flow structure transition and identification of two-phase fluid flow through rough rock fractures. Eur Phys J Plus 2023, 138, doi: 10.1140/epjp/s13360-023-03977-4.

Reviewer 3 Report

Comments and Suggestions for Authors

Authors made good effort to revise the manuscript based on the comments. I have few additional minor cases, including language (I am not an English expert so those are what I found "suspicious" or could not understand):

34 "is widely existed" maybe wrong
44-45 likely incorrect subject-verb basis, not clear is asingle sentence or multiple sentence (check as/are/it/is)
50 roughness and aperture "affect" the geometric properties (I find proper meaning is more like "are examples of" than "affect")
57-58 unclear subject-verb basis
94 extend the reference to [29-33] as listed below in the text
ref [32] order of given name / surname Xin and Huang to fit the text reference
tab.1+fig.1 I am not sure whether I commented this before, there is a conflict either 5mm of 10mm length
2.3 or 3.2 explanation for previous comment 3 could be incorporated into the manusript (one sentence to note the issue) - if I understand well, the added values of saturation change are your response, but their context is not clear.
2.3 the title could also cover the physical parameters (not only the numerical scheme and boundary)
216 I do not understand the word "encryption" in the context. Did you mean adaptive refinement?
220 "the mesh size was checked independently" does not make sense (did you mean that you somehow recorded/reported the final element count and decided which mesh to use?)

Fig.4 I am sorry I made an error in my comment no.9, it should aim to fig.4b and 6b (not 2b). So you revised fig.2 (also fine) but I do not see any revision of fig.4b. My idea was that the nine symbols in the plot are placed in discrete values on axes, so the plot is quite large but the information corresponds to just 3x3 table and could be presented more efficiently (one option, as part of 4a and 6a)

461-467 In my feeling, one feature, for which the models could be used in practice, is the bulk permeability of fracture. I guess such value (flow rate of gas and water versus pressure difference) is also among the model variables. It would be worth to comment how the results are relevant for applications in this context (e.g. is it desired in the CO2 or oil, to operate in slug or in annular regime? can the model help to set e.g. pumping control variables?)

Author Response

Author Responses:

Authors made good effort to revise the manuscript based on the comments. I have few additional minor cases, including language (I am not an English expert so those are what I found "suspicious" or could not understand):

Response: Thanks a lot for your time reviewing our paper and helping us improve this work! We appreciate it very much!

Comment 1: &nbsp"34 ‘is widely existed’ maybe wrong."

Response: Thanks a lot for your comment! We have changed “Rock fracture is widely existed in various types of rock formations, particularly in surface-exposed or shallowly buried regions” to “Rock fractures are widespread in various types of rock formations, particularly in surface-exposed or shallowly buried regions” in line 54 of the revised manuscript.

Comment 2: &nbsp"44-45 likely incorrect subject-verb basis, not clear is asingle sentence or multiple sentence (check as/are/it/is)"

Response: Thank you for your rigorous comment! We have changed “Single fracture as the fundamental element of the fracture network, it is essential to analyze the multiphase fluid flow characteristics within individual fractures is in order to investigate the multiphase fluid flow in fractured rocks.” to “Since single fractures constitute the fundamental units of fracture networks, it is essential to investigate the multiphase fluid flow behavior within individual fractures to better understand flow processes in fractured rock masses.” in lines 44-46 of the revised manuscript.

Comment 3: &nbsp"50 roughness and aperture "affect" the geometric properties (I find proper meaning is more like "are examples of" than "affect")"

Response: Thank you for your rigorous comment! We have changed “Among them, surface roughness and fracture aperture are the most fundamental parameters affecting the geometric properties of fractures and have a critical impact on their fluid flow characteristics.” to “Among them, surface roughness and fracture aperture are key parameters that describe the geometric properties of fractures and critically influence their fluid flow behavior.” in lines 50-52 of the revised manuscript.

Comment 4: &nbsp"57-58 unclear subject-verb basis"

Response: Thank you for your rigorous comment! We have changed “The study of two-phase fluid flow migration patterns in fracture media, thereby providing a foundation for oil and gas extraction” to “Investigating the migration patterns of two-phase fluid flow in fractured media lays the groundwork for enhancing oil and gas extraction efficiency” in lines 57-58 of the revised manuscript.

Comment 5: &nbsp"94 extend the reference to [29-33] as listed below in the text"

Response: Thank you for your rigorous comment! We have expanded the reference in line 94 of the revised manuscript from [29-32] to [29-33].

Comment 6: &nbsp"ref [32] order of given name / surname Xin and Huang to fit the text reference"

Response: Thank you for your rigorous comment! We apologize for using an inappropriate reference format in the text of reference 32, and to ensure the rigor of this study, we have corrected the format of reference 32 in the revised manuscript to the format required by the journal.

Comment 7: &nbsp"tab.1+fig.1 I am not sure whether I commented this before, there is a conflict either 5mm of 10mm length "

Response: Thank you for your insightful comment! We are unsure if this issue was raised in a previous comment, the issue may have been raised by other reviewers, we have carefully reviewed Tab. 1 and Fig. 1. We found that there is a discrepancy regarding the 5mm and 10mm lengths. This has now been clarified, and we have updated the table accordingly.

Comment 8: &nbsp"2.3 or 3.2 explanation for previous comment 3 could be incorporated into the manusript (one sentence to note the issue) - if I understand well, the added values of saturation change are your response, but their context is not clear."

Response: Thank you for your valuable suggestions, and as you suggested, we have added a setting for this condition in section 2.3 (Lines 203-207) of the revised manuscript as follows: “In fact, due to the hydrophilicity of the fracture wall and the consideration about the two-phase fluid flow state in the actual engineering, this paper sets up the two-phase fluid inlet conditions in a segmented way, and divides the fissure inlet into three parts, with the upper 25% and lower 25% as the water-phase inlet, and the mid-dle 50% as the gas-phase inlet.”

Comment 9: &nbsp"2.3 the title could also cover the physical parameters (not only the numerical scheme and boundary)"

Response: Thank you for your insightful comment! To ensure accuracy of expression, we have changed the title of section 2.3 in the revised manuscript from “2.3. Numerical solution scheme and boundary conditions” to “2.3. Numerical Solution Scheme, Boundary Conditions, and Physical Parameters”.

Comment 10: &nbsp"216 I do not understand the word "encryption" in the context. Did you mean adaptive refinement?"

Response: Thank you for your valuable comment! We acknowledge that the use of the term “encryption” in this context was incorrect. In this study, we intended to describe a “local adaptive refinement” of the mesh to ensure the accuracy of the simulation results. We have revised lines 221-222 of the manuscript to reflect this change, and the corrected text is: "In order to ensure the accuracy of the simulation results, local adaptive refinement of the mesh was carried out in this study."

Comment 11: &nbsp"220 "the mesh size was checked independently" does not make sense (did you mean that you somehow recorded/reported the final element count and decided which mesh to use?)"

Response: Thank you for your insightful comment! We agree that the phrase “the mesh size was checked independently” was unclear. What we intended to convey is that we evaluated the final mesh by recording the element count and determining the most suitable mesh resolution for our simulations. We have revised lines 225-226 the manuscript to reflect this more accurately: “The mesh was evaluated by recording the element count and selecting the most appropriate mesh resolution for the simulations.”

Comment 12: &nbsp"Fig.4 I am sorry I made an error in my comment no.9, it should aim to fig.4b and 6b (not 2b). So you revised fig.2 (also fine) but I do not see any revision of fig.4b. My idea was that the nine symbols in the plot are placed in discrete values on axes, so the plot is quite large but the information corresponds to just 3x3 table and could be presented more efficiently (one option, as part of 4a and 6a)"

Response: Thank you for your thoughtful comment. Apologies for the error in my previous comment (#9). I now understand that you were referring to Fig. 4b and Fig. 6b (rather than Fig. 2b). Regarding your suggestion to the optimization, we have optimized Figures 4b and 6b by adding boundary lines between different flow structures. Additionally, we have included relevant images of the actual flow structures within each flow region to better convey specific information from the figures, the revised figures are as follows:

Figure 4(b):

Figure 6(b):

 

Comment 13: &nbsp"461-467 In my feeling, one feature, for which the models could be used in practice, is the bulk permeability of fracture. I guess such value (flow rate of gas and water versus pressure difference) is also among the model variables. It would be worth to comment how the results are relevant for applications in this context (e.g. is it desired in the CO2 or oil, to operate in slug or in annular regime? can the model help to set e.g. pumping control variables?)"

Response: Thank you for your valuable comment! We agree that the bulk permeability of fractures is an important feature for practical applications, such as CO₂ sequestration and oil recovery. While we acknowledge that the flow rate of gas and water versus pressure difference is indeed a key variable in our model, we were unable to fully explore this aspect in the current study. We recognize the relevance of understanding the flow regime (e.g., slug or annular flow) and how the model could assist in setting operational parameters like pumping control variables. Unfortunately, due to the scope of the current work, we are not able to delve deeply into these applications at this stage. However, we plan to address these points in future research, where we will explore the practical implications of the model in greater detail. Thank you again for your thoughtful suggestion, which will guide our future efforts.

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

After the authors' careful reversion, this paper can be accepted for publication now.

Author Response

thanks for your work help us improve this manuscript.

Reviewer 5 Report

Comments and Suggestions for Authors

The paper can be accepted now.

Author Response

thanks for your work help us improve this manuscript.