Study on Applicability of Ball-and-Stick Model in Reservoir Pore-Throat Network Simulation

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Review

Journal: Processes (ISSN 2227-9717)

Manuscript ID: processes-3413687

Type: Article

Title: Study on applicability of ball-and-stick model in reservoir pore-throat network simulation

Section: Advanced Digital and Other Processes

Comments: The ball-and-stick model is no longer applicable, and the capillary model is more suitable. The ball-and-stick model combined with the capillary model can simulate the full scale pore throat network of the reservoir. This study provides a method to calibrate the application zone of ball-stick model and capillary model by using constant velocity mercury injection curve configuration, which has important guiding significance for the simulation of reservoir pore throat network and the study of seepage law.

The ball-and-stick model has been widely used to simulate reservoir pore networks and throats. However, due to the large span of the reservoir pore throat, whether the ball-and-stick model is fully applicable has still not been successfully verified. Authors analyzed the configuration of the constant-velocity mercury injection curve using configuration theory and the hierarchical analysis method. The suitability of the ball-and-stick model in simulating the reservoir pore-throat network was discussed by interpreting the information about the reservoir pore-throat structure contained in the configuration. Authors' findings that there are two areas of configuration A and B on the constant mercury injection rate curve. In configuration area A, the mercury saturation of the pore, pore-channel and throat increased monotonically with increasing mercury inlet pressure, indicating that the pore-channel and throat coexist in this configuration area, and the pore-to-throat ratio is greater than 1, and the ball-and-stick model applies. In configuration area B, mercury saturation in pores and throats increased monotonically with increasing mercury inlet pressure, while mercury saturation in the pore channel remained unchanged, which indicated, according to the authors, that this configuration area is mainly throats with a pore-to-throat ratio of 1.

According to Authors, the ball-pattern model is no longer applicable, and the capillary model is more suitable. The ball-pattern model combined with the capillary model can simulate the full-scale network of the reservoir pore throat. Authors' research by the zone calibration method of the application of the ball-stick model and capillary model using a constant velocity mercury injection curve configuration, which is important for simulating the reservoir pore throat network and studying the seepage law.

 

Decision: The article needs supplementation and re-review.

1. On lines 94-104, no literature sources are given to support the accepted theses.

2. The research was conducted on only 3 samples. This is not enough in the reviewer's opinion. For isotropic and homogeneous rocks, 5-7 samples are usually studied. Here, the results of testing 3 samples are shown, with the similarity of mercury pressure values for samples 2 and 3 and different for sample 1 clearly visible. The authors should present the results of testing for more samples.

3. Line 107 includes a brief description of Yishan Slope. Some sort of location map on a map of China is missing so that we know where it is.

4. In line 110, Authors provide average porosity and permeability. Authors then select samples. But no criteria are given for the Authors' selection of samples.

5. The laboratory tests are not documented in any way. There are no photos of the tests, no photos of the samples, no photos of the test apparatus/test stand.

6. Figure 1. The description lacks an explanation of why for the “Pore channel mercury injection curve” the characteristics end at lower values of “Mercury inlet pressure.”

7. In line 156, Authors refer to the use of the Washburn equation, but in no way state either the equation or how they applied it.

8. Further analysis is done only for Sample 1#. This is very weak. There is no justification why only for Sample 1#, why not for the other samples 2# and 3#, well, and why only for three samples.

9.The justification of Figure 4 is weak if it was developed only on the basis of the results of Sample 1#? (because the article does not include the results of the other samples).

10. In the context of the description of Figure 4, the division in Figure 2 into “Configurational region A and B” is hardly proven. No strong mathematical / analytical / statistical justification is given for the “Mercure inlet pressure” limit of 4MPa.

11. It is not clear whether the breakdown of the “Pore-throat combination” in Figure 4 is an achievement of the Authors or a citation, because as I wrote, if these are conclusions based on Sample 1# then the documentation of this is insufficient.

 

In summary, the article needs major additions, which are given in points 1-11.

  

Editorial errors noticed in *.pdf.

Author Response

Decision: The article needs supplementation and re-review.

1. On lines 94-104, no literature sources are given to support the accepted theses.Reply:Revised， in the Introduction,(33-125)
2. The research was conducted on only 3 samples. This is not enough in the reviewer's opinion. For isotropic and homogeneous rocks, 5-7 samples are usually studied. Here, the results of testing 3 samples are shown, with the similarity of mercury pressure values for samples 2 and 3 and different for sample 1 clearly visible. The authors should present the results of testing for more samples.Reply:Revised，Experimental units were added (only 3 samples were made).
3. Line 107 includes a brief description of Yishan Slope. Some sort of location map on a map of China is missing so that we know where it is.Reply:Revised，in 2.1 Characteristics of constant velocity mercury injection curve(127-160), added map and sample location.
4. In line 110, Authors provide average porosity and permeability. Authors then select samples. But no criteria are given for the Authors' selection of samples.Reply:Revised，the criteria for sample selection are given, in the 2.1 Characteristics of constant velocity mercury injection curve(127-160).
5. The laboratory tests are not documented in any way. There are no photos of the tests, no photos of the samples, no photos of the test apparatus/test stand.Reply:Revised，added a photo of the sample,in the 2.1 Characteristics of constant velocity mercury injection curve(127-160).
6. Figure 1. The description lacks an explanation of why for the “Pore channel mercury injection curve” the characteristics end at lower values of “Mercury inlet pressure.”Reply:Revised，in the 2.1 Characteristics of constant velocity mercury injection curve(127-160).
7. In line 156, Authors refer to the use of the Washburn equation, but in no way state either the equation or how they applied it.Reply:Revised, in the 3.1. The pore throat structure information behind the curve configuration(183-232)
8. Further analysis is done only for Sample 1#. This is very weak. There is no justification why only for Sample 1#, why not for the other samples 2# and 3#, well, and why only for three samples.Reply:Revised,in the 4.2. The significance of capillary model for the simulation of pore-throat network (321-400).(Statistical analysis of all sample configurations).

    

9.The justification of Figure 4 is weak if it was developed only on the basis of the results of Sample 1#? (because the article does not include the results of the other samples).Reply:Revised,in the 4.2. The significance of capillary model for the simulation of pore-throat network (321-400).(Statistical analysis of all sample configurations).

10. In the context of the description of Figure 4, the division in Figure 2 into “Configurational region A and B” is hardly proven. No strong mathematical / analytical / statistical justification is given for the “Mercure inlet pressure” limit of 4MPa. Reply:revised, in the 2.2. Constant velocity mercury injection curve configuration(161-181),(Added the description of the division standard).

     

11. It is not clear whether the breakdown of the “Pore-throat combination” in Figure 4 is an achievement of the Authors or a citation, because as I wrote, if these are conclusions based on Sample 1# then the documentation of this is insufficient.Reply:revised,in the 3.2. Reservoir pore throat structure model and applicability of ball-and-stick model (233-283),(pore-throat combination is cited, standard reference).

     

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

This paper addresses the simulation of reservoir pore-throat networks using different models, primarily the ball-and-stick model and capillary model. The study explores the structure of pore-throat networks through mercury injection experiments, utilizing constant velocity mercury injection curves to interpret the distribution of reservoir pores, pore channels, and throats. The paper identifies two configuration regions (A and B) in the reservoir based on throat radius and evaluates the applicability of the ball-and-stick model and capillary model in these regions. The research suggests that a hybrid approach combining both models is more suitable for simulating the pore-throat network in certain configurations.

 

Suggestions for the Paper:

1. Introduction Section:

Clarification of Key Terms: The introduction mentions several key terms like the ball-and-stick model, pore-throat network, and capillary model, which are central to the paper. However, these terms are not clearly defined for readers who may not be familiar with them. To improve clarity, it would be helpful to provide concise definitions or a brief overview of each model. For instance:

 

The ball-and-stick model can be explained as a simplified representation of the pore-throat network, where the balls represent pores, and the sticks represent throats or connections between them.

The capillary model could be briefly explained in terms of its use in simulating fluid behavior in porous media, particularly when dealing with small pores and low permeability conditions.

Explanation of "Configuration": The term configuration is used in a specific context, but its meaning is not fully clarified. It seems to refer to a topological property or relationship between parts of a network, but this concept could be introduced with a brief explanation. It would be useful to provide a definition or background on configuration theory, especially its relevance to pore-throat networks and why it is significant for understanding reservoir characteristics.

 

Expanding on Previous Research: The introduction briefly mentions previous work on the ball-and-stick model but lacks a more detailed discussion of its limitations. It would be beneficial to expand on this by mentioning what earlier studies have found regarding the applicability of the ball-and-stick model to pore-throat networks at varying scales. Specifically, how do these studies fall short in addressing complex pore-throat structures in reservoirs? By discussing the gaps in the current research, the introduction can better highlight how the current study fills those gaps.

 

Comparison with Previous Work: To give readers a clearer understanding of the progression of research in this field, it would be helpful to provide more detailed comparisons with previous studies. Highlighting the contributions of the current study within the broader context of reservoir simulation would underline the novelty and importance of the research.

 

2. Results Section:

Clarify Ball-and-Stick Model Limitations: In the section discussing the ball-and-stick model’s applicability, it’s essential to clarify why the model fails in certain regions (e.g., the B region) and why the capillary model is more suitable in these cases. Readers would benefit from a clearer explanation of the limitations of the ball-and-stick model, especially in regions with micropores and microthroats where fluid dynamics are governed by capillary forces. For example, the ball-and-stick model may oversimplify the behavior of fluid in fine throats, which is more accurately represented by the capillary model.

 

Discuss Hybrid Model Benefits in More Detail: When concluding that a combination of the ball-and-stick and capillary models is more appropriate, the paper should further explain how these models complement each other. It would be useful to describe the specific aspects of reservoir simulation that each model handles better. For example, the ball-and-stick model might be more effective for simulating larger pore structures and flow through interconnected pores, while the capillary model could excel at representing the behavior of fluids in smaller, low-permeability regions. Discussing under what conditions one model might dominate over the other would provide a more nuanced understanding of the models’ relative advantages.

 

3. Discussion Section:

Deeper Explanation of Capillary Model Applicability: The paper does a good job of addressing the relationship between the capillary model and reservoir physical properties, but it could go further in explaining why the capillary model works better in B-configuration regions, which have poor reservoir properties. A more detailed explanation of how the pore-throat structure in these regions impacts fluid dynamics would strengthen the argument. For instance, the small pore sizes and narrow throats in the B-region could lead to higher capillary forces, making the capillary model more appropriate for simulating fluid behavior.

 

Why the Ball-and-Stick Model Works Well for A-Configuration: The discussion section mentions the suitability of the ball-and-stick model for A-configuration but only briefly touches on the reasons for this. A more detailed explanation of why the model is effective in this configuration (beyond the pore-throat ratio argument) would improve the depth of the discussion. This could involve describing how the larger pores and throats in this region allow for more efficient fluid flow, which aligns well with the assumptions of the ball-and-stick model.

 

Implications of Movable Micropores in B-Configuration: When the paper states that "a large part of the micropores and microthroats in the B-configuration region are in the movable range," it would be helpful to elaborate on the implications of this for oil and gas extraction. Specifically, how do these movable pores and throats affect the efficiency of oil recovery? The paper could explore how the ability of fluids to move through smaller, more tortuous pathways in the B-configuration might lead to improved oil recovery, particularly under conditions where capillary forces play a dominant role.

 

Practical Implementation of Models: While the paper compares the two models in terms of their theoretical applicability to different configurations, it would be helpful to also discuss the practical challenges associated with each model. For example, the ball-and-stick model may be computationally simpler but may not capture the complexities of fine pore structures, while the capillary model may be more accurate but computationally expensive. A brief discussion of the trade-offs between these models in real-world applications, such as computational cost and model complexity, would add value to the paper.

 

Overall, the paper provides a valuable contribution to understanding reservoir pore-throat networks using both the ball-and-stick and capillary models. By addressing the suggestions above, particularly regarding the clarification of key concepts, deeper analysis of model applicability, and practical implications for oil recovery, the paper will be even more informative and accessible to readers from a range of disciplines.

Author Response

1. 介绍部分：

关键术语的澄清：引言提到了几个关键术语，如球棒模型、孔喉网络和毛细管模型，它们是论文的核心。但是，对于可能不熟悉这些术语的读者来说，这些术语没有明确的定义。为了提高清晰度，提供每个模型的简明定义或简要概述会很有帮助。例如：

 

球棒模型可以解释为孔喉网络的简化表示，其中球代表孔，棒代表喉咙或它们之间的连接。

回复：已修订，在引言中。(34-125)

毛细管模型可以简要解释它在模拟多孔介质中的流体行为方面的用途，特别是在处理小孔和低渗透性条件时。

回复：已修订，在引言中。(34-125)

“配置”说明：术语配置用于特定上下文，但其含义尚未完全阐明。它似乎指的是网络各部分之间的拓扑属性或关系，但可以通过简要说明来介绍这个概念。提供构型理论的定义或背景将很有用，尤其是它与孔喉网络的相关性以及为什么它对理解储层特征具有重要意义。

回复：已修订，在引言中。(34-125)

 

扩展以前的研究：引言简要提到了以前关于球棒模型的工作，但缺乏对其局限性的更详细讨论。通过提及早期研究发现的关于球棒模型在不同尺度上对孔喉网络的适用性，将对此进行扩展将是有益的。具体来说，这些研究在解决储层中复杂的孔喉结构方面有何不足？通过讨论当前研究中的空白，引言可以更好地突出当前研究如何填补这些空白。

回复：已修订，在引言中。(34-125)

与前人工作的比较：为了让读者更清楚地了解该领域的研究进展，提供与前人研究的更详细比较会有所帮助。在油藏模拟的更广泛背景下强调当前研究的贡献将强调该研究的新颖性和重要性。

回复：已修订，在引言中。(34-125)

2. 结果部分：

阐明球棒模型的限制：在讨论球棒模型的适用性的部分中，必须阐明为什么模型在某些区域（例如 B 区域）失败，以及为什么毛细管模型更适合这些情况。读者将受益于对球棒模型局限性的更清晰解释，尤其是在流体动力学受毛细管力控制的微孔和微喉区域。例如，球棒模型可能会过度简化液体在细喉中的行为，而毛细管模型可以更准确地表示这一点。

回复： 修订，在 4.1 中。球棒模型模拟的储层孔喉网破坏原因（285-320）

 

更详细地讨论混合模型的好处：当得出结论认为球棒和毛细管模型的组合更合适时，本文应进一步解释这些模型如何相互补充。描述每个模型更好地处理储层模拟的特定方面会很有用。例如，球棒模型可能更有效地模拟较大的孔隙结构和流经互连孔隙的流动，而毛细管模型可能擅长表示较小、低渗透性区域中流体的行为。讨论一个模型在什么条件下可能优于另一个模型，将有助于更细致地理解模型的相对优势。

回复： 修订，在 3.2 中。储层孔喉结构模型及球棒模型适用性 （233-283）

 

3. 讨论部分：

毛细管模型适用性的更深入解释：本文在解决毛细管模型与储层物理特性之间的关系方面做得很好，但它可以进一步解释为什么毛细管模型在储层特性较差的 B 型区域效果更好。更详细地解释这些区域的孔喉结构如何影响流体动力学将加强这一论点。例如，B 区的小孔径和狭窄的喉部可能导致更高的毛细管力，使毛细管模型更适合模拟流体行为。

回复： 修订，在 3.2 中。储层孔喉结构模型及球棒模型适用性 （233-283）

为什么球棒模型适用于 A 配置：讨论部分提到了球棒模型对 A 配置的适用性，但仅简要地触及了其原因。更详细地解释为什么该模型在这种配置中有效（超越孔喉比论点）将提高讨论的深度。这可能涉及描述该区域中较大的孔隙和喉部如何实现更高效的流体流动，这与球棒模型的假设非常吻合。

回复： 修订，在 3.2 中。储层孔喉结构模型及球棒模型适用性 （233-283）

B 型中可移动微孔的含义：当论文指出“B 型区域中的大部分微孔和微喉都在可移动范围内”时，详细说明这对石油和天然气开采的影响会有所帮助。具体来说，这些可移动的孔隙和喉咙如何影响石油回收的效率？本文可以探讨流体在 B 构型中通过更小、更曲折的路径的能力如何提高石油采收率，尤其是在毛细管力起主导作用的条件下。

回复： 修订，在 4.2 中。毛细管模型对孔喉网络模拟的意义

(321-400)

模型的实际实施：虽然本文根据两种模型对不同配置的理论适用性进行了比较，但讨论与每种模型相关的实际挑战也会有所帮助。例如，球棒模型在计算上可能更简单，但可能无法捕捉到细孔结构的复杂性，而毛细管模型可能更准确，但计算成本更高。简要讨论这些模型在实际应用中的权衡，例如计算成本和模型复杂性，将增加本文的价值。

回复： 修订，在 4.3 中。协同仿真的思路与挑战 （401-419）

总的来说，该论文为使用球棒和毛细管模型理解储层孔喉网络做出了有价值的贡献。通过解决上述建议，特别是关于关键概念的澄清、对模型适用性的深入分析以及对石油采收的实际影响，本文将提供更多信息，并为来自各个学科的读者提供更多信息。

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Dear Editors and Authors,

Below are points from my previous review that have not been clarified so far.

First of all, the main complaint is the lack of documentation of the studies / tests, the small number of samples (only 3) and the de facto analysis presented for only one sample.

 

2. The research was conducted on only 3 samples. This is not enough in the reviewer's opinion. For isotropic and homogeneous rocks, 5-7 samples are usually studied. Here, the results of testing 3 samples are shown, with the similarity of mercury pressure values for samples 2 and 3 and different for sample 1 clearly visible. The authors should present the results of testing for more samples.

Update: The photo does not show samples only fragments of drill cores. No photo documentation of either the prepared samples or the samples before or after testing.

5. The laboratory tests are not documented in any way. There are no photos of the tests, no photos of the samples, no photos of the test apparatus/test stand.

Update: W dalszym ciagu nie ma żadnego udokumentowania stanowisk badawczych, aparatury, przeprowadzania badań.

8. Further analysis is done only for Sample 1#. This is very weak. There is no justification why only for Sample 1#, why not for the other samples 2# and 3#, well, and why only for three samples.

9.The justification of Figure 4 (5) is weak if it was developed only on the basis of the results of Sample 1#?

Update: It is not possible, in my opinion, to formulate such universal and large conclusions on the basis of the study of three, in fact one sample.

Decision: Again, I ask the authors to complete / document the research part and the characteristics presented.

The article can be published only after these errors are corrected.

Author Response

First of all, the main complaint is the lack of documentation of the studies / tests, the small number of samples (only 3) and the de facto analysis presented for only one sample.

Reply: Modified: In this paper, the open literature of constant velocity mercury injection test of 38 samples from a wider range of Ordos Basin (Longdong, Jiyuan, Xifeng, Nanliang-Huachi) and horizon (Chang 6, Chang 7 and Chang 8 oil groups) by scholars (Li Weicheng et al. 2012, He Tao et al. 2013, Zhang Xiaohui et al. 2021) is supplemented, which is of general significance for the characteristics and variation rules of constant velocity curves. It does not change because of different regions or layers, and also provides a basis for configuration division.

2. The research was conducted on only 3 samples. This is not enough in the reviewer's opinion. For isotropic and homogeneous rocks, 5-7 samples are usually studied. Here, the results of testing 3 samples are shown, with the similarity of mercury pressure values for samples 2 and 3 and different for sample 1 clearly visible. The authors should present the results of testing for more samples. Reply:Modified, The characteristics and change rules of constant velocity curves have universal significance, and the number of curves is not the main influencing factor.

Update: The photo does not show samples only fragments of drill cores. No photo documentation of either the prepared samples or the samples before or after testing.

Modified: Core debris pictures removed; But unfortunately, the test samples and related test pictures could not be provided.

5. The laboratory tests are not documented in any way. There are no photos of the tests, no photos of the samples, no photos of the test apparatus/test stand.

Reply:This paper mainly uses the test result data.

8. Further analysis is done only for Sample 1#. This is very weak. There is no justification why only for Sample 1#, why not for the other samples 2# and 3#, well, and why only for three samples. Reply: Modified: The configuration diagram 2# and 3# and the distribution curves of pores, pore channels and throats are added;

9.The justification of Figure 4 (5) is weak if it was developed only on the basis of the results of Sample 1#?

 Instructions: The regularity of configuration does not change with the number of samples.

 

Author Response File: Author Response.docx

Round 3

Reviewer 1 Report

Comments and Suggestions for Authors

Dear Editors and Authors,
I have no further comments after the clarifications and corrections sent by the Authors.
The article can be published.
Thank you for the clarifications and replies.
Yours faithfully.