The Problem of Formation Destruction in Carbon Dioxide Storage: A Microscopic Model

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The article is quite interesting. It offers a detailed microscopic model for studying the long-term processes of rock dissolution during geological CO₂ storage. The model takes into account key chemical reactions, diffusion, phase saturation changes, and the evolution of the porous structure. It is generally well written, but the authors should consider the following issues: 

1. The authors state, "A cube with an edge of 1 μm was selected for modeling," but provide no justification for this scale or its relevance to real reservoir pores, which vary widely in size.
2. Justify the thickness of the transition layer d.
3. The article lacks clearer explanations of complex concepts and a more detailed discussion of the limitations of the model, especially with regard to the assumption of uniformity of the porous medium. In addition, a more detailed description of computational methods could enhance the article.

After eliminating these comments and careful revision, the article can become a valuable publication in the field of modeling geological carbon storage.

Author Response

The authors would like to thank the distinguished Reviewer for his valuable comments, which were all taken into account in order to improve our paper.

Comment 1. The authors state, "A cube with an edge of 1 μm was selected for modeling," but provide no justification for this scale or its relevance to real reservoir pores, which vary widely in size.

The subsection 2.2 "An object for testing the model" was introduced into the Section 2 with the text included:

"A cube with an edge of 1 $\mu m$ was selected for modeling. The cube is filled with rock with a porosity of 0.33. According to the results of laboratory studies of core samples from the Cenomanian deposit, the effective pore diameter lies in the range of 0.01 $\mu m$ -- 0.2 $\mu m$. These data justify the choice of the computational domain size, since it corresponds to 10 -- 100 times the pore diameter. Note that the volume of one calcite molecule is $12.295∙10^{-12} \mu m^3$. Thus, the computational domain is, on the one hand, large enough to visualize the chemical processes in the pores, and on the other hand, small enough that the number of grid nodes with a step of $10^{-2} \mu m$ is acceptable for numerical calculations on a personal computer, in particular with the use of distributed computing using CUDA technology. "

Comment 2. Justify the thickness of the transition layer d.

The text was introduced into the Section 2.5 (the 3^d paragraph):

To obtain an approximate estimate of the transition layer thickness, we used the results from the research~\cite{Afanasyev(2020)}, which presents modeling of ground displacement in geological porous media in petroleum reservoirs. That study includes a numerically derived model of the reservoir boundary structure. We assume that the widths of boundary (transition) layers in different porous media are likely to be of the same order of magnitude. Therefore, we adopted the transition layer thickness value of $d \approx 0.5$ km as it is reported in that work.

Comment 3. The article lacks clearer explanations of complex concepts and a more detailed discussion of the limitations of the model, especially with regard to the assumption of uniformity of the porous medium. In addition, a more detailed description of computational methods could enhance the article.

1) The concepts of saturation and porosity were defined and highlighted in separate lines, respectively, in the sections 2.1 "An object for testing the model" and 2.3. "The choice of the model equations"

2) We included the model limitations in a separate paragraph in the Conclusion section

3) The text was included in the end of a new Section 3.1. Parameters for the Numerical Implementation

"For the numerical implementation of the proposed algorithm, a C++ code was developed using CUDA-based parallel computing technology. The computations were carried out using the Method of Lines in combination with a one-stage Rosenbrock scheme with a coefficient of 1/2, incorporating factorization with respect to the spatial variables"

Reviewer 2 Report

Comments and Suggestions for Authors

Revision Report
Manuscript Title: The problem of formation destruction in carbon dioxide storage:
a microscopic model
Authors: Natalia Levashova , Pavel Levashov Dmitry Erofeev  and Alla Sidorova
Overall Evaluation:

The manuscript focuses on in-depth study of the modern trend aimed at low-carbon energy, the issue of CO2 utilization arises. One of the most interesting natural objects of CO2 disposal are
layers located within the boundaries of terrigenous sedimentary formations of oil and
gas basins and coal basins. It is assumed that CO2 will be stored in this form indefinitely. 
However, as a result of carbon dioxide dissolution in the water contained underground,
the pH level decreases and part of the formation may dissolve, which will change the
structure of the earth’s crust in the injection area. This process is quite long (presumably
can take tens and even hundreds of years), and to understand its possible consequences,
It is worth using mathematical modeling.

 I advise the authors to revise the manuscript thoroughly to enhance its quality and align it with the standards of the field.

1) The full term should be provided when an abbreviation first appears in the text.

2) Authors are advised to revise the graphics from Figure 3 to Figure 5. The parameter values used for generating these figures are not provided. Additionally, please avoid using the color black, as it obscures the details and hinders proper interpretation of the figures.

3) Paragraph 5 and Paragraph 6 should be consolidated to provide a comprehensive description of the simulation results.

4) Please include a dedicated section explaining the significance and interpretation of these figures. The 2D plots should also be improved for better clarity and presentation. The authors are strongly advised to completely revise these figures with the appropriate parameter details and proper justification.

5) The manuscript should be checked carefully to improve the English expression.

 

Comments on the Quality of English Language

The English could be improved to more clearly express the research

Author Response

We are very grateful to the distinguished Reviewer for his valuable comments, which we took into account in order to improve our manuscript.

Comment 1. The full term should be provided when an abbreviation first appears in the text.

Words similar to the abbreviations in the introduction are not actually abbreviations. These are the names of the packages used for mathematical modeling. The names were invented by the developers based on some personal considerations, and cannot be deciphered. In order not to annoy readers, we have removed them from the text, replacing them with some explanations regarding the essence of these packages.

Comment 2. Authors are advised to revise the graphics from Figure 3 to Figure 5. The parameter values used for generating these figures are not provided. Additionally, please avoid using the color black, as it obscures the details and hinders proper interpretation of the figures.

1) We have created a separate Section 3.1. Parameters for the Numerical Implementation  in which we have specified all the parameters necessary for numerical calculation.

2) The black color was replaced by brown

Comment 3.  Paragraph 5 and Paragraph 6 should be consolidated to provide a comprehensive description of the simulation results.

We have combined the results and the discussion into one section.

Comment 4.  Please include a dedicated section explaining the significance and interpretation of these figures. The 2D plots should also be improved for better clarity and presentation. The authors are strongly advised to completely revise these figures with the appropriate parameter details and proper justification.

We have included a detailed explanation of what is drawn on two-dimensional graphs in section "Results and Discussion". We also made additional one-dimensional graphs.

Comment 5.  The manuscript should be checked carefully to improve the English expression.

The English has been corrected by a professional translator.

 

Reviewer 3 Report

Comments and Suggestions for Authors

This manuscript presents a pore-scale model to simulate formation changes during CO₂ geological storage, with a focus on geochemical interactions. The study addresses an important topic, but several issues need to be clarified or improved:

1. The title "formation destruction" is too broad and could be misleading. Formation degradation can result from both physical and chemical mechanisms. Since the study focuses specifically on chemical dissolution (e.g., calcite dissolution induced by CO₂-acidified water), the title should be revised to reflect the geochemical nature of the formation degradation. This clarification should also be explicitly stated in the abstract and introduction.
2. While the Introduction discusses various numerical modeling efforts, it neglects to address experimental studies at the pore scale. It is recommended to briefly introduce laboratory methods such as high-pressure microfluidic experiments, especially considering their increasing relevance in validating pore-scale reactive transport processes. For example: Zhang J, Song Z, Zhou K, et al. Pore-Scale Analysis of the Permeability and Effective Thermal Conductivity of Hydrate-Bearing Sediments Based on a High-Pressure Microfluidics Approach. Energy & Fuels, 2024, 38(22): 22192-22204.
3. Line 101 states that the reservoir temperature is between 18–36 °C at a depth of 1100–1700 m. This seems underestimated, as typical formation temperatures at these depths are often higher. Please clarify the basis for this assumption and whether it corresponds to a specific geological context.
4. Equations (3)–(5) contain many parameters (e.g., K, t*, S_CO2) that are not sufficiently explained. The definition and physical meaning of each should be clearly described in the text, particularly the derivation and setting of the calcite dissolution rate constant and specific surface area.
5. Figure 5 presents simulation results over 1000 years, whereas Figure 6 shows porosity evolution over only 1 year. This inconsistency should be addressed. Why is porosity only shown for 1 year? How does it evolve beyond this time frame, especially given the timescale in Figure 5?
6. The study would benefit from more quantitative analysis. Currently, only porosity changes are shown in Figure 6. The authors should provide additional plots or data showing temporal evolution of key parameters, such as ion concentrations, dissolution volume, and spatial heterogeneity in dissolution patterns. These will help substantiate the conclusions.

Author Response

The authors would like to thank the distinguished Reviewer for his valuable comments, which were all taken into account in order to improve our article.

Comment 1. The title "formation destruction" is too broad and could be misleading. Formation degradation can result from both physical and chemical mechanisms. Since the study focuses specifically on chemical dissolution (e.g., calcite dissolution induced by CO₂-acidified water), the title should be revised to reflect the geochemical nature of the formation degradation. This clarification should also be explicitly stated in the abstract and introduction.

The title was changed to 

The problem of calcite destruction by CO2-acidified water in carbon dioxide storage: a microscopic model.

The text was included into the Abstract and Introduction:

"In this paper, we present an applied mathematical model that describes a complex set of processes, such as mass transfer, surface chemical reactions, and changes in the configuration of the pore space of a geological formation at the microscopic level. In order to ensure that the model is not divorced from reality, we relied on geological exploration data concerning the composition and structure of the pore space, characteristic of the Cenomanian suite in the north of Western Siberia. We introduced in the model the main chemical reactions based on calcium carbonate (calcite, $CaCO_3$) characteristic of the Cenomanian deposits. The model describes the processes of $CO_2$ dissolution in the pore space. Changes in the concentrations of $H^+$, $Ca^{2+}$, $HCO_3^-$ ions are considered. The input parameters of the model are based on experimental data."

Comment 2. While the Introduction discusses various numerical modeling efforts, it neglects to address experimental studies at the pore scale. It is recommended to briefly introduce laboratory methods such as high-pressure microfluidic experiments, especially considering their increasing relevance in validating pore-scale reactive transport processes. For example: Zhang J, Song Z, Zhou K, et al. Pore-Scale Analysis of the Permeability and Effective Thermal Conductivity of Hydrate-Bearing Sediments Based on a High-Pressure Microfluidics Approach. Energy & Fuels, 2024, 38(22): 22192-22204.

In the Introduction, a paragraph (12^th paragraph) was introduced with an overview of works containing studies of the rock at the microscopic level. The specified work was cited (reference [18]).

Comment 3. Line 101 states that the reservoir temperature is between 18–36 °C at a depth of 1100–1700 m. This seems underestimated, as typical formation temperatures at these depths are often higher. Please clarify the basis for this assumption and whether it corresponds to a specific geological context.

 Based on thermometric measurements conducted in the Cenomanian deposits of Northwestern Siberia, the reservoir temperature is estimated to be in the range of +18$^\circ$C to +36$^\circ$C, and the pressure varies from 9 to 15 MPa. 

The above text was included into the 1^st paragraph of the Subsection 2.3 "The choice of the model equations".

Comment 4. Equations (3)–(5) contain many parameters (e.g., K, t*, S_CO2) that are not sufficiently explained. The definition and physical meaning of each should be clearly described in the text, particularly the derivation and setting of the calcite dissolution rate constant and specific surface area.

Indeed, there are a lot of parameters, and we apologize for posting them in a continuous text, making the text unreadable. In the new version, we divided our explanations into sub-items, which we liked much more and introduced a new subsection 2.4 "The explanation of the terms in the equation system (4) – (6)". Thank you for the useful comment.

Comment 5.  presents simulation results over 1000 years, whereas Figure 6 shows porosity evolution over only 1 year. This inconsistency should be addressed. Why is porosity only shown for 1 year? How does it evolve beyond this time frame, especially given the timescale in Figure 5?

We have included detailed explanations regarding the model's ability to account for different time scales in the Results and Discussion section as explanations to Figures 7 and 8.

Comment 6. The study would benefit from more quantitative analysis. Currently, only porosity changes are shown in Figure 6. The authors should provide additional plots or data showing temporal evolution of key parameters, such as ion concentrations, dissolution volume, and spatial heterogeneity in dissolution patterns. These will help substantiate the conclusions.

The Results and Discussion section included Figure 4, which contains the change in concentrations over time, and Figure 5, which shows the distribution along a selected line crossing the pore space.

Reviewer 4 Report

Comments and Suggestions for Authors

Dear Authors,

The manuscript presents an interesting study; however, there are several significant concerns, particularly regarding the micromodel design and its geological context. I outline my main comments below:

1. Lack of Geological Context: After the introduction, the manuscript shifts directly into mathematical modeling without providing any geological rationale or background for the micromodel. This weakens the relevance and applicability of the study.

2. Unclear Geological Target: It is not clear which type of geological formation the study focuses on—whether sandstone, carbonate, or another type. Clarifying the geological setting is essential for understanding the relevance of the micromodel design.

3. Missing Micromodel Design Rationale: The manuscript does not include any explanation or justification for how the micromodel was constructed. Without this, it is difficult to assess the validity or realism of the simulation results.

4. Recommendation: I strongly recommend the authors include a dedicated section describing the micromodel setup in detail. This should explain the design parameters, the geological motivation behind the design, and why this specific micromodel was chosen for the study. This context is crucial and should be presented before the modeling results.

In its current form, the manuscript lacks critical methodological information and cannot be fully evaluated. I encourage the authors to revise accordingly.

Thanks 

 

Author Response

Many thanks to the distinguished reviewer for the helpful comments that made it possible to give the paper a brighter look.

Comment 1. Lack of Geological Context: After the introduction, the manuscript shifts directly into mathematical modeling without providing any geological rationale or background for the micromodel. This weakens the relevance and applicability of the study.

A subsection "An object for testing the model" with a brief description of the Cenomanian deposit in Western Siberia was included in section 2. Based on the data on the geological composition of the Cenomanian deposit rocks, our model was developed.

Comment 2. Unclear Geological Target: It is not clear which type of geological formation the study focuses on—whether sandstone, carbonate, or another type. Clarifying the geological setting is essential for understanding the relevance of the micromodel design.

In Subsection 2.1 "An object for testing the model"  The text was included:

"According to scientific assessments, the Cenomanian gas reserves are gradually being depleted. Once production has ceased, the depleted reservoir may be repurposed as a geological $CO_2$ storage site. This prospect necessitates a detailed investigation and modeling of $CO_2$ storage processes, utilizing existing data on the geological composition and microscopic structure of the Cenomanian reservoir rocks".

Comment 3. Missing Micromodel Design Rationale: The manuscript does not include any explanation or justification for how the micromodel was constructed. Without this, it is difficult to assess the validity or realism of the simulation results.

A subsection "Micromodel setup" has been added to section 2, in which we explained in detail how we designed the micromodel based on experimental exploration data regarding the pore size of the rock core sampled at the Cenomanian deposit.

Comment 4. Recommendation: I strongly recommend the authors include a dedicated section describing the micromodel setup in detail. This should explain the design parameters, the geological motivation behind the design, and why this specific micromodel was chosen for the study. This context is crucial and should be presented before the modeling results.

The design of the micromodel and its rationale were separated into a separate section "Micromodel setup"

 

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

After corrections, the article is ready for publication.

Reviewer 3 Report

Comments and Suggestions for Authors

The authors have made adequate revisions. it can be recommended now.

Reviewer 4 Report

Comments and Suggestions for Authors

Dear Author 

i am satisfied with the changes and will recommend publication. 

Thanks