A Cement Bond Quality Prediction Method Based on a Wide and Deep Neural Network Incorporating Embedded Domain Knowledge
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe article proposes an analytical method that allows estimating the bonding quality of the cement slurry in the cementing process of oil wells with a percentage of effectiveness higher than 80%, which is of great interest and relevance for this area of research and industry. However, it does not consider variables of mechanical character and design of the slurry in question, these variables could strongly influence the percentage of effectiveness of the model presented. It is suggested to the authors to consider the following aspects.
1.-Methodology, page 19, lines 103 and 104, “(such as cement slurry density, viscosity, preflush density, and slurry flow rate) directly impact cement bond quality”. This statement should be supported with bibliographic citations.
2.- Why is not considered in the analysis any mechanical parameter of bond at laboratory level made to a cement slurry of the same characteristics as the one injected in the well? It would be prudent to include this variable or justify why it is not considered in this analysis.
3.- Neither is the water-cement ratio considered, nor the plastic contractions by setting of the cement slurry used for cementing (the plastic contractions by setting increase with the temperature of curing or of the injection zone of the slurry). You could use literature data and include such variables in your analysis. It would be prudent to include such variables or justify why they are not considered in this analysis.
4.- No equation is observed that correlates the rheological characteristics of the cement slurry with the quality of adhesion or does not clearly show such a relationship. Perhaps with a specific graph or analysis.
Author Response
Q1.-Methodology, page 19, lines 103 and 104, “(such as cement slurry density, viscosity, preflush density, and slurry flow rate) directly impact cement bond quality”. This statement should be supported with bibliographic citations.
A1:
We thank the reviewer for the valuable suggestion. Regarding your comment that parameters such as cement slurry density, viscosity, preflush density, and slurry flow rate directly influence cement bond quality, we have reviewed several relevant studies to ensure scientific rigor. Accordingly, we revised lines 383 and 385 in the manuscript. We have now added supporting references (Refs. 27, 28, 29, and 30) immediately after the related paragraph. These studies consistently indicate that the flowability of the cement slurry has a significant impact on cement bond quality. By incorporating these citations, we have strengthened the scientific basis of our discussion and made the argument more convincing. In addition to the literature support, some of our co-authors are engineers with extensive field experience in cementing operations. Their long-term practical insights have guided our work, confirming that these parameters have a direct and pronounced influence on cement bond quality during the cementing process.
Q2.- Why is not considered in the analysis any mechanical parameter of bond at laboratory level made to a cement slurry of the same characteristics as the one injected in the well? It would be prudent to include this variable or justify why it is not considered in this analysis.
A2:
Comprehensive laboratory mechanical testing of the same cement slurry injected downhole requires significant resources and specialized equipment to accurately simulate downhole conditions such as high temperature and high pressure. Within the scope of this study, we adopted a field-based evaluation method, which is more cost-effective and capable of directly reflecting real downhole conditions. In future work, we plan to integrate laboratory and field data to further improve the cement bond quality evaluation system. While laboratory testing provides valuable insights into the fundamental properties of cement slurry, we prioritized field data and numerical simulation in this study to ensure that the results closely reflect actual downhole performance. We sincerely appreciate the reviewer’s insightful suggestion, and we will consider incorporating both laboratory and field data in future research to enhance the comprehensiveness and accuracy of cement bond quality assessments.
Q3.- Neither is the water-cement ratio considered, nor the plastic contractions by setting of the cement slurry used for cementing (the plastic contractions by setting increase with the temperature of curing or of the injection zone of the slurry). You could use literature data and include such variables in your analysis. It would be prudent to include such variables or justify why they are not considered in this analysis.
A3:
We sincerely thank the reviewer for the valuable suggestion. We have addressed this comment in two parts:
- Water–cement ratio consideration:
We have now included the water–cement ratio as an influencing factor in our analysis (feature x20 in Table 1). The correlation coefficient of this parameter has been recalculated and is shown in the updated Figure 2. Furthermore, the neural network model was retrained using the updated dataset. The results confirm that this variable has a significant impact on cement bond quality and contributes to improved prediction accuracy. All relevant results in the revised manuscript are based on this updated analysis.
- Plastic contractions by setting:
We fully recognize the importance of plastic contractions during the setting phase of cement slurry, especially under elevated temperature conditions. However, at this stage, we are unable to include this variable in our analysis due to practical limitations. Our research team is part of a petroleum production company rather than a dedicated research institute. The data used in this study were collected from actual field operations. While rheological measurements are mandated by standard procedures, plastic contraction tests are not included in the routine testing scope, and we are not in a position to request additional laboratory testing beyond operational requirements.
We understand the reviewer’s suggestion to utilize literature data. However, the plastic contraction behavior is highly specific to the exact cement formulation, temperature, and pressure conditions. Literature data may not accurately represent the unique characteristics of the slurries used in our operations. Incorporating such generalized data could compromise model accuracy or introduce misleading correlations. Furthermore, as plastic contractions are temperature-dependent, their inclusion without direct measurements could lead to inconsistencies in the correlation analysis.
That said, we consider this a very important point and have incorporated it into our future work plan. We plan to conduct controlled laboratory experiments to measure plastic contractions under realistic downhole conditions and to integrate such results in a more comprehensive model (see lines 592~601 in the revised manuscript). We believe this future direction will significantly enhance the physical realism and predictive power of our model.
Once again, we thank the reviewer for the thoughtful comment and believe it has led to meaningful improvements in our work.
Q4.- No equation is observed that correlates the rheological characteristics of the cement slurry with the quality of adhesion or does not clearly show such a relationship. Perhaps with a specific graph or analysis.
We appreciate the reviewer’s valuable comment. In response, we have made specific revisions in lines 447–467 of the manuscript to clarify the relationship between the rheological characteristics of the cement slurry and cement bond quality.
First, both published literature and field engineering experience have consistently shown that the rheological properties of cement slurry significantly affect cementing quality. In our dataset, all wells used power-law fluid cement systems, for which the consistency coefficient (k) and flow behavior index (n) are the most representative parameters describing slurry flowability.
We first conducted a correlation analysis between the original rheological parameters (k, n) and cement bond quality. The correlation coefficients were found to be around 0.2. Since these parameters are temperature-sensitive, we applied a temperature correction to obtain k(T) and n(T), and repeated the correlation analysis. The corrected parameters showed improved correlation coefficients above 0.3, indicating that temperature correction plays a critical role. These results are illustrated in Figure 11 of the revised manuscript.
To further enhance clarity, we added a detailed explanation of how the temperature-corrected rheological parameters are embedded into the neural network structure. Additionally, to support the validity of this method, we analyzed the gradient flow of the model during training, as shown in lines 476–508. This provides further evidence that the proposed embedding method improves the model’s sensitivity to key physical features and enhances prediction performance.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsI read the article with great interest. The research is welcome in the scientific community. The authors addressed a relevant topic. However, I noted a few remarks and weaknesses in the document. First, the objective (in the introduction section, even in the abstract) of the cement bond quality in the oil well is not clearly argued and specified. The reader has difficulty understanding this aspect of the matter.
The introduction is not well presented; the authors did not sufficiently research the literature. There are only nine works that are discussed. This does not allow for a good understanding of the context and the problem, what has already been done and what needs to be done in the field. The state of the art should be added in this section. I suggest the authors add a minimum of 15 references (including 6 more recent ones from 2024, and the rest from at least 2021); this will add value to this article.
The methodology should be improved, by clearly specifying the objective of this research, and the methods and techniques to be used, to achieve the expected objectives.
Figure 1 needs to be improved: the arrow leaving "Test dataset" should point to the correct box (either to "Model evaluation" or to "Temperature correction"?). Also, the arrow leaving "validation dataset" and "Training dataset" should point to the correct location. Explain the meaning of the dotted and solid lines separating the three configurations.
Figure 2 is unclear; please improve it.
What conditions allowed Figure 3 to be created? Please specify in the manuscript.
Figures 7 and 12 are not clear. The color code may need to be changed!
The conclusion is too brief; the results are not included. Future prospects are not addressed. The authors should improve this section.
Publication of this article requires appropriate responses to the comments mentioned above.
Author Response
Q1: First, the objective (in the introduction section, even in the abstract) of the cement bond quality in the oil well is not clearly argued and specified. The reader has difficulty understanding this aspect of the matter.
A1:
Thank you for your valuable comment. In response, we have revised the abstract (lines 13–35) and the introduction section (lines 46–48 & lines 111~120) to more clearly highlight the objective of cement bond quality prediction in oil wells. We hope this revision improves the clarity and helps readers better understand the focus and motivation of our study.
Q2: The introduction is not well presented; the authors did not sufficiently research the literature. There are only nine works that are discussed. This does not allow for a good understanding of the context and the problem, what has already been done and what needs to be done in the field. The state of the art should be added in this section. I suggest the authors add a minimum of 15 references (including 6 more recent ones from 2024, and the rest from at least 2021); this will add value to this article.
A2:
Thank you for your constructive suggestion. As cement bond quality prediction remains a relatively niche topic with limited existing literature, we carefully re-investigated the available research. In the revised manuscript, the literature review section has been reorganized as follows: references [1] ~ [9] cover traditional cement bond evaluation methods, while references [10] ~ [18] focus on intelligent prediction approaches. In particular, references [15] ~ [18] are recent studies published in 2022~2024, as recommended. Furthermore, in lines 91~110, we have added a concise summary of the literature and clearly outlined the research gap that this study aims to address.
Q3: The methodology should be improved, by clearly specifying the objective of this research, and the methods and techniques to be used, to achieve the expected objectives.
A3:
Thank you for your insightful suggestion. In the revised manuscript, we have further clarified the objective of this research and provided a more detailed explanation of the methods and techniques used to achieve it. The updated content in the methodology section (see lines 122–132 and lines 143–154), along with the revised Figure 1, reflects these improvements.
Q4: Figure 1 needs to be improved: the arrow leaving "Test dataset" should point to the correct box (either to "Model evaluation" or to "Temperature correction"?). Also, the arrow leaving "validation dataset" and "Training dataset" should point to the correct location. Explain the meaning of the dotted and solid lines separating the three configurations.
A4:
Thank you for your valuable suggestion. In the revised version, Figure 1 has been updated to more accurately reflect the data flow and model development process. Specifically, the training and validation datasets are used during model training and parameter tuning, while the test dataset is kept completely separate and is only used to evaluate the model's predictive performance. Additionally, data from one well, not involved in the training or validation process, is used for field testing to further verify the model's applicability under real-world conditions.
Figure 2 is unclear; please improve it.
In response to the comment, the two subplots in Figure 2 have been enlarged to enhance clarity and make the visual information more accessible to readers.
What conditions allowed Figure 3 to be created? Please specify in the manuscript.
Thank you for your helpful suggestion. Figure 3 presents the correlation between centralizer positions and cement bond quality at the two interfaces. Since the centralizer position is represented using one-hot encoding and is therefore categorical rather than continuous, the Spearman correlation coefficient is not suitable in this context. Instead, we employed Cramér’s V coefficient for the correlation analysis, as defined in Equation (3). The results are visually presented in the updated Figure 3. In the revised manuscript (lines 266–270), we have added a detailed explanation of this methodological change.
Figures 7 and 12 are not clear. The color code may need to be changed!
As suggested, Figures 7 and 12 have been redrawn. In addition, all confusion matrix figures throughout the manuscript have been revised for improved visual quality and presentation consistency.
Q5: The conclusion is too brief; the results are not included. Future prospects are not addressed. The authors should improve this section.
A5：
We have revised the Future Development Directions section (lines 592–601). In this updated section, we propose the integration of laboratory testing and intelligent modeling as a key avenue for future research. This will allow for a more precise simulation of downhole conditions by incorporating cement slurry properties—such as plastic contractions and thickening time—into the model prior to field operations.
We have further enriched the Conclusion section (lines 603–630) by incorporating a more comprehensive summary of the model’s predictive results and explicitly discussing the mechanism by which physical equation embedding enhances neural network performance.
Specifically, we summarized the improvements in prediction accuracy (up to 89% in field tests), the effectiveness of the model in identifying poor-quality cement bonds, and the generalization performance across different data distributions. Additionally, we elaborated on the role of embedding temperature-corrected rheological equations, showing how they influence gradient flow during training, promote model convergence, and enhance learning efficiency. These enhancements help to clarify both the practical outcomes and theoretical contributions of our study.
Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for AuthorsThe article employs Wide & Deep neural networks to propose an enhanced method for predicting cement bond quality in oil wells. It presents an intelligent tool aimed at evaluating cementing performance in such environments and mitigating operational risks.
The following suggestions to improve the manuscript:
1- Is there a specific methodology for incorporating real-world variables into the model? It is important to clarify how physical variables are integrated into the proposed architecture.
2- Were the source data obtained from actual field conditions? It would be beneficial to include details regarding data preprocessing steps such as normalization, cleaning, and other treatments.
3- Provide a detailed explanation of the procedures used for validating the original dataset.
4- It is advisable to include examples demonstrating the application of the data, as well as a discussion on the potential for future research developments.
Author Response
Q1- Is there a specific methodology for incorporating real-world variables into the model? It is important to clarify how physical variables are integrated into the proposed architecture.
A1：
We thank the reviewer for this important observation. In the revised manuscript, we have elaborated on the method used to embed domain knowledge into our intelligent model. Specifically, we adopt a physics-informed neural network approach by directly integrating domain-specific temperature correction equations into the network structure. This allows the model to account for the physical relationships governing the rheological behavior of cement slurry under varying temperature conditions.
We have revised Figure 12 and added a detailed explanation in lines 476–507 to illustrate the embedding process. Comparative experiments were conducted to demonstrate the effectiveness of this approach. The results show that incorporating temperature-corrected parameters k(T) and n(T) influences the gradients of the corresponding neurons during backpropagation. This enables faster model convergence and improves prediction accuracy. These findings support the validity and benefit of integrating domain physical equations into the model architecture.
We appreciate the reviewer’s suggestion, which helped us clarify and emphasize this important aspect of our methodology.
Q2- Were the source data obtained from actual field conditions? It would be beneficial to include details regarding data preprocessing steps such as normalization, cleaning, and other treatments.
Thank you for this important comment. As clarified in the revised manuscript (lines 174–192), all data used in this study were obtained from actual field operations conducted in an oilfield located in western China. The dataset includes real-time measurements collected during cementing and logging operations, encompassing parameters such as temperature, pressure, rheological properties, and cement bond quality indicators.
These first-hand field measurements provide a reliable and realistic foundation for both model development and performance evaluation. We have revised the corresponding section in the manuscript to more clearly state the source and authenticity of the data.
We appreciate the reviewer’s emphasis on data reliability, which we agree is essential to the integrity of our research.
Q3- Provide a detailed explanation of the procedures used for validating the original dataset.
A3:
We appreciate the reviewer’s attention to data quality, which is indeed essential for the credibility of any predictive model. Although the total dataset used in this study comprises approximately 30,000 samples, we emphasize that all data were carefully verified to ensure authenticity and accuracy.
One of the co-authors is a senior cementing engineer with extensive field experience. He was responsible for performing a thorough cross-check of all preprocessed data against field operation logs and engineering records from the oilfield. During this process, data collected by downhole sensors and surface equipment were meticulously compared with manually recorded values. No anomalies or inconsistencies were observed throughout this verification.
As this process did not involve complex technical procedures or additional algorithms, we did not highlight it prominently in the manuscript. However, we will be happy to add a brief note regarding this verification process if the reviewer deems it necessary.
If this was not the intended concern in your comment, we kindly invite you to elaborate further so we may address it accordingly in the next revision.
Q4- It is advisable to include examples demonstrating the application of the data, as well as a discussion on the potential for future research developments.
A4:
We thank the reviewer for the helpful suggestion. In the revised manuscript, we have added Section 5: Field Test, where we validated the model using third-stage casing data from a real well. The model demonstrated robust performance under actual field conditions, achieving an accuracy rate of over 89%, which confirms the model’s applicability and reliability.
In addition, we have revised the Future Development Directions section (lines 592–601). In this updated section, we propose the integration of laboratory testing and intelligent modeling as a key avenue for future research. This will allow for a more precise simulation of downhole conditions by incorporating cement slurry properties—such as plastic contractions and thickening time—into the model prior to field operations.
We believe these revisions enhance the practical significance and scientific rigor of the study.
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
Comments and Suggestions for AuthorsThe authors have meaningfully addressed my concerns. The article is significantly improved.
I therefore agree to the article being published.
