Machine Learning-Based Virtual Sensor for Bottom-Hole Pressure Estimation in Petroleum Wells

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper proposes a machine learning-based soft sensor method for estimating bottom-hole flowing pressure (BHP) in oil wells. It demonstrates outstanding performance in methodology design, data scale, and experimental validation, with strong practical engineering value and academic significance. The proposed clustering-integration framework achieves high-precision BHP estimation under complex reservoir conditions, while the model exhibits interpretability and real-time application potential. Although there is room for improvement in innovative presentation and comparative experiments, the overall work is solid and contributions are well-defined. It is recommended to accept the paper after minor revisions, with a focus on strengthening comparisons with existing methods, deepening the rationale for clustering selection, and refining the presentation of innovations.

The primary limitation of the paper in parameter selection lies in decomposing a highly coupled system that should have been jointly optimized into several independent, sequential steps. While this simplifies the experimental process, it sacrifices the possibility of finding a globally optimal solution. Please explain the errors or reliability associated with this approach.
2 Briefly explain in the paper whether the hyperparameter ranges are based on preliminary experiments, literature recommendations, or computational resource constraints to enhance the transparency and reproducibility of the experiments.
The model explains that only dynamic parameters are considered in terms of parameter evaluation. It is necessary to add a discussion on the model's limitations and future prospects, providing relevant research directions.
4. Figures 19 and 22 require adjustment of the vertical axis range to make the curve variations more pronounced.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Dear Authors,
Please find my comments and suggestions in the annexed file. I hope these  will be helpful in strengthening your manuscript.
Best regards

Comments for author File: Comments.pdf

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

Dear Editor and Authors,

Thank you for the opportunity to review your manuscript titled "Machine Learning-Based Virtual Sensor for Bottom-Hole Pressure Estimation in Petroleum Wells". Below is my detailed feedback:

1) General Comments

The study proposes an innovative soft sensor methodology based on ensemble machine learning with fuzzy clustering to estimate bottom-hole pressure (BHP) in complex offshore wells. By partitioning the data into clusters corresponding to physical flow regimes, the final model (such as, linear regression with clusters) achieves excellent and stable accuracy, with errors below 2%, demonstrating scalability and robustness across diverse production conditions.

2) Specific Comments

a) The study possesses high overall merit and excellent scientific rigor, demonstrating a novel and efficient solution (approximately 2% MAPE accuracy) for a critical industrial problem. However, there is a single methodological gap requiring explicit clarification.

b) The Introduction mentions the objective of "partitioning" the data space to make the problem more manageable. In Section 3.5, the authors show that this clustering separates physical flow regimes, but the specific input variables used to run the Fuzzy C-means algorithm are not explicitly stated. Knowledge of the clustering variables is important for understanding the space in which the partitioning is performed. The method's success depends on the efficient separation of multiphase flow regimes into clusters, and this is directly determined by the variables used as inputs to the clustering algorithm.

Please specify the exact set of input variables used to train the Fuzzy C-means clustering algorithm.

c) The Choke Ap variable, an important control variable in flow physics, was eliminated based on a low Pearson linear correlation. A direct comparison of the model's performance (error metrics) was not presented to demonstrate that the complete feature set (Set 1) did not yield improvements over the reduced sets (for example, Set 4). The model utilizes nonlinear algorithms (XGBoost, NN), but a low linear correlation does not guarantee a lack of relevance. The justification for excluding a control variable should be based on clear evidence, demonstrating that it did not provide an improvement to the model's final performance.

Was an explicit comparison of performance metrics (MAPE/RMSE) conducted between the fully trained model (Input Set 1) and the best selected final model (for example, Set 4 or 6) to justify the final elimination of low-linear-correlation variables, such as Choke Ap?

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The paper has been significantly improved through revision, and I have no further questions. Recommended for acceptance.

Reviewer 2 Report

Comments and Suggestions for Authors

The authors have provided a clear and comprehensive response to the previous questions raised, and the revised manuscript now addresses the methodological and clarity concerns that were flagged. 

The contribution of the work remains primarily applied and incremental, rather than introducing methodological innovation. However, the presented approach is adequately validated, technically sound, and relevant within the scope of the journal.

On this basis, I consider the paper suitable for publication in its current form

Wishing the authors the best!

Reviewer 3 Report

Comments and Suggestions for Authors

Dear Editor,

Please find below my final evaluation of the revised manuscript.

I have carefully analyzed the authors' detailed responses to the review comments and the way they addressed and clarified all the methodological and substantive aspects I had raised. I appreciate the effort made to address and clarify each point.

I consider the revised version of the manuscript to be significantly improved and to adequately address all objections.

I recommend the continuation of the editorial process towards the publication of this study.

Sincerely,