Spatiotemporal Optimization of Oilfield Electricity Consumption: A Multi-Objective Modeling Approach with Machine Learning

Comments 1: The title of Table 6 on Page 13 is labeled as Annual Production Data, but the table actually presents monthly production and electricity data. The title is inconsistent with the content and should be revised accordingly.

Response 1: We thank the reviewer for carefully identifying this inconsistency. We agree that the original title “Annual Production Data” is misleading because Table 6 reports monthly values (planned vs. actual production and electricity consumption) for each month of 2022.

To resolve this issue, we have revised the title to:” Table 6. Monthly Production and Electricity Data for 2022” (Line 512).

Comments 2: The abbreviation of Light Gradient Boosting Machine is not unified in the manuscript. Although Light Gradient Boosting Machine (LGBM) is defined on Page 6, the form LightGBM still appears in the subsequent text. Please uniformly use the abbreviation LGBM throughout the manuscript.

Response 2: We thank the reviewer for pointing out this inconsistency. We have carefully checked the entire manuscript and replaced all occurrences of “LightGBM” (except where it appears as part of a proper noun or citation key) with the unified abbreviation “LGBM”.”

Comments 3: The term liquid production is consistently used in the main text, but oil production incorrectly appears in the abstract. These two terms represent different technical concepts in oilfield engineering. Please maintain terminological consistency and use liquid production for the entire manuscript.

Response 3: We thank the reviewer for pointing out this terminological inconsistency. We have replaced ‘oil production’ with ‘liquid production’ in the abstract and verified that the entire manuscript now uses ‘liquid production’ consistently.

Comments 4: The constraints of ±20% monthly adjustment limit and no less than 85% of the original plan for key units (Page 9) are presented without any explanation or justification. Please supplement the industrial basis, field specifications or practical considerations for selecting these threshold values.

Response 4: We thank the reviewer for the comment. In the revised manuscript, we have added the following note in Section 2.4.2:“Note: These threshold values are derived from Daqing Oilfield’s practical experience. Users of the framework may modify them to suit their own operational contexts.”This clarifies that the ±20% and 85% thresholds are empirical parameters from Daqing Oilfield, and other enterprises can adjust them accordingly. (Line 356-357)

Comments 5: In Section 2.3.2 Machine Learning-Based Production Prediction, the description of the machine learning methods and their predictive performance is insufficient. It is strongly suggested to add a fitting curve (e.g., actual values versus predicted values) to visually illustrate the prediction accuracy of the model.

Response 5: We thank the reviewer for this constructive suggestion. In the revised manuscript, we have added a visual comparison of prediction outcomes from three representative models (LGBM, DT, and LASSO) in the new Figure 3, along with a corresponding description in Section 2.3.2 (immediately below Table 1). The figure clearly shows that the LGBM predictions (red curve) align most closely with the ground truth values (dotted black line), which qualitatively supports the quantitative metrics reported in Table 1.(Line 268-279)

Comments 6: In Section 2.3.2 Machine Learning-Based Production Prediction, the key parameter settings of the LGBM model are missing, including learning rate, maximum tree depth, number of iterations and other critical hyperparameters. Please supplement these details to ensure the reproducibility of the modeling results.

Response 6: We thank the reviewer for the suggestion. In the revised manuscript (Section 2.3.2), we have added a paragraph describing the hyperparameter optimization of the LGBM model. The description now follows the performance comparison in Table 1 and explains that to achieve the reported performance, we used the Optuna framework with 30 trials. The search ranges and optimization settings are provided in detail to ensure reproducibility and clarity. (Line256-266)

Comments 7: Detailed information about the SLSQP optimization algorithm is missing. Please provide the specific algorithmic parameters, software library version, solver configuration and convergence criteria adopted in this study.

Response 7: We thank the reviewer for the comment. In the revised manuscript (Section 2.4.2), we have supplemented the missing algorithmic parameters. Specifically, we now explicitly state that the SLSQP solver was called with maxiter=1000 and ftol=1e-6, in addition to the previously reported convergence criteria (objective change < 1e-6, constraint violation < 1e-4). All solver configurations are now fully reported to ensure reproducibility.(Line 367-Line 372)

Comments 8: Machine learning models are employed in the field data validation, whereas no related machine learning algorithm is involved or illustrated in the simulation data section. Please add a clear and reasonable introduction to the algorithmic design in the simulation part.

Response 8: We thank the reviewer for the comment. As noted in the revised manuscript (Section 2.2.1, last paragraph), we have added the following clarification:

“Because the simulated data follow a linear electricity-to-production relationship by design, the optimization efficiency term uses this linear model directly, in contrast to the field data where a machine learning model (LGBM) is required.”

Thus, the absence of machine learning in the simulation part is intentional: the simulated data are generated from a known linear relationship, making a simple linear model sufficient. For the real-world field data, where the relationship is nonlinear, we employ LGBM to ensure accurate production prediction. The current revision clearly explains this difference in algorithmic design.(Line147-149)

Comments 9: The Conclusion section redundantly elaborates detailed procedural steps (such as decomposing electricity consumption into three functional components), which makes the content lengthy and repetitive. The conclusion should focus on the core findings, research contributions, practical implications and future prospects, rather than restating the methodological procedures.

Response 9: We thank the reviewer for the suggestion. The Conclusion section has been rewritten into three concise paragraphs, without restating methodological details. It now focuses on core findings (18.0% and 32.5% production loss reduction), the main contribution (differentiated allocation strategy), practical implications (low data requirements, scalability), and future research directions. Repetitive procedural descriptions have been removed. (Line574-594)

Comments 1: I suggest explicitly mentioning the key method names in the abstract, not only the general framework. For example, the authors may state that production is predicted using LightGBM and that the constrained multi-objective optimization problem is solved using SLSQP. This would make the abstract more informative, improve transparency, and attract readers by clearly highlighting the technical tools behind the proposed approach.

Response 1:  We thank the reviewer for the suggestion. In the revised abstract, we have explicitly added the two key method names. Specifically, we now state that liquid production is predicted via the LightGBM machine learning model, and we have added a sentence indicating that the optimization problem is solved using the SLSQP algorithm. (Line24-26)

Comments 2: I identified 8 references that need rechecking for consistency with the text, namely [11], [12], [14], [15], [18], [19], [24], and [29]. Some appear too broad, while others do not seem to directly support the specific methodological or background statements they are cited for. The authors are encouraged to revise these citations and use more precise references that better match the corresponding text.

Response 2: We apologize for the inappropriate citations. We thank the reviewer for identifying these issues. In the revised manuscript, we have carefully rechecked all eight references ([11], [12], [14], [15], [18], [19], [24], and [29]) and replaced them with more precise and directly supporting sources. The revised citations now accurately support the corresponding statements in the text. We greatly appreciate the reviewer’s meticulous reading, which has improved the quality of our references.

Comments 3: The simulation study is methodologically weak because it is based on a self-constructed toy scenario rather than any established benchmark, and therefore it does not provide a sufficiently credible basis for claiming real-world effectiveness. A 3-unit, 12-month controlled setup with only 1% injected random noise cannot adequately reproduce the complexity, heterogeneity, and stochastic disturbances of actual oilfield operations. Moreover, the manuscript does not support the simulation with a proper probabilistic framework: no distributional assumptions, no Monte Carlo repetitions, no uncertainty propagation, and no confidence-based statistical analysis are reported. Consequently, the simulation section has limited scientific value beyond basic demonstration, and the authors should substantially strengthen it before drawing strong conclusions from it.

Response 3: We thank the reviewer for this critical comment. We agree that our simulation lacks probabilistic rigor and is not a benchmark. We would like to clarify its limited role.

First, to our knowledge, there is no widely accepted benchmark or standard simulation framework for the specific problem of electricity consumption allocation among multiple oilfield production units. Our simulation was designed merely as a proof‑of‑concept to illustrate the optimization logic under transparent, controlled conditions. Second, we fully recognize its limitations and therefore do not draw strong conclusions from the simulation alone. The main conclusions rely on the field data validation from Daqing Oilfield (32.5% production loss reduction), which captures real‑world complexity. The simulation only helps to demonstrate the internal mechanics of the method.

In light of the reviewer’s suggestion, we have revised the manuscript (Section 3.1.1) to explicitly state these limitations and removed any over‑generalized claims. We have also noted that future work should incorporate a probabilistic framework. We appreciate the reviewer’s thorough critique, which has improved the clarity of our paper. (Line 388-393)

Comments 4: Although the manuscript presents the problem as multi-objective optimization, the proposed formulation is actually implemented as a weighted aggregated single-objective model solved by SLSQP, rather than as a genuine Pareto dominance-based multi-objective optimization approach. In addition, the manuscript does not compare the optimization method against established multi-objective baselines such as NSGA-II, NSGA-III, or MOEA/D, and no standard Pareto-performance indicators such as hypervolume, IGD, or Pareto front visualizations are reported. Therefore, the current validation is insufficient to support the broader multi-objective optimization claim in the evolutionary/Pareto sense.

Response 4: We thank the reviewer for this important methodological observation. We fully agree that our formulation solves a weighted aggregated single‑objective problem rather than a genuine Pareto‑dominance‑based multi‑objective optimization. We apologize for any confusion caused by the original wording.

We would like to respectfully explain the reasons for this design choice in our industrial context.

First, in actual oilfield production management, decision‑makers require a single, deterministic, and immediately executable electricity allocation plan for each operation area and each month. A full Pareto front, while valuable for exploring trade‑offs, would require an additional preference‑based selection step before deployment. The weighted‑sum approach directly incorporates the managers’ priorities (weights for efficiency, stability, and protection), yields a unique solution, and is computationally efficient using SLSQP – all desirable for routine operational use.

Second, the primary objective of this study is not to benchmark against evolutionary multi‑objective optimizers (such as NSGA‑II, NSGA‑III, or MOEA/D), but to demonstrate that the proposed spatiotemporal allocation framework outperforms the conventional ton‑per‑kWh method in reducing production loss under real‑world constraints. A systematic comparison with Pareto‑based methods, including reporting hypervolume, IGD, or Pareto front visualizations, is an independent algorithmic research direction that goes beyond the engineering application focus of our paper.

Nevertheless, we acknowledge the limitation: our current validation does not support a claim of “Pareto‑optimality” or “superiority over evolutionary multi‑objective algorithms”. We have therefore revised the manuscript to use more precise language (e.g., “scalarized multi‑objective optimization using a weighted sum”) and have explicitly stated in the Conclusions that a systematic comparison with Pareto‑based methods is left for future work. We also added a brief note that for decision‑makers who wish to explore the entire trade‑off surface, our framework can be readily extended with an MOEA module – a promising direction we plan to pursue. (Line 290-291, Line591-594)

Comments 1: LightGBM configuration is used in this paper as a widely recognized algorithm, and it is also referenced in the paper, but its configuration and properties should be described in more detail in the paper. Also, it should be explained how the hyperparameters were selected and validated.

Response 1:  We thank the reviewer for the suggestion. In the revised manuscript (Section 2.3.2), we have added a detailed description of the LightGBM model, including its key properties (GOSS and EFB) and the hyperparameter optimization process using Optuna (search space, 30 trials, validation MAE minimization). The final configuration is reported to ensure clarity and reproducibility. ( Line249 - 255)

Comments 2: One more question to be answered is why SLSQP algorithm was chosen over other optimization methods.

Response 2: The optimization problem is solved using the SLSQP algorithm, a mature constrained optimization solver in SciPy. It is well-suited for medium-scale constrained nonlinear continuous problems, efficiently handling variable bounds, equality constraints, and inequality constraints with good convergence and practical convenience. (Line 361-364)

Comments 3: There are 4 figures in the paper, but captions for the figures are too long. They should be much shorter and explained in a detail in a text, not in a caption.

Response 3: We thank the reviewer for the suggestion. In the revised manuscript, we have shortened all figure captions to one concise sentence each. Detailed descriptions that were previously in the captions have either been removed (if already explained elsewhere) or moved to the corresponding main text where each figure is first cited.

Comments 4: Also, text in the Fig. 2 is in a very small font – it must be enlarged. There are also 7 tables in the paper, but data is presented clearly in them.

Response 4: We thank the reviewer for this valuable suggestion. In the revised manuscript, we have enlarged all text in Fig. 2 (including axis labels, tick labels, legends, and any annotations) to ensure good readability. Regarding the seven tables, we have carefully checked them and confirm that the data are presented clearly and logically; therefore, no further modifications have been made to the tables. We appreciate the reviewer’s positive comment on the clarity of the tables.

Comments 5: The reference list is relevant and up-to-date, but it would be nice to cite more recent review articles or state-of-the-art studies that utilize machine learning applications in oil and gas systems.

Response 5: We have added two recent review articles (new reference [25-26]) and updated the sentence in the Introduction to highlight the growing role of machine learning in oil and gas, as suggested. (Line 83-84)