the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 14 May 2025
Research on the correction method of hydraulic fracturing in-situ stress testing based on MLP-KFold
Abstract. Hydraulic fracturing serves as a critical in-situ stress testing technique, where the accurate determination of rock fracture pressure and closure pressure in fracturing intervals is essential for precise in-situ stress estimation. During hydraulic fracturing stress measurement, parameters including injection rate, viscosity, density, and compressibility ratio of fracturing fluid significantly affect the measurement accuracy of fracture and closure pressures, potentially introducing substantial errors in in-situ stress calculations. This study develops an MLP-KFold-based correction model for rock mechanical measurements by establishing a dataset derived from laboratory hydraulic fracturing simulations, incorporating fracturing fluid density, viscosity, injection rate, and corresponding rock fracture/closure pressures. Evaluation results demonstrate that the MLP-KFold model achieves superior performance with a coefficient of determination (R²=0.9937) on test sets, outperforming Random Forest (Δ+1.89 %), Support Vector Regression (Δ+4.05 %), and BiLSTM (Δ+5.34 %). Key error metrics including MAE (0.518), MSE (0.646), and maximum error (1.945 MPa) remain at minimal levels. The model exhibits enhanced data utilization efficiency and evaluation stability with small-scale datasets while effectively preventing overfitting and improving generalization capabilities. Field applications in in-situ stress measurements demonstrate significant reduction in average percentage differences of calculated stresses under different fracturing fluids (σH: -21.48 %, σh:-29.03 %), confirming its superior compensation effects. This research establishes a reliable compensation model for hydraulic fracturing pressures, providing an effective technical approach for correcting field measurement data and compensating in-situ stress calculation results, thereby contributing to the accurate assessment of regional stress profile states.
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RC1: 'Comment on egusphere-2025-1895', Anonymous Referee #1, 03 Jun 2025
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This paper proposed an interesting method for improving the accuracy of in-situ stress measurement. This method based on the MLP-KFold displayed good calibration performance, and preventing overfitting and improving generalization capabilities. If this method can be extended to the field of hydraulic fracturing stress measurement, it will have a positive impact on the accurate acquisition of regional stress field.
To sum up, combining AI learning algorithms with hydraulic fracturing in-situ stress measurement is a useful and interesting attempt. Therefore, I support the publication of this paper on GI. Of course, this paper requires some minor revisions before it can be published.
Specific modification and suggestions：
- Some references are outdated, slightly lacking an understanding of the latest research progress. I suggest adding some latest literature related to this study.
- Insufficient Dataset Scale and Diversity. Although the model shows good data utilization efficiency and evaluation stability on a small-scale dataset, a small dataset may not be able to fully cover various situations in actual applications. And this article only discusses the fracturing situation of granite rock cores. It is recommended to add fracturing comparisons of other rock cores in subsequent research.
- Model Generalization Capability: Although the model performs well on the test set (R²=0.9937), the diversity of rock types, formation conditions, and construction parameters in actual applications may limit the model's generalization capability. How can the generalization capability of the model under different geological environments and construction conditions be further verified? These should be mentioned in the discussion.
- The content of the Conclusions is too extensive and should be more refined.
Format issues:
- Table 5 is too large and should not appear in the main text. It should be placed in the appendix.
- The font in Figure 3 is too small, but the font in Figure 4 is too large, which should be consistent with the font in the main text. The rest of the pictures also have this issue, please adjust them.
Citation: https://doi.org/10.5194/egusphere-2025-1895-RC1 -
AC1: 'Reply on RC1', Yimin liu, 09 Jun 2025
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Dear reviewer 1#：
We are very grateful to your comments, and we have carefully read and considered the referee’s comments, and these comments are important for improving the quality of this manuscript. Based on these comments, we have made carefully modification and proofreading on the original manuscript, the revised parts have been marked in red in revised version, and the detail modifications are shown in next chapter.
Thank you very much for your suggestion and consideration, and we look forward to hearing from you.
Best regards,
Yimin Liu and Jinwu Luo.
Detailed revision:
- Some references are outdated, slightly lacking an understanding of the latest research progress. I suggest adding some latest literature related to this study.
Modification: In the revised manuscript, a new reference to Liu et al. (2024) has been added to the literature review section. This latest reference is particularly relevant to our research as it introduces an advanced in-situ stress calculation model, and addition strengthens our literature review by providing a more precise and up-to-date method for in-situ stress calculation. And Ma et al. (2024) and Zou et al. (2024) in the first draft also reflect the real-time and relevance of literature review.
Liu J, Cheng Y, Shu H, et al. 2024. Geostress Calculation Model of Horizontal Hole Hydraulic Fracturing Method Considering Different Fracturing Fluid Flow Rates [J]. Yellow River, 46(12):131-136. (abstract in English)
- Insufficient Dataset Scale and Diversity.
Explanation and modification: Thank you for your valuable feedback and suggestions regarding the scale and diversity of our dataset. We fully acknowledge the importance of a diverse and sufficiently large dataset in ensuring the comprehensive applicability of our model. In our study, we have utilized 35 sets of hydraulic fracturing experimental data. It's crucial to note that hydraulic fracturing is a destructive testing method, and the success rate of such experiments is relatively low. Each successful experiment requires significant time and resources, including the preparation of rock cores and the careful calibration of experimental conditions. Given these constraints, obtaining 35 valid datasets represents a substantial effort and a rare accumulation of data in this field.
The primary focus of this paper is to explore the feasibility and effectiveness of the MLP-KFold model in correcting rock mechanics measurements based on the available dataset. The model has demonstrated excellent data utilization efficiency and evaluation stability, which is particularly significant given the limited data scale. We agree that expanding the dataset to include a wider variety of rock types would further enhance the model's generalization ability and robustness. In our subsequent research, we plan to conduct hydraulic fracturing experiments on rock cores of different lithologies to collect more diverse data and address the current limitations of dataset scale and diversity.
We appreciate your understanding of the challenges associated with experimental data collection in this field and hope that our current work can serve as a preliminary exploration, with more comprehensive improvements to follow in future studies.
- Model Generalization Capability.
Explanation and modification: Thank you for raising the important issue of the model's generalization capability. We recognize the need to further validate and discuss the model's applicability across diverse geological environments and construction conditions. While the MLP-KFold model demonstrated remarkable performance on the test set with a coefficient of determination (R²=0.9937), it is acknowledged that the diversity of rock types, formation conditions, and construction parameters in real-world applications could pose challenges to the model's generalization capability, and the following aspects discussed in section 5.3 in red.
(1) Cross-Validation with diverse datasets: by merging cross-validation with datasets spanning various geological settings and construction conditions with field trials in multiple locations, we can comprehensively assess the model's performance in real-world applications. This integrated method not only identifies potential weaknesses or biases in the model but also provides empirical data from different geological environments, thereby enabling targeted adjustments to improve generalization.
(2) Incorporation of additional features: to further bolster the model's adaptability, we advocate for the incorporation of additional features that encapsulate the variability in geological and construction parameters. These features may encompass rock anisotropy, formation fluid properties, and dynamic construction variables, among others. In parallel, establishing a framework for continuous model updating based on new data and feedback from field applications ensures the model evolves with emerging geological and construction challenges, maintaining its accuracy and relevance.
In summary, these strategies aim to enhance the model's generalization capability and reliability across a broad spectrum of practical applications. Future efforts will concentrate on expanding the dataset, conducting extensive field trials, and refining the model to address the intricacies of real-world hydraulic fracturing operations.
- The content of the Conclusions is too extensive and should be more refined.
Modification: We have rewritten the conclusion based on the revision suggestions.
Format issues:
- Table 5 is too large and should not appear in the main text. It should be placed in the appendix.
Modification: We have included Table 5 as an appendix at the end of the manuscript.
- The font in Figure 3 is too small, but the font in Figure 4 is too large, which should be consistent with the font in the main text. The rest of the pictures also have this issue, please adjust them.
Modification: We adjusted the dimensions of Figures 3, 4, 5 and 9 to be consistent with the font in the main text.
Citation: https://doi.org/10.5194/egusphere-2025-1895-AC1 -
AC2: 'Reply on RC1 for supplement', Yimin liu, 10 Jun 2025
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