Оптимизация технологий нефтесервисного обслуживания на основе математического моделирования и анализа данных / Optimization of Oilfield Services Technologies Based on Mathematical Modeling and Data Analysis тема диссертации и автореферата по ВАК РФ 00.00.00, кандидат наук Морозов Антон Дмитриевич

• Морозов Антон Дмитриевич
• кандидат наук
• 2026

Оглавление диссертации кандидат наук Морозов Антон Дмитриевич

Content

Introduction

1. Overview of primary data sources describing unconventional field

1.1 Reservoir data sources, measurement tools and methods, and limitations

1.1.1 Core analysis

1.1.2 PVT analysis

1.1.3 Well testing methods

1.1.4 Well logging technologies

1.1.5 Seismic data

1.1.6 Integrated reservoir characterization workflows

1.2 Reservoir data quality assurance and quality control methods

2. Overview of hydraulic fracturing modeling in tight oil reservoirs

2.1 Physics-based analytical and semi-analytical models

2.2 Numerical continuum/discontinuum/hybrid methods

2.3 Numerical model for fracture cleanup (flowback)

2.3.1 Governing equations for multiphase flow with fines transport

2.3.2 Constitutive relations and flow equations

2.3.3 Geomechanical coupling: dynamic aperture and porosity

2.3.4 Geomechanical submodels

2.3.5 Numerical solution scheme

2.3.6 Model significance and application

2.4 Data-driven modeling

2.4.1 Supervised machine learning

2.4.2 Physics-informed machine learning

2.4.3 Application of machine learning in hydraulic fracturing optimization

3. Database

3.1 Data parsing and preprocessing

3.1.1 Frac-list

3.1.2 MPR

3.1.3 Operating practices

3.1.4 Facies

3.2 Data matching

3.3 Data aggregation

3.4 Data postprocessing

3.4.1 Manual postprocessing

3.4.2 Parameter merging

3.4.3 Feature engineering

3.4.4 Categorical parameters

3.5 Database discussion

4. Exploratory data analysis and domain-aware dataset

4.1 Target selection

4.2 Missing data mechanism analysis

4.2.1 Missingness analysis results

4.3 Data imputation pipeline

4.3.1 Data imputation results

4.4 Feature analysis using Mutual Information

4.4.1 Mutual Information results

4.5 Feature correlation analysis

4.5.1 Feature correlation analysis results

4.6 Exploratory spatial data analysis

4.6.1 Spatial autocorrelation analysis

4.6.2 Spatial features

4.7 Object-based clustering

4.7.1 Object-based clustering results

4.8 IID assumption and domain shift

4.8.1 Domain shift diagnostics

4.8.2 Domain shift results

4.8.3 Anchor data selection strategies

4.9 Aggregation-based clustering

4.9.1 Aggregation-based clustering results

4.10 Physically-informed data filtering by Productivity Index

4.10.1 Lower bound: Productivity Index of vertical well

4.10.2 Upper bound: Productivity Index of multistage horizontal well

4.10.3 Reconciliation of low-fidelity data

4.10.4 Physically-informed data filtering results

4.11 High-fidelity data sanity check via numerical fracture cleanup model 133 4.11.1 Fracture cleanup model adaptation on pilot well

4.12 Application of numerical model to high-fidelity wells

4.12.1 High-fidelity data sanity check results

4.13 EDA discussion

5. Forward and inverse problem

5.1 Forward problem

5.1.1 Model baseline architecture selection

5.1.2 Data splitting and cross-validation strategy

5.1.3 Objective loss function

5.1.4 Evaluation metrics

5.1.5 Candidate datasets for model training

5.1.6 Hyperparameter optimization

5.1.7 Advanced model architectures

5.1.8 Model interpretation

5.1.9 Bootstrap-based uncertainty quantification

5.2 Inverse problem

5.2.1 Uncertainty-aware optimization objective

5.2.2 Hydraulic fracturing design parameter set selection

5.2.3 Inverse problem experiment design

5.2.4 Evaluation and interpretation methodology

5.2.5 Inverse optimization results

5.3 Forward and inverse problem discussion

Conclusion

List of abbreviations

Glossary of terms

References

List of Figures

List of Tables

Appendix A. List of features

Appendix B. Model interpretation for the whole dataset

Appendix C. HFML database completeness

Appendix D. Parameter statistics

Appendix E. Correlation matrix

Appendix F. Database design

Введение диссертации (часть автореферата) на тему «Оптимизация технологий нефтесервисного обслуживания на основе математического моделирования и анализа данных / Optimization of Oilfield Services Technologies Based on Mathematical Modeling and Data Analysis»

Introduction

The relevance of the research area. Most oil fields are currently mature and produce more water than oil due to breakthrough, coning, channeling or water fronts. This makes it difficult to extract the remaining reserves cost-effectively. In addition, relatively expensive technologies or equipment are not of interest to any oil and gas company due to rapidly changing oil prices. Such factors provoked different types of enhanced oil recovery (EOR) and well stimulation techniques. Hydraulic fracturing (will be referred to interchangeably as HF) is a transformative well stimulation technology for developing unconventional, low-permeability reservoirs, yet its performance remains difficult to optimize due to strong geological heterogeneity, complex geomechanical behavior, and high sensitivity of production response to design decisions.

At the same time, the increasing availability of large volumes of operational and production data in hydraulic fracturing has shifted attention toward data-driven forecasting and analysis methods. Recent advancements in data-driven methodologies—including machine learning (will be referred to interchangeably as ML) and big data analytics have introduced new opportunities to enhance hydraulic fracturing design, improve well performance, and reduce operational costs. Data-driven approaches leverage historical well data, real-time monitoring, and predictive modeling to identify optimal hydraulic fracturing design parameters, such as fluid and proppant volumes, proppant concentration, and injection rates. These techniques can uncover hidden patterns in large datasets, enabling more efficient decision-making and reducing uncertainties associated with reservoir behavior. The availability of large amounts of data allows the use of ML methods to speed up approximation and improve accuracy of modeling of production processes, acting as "gray box" models, where the physics-based part compensates for the lack of actual field data.

In industrial practice, however, the effectiveness of such approaches is often limited by data inconsistency, noise, and the lack of physically meaningful validation mechanisms. The dissertation addresses these limitations by proposing a data-centric and physically-informed framework for integrating heterogeneous field data, diagnosing data quality, and supporting reliable modeling under uncertainty. The relevance of the dissertation topic is driven by the need to bridge the gap between

numerical modeling and machine-learning-based analysis, enabling robust and interpretable decision-making in hydraulic fracturing design and evaluation.

Goals and problems addressed. The central hypothesis of the dissertation is that machine learning models trained on datasets whose physical consistency has been explicitly verified and enforced can provide reliable, interpretable, and practically meaningful production forecasts. Such consistency can be achieved through a combination of exploratory data analysis, domain diagnostics, physically-informed data filtering, and independent physics-based validation of target variables. Testing this hypothesis enables the development of robust data verification methodologies that assess the physical plausibility of input parameters and model outputs. These methodologies, in turn, support the derivation of consistent and insightful hydraulic fracturing design trends in a retrospective analysis framework.

Based on the proposed hypothesis, the goal of the dissertation is to develop a data-driven modeling framework based on the machine learning model trained on the high-fidelity physically-informed data for assessing optimal uncertainty-aware hydraulic fracturing design trends under specified reservoir and operational constraints. To achieve this aim, the following objectives were formulated and addressed in the dissertation:

- To analyze and systematize: (i) primary data sources describing hydraulic fracturing treatments, including completion parameters, operational data, and production histories, with an emphasis on data consistency and practical availability in industrial workflows; (ii) hydraulic fracturing analytical, numerical modeling and data-driven methods with a particular focus on the advantages and limitations of each type of model.

- To design a comprehensive digital database describing hydraulically fractured wells, integrating geological, petrophysical, operational, and spatial information including a preprocessing pipeline.

- To perform a structured exploratory data analysis (EDA) aimed at characterizing feature distributions, correlation structures, missing data patterns, and spatial dependencies, thereby establishing a transparent baseline for subsequent data-driven modeling.

- To investigate dataset heterogeneity and domain structure using statistical diagnostics and clustering techniques in conjunction with physically-informed methods to obtain a high-fidelity homogeneous dataset applicable

for assessing hydraulic fracturing design potential via machine learning methods.

- To formulate and solve the forward problem of 90-day cumulative fluid production forecasting, using machine learning models trained on the constructed datasets, and to systematically evaluate model architectures, validation strategies, and performance metrics.

- To formulate and solve the inverse problem of retrospective hydraulic fracturing design optimization trends on representative number of wells, where the trained machine learning model is used to identify design parameter configuration trends that maximize predicted production under geological and operational constraints.

Together, these objectives define a unified framework for assessing data-driven hydraulic fracturing optimization trends, where data validation, physical consistency, and predictive modeling are treated as interdependent components rather than isolated steps.

Scientific novelty. The proposed work to assessing uncertainty-aware HF design optimization is one of the first (to the author's knowledge) to utilize a comprehensive dataset, owing to extensive collaboration with the industrial partners. The scientific novelty of the dissertation consists in the development of an integrated, data-centric and physically-informed approach to the analysis and evaluation of hydraulic fracturing treatments under conditions of data uncertainty and heterogeneity. The pipeline is based on the comprehensive digital database consisting of 6 715 wells validated by EDA, analytical and numerical methods related to hydraulic fracturing processes. This framework enables the application of machine learning methods that produce highly accurate predictions, capable of capturing relationships inaccessible to other traditional methods. Furthermore, the data-driven approach does not demand on a complete set of input data, is flexible in defining the objective function, and can immediately produce statistical ranges of optimal hydraulic fracturing design trends for a large number of wells.

Theoretical and practical significance. The proposed approach demonstrates the theoretical feasibility of using data-driven modeling, offering its advantages. Specifically, the presented ML-based methodology was first tested on pilot wells and is used by HF engineers as a software tool for quickly assessing the potential of HF designs. Thanks to feedback, the work was expanded to validate the dataset using analytical and numerical methods for more accurate HF optimizations.

The current research represents a set of best engineering practices related to data-driven approaches in hydraulic fracturing discipline developed over more than 5 years, on the basis of which flexible industrial tools exist for rapid assessment of well potential and uncertainty-aware optimal hydraulic fracturing design.

The practical significance lies in the development of the proposed workflow that can be directly applied in industrial practice for the analysis, evaluation, and optimization of hydraulic fracturing treatments under conditions of limited, noisy, and heterogeneous data. The results of obtaining hydraulic fracturing design optimal trends enable more efficient decision-making and can be used to develop optimal pumping schedules based on retrospective analysis. The use of hydraulic fracturing-based analytical methods and numerical fracture flowback model serving as a sanity-check tool provides an additional level of physical validation, allowing engineers to identify inconsistent input parameters and unrealistic modeling outcomes at early stages of analysis. The combined forward and inverse problem approaches support the identification of uncertainty-aware, statistically and physically meaningful trends, assisting in the selection and prioritization of design variables for further optimization.

Methodology and research methods. The research utilizes statistical methods including machine learning, and numerical fracture flowback model. The algorithms were developed in Python programming language. Also, the foundations of reservoir and production engineering were applied to develop the analytical Productivity Index approach.

Main results submitted for the defense:

1. It is substantiated that the field identifier parameter represents a primary source of domain shift in the considered hydraulic fracturing database and must be explicitly accounted for prior to solving the forward problem. The presence of multiple underlying data distributions demonstrates that a single global data-driven model is insufficient to reliably generalize across the entire dataset.

2. Based on the results of domain shift diagnostics, a field aggregation-based clustering approach using KMeans combined with a stabilization pipeline is developed to enable domain-aware learning. This procedure results in the identification of two distinct clusters: a dominant cluster comprising the largest field and its neighboring fields (accounting for more than 50% of the dataset), and a second, heterogeneous cluster.

3. A physically informed data filtering procedure, incorporating the Productivity Index and a numerical fracture cleanup model, is proposed and applied to the dominant cluster. This procedure constrains the dataset to physically plausible operating regimes and yields a high-fidelity subset consisting of 1 081 wells suitable for subsequent data-driven analysis.

4. It is demonstrated that the use of the high-fidelity homogeneous subset leads to a significant improvement in machine-learning model predictive performance and interpretability, despite a reduction in the overall training sample size.

5. On the basis of machine-learning models trained on the refined dataset, stable and physically interpretable optimal trends in hydraulic fracturing design parameters are identified, accompanied by uncertainty quantification.

Personal contribution of the author. All the results of the dissertation were obtained personally by the applicant or with his direct involvement. Field data was provided through a collaboration between Skolkovo Institute of Science and Technology and LLC "Gazpromneft-STC". The applicant performed the search and analysis of the literature related to the research topic. The author together with the scientific supervisor, A.A. Osiptsov, D. Sc., and the scientific co-supervisor, S.A. Boronin, Cand. Sc., participated in the formulation of aims and objectives of the dissertation. The development of the experimental methodology was conducted personally by the author. The results were obtained and analyzed personally by the author.

In particular, the collection and preprocessing of the provided data to formulate the digital database was performed by the author in collaboration with research engineers D.O. Popkov (Skoltech) and V.M. Duplyakov, Ph.D. (Skoltech). The development of the ML methods (the forward problem, the inverse problem) was initially designed by the author and further experimentally improved by himself with the participation of D.O. Popkov and V.M. Duplyakov. The exploratory data analysis and data quality methods including the analytical approach and the application of the flowback model approach were developed by the author. The numerical model was provided by the co-supervisor S.A. Boronin while implemented personally by the author.

Validity of the obtained results. The dissertation work was performed at the high scientific level. The research results and conclusions are grounded in rigorous

scientific methodology and validated through multiple complementary approaches. The large dataset used was thoroughly analyzed and verified via novel physically-based analytical methods and numerical modeling, ensuring high data fidelity. Multiple ML models were trained and validated with appropriate cross-validation techniques on verified data subsets, demonstrating consistency and robustness of predictions. The fracture cleanup numerical model was adapted on field data, further confirming the accuracy of reservoir parameter estimations. Collaborative data provision by industry partners and extensive literature support reinforces the validity of the research. Peer-reviewed journal publications and presentations at international scientific conferences serve as qualified external validation and recognition of the scientific contributions. The materials of the dissertation are presented in the following two published works in the peer-reviewed journals, one Russian patent, three certificates of software state registration and four conferences.

Approbation. The results and main provisions of the work were presented at international and Russian conferences:

- First EAGE Digitalization Conference and Exhibition. November 2020, Vienna, Austria.

- SPE Symposium: Hydraulic Fracturing, Russia. September 2020, Moscow, Russia.

- Intelligent data analysis in oil and gas industry 2022. 2022, Novosibirsk, Russia.

- RN Digital Transparency 2022. October 2022, Ufa, Russia.

Publications. The results of the work are presented in 6 publications,

including 2 papers in scientific Q1 and Q2 ranked journals indexed by Scopus and Web of Science, 1 patent, and 3 certificates of software state registration.

Papers:

1. Morozov A., Popkov D., Duplyakov V., Mutalova R., Osiptsov A., Vainshtein A., Burnaev E., Shel E., Paderin G.. Data-driven model for hydraulic fracturing design optimization: Focus on building digital database and production forecast //Journal of Petroleum Science and Engineering. - 2020. - T. 194. - P. 107504.

2. Duplyakov V., Morozov A., Popkov D., Shel E., Vainshtein A., Burnaev E., Osiptsov A., Paderin G.. Data-driven model for hydraulic fracturing design optimization. Part II: Inverse problem //Journal of Petroleum Science and Engineering. - 2022. - T. 208. - P. 109303.

Patents and certificates:

1. Patent for invention No. 2775034 Russian Federation. A way to select the optimal fracturing design based on intelligent analysis of field data to increase hydrocarbon production. Application No. 2021122523. Filed on July 28, 2021. Registered in the State Register of Inventions of the Russian Federation on June 27, 2022 / Paderin G.V., Shel E.V., Kabanova P.K., Osiptsov A.A., Burnaev E.V., Vainshtein A.L., Duplyakov V.M., Morozov A.D., Popkov D.O. - 27 pages.

2. Certificate of software state registration No. 2023668422 Russian Federation. Well analog selection in terms of hydraulic fracturing module. Application No. 2023667686. Date of receipt: August 28, 2023. Registered in the Register of Computer Programs on August 28, 2023 / Paderin G.V., Shel E.V., Kabanova P.K., Osiptsov A.A., Burnaev E.V., Vainshtein A.L., Duplyakov V.M., Morozov A.D., Popkov D.O.

3. Certificate of software state registration No. 2023668421 Russian Federation. Fracturing design optimization based on well production prediction after hydraulic fracturing module. Application No. 2023667685. Registered in the Register of Computer Programs on August 28, 2023 / Paderin G.V., Shel E.V., Kabanova P.K., Osiptsov A.A., Burnaev E.V., Vainshtein A.L., Duplyakov V.M., Morozov A.D., Popkov D.O.

4. Certificate of software state registration No. 2023668393 Russian Federation. Production prediction after hydraulic fracturing based on geology and hydraulic fracture parameters. Application No. 2023667671. Registered in the Register of Computer Programs on August 28, 2023 / Paderin G.V., Shel E.V., Kabanova P.K., Osiptsov A.A., Burnaev E.V., Vainshtein A.L., Duplyakov V.M., Morozov A.D., Popkov D.O.

Dissertation structure. The dissertation consists of an introduction, 5 chapters, and a conclusion. The dissertation is 233 pages long, including 50 figures and 14 tables. The list of references contains 154 titles.

Заключение диссертации по теме «Другие cпециальности», Морозов Антон Дмитриевич

Conclusion

This dissertation demonstrates a data-driven framework for analyzing and predicting hydraulic fracturing performance under uncertainty, with explicit emphasis on data quality, domain structure, and physical consistency. The work integrates exploratory data analysis, forward data-driven predictive modeling, and uncertainty-aware inverse optimization into a unified methodological pipeline that explicitly links data verification, predictive modeling, and retrospective design assessment.

A key result of the study is the quantitative demonstration that data quality and domain homogeneity decisively affect predictive stability and interpretability in large-scale hydraulic fracturing datasets. Through systematic exploratory analysis, clustering, and physically motivated filtering, a high-fidelity dataset was constructed that enabled both improved predictive accuracy and meaningful physical interpretation.

The forward modeling results confirmed that machine learning models can predict 90-day cumulative fluid production with stable generalization performance across homogeneous domains. Uncertainty estimation via ensemble techniques provided robust measures of predictive confidence, which enabled differentiation between genuinely high-performing design regions and artifacts of data heterogeneity.

Building upon the forward model, an uncertainty-aware inverse optimization framework was developed to assess hydraulic fracturing design potential. The inverse analysis revealed systematic and physically consistent design trends and demonstrated that optimization potential strongly depends on completion type and fracture staging, with diminishing returns observed for highly complex multi-stage treatments. Importantly, the inverse problem was formulated and interpreted as a retrospective analysis, aimed at identifying latent improvement potential rather than issuing direct operational prescriptions.

From a practical perspective, the proposed framework offers substantial advantages over traditional physics-based workflows in terms of computational efficiency and flexibility. While detailed numerical physics-based simulations may require hours to days of computation, the data-driven model and inverse optimization can be executed within minutes. This enables rapid screening,

benchmarking of existing practices, and exploration of alternative design strategies. In particular, the identified optimal trends in hydraulic fracturing design parameters support more efficient decision-making and may be used to inform the development of pumping schedules based on retrospective analysis.

While economic considerations were intentionally excluded to isolate technical effects, the framework is inherently extensible. Given appropriate cost and economic data, the objective function can be reformulated to maximize economic metrics such as net present value or risk-adjusted returns without fundamental changes to the methodology.

The main limitations of the study arise from the assumption of approximate well independence and the retrospective nature of the analysis. In real-field conditions, inter-well interference and reservoir-scale interactions may influence production response. Addressing these effects represents a natural direction for future work and may involve coupling the proposed data-driven framework with physics-based reservoir simulation or hybrid physics-machine learning models.

This dissertation demonstrates that uncertainty-aware, domain-restricted machine learning provides a powerful and practical tool for hydraulic fracturing analysis. The proposed approach bridges the gap between purely empirical modeling and physics-based simulation, offering a fast, flexible, and interpretable methodology that can be readily integrated into the operational workflows of vertically integrated oil and gas companies.

The author expresses gratitude and deep appreciation to his supervisor, A. A. Osiptsov, for the opportunity to work on this cutting-edge engineering project, as well as his support, assistance, and scientific guidance. He also thanks his co-supervisor, S. A. Boronin, and oil and gas industry expert, A. L. Vainshtein, for their assistance in formulating and solving applied problems, the successful results of which led to the active development of scientific thought. He also thanks his colleagues, D. O. Popkov and V. M. Duplyakov, for their shared contributions and the opportunity to work with true professionals. The author is also grateful to the management of LLC "Gazpromneft-STC" for organizational, financial support and field data provision of this scientific project. The author also thanks the educational staff of West Virginia University and Skolkovo Institute of Science and Technology for the opportunity to be part of the scientific community, acquire relevant professional skills and become who I wanted to be.

Список литературы диссертационного исследования кандидат наук Морозов Антон Дмитриевич, 2026 год

References

1. Khan Abdul Muqtadir, Luo Yin, Ugarte Esteban, Bannikov Denis. Physics-informed machine learning for hydraulic fracturing—part i: The backbone model // SPE EOR Conference at Oil and Gas West Asia / SPE. — 2024. — P. D021S016R002.

2. Li Weirong, Zhang Tianyang, Liu Xinju et al. Machine learning-based fracturing parameter optimization for horizontal wells in Panke field shale oil // Scientific Reports. — 2024. — Vol. 14, no. 1. — P. 6046.

3. Soroush Mohammad, Mohammadtabar Mohammad, Roostaei Morteza et al. An industry overview of downhole monitoring using distributed temperature sensing: Fundamentals and two decades deployment in oil and gas industries // SPE Western Regional Meeting / SPE. — 2021. — P. D031S014R001.

4. Soroush Mohammad, Mohammadtabar Mohammad, Roostaei Morteza et al. Downhole monitoring using distributed acoustic sensing: fundamentals and two decades deployment in oil and gas industries // SPE EOR Conference at Oil and Gas West Asia / SPE. — 2022. — P. D031S020R004.

5. Ma Yuanyuan, Eaton David W, Wang Chaoyi, Aklilu Alemayehu. Characterizing hydraulic fracture growth using distributed acoustic sensing-recorded microseismic reflections // Geophysics. — 2023. — Vol. 88, no. 6. — P. WC47-WC57.

6. Uchendu O., Omomo K. O., Esiri A. E. Theoretical Insights into Uncertainty Quantification in Reservoir Models: A Bayesian and Stochastic Approach // International Journal of Engineering Research and Development. — 2024. — Vol. 20, no. 11. — P. 987-997.

7. Fathy Mohammad, Haghighi Foojan Kazemzadeh, Ahmadi Mohammad. Uncertainty quantification of reservoir performance using machine learning algorithms and structured expert judgment // Energy. — 2024. — Vol. 288. — P. 129906.

8. Lu Chunhua, Jiang Hanqiao, Yang Jinlong et al. Simulation and optimization of hydraulic fracturing in shale reservoirs: A case study in the Permian Lucao-gou formation, China // Energy Reports. — 2022. — Vol. 8. — P. 2558-2573.

9. Luo Shangui, Zhao Yulong, Zhang Liehui et al. Integrated simulation for hydraulic fracturing, productivity prediction, and optimization in tight conglomerate reservoirs // Energy & Fuels. — 2021. — Vol. 35, no. 18. — P. 14658-14670.

10. McPhee Colin, Reed Jules, Zubizarreta Izaskun. Best practice in coring and core analysis // Developments in petroleum science. — Elsevier, 2015. — Vol. 64. — P. 1-15.

11. Wang Yamin, Wang Zhenlin, Zhang Zhengchen et al. Recent techniques on analyses and characterizations of shale gas and oil reservoir // Energy Reviews.

— 2024. — Vol. 3, no. 2. — P. 100067.

12. Yang R, Jia A., He S. et al. Pore structure characterization and reservoir quality evaluation of analcite-rich shale oil reservoir from the bohai bay basin // Energy & Fuels. — 2021. — Vol. 35, no. 11. — P. 9349-9368.

13. Martinez Jenny Paola Rueda, Mendoza Jose Luis et al. Best laboratory practices for reducing uncertainty in the pressure differential (AP) measurements in core-flooding tests for the petrophysical characterization of reservoirs // ITEGAM-JETIA. — 2023. — Vol. 9, no. 39. — P. 42-51.

14. Rouainia Mohamed, Goodarzi Majid, Charlton Tom et al. Assessment of the elastic response of shale using multiscale mechanical testing and homogenisation. — 2020. — Vol. 205. — P. 04013.

15. Al-Aamri Mohammed, Al-Kindi Ahmed, Terras Yan et al. Using Continuous Core Measurements to Reduce the Uncertainty on Rock Strength vis-à-vis Ge-omechanical Modeling in a Tight Gas Reservoir in Sultanate of Oman. — 2022.

— P. D021S016R003.

16. Mehmani Ayaz, Kelly Shaina, Torres-Verdin Carlos. Leveraging digital rock physics workflows in unconventional petrophysics: A review of opportunities, challenges, and benchmarking // SPWLA Annual Logging Symposium / SP-WLA. — 2019. — P. D043S013R004.

17. Amabeoku Maclean O, Al-Ghamdi Tariq M, Mu Yaoming et al. Evaluation and application of digital rock physics (DRP) for special core analysis in carbonate formations // IPTC 2013: International Petroleum Technology Conference / European Association of Geoscientists & Engineers. — 2013. — P. cp-350.

18. Wei Jianguang, Li Jiangtao, Yang Ying et al. Digital-rock construction of shale oil reservoir and microscopic flow behavior characterization // Processes.

— 2023. — Vol. 11, no. 3. — P. 697.

19. Liu Qing, Sun Mengdi, Sun Xianda et al. Pore network characterization of shale reservoirs through state-of-the-art X-ray computed tomography: A review // Gas Science and Engineering. — 2023. — Vol. 113. — P. 204967.

20. El Din S Serag, Dernaika MR, Al Hosani I et al. Whole core versus plugs: Integrating log and core data to decrease uncertainty in petrophysical interpretation and STOIP calculations. — 2010. — P. SPE-137679.

21. Ahmed Tarek. Equations of state and PVT analysis. — Elsevier, 2013. — P. 278.

22. Esposito Rogerio Oliveira, Alijo Pedro Henrique Rodrigues, Scilipoti Jose Antonio, Tavares Frederico Wanderley. Compositional grading in oil and gas reservoirs. — Gulf Professional Publishing, 2017. — P. 278.

23. Ibeh SU, Chubueze SE. PVT analysis: validity checks and EOS tuning techniques for retrograde gas condensate reservoirs. — 2016. — P. SPE-184314.

24. Anyadiegwu Charley Iyke, Okalla Christian Emelu, Kerunwa Anthony et al. Data-Driven Modeling and Analysis of Reservoir Fluid Behavior: A Machine Learning Approach to PVT Characterization in Heterogeneous Reservoirs // Engineering World. — 2025. — Vol. 7. — P. 99 - 111.

25. Wu Zhongwei, Cui Chuanzhi, Jia Peifeng et al. Advances and challenges in hydraulic fracturing of tight reservoirs: A critical review // Energy Geoscience.

— 2022. — Vol. 3, no. 4. — P. 427-435.

26. Cipolla Craig L, Lolon EP, Mayerhofer Michael J. Resolving Created, Propped, and Effective Hydraulic Fracture Length. — 2008. — P. cp-148.

27. Rosberg Jan-Erik. Well Testing, Methods and Applicability. — 2010. — P. 56.

28. Kim Tae Hong, Lee Sung Jun, Lee Kun Sang. Estimation of Permeability and Initial Pressure in Reservoir by DFIT Data Analysis // Tunnel and Underground Space. — 2013. — Vol. 23, no. 3. — P. 169-179.

29. Benish TG, Brown JS, Chhatre SS et al. Evaluation of completion designs and fracture heterogeneity via an instrumented slant monitor well. — 2024. — P. D011S001R001.

30. Bahrami Nick. Well test analysis for characterizing unconventional gas reservoirs // Sustainable Natural Gas Reservoir and Production Engineering. —

2022. — P. 217-242.

31. Nwankwo Cosmas, Alade Samuel M, Agbakwuru O.A et al. Investigating the Frontiers of Deep Learning and Machine Learning: A Comprehensive Overview of Key Challenges in Missing Well Log Estimation // International research journal of innovations in engineering and technology. — 2024. — Vol. 08. — P. 01 - 15.

32. Mondol Nazmul Haque. Well logging: Principles, applications and uncertainties // Petroleum geoscience: From sedimentary environments to rock physics.

— Springer, 2015. — P. 385-425.

33. Zhongliang SUN, Zhiming LI, Baojian SHEN et al. NMR technology in reservoir evaluation for shale oil and gas // Petroleum Geology Experiment (Chinese). — 2022. — Vol. 44, no. 5. — P. 930-940.

34. Jiang Tianmin, Bonnie Ron JM, Correa Thiago Simoes et al. Integrated Reservoir Characterization Using Unsupervised Learning on Nuclear Magnetic Resonance (NMR) T 1-T 2 Logs // Petrophysics. — 2022. — Vol. 63, no. 03.

— P. 277-289.

35. Gainitdinov Batyrkhan, Meshalkin Yury, Orlov Denis et al. Predicting miner-alogical composition in unconventional formations using machine learning and well logging data. — 2024. — P. IPTC-23487.

36. Hu Kezhen, Liu Xiaojun, Chen Zhuoheng, Grasby Stephen E. Mineralogical characterization from geophysical well logs using a machine learning approach: Case study for the Horn River Basin, Canada // Earth and Space Science. —

2023. — Vol. 10, no. 12. — P. e2023EA003084.

37. Chowdhury Mohammad Sumon, Tanjil H Al, Akter Sigma et al. Production Logging and its Implementation: A Technical Review // International Journal of Petroleum and Petrochemical Engineering. — 2019. — Vol. 5, no. 2. — P. 42-51.

38. Maity S, Manzar A, Alshabibi H et al. Enhancing Confidence in Multiphase Flow Profiling with Innovative Downhole Sensors // International Petroleum Technology Conference / IPTC. — 2024. — P. IPTC-23924.

39. Alanazi AA, Alharthi A, Ogunsanwo T, Amjad B. A Methodology for Precise Flow Contribution and Allocation in Multi-lateral Wells // Abu Dhabi International Petroleum Exhibition and Conference / SPE. — 2024. — P. D041S131R001.

40. Upadhye Vishwajit, Malyavko Evgeny, Kashapov Denis. Using Tracer-Based Technologies for Production Profiling in a Hydraulic Fracture to Optimise the Hydraulic Fracturing Design // SPE Middle East Oil and Gas Show and Conference / SPE. — 2023. — P. D021S070R005.

41. Katashov Alexander, Ovchinnikov Kirill, Belova Anna et al. Using markers for Production Logging in horizontal gas wells with multistage hydraulic fracturing // SPE Annual Technical Conference and Exhibition? / SPE. — 2020. — P. D031S033R002.

42. Velychko Oleh, Dovhan Vasyl, Nikitenko Denys, Brezytskyi Jaroslav. Evaluation of the long-term drift of high precision resistance measures // Measurement: Sensors. — 2025. — Vol. 38. — P. 101430.

43. Shahraeeni Mohammad, Curtis Andrew. Facies uncertainty in petrophysical forward function: A West Africa offshore field example // SEG Technical Program Expanded Abstracts 2011. — Society of Exploration Geophysicists, 2011. — P. 2261-2265.

44. Adams SJ. Quantifying petrophysical uncertainties. — 2005. — P. SPE-93125.

45. Archer STEWART H, King GA, Uden RICHARD C. An integrated approach to reservoir characterization using seismic and well data. — 1993. — P. cp-46.

46. Kumar Dhananjay. Seismic AVO analysis for reservoir characterization // Developments in Structural Geology and Tectonics. — Elsevier, 2023. — Vol. 6.

— P. 259-284.

47. Ochai-Audu Eudorah. Technology Focus: Seismic (February 2025) // Journal of Petroleum Technology. — 2025. — Vol. 77, no. 02. — P. 90-91.

48. Cai Yanjun, Wu Jianping, Liu Yaning, Gao Shijie. Advances in seismological methods for characterizing fault zone structure // Earthquake Science. — 2024.

— Vol. 37. — P. 122 - 138.

49. Dupuy Bastien, Garambois Stéphane, Asnaashari Amir et al. Estimation of rock physics properties from seismic attributes—Part 2: Applications // Geophysics. — 2016. — Vol. 81, no. 4. — P. M55-M69.

50. Amaru Maisha, Hoelting Cory James, Ivanova Natalia, Osypov Konstantin. Introduction to this special section: Velocity-model uncertainty // Geophysics.

— 2017. — Vol. 36. — P. 126.

51. Wang Shuang, Gong Xiangbo, Huang Xingguo et al. Bayesian reverse time migration with quantified uncertainty // Geophysics. — 2024. — Vol. 89, no. 2. — P. S145-S154.

52. Oliveira Sérgio Adriano Moura, Franco Annalisa, Moraes Fernando et al. A robust workflow for quantitative seismic reservoir characterization: example from noisy land data // Interpretation. — 2025. — P. 1 - 53.

53. Bakku Sudhish K, Wills Peter, Fehler Michael et al. Vertical seismic profiling using distributed acoustic sensing in a hydrofrac treatment well. — 2014. — P. SEG-2014.

54. Mateeva Albena, Lopez Jorge, Potters Hans et al. Distributed acoustic sensing for reservoir monitoring with vertical seismic profiling // Geophysical Prospecting. — 2014. — Vol. 62, no. 4. — P. 679-692.

55. Al-Qasim Abdulaziz, Alabduh Sharidah, Alabdullateef Muhannad, Alsubhi Mu-taz. Expanding the envelope of fiber-optic sensing for reservoir description and dynamics. — 2021. — P. D011S004R002.

56. DeMerchant Michael D, Brown Anthony W, Bao Xiaoyi, Bremner Theodore W. Brillouin-scattering-based strain sensing // Smart Structures and Materials 1999: Sensory Phenomena and Measurement Instrumentation for Smart Structures and Materials / SPIE. — Vol. 3670. — 1999. — P. 352-358.

57. Farhadiroushan M, Parker Tom, С. В. Шаталин et al. Integrated Distributed Strain Sensing for Wellbore and Reservoir Monitoring // Geophysical monograph. — 2024. — P. 17 - 28.

58. Li Meng, Wang Hua, Tao Guo. Current and future applications of distributed acoustic sensing as a new reservoir geophysics tool // The Open Petroleum Engineering Journal. — 2015. — Vol. 8, no. 1. — P. 272-281.

59. Esiri Andrew Emuobosa, Jambol Dazok Donald, Ozowe Chinwe. Enhancing reservoir characterization with integrated petrophysical analysis and geostatis-tical methods // Open access research journal of multidisciplinary studies. — 2024. — Vol. 7. — P. 168 - 179.

60. Soares Amilcar, Azevedo Leonardo. Geostatistics for seismic characterization of oil reservoirs // Handbook of Mathematical Geosciences: Fifty Years of IAMG. — Springer International Publishing Cham, 2018. — P. 483-504.

61. Doligez Brigitte, Ravalec Mickaele Le, Bouquet Sarah, Adelinet M. A Review of Three Geostatistical Techniques for Realistic Geological Reservoir Modeling Integrating Multi-scale Data // Bulletin of Canadian Petroleum Geology. — 2015. — Vol. 63. — P. 277 - 286.

62. Caers Jef, Srinivasan Sanjay. Chapter 23 Combining geological information with seismic and production data. — Elsevier, 2003. — Vol. 51. — P. 499 -525.

63. Esiri Andrew Emuobosa, Jambol Dazok Donald, Ozowe Chinwe. Enhancing reservoir characterization with integrated petrophysical analysis and geostatistical methods // Open access research journal of multidisciplinary studies. — 2024. — Vol. 7. — P. 168 - 179.

64. Rasoulzadeh S, Tehrani A Moradi. Integrating data and knowledge into highly detailed 3D reservoir models using Geostatistical Seismic Reservoir Characterization. — 2022. — Vol. 2022, no. 1. — P. 1-5.

65. Shutov Grigoriy, Duplyakov Viktor, Davoodi Shadfar et al. A deep learning-aided approach for estimating field permeability map by fusing well logs, well tests, and seismic data // Petroleum. — 2025. — Vol. 11, no. 6. — P. 813-824.

66. Fayyad Usama, Piatetsky-Shapiro Gregory, Smyth Padhraic. From Data Mining to Knowledge Discovery in Databases // AI Magazine. — 1996. — Mar. — Vol. 17, no. 3. — P. 37.

67. Kikani Jitendra. Reservoir surveillance. — Sociaty Of Petroleum Engineers, 2013. — P. 138-159.

68. Ouyang Liang-Biao, Kikani Jitendra. Improving Permanent Downhole Gauge (PDG) Data Processing via Wavelet Analysis // Society of Petroleum Engineers. — 2002. — URL: http://dx.doi.org/10.2118/78290-MS.

69. Akbar Bibi Hussain, Al-Aradi Huda Jassim, Achmad Pajar Rachman, Khan Waqar Ullah. Achieving Productivity and Operational Efficiency, and High-Quality Data Through Automation in Well Log Data Quality Control and Acceptance Process Using AI/ML Techniques // Abu Dhabi International Petroleum Exhibition and Conference / SPE. — 2022. — P. D021S068R004.

70. Al Hinai Adnan Saif, Florez Juan Chavez, Al Hinai Mohamed Said et al. Qualitative & Quantitative Digital Frac Platform for Reservoir Stimulation Operations in Oman Fields // SPE EOR Conference at Oil and Gas West Asia / SPE. — 2022. — P. D032S067R002.

71. Petersen Egil Boye, Larsen Alex, Craig Lee et al. Rock and Fluid Data: An Integrated Effort on Improving Subsurface Analysis and Modelling Workflows // SPE Norway Subsurface Conference / SPE. — 2022. — P. D011S003R003.

72. Andrianova Alla, Simonov Maxim, Perets Dmitry et al. Application of machine learning for oilfield data quality improvement // SPE Russian Petroleum Technology Conference / SPE. — 2018. — P. D023S029R005.

73. Perkins Thomas K, Kern Loyd R. Widths of hydraulic fractures // Journal of Petroleum Technology. — 1961. — Vol. 13, no. 09. — P. 937-949.

74. Nordgren Rolf P. Propagation of a vertical hydraulic fracture // Society of Petroleum Engineers Journal. — 1972. — Vol. 12, no. 04. — P. 306-314.

75. Khristianovich S. A., Zheltov Y. P. On hydraulic fracturing of oil strata // Izvestiya Akademii Nauk SSSR, Otdelenie Tekhnicheskikh Nauk. — 1955. — no. 5. — P. 3-41.

76. Geertsma Jan, de Klerk F. A comparison of the theories for predicting width and extent of vertical hydraulically induced fractures // Journal of Petroleum Technology. — 1969. — Vol. 21, no. 01. — P. 1571-1581.

77. Sneddon Ian Naismith. The distribution of stress in the neighbourhood of a crack in an elastic solid // Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences. — 1946. — Vol. 187, no. 1009. — P. 229-260.

78. Ismail Atif, Azadbakht Saman. A comprehensive review of numerical simulation methods for hydraulic fracturing // International Journal for Numerical and Analytical Methods in Geomechanics. — 2024. — Vol. 48, no. 5. — P. 1433-1459.

79. Adachi José, Siebrits Emmanuel, Peirce Anthony, Desroches Jean. Computer simulation of hydraulic fractures // International Journal of Rock Mechanics and Mining Sciences. — 2007. — Vol. 44, no. 5. — P. 739-757.

80. Zhou Jing. Hydraulic fracture propagation modeling and data-based fracture identification // The University of Utah. — 2016. — P. 6.

81. SADD MARTIN H. 5 - Formulation and Solution Strategies // Elasticity / Ed. by Martin H. Sadd. — Burlington: Academic Press, 2005. — P. 83-102.

82. Zheng An-xing, Luo Xian-qi. Hydro-mechanical modeling of impermeable discontinuity in rock by extended finite element method // Journal of Central South University. — 2015. — Vol. 22, no. 11. — P. 4337-4346.

83. Li Xiaogang, Liu Changyin, Yi Liang-Ping et al. A Review and Prospect of Numerical Simulation of Complex Hydraulic Fracture Propagation in Unconventional Reservoirs // international conference on Modelling and simulation. — 2017. — P. 87 - 90.

84. Cundall Peter, Strack Otto D. L. Discussion: A discrete numerical model for granular assemblies // Geotechnique. — 1980. — Vol. 30. — P. 331 - 336.

85. Crouch S. L. Solution of plane elasticity problems by the displacement discontinuity method. I. Infinite body solution // International Journal for Numerical Methods in Engineering. — 1976. — Vol. 10, no. 2. — P. 301-343.

86. Chen Bin, Barboza B., Sun Yanan et al. A Review of Hydraulic Fracturing Simulation // Archives of Computational Methods in Engineering. — 2021. — Vol. 29. — P. 1 - 58.

87. Osiptsov Andrei A. Fluid mechanics of hydraulic fracturing: a review // Journal of petroleum science and engineering. — 2017. — Vol. 156. — P. 513-535.

88. Osiptsov AA, Garagash IA, Boronin SA et al. Impact of flowback dynamics on fracture conductivity // Journal of Petroleum Science and Engineering. — 2019. — P. 106822.

89. Vainshtein Albert, Fisher Georgii, Boronin Sergei et al. Field Testing of the Flowback Technology for Multistage-Fractured Horizontal Wells: Test Results and Primary Interpretation of the Results. — Vol. Day 4 Thu, October 29, 2020 of SPE Russian Petroleum Technology Conference. — 2020. — 10. — P. D043S023R001.

90. Hastie T., Tibshirani R., Friedman J.H. The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer series in statistics. — Springer, 2009. — P. 160, 356.

91. Belson William A. Matching and Prediction on the Principle of Biological Classification // Journal of the Royal Statistical Society. Series C (Applied Statistics). — 1959. — Vol. 8, no. 2. — P. 65-75.

92. Arik Sercan O, Pfister Tomas. Tabnet: Attentive interpretable tabular learning. — 2021. — Vol. 35, no. 8. — P. 6679-6687.

93. Gorishniy Yury, Rubachev Ivan, Khrulkov Valentin, Babenko Artem. Revisiting deep learning models for tabular data // Advances in neural information processing systems. — 2021. — Vol. 34. — P. 18932-18943.

94. Friedman Jerome H. Greedy function approximation: a gradient boosting machine // Annals of statistics. — 2001. — P. 1189-1232.

95. Sharma Pushan, Chung Wai Tong, Akoush Bassem, Ihme Matthias. A review of physics-informed machine learning in fluid mechanics // Energies. — 2023.

— Vol. 16, no. 5. — P. 2343.

96. Karniadakis George Em, Kevrekidis Ioannis G, Lu Lu et al. Physics-informed machine learning // Nature Reviews Physics. — 2021. — Vol. 3, no. 6. — P. 422-440.

97. Meng Chuizheng, Griesemer Sam, Cao Defu et al. When physics meets machine learning: A survey of physics-informed machine learning // Machine Learning for Computational Science and Engineering. — 2025. — Vol. 1, no. 1. — P. 20.

98. Xue Liang, Liu Yuetian, Xiong Yifei et al. A data-driven shale gas production forecasting method based on the multi-objective random forest regression // Journal of Petroleum Science and Engineering. — 2021. — Vol. 196.

— P. 107801. — URL: https://www.sciencedirect.com/science/article/pii/ S0920410520308627.

99. Yang Huohai, Liu Xuanyu, Chu Xiangshu et al. Optimization of tight gas reservoir fracturing parameters via gradient boosting regression modeling // Heliyon. — 2024. — Vol. 10, no. 5. — P. e27015.

100. Ockree Matthew, Brown Kenneth G, Frantz Joseph et al. Integrating big data analytics into development planning optimization // SPE Eastern Regional Meeting / SPE. — 2018. — P. D043S005R001.

101. Pan Yuewei, Bi Ran, Zhou Peng et al. An effective physics-based deep learning model for enhancing production surveillance and analysis in unconventional reservoirs // SPE/AAPG/SEG Unconventional Resources Technology Conference / URTEC. — 2019. — P. D023S035R001.

102. Singleton Scott, Clar F Herrero, Monaco A. Data-driven approach to optimize stimulation design in eagle ford formation // Unconventional Resources Technology Conference, Denver, Colorado, 22-24 July 2019 / GeoScienceWorld. — 2019. — P. 4317-4336.

103. Lizhe Li, Fujian Zhou, You Zhou et al. The prediction and optimization of Hydraulic fracturing by integrating the numerical simulation and the machine learning methods // Energy Reports. — 2022. — Vol. 8. — P. 15338-15349.

104. Park Jaeyoung, Datta-Gupta Akhil, Singh Ajay, Sankaran Sathish. Hybrid physics and data-driven modeling for unconventional field development and its application to US onshore basin // Journal of Petroleum Science and Engineering. — 2021. — Vol. 206. — P. 109008.

105. Morozov Anton D, Popkov Dmitry O, Duplyakov Victor M et al. Data-driven model for hydraulic fracturing design optimization: Focus on building digital database and production forecast // Journal of Petroleum Science and Engineering. — 2020. — Vol. 194. — P. 107504.

106. Karami Ali, Akbari Ali, Kazemzadeh Yousef, Nikravesh Hamed. Enhancing hydraulic fracturing efficiency through machine learning // Journal of Petroleum Exploration and Production Technology. — 2025. — Vol. 15, no. 1. — P. 5.

107. Ma Yulin, Ye Man. Application of Machine Learning in Hydraulic Fracturing: A Review // ACS Omega. — 2025. — Vol. 10. — P. 10769 - 10785.

108. Lu Y., Yang F., Bai T. et al. Shale oil occurrence mechanisms: A comprehensive review of the occurrence state, occurrence space, and movability of shale oil // Energies. — 2022. — Vol. 15, no. 24. — P. 9485.

109. Xiao Cong, Zhang Shicheng, Ma Xinfang et al. Surrogate-assisted hydraulic fracture optimization workflow with applications for shale gas reservoir development: A comparative study of machine learning models // Natural Gas Industry B. — 2022. — Vol. 9, no. 3. — P. 219-231.

110. Ibrahim Ahmed Farid, Alarifi Sulaiman A, Elkatatny Salaheldin. Application of machine learning to predict estimated ultimate recovery for multistage hydrauli-cally fractured wells in niobrara shale formation // Computational Intelligence and Neuroscience. — 2022. — Vol. 2022, no. 1. — P. 7084514.

111. Duplyakov V.M., Morozov A.D., Popkov D.O. et al. Data-driven model for hydraulic fracturing design optimization. Part II: Inverse problem // Journal of Petroleum Science and Engineering. — 2022. — Vol. 208. — P. 109303.

112. Wang Sen, Qin Chaoxu, Feng Qihong et al. A framework for predicting the production performance of unconventional resources using deep learning // Applied Energy. — 2021. — Vol. 295. — P. 117016.

113. Yu Tianjun, Li Ming, Wang Taiji et al. Machine Learning Application for Hydraulic Fracturing Optimization in a China Tight Gas Field // International Petroleum Technology Conference / IPTC. — 2024. — P. D031S113R008.

114. Mwakipunda Grant Charles, Komba Norga Alloyce, Ayimadu Edwin Twum, Yu Long. Model Development for Brittleness Index Estimation and Depth Determination in Hydraulic Fracturing Operations in Shale Gas Reservoirs Using Machine Learning Algorithms // SPE Journal. — 2025. — P. 1-22.

115. Li Dongshuang, You Shaohua, Liao Q. et al. Prediction of Shale Gas Production by Hydraulic Fracturing in Changning Area Using Machine Learning Algorithms // Transport in Porous Media. — 2023. — Vol. 149. — P. 373-388.

116. Bangi Mohammed Saad Faizan, Kwon J. Deep hybrid modeling of chemical process: Application to hydraulic fracturing // Comput. Chem. Eng. — 2020.

— Vol. 134. — P. 106696.

117. Nashed Samuel, Moghanloo Rouzbeh. Replacing Gauges with Algorithms: Predicting Bottomhole Pressure in Hydraulic Fracturing Using Advanced Machine Learning // Eng. — 2025. — Vol. 6, no. 4. — P. 73.

118. Ben Yuxing, Perrotte Michael, Ezzatabadipour Mohammadmehdi et al. Realtime hydraulic fracturing pressure prediction with machine learning // SPE hydraulic fracturing technology conference and exhibition / SPE. — 2020. — P. D031S008R003.

119. Yonggang Xie, Qian Ma, Zengqiang Jia et al. Hydraulic Fracturing Pressure Prediction with Deep Learning Approach // SPE Oklahoma City Oil and Gas Symposium/Production and Operations Symposium / SPE. — 2025. — P. D021S002R002.

120. Butler Erin, Pertuso Dryonis, Hua Gerald, Stark Price. Automated Hydraulic Fracturing Integrated with Predictive Machine Learning // SPE Hydraulic Fracturing Technology Conference and Exhibition / SPE. — 2022.

— P. D021S005R005.

121. Lundberg Scott M, Lee Su-In. A unified approach to interpreting model predictions // Advances in neural information processing systems. — 2017. — Vol. 30. — Accessed: 29.01.2026. URL: https://arxiv.org/abs/1705.07874.

122. Ribeiro Marco Tulio, Singh Sameer, Guestrin Carlos. "Why should i trust you?"Explaining the predictions of any classifier // Proceedings of the 22nd ACM SIGKDD international conference on knowledge discovery and data mining. — 2016. — P. 1135-1144.

123. Goldstein Alex, Kapelner Adam, Bleich Justin, Pitkin Emil. Peeking inside the black box: Visualizing statistical learning with plots of individual conditional expectation // journal of Computational and Graphical Statistics. — 2015. — Vol. 24, no. 1. — P. 44-65.

124. Chen Yun-Tian, Zhang Dong-Xiao, Zhao Qun, Liu De-Xun. Interpretable machine learning optimization (InterOpt) for operational parameters: A case study of highly-efficient shale gas development // Petroleum Science. — 2023.

— Vol. 20, no. 3. — P. 1788-1805.

125. Sheikhi Garjan Yousef, Ghaneezabadi Mehdi. Machine Learning Interpretabil-ity Application to Optimize Well Completion in Montney // SPE Canada Unconventional Resources Conference / SPE. — 2020. — P. D033S004R003.

126. Gaurav Abhishek // SPE Liquids-Rich Basins Conference-North America / SPE. — 2017. — P. D011S001R002.

127. Bowman Dan. Definitions and Setting. — Dordrecht: Springer Netherlands, 2019. — P. 1-11.

128. Альтемиров Дмитрий Валерьевич. Характеристика Приобского нефтяного месторождения // Молодой ученый. — 2017. — no. 3. — P. 204-207.

129. Little Roderick J. A. A Test of Missing Completely at Random for Multivariate Data with Missing Values // Journal of the American Statistical Association.

— 1988. — Vol. 83, no. 404. — P. 1198-1202.

130. Azur Melissa J., Stuart Elizabeth A., Frangakis Constantine, Leaf Philip J. Multiple imputation by chained equations: What is it and how does it work? //

International Journal of Methods in Psychiatric Research. — Vol. 20, no. 1. — P. 40-49.

131. Kraskov Alexander, Stögbauer Harald, Grassberger Peter. Estimating mutual information // Physical Review E. — 2004. — Vol. 69, no. 6. — P. 066138.

132. Marquardt Donald W. Generalized inverses, ridge regression, biased linear estimation, and nonlinear estimation // Technometrics. — 1970. — Vol. 12, no. 3.

— P. 591-612.

133. Peres Fernanda Fiel. Effect sizes for nonparametric tests // Biochemia Medica.

— 2025. — Vol. 36, no. 1. — P. 4.

134. Moran P. A. P. The statistical significance of geographical series // Journal of the Royal Statistical Society. Series B (Methodological). — 1950. — Vol. 12, no. 2. — P. 247-258.

135. van der Maaten Laurens, Hinton Geoffrey. Visualizing Data using t-SNE // Journal of Machine Learning Research. — 2008. — Vol. 9. — P. 2579-2605.

136. Ester Martin, Kriegel Hans-Peter, Sander Jorg, Xu Xiaowei. A density-based algorithm for discovering clusters in large spatial databases with noise // Proceedings of the Second International Conference on Knowledge Discovery and Data Mining. — KDD'96. — AAAI Press, 1996. — P. 226-231.

137. Hubert Lawrence, Arabie Phipps. Comparing partitions // Journal of Classification. — 1985. — Vol. 2, no. 1. — P. 193-218.

138. Scholz F. W., Stephens M. A. K-Sample Anderson-Darling Tests // Journal of the American Statistical Association. — 1987. — Vol. 82, no. 399. — P. 918-924.

139. Massey Frank J. Jr. The Kolmogorov-Smirnov Test for Goodness of Fit // Journal of the American Statistical Association. — 1951. — Vol. 46, no. 253.

— P. 68-78.

140. Muskat Morris. The flow of homogeneous fluids through porous media // Soil Science. — 1938. — Vol. 46, no. 2. — P. 169.

141. Peaceman D.W. Interpretation of Well-Block Pressures in Numerical Reservoir Simulation(includes associated paper 6988 ) // Society of Petroleum Engineers Journal. — 1978. — 06. — Vol. 18, no. 03. — P. 183-194.

142. Economides M.J. Petroleum Production Systems. — Prentice Hall, 2013. — URL: https://books.google.ru/books?id=Ej9iAwAAQBAJ (online; accessed: 2026-01-29).

143. Каневская Регина Дмитриевна. Математическое моделирование гидродинамических процессов разработки месторождений углеводородов.

— Автономная некоммерческая организация Ижевский институт компьютерных исследований, 2002. — P. 74-80.

144. Bear J. Dynamics of Fluids in Porous Media. Dover Civil and Mechanical Engineering Series. — Dover, 1988. — P. 122.

145. Cinco-Ley Heber, Samaniego-V. Fernando. Transient Pressure Analysis for Fractured Wells // Journal of Petroleum Technology. — 1981. — 09. — Vol. 33, no. 09. — P. 1749-1766.

146. Ozkan Erdal, Brown M, Raghavan Rajagopal, Kazemi Hossein. Comparison of fractured-horizontal-well performance in tight sand and shale reservoirs // SPE Reservoir Evaluation & Engineering. — 2011. — Vol. 14, no. 02. — P. 248-259.

147. Rahmanifard Hamid, Gates Ian. A Comprehensive review of data-driven approaches for forecasting production from unconventional reservoirs: best practices and future directions // Artificial Intelligence Review. — 2024. — Vol. 57, no. 8. — P. 213.

148. Wilcoxon Frank. Individual Comparisons by Ranking Methods // Biometrics Bulletin. — 1945. — Vol. 1, no. 6. — P. 80-83.

149. Breiman Leo. Random forests // Machine learning. — 2001. — Vol. 45, no. 1.

— P. 5-32.

150. Pedregosa F., Varoquaux G., Gramfort A. et al. Scikit-learn: Machine Learning in Python // Journal of Machine Learning Research. — 2011. — Vol. 12. — P. 2825-2830.

151. Chen Tianqi, Guestrin Carlos. XGBoost: A Scalable Tree Boosting System // Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. — ACM. — P. 785-794.

152. Ke Guolin, Meng Qi, Finley Thomas et al. LightGBM: A Highly Efficient Gradient Boosting Decision Tree. — 2017. — 12. — P. 7.

153. Prokhorenkova Liudmila, Gusev Gleb, Vorobev Aleksandr et al. CatBoost: unbiased boosting with categorical features // Proceedings of the 32nd International Conference on Neural Information Processing Systems. — NIPS'18. — Red Hook, NY, USA: Curran Associates Inc., 2018. — P. 6639-6649.

154. Akiba Takuya, Sano Shotaro, Yanase Toshihiko et al. Optuna: A Next-Generation Hyperparameter Optimization Framework // The 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining. — 2019. — P. 2623-2631.