Cover
Vol. 2 No. 2 (2026)

Published: June 30, 2026

Pages: 1-21

Review Article

Response Surface Methodology Applications in Drilling Engineering: Toward Multi-Objective Optimization of Bit Hydraulic Performance—A Critical Review

Dena Mahmood 1 Nada S. Al-Zubaidi 2 Akhmal Sidek 1 Kenny A. Ganie 1 Muftahu N Yahya 3 Fahad Mir 4 Ahmed R. Al-Bajalan 1 Muhammad Shahid 5
1 Petroleum Engineering Department, Faculty of Chemical and Energy Engineering, Universiti Teknologi Malaysia, Johor, 81310 Malaysia
2 Department of Petroleum Engineering, College of Engineering, Al-Naji University, Baghdad10001, Iraq
3 Department of Chemical and Petroleum Engineering, Bayero University Kano, Nigeria
4 Advanced Membrane Technology Research Centre (AMTEC), Universiti Teknologi Malaysia (UTM), 81310 Johor Bahru, Johor, Malaysia
5 UTM Skudai: Universiti Teknologi Malaysia
History
  • Received: April 13, 2026
  • Revised: June 8, 2026
  • Accepted: June 12, 2026
  • Available Online: June 30, 2026
DOI

https://doi.org/10.65505/ETES-26-0005

Abstract

Response Surface Methodology (RSM) has been widely applied in drilling engineering to model and optimize multivariable operational systems. This review critically evaluates recent RSM applications in drilling engineering, identifies their methodological limitations, and examines the extent to which bit-level hydraulic performance parameters have been incorporated into drilling optimization frameworks. A structured review of studies published between 2021 and 2026 was conducted. The selected studies were classified into three categories: mechanical performance optimization, drilling-fluid optimization, and hybrid optimization approaches. Each study was evaluated according to its input variables, response variables, modeling techniques, optimization objectives, reported performance improvements, consideration of physical and operational constraints, and integration of data-driven methods such as Artificial Neural Networks (ANN). The review indicates that most RSM-based studies prioritize outcome-based indicators, particularly rate of penetration (ROP), drilling-fluid rheology, and operational parameter selection. In contrast, bit-level hydraulic parameters, specifically Bit Hydraulic Horsepower (BHHP) and Jet Impact Force (JIF), are rarely treated as primary optimization objectives despite their direct influence on hydraulic energy transfer, rock fragmentation, and cuttings removal at the bit–rock interface. The findings also show that most existing studies employ single-objective optimization and second-order polynomial models, which may limit their ability to represent nonlinear and coupled hydraulic behavior under field operating conditions. This review adds to the existing literature by systematically identifying the limited integration of physics-based hydraulic indicators into RSM-driven drilling optimization and by defining a research direction for hybrid frameworks that combine RSM-based design-space validation, ANN-based nonlinear prediction, and constrained multi-objective optimization of BHHP and JIF. Such frameworks could support more robust, scalable, and field-applicable drilling optimization strategies.

Keywords

References

  1. A. Schultz and R. Rallo, "Toward Drilling the Perfect Geothermal Well: An International Research Coordination Network for Geothermal Drilling Optimization Supported by Deep Machine Learning and Cloud Based Data Aggregation," Golden Field Office, Golden, CO (United States), 2025.
  2. A. N. Al-Dujaili, M. S. Asad, N. Saeed, and N. Tileuberdi, "Optimizing polycrystalline diamond compact bit selection and drilling parameters for deviated wells in the Majnoon Field, Iraq," Scientific Reports, vol. 15, no. 1, p. 3178, 2025, doi: https://doi.org/10.1038/s41598-025-87484-9.
  3. A. Bani Mustafa, A. K. Abbas, M. Alsaba, and M. Alameen, "Improving drilling performance through optimizing controllable drilling parameters," Journal of Petroleum Exploration and Production, vol. 11, pp. 1223-1232, 2021, doi: https://doi.org/10.1007/s13202-021-01116-2.
  4. G. Bi et al., "Study on the mechanism of high-efficiency rock breaking by hydraulic jet based on explicit dynamics," Processes, vol. 11, no. 7, p. 2165, 2023, doi: https://doi.org/10.3390/pr11072165.
  5. M. Al-Rubaii, M. Al-Shargabi, D. Al-Shehri, A. Alyami, and K. M. Minaev, "A novel efficient borehole cleaning model for optimizing drilling performance in real time," Applied Sciences, vol. 13, no. 13, p. 7751, 2023, doi: https://doi.org/10.3390/app13137751.
  6. S. Tewari, U. D. Dwivedi, and S. Biswas, "Intelligent drilling of oil and gas wells using response surface methodology and artificial bee colony," Sustainability, vol. 13, no. 4, p. 1664, 2021, doi: https://doi.org/10.3390/su13041664.
  7. W. Zhu et al., "A Hybrid Deep Learning Approach for Rate of Penetration Prediction in Deepwater Drilling," in Offshore Technology Conference, 2025: OTC, p. D011S007R004, doi: https://doi.org/10.4043/35771-MS.
  8. A. Al-Dujaili, "New advances in drilling operations in sandstone, shale, and carbonate formations: a case study of five giant fields in the Mesopotamia Basin, Iraq," Mining Science and Technology (Russia), vol. 9, no. 4, pp. 308-327, 2024, doi: https://doi.org/10.17073/2500-0632-2023-08-146.
  9. D. Mahmood, A. Sidek, K. A. Ganie, and N. S. Al-Zubaidi, "Enhancing Drilling Efficiency: A Comprehensive Review of Bit Hydraulic Optimization in Rotary Drilling Operations," Petroleum Chemistry, vol. 65, no. 5, pp. 550-557, 2025, doi: https://doi.org/10.1134/S0965544125040097.
  10. M. M. Al-Rubaii, "Real-Time Models of Rig and Drill Bit Hydraulics Optimizes Drilling Efficiency," presented at the Offshore Technology Conference Asia, Kuala Lumpur, Malaysia, 2026. [Online]. Available: https://doi.org/10.4043/36336-MS.
  11. A. H. Asmungi, N. A. Ghazali, S. F. Abdul Manaf, O. S. Jehan Elham, and N. I. Hammizul, "Optimisation of Rheological Properties of Water-Based Mud (WBM) with Natural Additives by Using Response Surface Methodology (RSM)," Key Engineering Materials, vol. 939, pp. 103-114, 2023, doi: https://doi.org/10.4028/p-zcg62q.
  12. H. Chen, Y. Jin, W. Zhang, J. Zhang, L. Ma, and Y. Lu, "Deep neural network prediction of mechanical drilling speed," Energies, vol. 15, no. 9, p. 3037, 2022, doi: https://doi.org/10.3390/en15093037.
  13. L. Velásquez, A. Rubio-Clemente, D. Tobón, F. Botero, C. Arrieta, and E. Chica, "Experimental Optimization of the Propeller Turbine Performance Using the Response Surface Methodology," Sustainability, vol. 16, no. 19, p. 8476, 2024, doi: https://doi.org/10.3390/su16198476.
  14. X. Feng, Y. Xie, S. Liu, and F. Yang, "Influence and Optimization of Geometric Parameters for Small-Radius Curved Tunnel Based on Response Surface Method," Applied Sciences, vol. 13, no. 6, p. 3800, 2023, doi: https://doi.org/10.3390/app13063800.
  15. M. O. Okwu et al., "Investigating the accuracy of artificial neural network models in predicting surface roughness in drilling processes," Procedia Computer Science, vol. 232, pp. 1982-1990, 2024, doi: https://doi.org/10.1016/j.procs.2024.02.020.
  16. S. J. Arunachalam, R. Saravanan, S. Thanikodi, G. Vinuja, and A. J. Santhosh, "Hybrid ANN‐Based Modeling and Optimization of Drilling Performance in Basalt Fiber Composites," Engineering Reports, vol. 8, no. 3, p. e70651, 2026, doi: https://doi.org/10.1002/eng2.70651.
  17. R. H. Allawi, W. J. Al-Mudhafar, M. A. Abbas, and D. A. Wood, "Leveraging Boosting Machine Learning for Drilling Rate of Penetration (ROP) Prediction Based on Drilling and Petrophysical Parameters," Artificial Intelligence in Geosciences, p. 100121, 2025, doi: https://doi.org/10.1016/j.aiig.2025.100121.
  18. M. Mansouri, M. Shayanmehr, and A. Ghaemi, "Exploring the adsorption desulfurization efficiency using RSM and ANN methodologies," Scientific Reports, vol. 15, no. 1, p. 20869, 2025, doi: https://doi.org/10.1038/s41598-025-05688-5.
  19. R. H. Myers, D. C. Montgomery, and C. M. Anderson-Cook, Response surface methodology: process and product optimization using designed experiments. John Wiley & Sons, 2016.
  20. A. Witek-Krowiak, K. Chojnacka, D. Podstawczyk, A. Dawiec, and K. Bubała, "Application of response surface methodology and artificial neural network methods in modelling and optimization of biosorption process," Bioresource technology, vol. 160, pp. 150-160, 2014, doi: https://doi.org/10.1016/j.biortech.2014.01.021.
  21. F. Mohammadinia, A. Ranjbar, F. Ghazi, and S. T. Hosseini, "Rate of penetration prediction in drilling operations: a comparative study of AI models and meta-heuristic approaches," Journal of Petroleum Exploration and Production Technology, vol. 15, no. 7, p. 115, 2025, doi: https://doi.org/10.1007/s13202-025-02020-9.
  22. A. M. Awad, I. A. Hussein, M. S. Nasser, S. A. Ghani, and A. O. Mahgoub, "A CFD-RSM study of cuttings transport in non-Newtonian drilling fluids: Impact of operational parameters," Journal of Petroleum Science and Engineering, vol. 208, p. 109613, 2022, doi: https://doi.org/10.1016/j.petrol.2021.109613.
  23. Y. Li, Z. Xu, J. Xi, H. Zhao, and Z. Fan, "Radial Basis Function Neural Network and Response Surface Methodology-Based Optimization of Glue Breakage in Waste Drilling Fluids," Processes, vol. 13, no. 2, p. 406, 2025, doi: https://doi.org/10.3390/pr13020406.
  24. X. Jia, N. Liu, and X. Zhao, "Optimizing Nanosilica-Enhanced Polymer Synthesis for Drilling Fluids via Response Surface Methodology: Enhanced Fluid Performance Analysis," Journal of Composites Science, vol. 9, no. 6, p. 263, 2025, doi: https://doi.org/10.3390/jcs9060263.
  25. B. Satiyawira et al., "Drilling Fluid Optimization Using Response Surface Methodology," Scientific Contributions Oil and Gas, vol. 48, no. 4, pp. 281-294, 2025, doi: https://doi.org/10.29017/scog.v48i4.1900.
  26. D. Z. Mantegazini, A. Nascimento, M. H. Mathias, O. J. Romero Guzman, and M. Reich, "Optimization of Rate of Penetration and Mechanical Specific Energy Using Response Surface Methodology and Multi-Objective Optimization," Applied Sciences, vol. 15, no. 3, p. 1390, 2025, doi: https://doi.org/10.3390/app15031390.
  27. F. S. Alakbari, M. E. Mohyaldinn, M. A. Ayoub, A. S. Muhsan, and A. Hassan, "Apparent and plastic viscosities prediction of water-based drilling fluid using response surface methodology," Colloids and Surfaces A: Physicochemical and Engineering Aspects, vol. 616, p. 126278, 2021, doi: https://doi.org/10.1016/j.colsurfa.2021.126278.
  28. M. Alhajabdalla, H. Mahmoud, M. S. Nasser, I. A. Hussein, R. Ahmed, and H. Karami, "Application of response surface methodology and Box–Behnken design for the optimization of the stability of fibrous dispersion used in drilling and completion operations," ACS omega, vol. 6, no. 4, pp. 2513-2525, 2021, doi: https://doi.org/10.1021/acsomega.0c04272.
  29. X. Bai, X. Zhang, Y. Xu, and X. Yong, "Synthesis and characterization of sodium carboxymethyl starch‐graft acrylamide/1‐vinyl‐2‐pyrrolidone copolymers via central composite design and using as filtration loss agent in drilling muds," Starch‐Stärke, vol. 73, no. 3-4, p. 2000151, 2021, doi: https://doi.org/10.1002/star.202000151.
  30. I. Ali, M. Ahmad, S. Ridha, C. C. Iferobia, and N. Lashari, "Enhancing drilling mud performance through CMITS-modified formulations: rheological insights and performance optimization," RSC advances, vol. 13, no. 47, pp. 32904-32917, 2023, doi: https://doi.org/10.1039/D3RA06008J.
  31. J. E. Ossai, E. A. Oyedoh, V. O. Magbuwe, and M. I. Atapia, "Optimization of the Formulation of Drilling Mud using Box–Behnken Design," NIPES-Journal of Energy Technology and Environment, vol. 7, no. 2, pp. 166-173, 2025, doi: https://doi.org/10.5281/zenodo.15609815.
  32. F. S. Alakbari, M. E. Mohyaldinn, S. M. Mahmood, A. M. Hassan, R. Ashena, and A. Al-Fakih, "A Statistics-Based Correlation for the Assessment of Water-Based Mud Performance: Yield Point Prediction," Arabian Journal for Science and Engineering, vol. 50, no. 7, pp. 4927-4942, 2025, doi: https://doi.org/10.1007/s13369-024-09415-6.
  33. L. A. da Silva et al., "Assessment of the rheological properties of a novel drilling fluid based on babassu esters for oil well applications," Petroleum Research, 2026, doi: https://doi.org/10.1016/j.ptlrs.2026.02.006.
  34. I. E. Ihua-Maduenyi and E. Oguta, "Modelling and Performance Analyses of Annular Equivalent Circulation Density in Extended Reach Wells Using Response Surface Methodology," Asian Journal of Engineering and Applied Technology, vol. 14, no. 2, pp. 1-17, 2025, doi: https://doi.org/10.70112/ajeat-2025.14.2.4298.
  35. C. Hao et al., "Investigation of the Effect of Casing-to-Wellbore Clearance on Equivalent Circulating Density During Casing Running," Processes, vol. 12, no. 12, p. 2894, 2024, doi: https://doi.org/10.3390/pr12122894.
  36. A. S. Youssef, S. Elkatatny, A. Abdulraheem, and T. Al-Shafloot, "Enhanced Rate of Penetration Prediction for Complex Bottom Hole Assemblies Using Advanced Artificial Intelligence Techniques," in SPE Gas & Oil Technology Showcase and Conference, 2025: SPE, p. D021S036R002, doi: https://doi.org/10.2118/224471-MS.
  37. B. A. Mokaimi et al., "Managed Pressure Drilling Technique Commingled High Pore Pressure Section with Depleted Section, Eliminate Drilling Hazard and Pore Pressure Uncertainty Related High-Pressure High-Temperature in West Kuwait Jurassic Deep Wells," in Abu Dhabi International Petroleum Exhibition and Conference, 2024: SPE, p. D031S085R004, doi: https://doi.org/10.2118/222742-MS.
  38. M. Al-Rubaii, M. Al-Shargabi, B. Aldahlawi, D. Al-Shehri, and K. M. Minaev, "A developed robust model and artificial intelligence techniques to predict drilling fluid density and equivalent circulation density in real time," Sensors, vol. 23, no. 14, p. 6594, 2023, doi: https://doi.org/10.3390/s23146594.
  39. A. Aliyeva et al., "MPD Technique Drive through Extreme Narrow Pressure Window, Eliminate Drilling Hazard Related to HPHT Salt Anhydrite & Limestone Formation in North Kuwait Jurassic Deep Well," in IADC/SPE Asia Pacific Drilling Technology Conference and Exhibition?, 2024: SPE, p. D021S005R005, doi: https://doi.org/10.2118/219571-MS.
  40. K. Amadi, I. Iyalla, and R. Prabhu, "Modeling and predicting performance of autonomous rotary drilling system using machine learning techniques," in SPE Nigeria Annual International Conference and Exhibition, 2021: SPE, p. D021S002R008, doi: https://doi.org/10.2118/208450-MS.
  41. M. Xiang, J. Li, H. Zhu, X. Wang, X. Zhang, and Z. Wang, "Study on the hydraulic parameter design method for managed pressure drilling in deepwater thick salt layers," in Sixth International Conference on Materials Science, Energy Technology, and Environmental Engineering (MSETEE 2025), 2026, vol. 13997: SPIE, pp. 32-44, doi: https://doi.org/10.1117/12.3098269.
  42. S. M. Tharayil, I. M. Azmi, A. L. M, and A. M. M, "A Machine Learning Approach to Optimize Drilling Operations in Real-Time," in Abu Dhabi International Petroleum Exhibition and Conference, 2025: SPE, p. D041S145R003, doi: https://doi.org/10.2118/228907-MS.
  43. S. Wessling, O. Hummes, F. Jonsbraten, C. Hansen, V. Klemme, and S. Haberer, "Closing the loop with the subsurface: First deployment of autonomous well placement following reservoir boundaries," in Abu Dhabi International Petroleum Exhibition and Conference, 2023: SPE, p. D022S177R002, doi: https://doi.org/10.2118/216251-MS.