Development of a new closed-form symbolic regression correlation for predicting multiphase flow wellhead pressure through chokes: A case study of Buzurgan oil field
DOI:
https://doi.org/10.31699/IJCPE.2026.3.6Keywords:
Wellhead Choke; Multiphase Flow; Wellhead Pressure; Symbolic Regression; Buzurgan Oil FieldAbstract
Accurate calculation and monitoring of multiphase choke-flow pressure drops present a critical engineering challenge for optimizing production rates and ensuring effective reservoir management. Traditional empirical correlations, such as Gilbert and Ros formulations, often show reduced accuracy when applied to fields like Buzurgan in Iraq. Although modern machine learning models offer high statistical accuracy, their “black-box” nature limits practical field deployment due to the lack of transparent, explicit formulas. To bridge this gap, this study introduces an artificial intelligence framework using Python symbolic regression (PySR) to develop a novel, transparent, and directly deployable closed-form algebraic correlation using 672 field datasets from the Buzurgan Oil Field based on choke size, liquid flow rate, and gas-liquid ratio. The derived equation achieved an R² of approximately 0.80, an RMSE of 162.6 psi, and a MAPE of 18.1% on test data, outperforming traditional correlations (R² = 0.60–0.65). Comparisons with random forest, DNN, XGBoost, and ANN showed that while random forest achieved the highest accuracy (R² = 0.94), the PySR model offers a practical compromise between accuracy and interpretability, providing a transparent engineering trade-off that sacrifices minor statistical precision for an explicit formula essential for immediate field deployment and daily operational optimization. The proposed explicit algebraic formula enables production engineers to implement the correlation directly in spreadsheets and field software, improving daily production optimization. This study contributes to solving the “black box” problem by providing a powerful, accurate, and straightforward tool tailored to Iraqi oil field conditions.
Received on 12/06/2026
Received in Revised Form on 01/08/2026
Accepted on 01/08/2026
Published on 30/09/2026
References
[1] B. Guo, W. C. Lyons, and A. Galiullin, Petroleum Production Engineering: A Computer-Assisted Approach. Amsterdam: Elsevier Science & Technology Books, 2007, pp. 59-67. https://doi.org/10.1016/B978-0-7506-8270-1.X5000-2
[2] M. J. Economides, A. D. Hill, C. Ehlig-Economides, and D. Zhu, Petroleum Production Systems, 2nd ed. Upper Saddle River, NJ: Prentice Hall, 2013, pp. 236–247.
[3] W. E. Gilbert, "Flowing and gas-lift well performance," API Drilling and Production Practice, vol. 1954, pp. 126-157, Jan. 1954.
[4] N. C. J. Ros, "An analysis of critical simultaneous gas-liquid flow through a restriction," Applied Scientific Research, Section A, vol. 9, no. 5, pp. 374-388, 1960. https://doi.org/10.1007/BF00382215
[5] A. N. Okon and D. Appah, "Neural Network Models for Predicting Wellhead Pressure-Flow Rate Relationship for Niger Delta Oil Wells," Journal of Scientific Research and Reports, vol. 12, no. 1, pp. 1–14, Jan. 2016. https://doi.org/10.9734/JSRR/2016/28715
[6] A. Lak, R. Azin, S. Osfouri, and R. Fatehi, "Modeling Critical Flow through Choke for a Gas-condensate Reservoir Based on Drill Stem Test Data," Iranian Journal of Oil & Gas Science and Technology, vol. 6, no. 3, pp. 29–40, 2017. https://doi.org/10.22050/ijogst.2017.69063.1371
[7] P. B. Baxendell, "Producing Wells on Casing Flow – An Analysis of Flowing Pressure Gradients," Transactions of the AIME, vol. 213, pp. 202–206, 1958. https://doi.org/10.2118/983-G
[8] M. S. Beiranvand, P. Mohammadmoradi, B. Aminshahidy, B. Fazelabdolabadi, and S. Aghahoseini, "New multiphase choke correlations for a high flow rate Iranian oil field," Mechanical Sciences, vol. 3, no. 1, pp. 43–47, Jun. 2012. https://doi.org/10.5194/ms-3-43-2012
[9] A. N. Okon, F. D. Udoh, and D. Appah, "Empirical Wellhead Pressure-Production Rate Correlations for Niger Delta Oil Wells," presented at the SPE Nigeria Annual International Conference and Exhibition, Lagos, Nigeria, Aug. 2015. https://doi.org/10.2118/178303-MS
[10] M. Khamis, M. Elhaj, and A. Abdulraheem, "Optimization of choke size for two-phase flow using artificial intelligence," Journal of Petroleum Exploration and Production Technology, vol. 10, no. 2, pp. 487–500, May 2020. https://doi.org/10.1007/s13202-019-0734-6
[11] A. Akbari and M. Rahimi, "Prediction of well performance parameters for wellhead choke flow optimization using MLP-GA," Geosystem Engineering, 2026. https://doi.org/10.1080/12269328.2026.2613005
[12] A. Barredo Arrieta et al., "Explainable Artificial Intelligence (XAI): Concepts, taxonomies, opportunities and challenges toward responsible AI," Information Fusion, vol. 58, pp. 82–115, Jun. 2020. https://doi.org/10.1016/j.inffus.2019.12.012
[13] W. Saeed and C. Omlin, "Explainable AI (XAI): A systematic meta-survey of current challenges and future opportunities," Knowledge-Based Systems, vol. 263, p. 110273, Mar. 2023. https://doi.org/10.1016/j.knosys.2023.110273
[14] I. U. Ekanayake, D. P. P. Meddage, and U. Rathnayake, "A novel approach to explain the black-box nature of machine learning in compressive strength predictions of concrete using Shapley additive explanations (SHAP)," Case Studies in Construction Materials, vol. 16, e01059, 2022. https://doi.org/10.1016/j.cscm.2022.e01059
[15] A. Akbari, F. Ghazi, and Y. Kazemzadeh, "Machine learning-based prediction of well performance parameters for wellhead choke flow optimization," Scientific Reports, vol. 15, art. 44182, Dec. 2025. https://doi.org/10.1038/s41598-025-27851-8
[16] F. S. Alakbari, M. A. Ayoub, M. A. Awad, T. Ganat, M. E. Mohyaldinn, and S. M. Mahmood, "A robust pressure drop prediction model in vertical multiphase flow: a machine learning approach," Scientific Reports, vol. 15, art. 13420, Apr. 2025. https://doi.org/10.1038/s41598-025-96371-2
[17] M. M. Mohammed, H. M. Salih, and K. H. Mnaty, "3D Reservoir Modeling of Buzurgan Oil Field, Southern Iraq," Iraqi Journal of Science, vol. 63, no. 2, pp. 596–607, Feb. 2022. https://doi.org/10.24996/ijs.2022.63.2.16
[18] M. A. Ahmed, J. M. Al Said Naji, A. Ali, and A. Qassim Al-Khafaje, "Asphaltene Phase Behavior Modeling Using Peng-Robinson 78A-EOS for a Crude Oil Sample from Buzurgan Oil Field," Petroleum Chemistry, vol. 64, no. 7, pp. 840–848, Oct. 2024. https://doi.org/10.1134/S096554412405013X
[19] B. Amiri-Ramsheh, S. Sahebalzamani, R. Zabihi, and A. Hemmati-Sarapardeh, "Predicting asphaltene precipitation during natural depletion of oil reservoirs by integrating SARA fractions with advanced intelligent models," Scientific Reports, vol. 15, art. 26214, Jul. 2025. https://doi.org/10.1038/s41598-025-11966-z
[20] M. S. Dabiri, F. Hadavimoghaddam, S. Ashoorian, M. Schaffie, and A. Hemmati-Sarapardeh, "Modeling liquid rate through wellhead chokes using machine learning techniques," Scientific Reports, vol. 14, no. 1, art. 6945, Mar. 2024. https://doi.org/10.1038/s41598-024-54010-2
[21] L. S. Keren, A. Liberzon, and T. Lazebnik, "A computational framework for physics-informed symbolic regression with straightforward integration of domain knowledge," Scientific Reports, vol. 13, art. 1249, Jan. 2023. https://doi.org/10.1038/s41598-023-28328-2
[22] A. Tonda, "Review of PySR: high-performance symbolic regression in Python and Julia," Genetic Programming and Evolvable Machines, vol. 26, art. 7, Dec. 2024. https://doi.org/10.1007/s10710-024-09503-4
[23] S. M. Koksbang, "Cosmic backreaction and the mean redshift drift from symbolic regression," Phys. Rev. D, vol. 107, p. 103522, May 2023, https://doi.org/10.1103/PhysRevD.107.103522
[24] Udrescu, S. M., and Tegmark, M., "AI Feynman: A physics-inspired method for symbolic regression," Science Advances, vol. 6, no. 16, p. eaay2631, Apr. 2020. https://doi.org/10.1126/sciadv.aay2631
[25] Chicco, D., Warrens, M. J., and Jurman, G., "The coefficient of determination R-squared is more informative than SMAPE, MAE, MAPE, MSE, and RMSE in regression analysis evaluation," PeerJ Computer Science, vol. 7, p. e623, Jul. 2021. https://doi.org/10.7717/peerj-cs.623
Downloads
Published
Issue
Section
License
Copyright (c) 2026 The Author(s). Published by College of Engineering, University of Baghdad.
This work is licensed under a Creative Commons Attribution 4.0 International License.
