Heterogeneous stacking strategy for modeling flowing bottom-hole pressure of oil wells

Authors

  • Deivid Campos Computational Modeling Program, Engineering Faculty, Federal University of Juiz de Fora, Juiz de Fora, 36036-900, Brazil Author
  • Bruno da Silva Macêdo Systems and Automation Engineering Graduate Program, Federal University of Lavras, Lavras, 37200-000, MG, Brazil Author
  • Oscar Ikechukwu Ogali Department of Petroleum and Gas Engineering, University of Port Harcourt, Port Harcourt, Nigeria Author
  • Matteo Bodini Dipartimento di Economia, Management e Metodi Quantitativi, Università degli Studi di Milano, Via Conservatorio 7, 20122 Milano, Italy Author
  • Dmitriy A. Martyushev Department of Oil and Gas Technologies, Perm National Research Polytechnic University, Perm, 614990, Russia Author
  • Farouk Abduh Kamil Al-Fahaidy Emirates International University image/svg+xml Author
  • Camila Martins Saporetti Department of Computational Modeling, Polytechnic Institute, Rio de Janeiro State University, Nova, Friburgo, 28625-570, Brazil Author
  • Leonardo Goliatt Department of Computational and Applied Mechanics, Federal University of Juiz de Fora, Juiz de Fora, 36036-900, Brazil Author

DOI:

https://doi.org/10.1016/j.uncres.2026.100331

Keywords:

Flowing bottom hole pressure , Machine learning , Stacking model , Artificial intelligence , Production optimization

Abstract

Accurately predicting Flowing Bottom-Hole Pressure (FBHP) is critical for optimizing oil and gas production. Existing predictive methods often rely on oversimplified or complex, yet computationally expensive, models that fail to capture the intrinsic nonlinearities of well dynamics, leading to inaccurate predictions and potential economic losses. This paper introduces a three-layer heterogeneous stacking ensemble model to address the latter challenge. In particular, the key novelty of the developed work is a hierarchical architecture that integrates five distinct Machine Learning (ML) base learners, two meta-learners, and a final super-learner, i.e., an additional meta-model that combines the outputs of the meta-learners to capture complex, non-linear relationships in the data. When evaluated on a field dataset (total dataset samples N=795; test set samples N=199), the proposed Super Learner Stacking model (ST-S) demonstrated superior predictive performance on the independent test set, achieving R-squared (R2) = 0.857±0.006 and Root Mean Squared Error (RMSE) = 146.382±2.806. In addition, the ST-S model outperformed all individual models and simpler stacking ensembles reported in the article. As a result, the developed ST-S model provides a robust, data-driven tool for FBHP prediction, achieving high predictive accuracy without resorting to computationally expensive methods, thereby supporting improved well management and production optimization.

References

A

Abdullahi, B., & Ezeh, M. (2024). Production optimization in oil and gas wells: A gated recurrent unit approach to bottom hole flowing pressure prediction. Paper presented at the SPE Nigeria Annual International Conference and Exhibition. https://doi.org/10.2118/223412-MS

Adekomaya, O., Fadairo, A. A., & Falode, O. (2008). Predictive tool for bottom-hole pressure in multiphase flowing wells. Petroleum & Coal, 50(3), 67–73.

Agwu, O. E., Alatefi, S., Alkouh, A., & Suppiah, R. R. (2025). Modelling the flowing bottom hole pressure of oil and gas wells using multivariate adaptive regression splines. Journal of Petroleum Exploration and Production Technology, 15(2), Article 22. https://doi.org/10.1007/s13202-024-01988-x

Al-Ghamdi, A. A., & Gajbhiye, R. N. (2024). Development of an AI model to estimate flowing bottom-hole pressure in high-pressure high-temperature gas well. Paper presented at the International Petroleum Technology Conference (IPTC). https://doi.org/10.2118/24IPTC-MS

Agamiri, K., & Govier, G. W. (1972). Pressure drop in wells producing oil and gas. The Journal of Canadian Petroleum Technology, 11(3), 38–49. https://doi.org/10.2118/72-03-04

B

Beheshtian, S., Roodbari, S. K., Ghorbani, H., Azodinia, M., Mudabbir, M., & Varkonyi-Koczy, A. R. (2024). Comparative evaluation of machine learning and Bayesian deep learning methods for estimating ultimate recovery in shale well reservoirs. Proceedings of the 2024 IEEE 11th International Conference on Computational Cybernetics and Cyber-Medical Systems (ICCC), 17–24. https://doi.org/10.1109/ICCC61024.2024.1054321

Beheshtian, S., Roodbari, S. K., Ghorbani, H., Azodinia, M., Mudabbir, M., & Varkonyi-Koczy, A. R. (2024). Advanced machine learning methods for accurate prediction of loss circulation in drilling well log. Proceedings of the 2024 IEEE 11th International Conference on Computational Cybernetics and Cyber-Medical Systems (ICCC), 31–36. https://doi.org/10.1109/ICCC61024.2024.1054327

Bian, S., & Wang, W. (2007). On diversity and accuracy of homogeneous and heterogeneous ensembles. International Journal of Hybrid Intelligent Systems, 4(2), 103–128. https://doi.org/10.3233/HIS-2007-4202

Breiman, L. (2001). Random forests. Machine Learning, 45(1), 5–32. https://doi.org/10.1023/A:1010933404324

C

Campos, D., Wayo, D. D. K., De Santis, R. B., Martyushev, D. A., Yaseen, Z. M., Duru, U. I., Saporetti, C. M., & Goliatt, L. (2024). Evolutionary automated radial basis function neural network for multiphase flowing bottom-hole pressure prediction. Fuel, 377, Article 132666. https://doi.org/10.1016/j.fuel.2024.132666

Chen, Front., Zhang, Y., Li, H., & ... (2022). Influence factors of the bottom hole flow pressure in a high-pressure and high-temperature condensate gas reservoir: Applicability analysis. Frontiers in Energy Research, 10Trace, Article 857354. https://doi.org/10.3389/fenrg.2022.857354

Chen, X., Zhang, Y., Li, H., & ... (2024). Further study on oil/water relative permeability ratio model and waterflooding performance prediction model for high water-cut oilfields sustainable development. Journal of Petroleum Exploration and Production Technology, 14(4), 812–824. https://doi.org/10.1007/s13202-024-01764-x

Cover, T., & Hart, P. (1967). Nearest neighbor pattern classification. IEEE Transactions on Information Theory, 13(1), 21–27. https://doi.org/10.1109/TIT.1967.1053964

Cui, S., Yin, Y., Wang, D., Li, Z., & Wang, Y. (2021). A stacking-based ensemble learning method for earthquake casualty prediction. Applied Soft Computing, 101, Article 107038. https://doi.org/10.1016/j.asoc.2021.107038

D

Du, K. .-L., Jiang, B., Lu, J., Hua, J., & Swamy, M. N. S. (2024). Exploring kernel machines and support vector machines: Principles, techniques, and future directions. Mathematics, 12(24), Article 3935. https://doi.org/10.3390/math12243935

Dukler, A. E., & Hubbard, M. G. (1975). A model for gas-liquid slug flow in horizontal and near horizontal tubes. Industrial & Engineering Chemistry Fundamentals, 14(4), 337–347. https://doi.org/10.1021/i160056a011

E

El-Saghier, R. M., Abu El Ela, M., & El-Banbi, A. (2020). A model for calculating bottom-hole pressure from simple surface data in pumped wells. Journal of Petroleum Exploration and Production Technology, 10(5), 2069–2077. https://doi.org/10.1007/s13202-020-00862-y

El-Shorbagy, S. A., El-Gammal, W. M., & Abdelmoez, W. M. (2018). Using SMOTE and heterogeneous stacking in ensemble learning for software defect prediction. Proceedings of the 7th International Conference on Software and Information Engineering (ICSIE '18), 44–47. https://doi.org/10.1145/3220267.3220274

El-Moniem, M. A. A., & El-Banbi, A. H. (2020). Effects of production, PVT and pipe roughness on multiphase flow correlations in gas wells. Journal of Petroleum Exploration and Production Technology, 10(7), 2953–2964. https://doi.org/10.1007/s13202-020-00912-x

Eltahan, E., Ganjdanesh, R., Yu, W., Kepehrnoori, K., Williams, R., & Nohavitsa, J. (2021). Machine learning approach to improve calculated bottom-hole pressure. Paper presented at the 9th Unconventional Resources Technology Conference (URTeC 2021). https://doi.org/10.15530/urtec-2021-5412

F

Fernandes, M. A., Gildin, E., & Sampaio, M. A. (2024). Data-driven estimation of flowing bottom-hole pressure in petroleum wells using long short-term memory. Proceedings of the 2024 International Conference on Machine Learning and Applications (ICMLA), 1530–1537. https://doi.org/10.1109/ICMLA61024.2024.1054210

Figueroa, J., Baraldi, P., Chouybat, I., Ursini, F., & Vignati, E. (2024). Estimation of real-time bottomhole parameters in CO2 injection wells during operations by means of an ensemble of neural networks. Paper presented at the SPE Europe Energy Conference and Exhibition. https://doi.org/10.2118/22EURO-MS

G

García, S., Luengo, J., & Herrera, F. (2015). Data preprocessing in data mining. Springer International Publishing. https://doi.org/10.1007/978-3-319-10247-4

Goliatt, L., Mohammad, R. S., Abba, S. I., & Yaseen, Z. M. (2023). Development of hybrid computational data-intelligence model for flowing bottom-hole pressure of oil wells: New strategy for oil reservoir management and monitoring. Fuel, 350, Article 128623. https://doi.org/10.1016/j.fuel.2023.128623

Goliatt, L., Saporetti, C., & Pereira, E. (2023). Super learner approach to predict total organic carbon using stacking machine learning models based on well logs. Fuel, 353, Article 128682. https://doi.org/10.1016/j.fuel.2023.128682

Goliatt, L., & Yaseen, Z. M. (2023). Development of a hybrid computational intelligent model for daily global solar radiation prediction. Expert Systems with Applications, 212, Article 118295. https://doi.org/10.1016/j.eswa.2022.118295

Gupta, R., & S. J. Nanda. (2021). Solving dynamic many-objective TSP using NSGA-III equipped with SVR-RBF kernel predictor. Proceedings of the 2021 IEEE Congress on Evolutionary Computation (CEC), 95–102. https://doi.org/10.1109/CEC45853.2021.9508612

H

Hari, S., Krishna, S., Patel, M., Bhatia, P., & Vij, R. K. (2022). Influence of wellhead pressure and water cut in the optimization of oil production from gas lifted wells. Petroleum Research, 7(2), 253–262. https://doi.org/10.1016/j.ptlrs.2021.09.004

Huang, R., Wei, C., B. Wang, Yang, J., Xu, X., Wu, S., & Huang, S. (2022). Well performance prediction based on long short-term memory (LSTM) neural network. Journal of Petroleum Science and Engineering, 208, Article 109686. https://doi.org/10.1016/j.petrol.2021.109686

I

Ibrahim, N. M., Alharbi, A. A., Alzahrani, T. A., Abdulkarim, A. M., Alessa, I. A., Hameed, A. M., Albabtain, S. S., Alqahtani, D. A., Alsawwaf, M. K., & Almuqhim, A. A. (2022). Well performance classification and prediction: Deep learning and machine learning long term regression experiments on oil, gas, and water production. Sensors, 22(14), Article 5326. https://doi.org/10.3390/s22145326

Isnaeni, R., Sudarmin, S., & Rais, Z. (2022). Analisis support vector regression (Svr) dengan kernel radial basis function (Rbf) untuk memprediksi laju inflasi di Indonesia. VARIANSI: Journal of Statistics and Its Application on Teaching and Research, 4(1), 30–38. https://doi.org/10.35585/variansi.v4i1.1245

Izgec, B., Hasan, A. R., Lin, D., & Kabir, C. S. (2009). Flow-rate estimation from wellhead-pressure and temperature data. SPE Production & Operations, 25(1), 31–39. https://doi.org/10.2118/116213-PA

J

Jin, M., & Emami-Meybodi, H. (2025). An integrated machine learning algorithm for unconventional flowing bottomhole pressure prediction during dynamic gas lift operation. SPE Journal, 30(5), 2726–2737. https://doi.org/10.2118/221234-PA

Jin, M., & Emami-Meybodi, H. (2025). Prediction of flowing bottomhole pressure in gas-lifted wells using LSTM-ANN models. Energy & Fuels, 39(31), 14992–15002. https://doi.org/10.1021/acs.energyfuels.4c12342

Jin, M., Emami-Meybodi, H., & Ahmadi, M. (2024). Flowing bottomhole pressure during gas lift in unconventional oil wells. SPE Journal, 29(5), 2432–2444. https://doi.org/10.2118/214532-PA

K

Kanin, E., Osiptsov, A., Vainshtein, A. L., & Burnaev, E. (2019). A predictive model for steady-state multiphase pipe flow: Machine learning on lab data. Journal of Petroleum Science and Engineering, 180Trace, 727–746. https://doi.org/10.1016/j.petrol.2019.05.084

Kanin, N., Zhou, A., Nazem, M., & Shen, S. .-L. (2021). Improved prediction of slope stability using a hybrid stacking ensemble method based on finite element analysis and field data. Journal of Rock Mechanics and Geotechnical Engineering, 13(1), 188–201. https://doi.org/10.1016/j.jrmge.2020.09.004

Kasuya, E. (2019). On the use of r and r squared in correlation and regression. Ecological Research, 34(1), 235–236. https://doi.org/10.1111/1440-1703.1245

L

Lasisi, A., & Attoh-Okine, N. (2019). Machine learning ensembles and rail defects prediction: Multilayer stacking methodology. ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering, 5(4), Article 04019016. https://doi.org/10.1061/AJRUA6.0001024

Liu, N., Gao, H., Zhao, Z., Hu, Y., & Duan, L. (2021). A stacked generalization ensemble model for optimization and prediction of the gas well rate of penetration: A case study in Xinjiang. Journal of Petroleum Exploration and Production Technology, 12(6), 1595–1608. https://doi.org/10.1007/s13202-021-01342-z

Lu, X., Wang, Z., Zhao, M., Peng, S., Geng, S., & Hhorbani, H. (2025). Data-driven insights into climate change effects on groundwater levels using machine learning. Water Resources Management, 39(7), 3521–3536. https://doi.org/10.1007/s11269-024-03912-w

Lundberg, S. M., & Lee, S. .-I. (2017). A unified approach to interpreting model predictions. Advances in Neural Information Processing Systems, 30, 4765–4774.

M

Marfo, S. A., Asante-Okyere, S., & Ziggah, Y. Y. (2021). A new flowing bottom hole pressure prediction model using M5 prime decision tree approach. Modeling Earth Systems and Environment, 8(2), 2065–2073. https://doi.org/10.1007/s40808-021-01201-w

McKinney, W., & ... (2011). Pandas: A foundational Python library for data analysis and statistics. Python for High Performance Scientific Computing, 14(9), 1–9. https://doi.org/10.2508/pyhpsc.2011.14.9

Mienye, I. D., & Sun, Y. (2022). A survey of ensemble learning: Concepts, algorithms, applications, and prospects. IEEE Access, 10, 99129–99149. https://doi.org/10.1109/ACCESS.2022.3201234

Molinari, D., & Sankaran, S. (2021). Merging physics and data-driven methods for field-wide bottomhole pressure estimation in unconventional wells. Paper presented at the Unconventional Resources Technology Conference, Houston, Texas. https://doi.org/10.15530/urtec-2021-D031S074R004

N

Nikitin, N. O., Revin, I., Hvatov, A., P. Vychuzhanin, & Kalyuzhnaya, A. V. (2022). Hybrid and automated machine learning approaches for oil fields development: The case study of Volve field, North Sea. Computers & Geosciences, 161, Article 105061. https://doi.org/10.1016/j.cageo.2022.105061

Nikitin, N. O., Pinchuk, M., Pokrovskii, V., Shevchenko, P., Getmanov, A., Aksenkin, Y., Revin, I., Stebenkov, A., Latypov, V., Poslavskaya, E., & ... (2024). Integration of evolutionary automated machine learning with structural sensitivity analysis for composite pipelines. Knowledge-Based Systems, 302, Article 112363. https://doi.org/10.1016/j.knosys.2024.112363

Nnaemeka, E., & Chinyereugo, V. M. (2025). Predictive modelling of flowing bottom hole pressure in sandstone reservoir formations using machine learning. Paper presented at the SPE Nigeria Annual International Conference and Exhibition. https://doi.org/10.2118/25NAIC-MS

Nwanwe, C. C., & Duru, U. I. (2023). An adaptive neuro-fuzzy inference system white-box model for real-time multiphase flowing bottom-hole pressure prediction in wellbores. Petroleum, 9(4), 629–646. https://doi.org/10.1016/j.petlm.2022.09.002

P

Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., Blondel, M., Prettenhofer, P., Weiss, R., Dubourg, V., Vanderplas, J., Passos, A., Cournapeau, D., Brucher, M., Perrot, M., & Duchesnay, É. (2011). Scikit-learn: Machine learning in Python. Journal of Machine Learning Research, 12(85), 2825–2830.

R

Ribeiro, M. T., Singh, S., & Guestrin, C. (2016). 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, 1135–1144. https://doi.org/10.1145/2939672.2939778

Rice, J. R. (1976). The algorithm selection problem. In M. Rubinoff & M. C. Yovits (Eds.), Advances in Computers (Vol. 15, pp. 65–118). Elsevier. https://doi.org/10.1016/S0065-2458(08)60520-1

S

Seni, G., & Elder, J. F. (2010). Ensemble methods in data mining: Improving accuracy through combining predictions. Springer International Publishing. https://doi.org/10.1007/978-3-319-04142-1

Shammari, A. (2011). Prediction of pressure drop for two-phase flow in vertical pipes using artificial intelligence [Master's thesis, King Fahd University of Petroleum and Minerals]. KFUPM Electronic Theses and Dissertations.

Shi, J., Li, C., & Yan, X. (2023). Artificial intelligence for load forecasting: A stacking learning approach based on ensemble diversity regularization. Energy, 262, Article 125295. https://doi.org/10.1016/j.energy.2022.125295

Song, Z., Han, G., Ren, Z., Su, H., Jia, S., Cheng, T., Li, M., & Liang, J. (2024). Research on oil–water two-phase flow patterns in wellbore of heavy oil wells with medium-high water cut. Processes, 12(11), Article 2404. https://doi.org/10.3390/pr12112404

Su, X., Yan, X., & Tsai, C. .-L. (2012). Linear regression. Wiley Interdisciplinary Reviews: Computational Statistics, 4(3), 275–294. https://doi.org/10.1002/wics.1197

Syed, F. I., Alnaqbi, S., Muther, T., Dahaghi, A. K., & Negahban, S. (2022). Smart shale gas production performance analysis using machine learning applications. Petroleum Research, 7(1), 21–31. https://doi.org/10.1016/j.ptlrs.2021.06.002

T

Tariq, Z., & ... (2020). Real-time prognosis of flowing bottom-hole pressure in a vertical well for a multiphase flow using computational intelligence techniques. Journal of Petroleum Exploration and Production Technology, 10Trace(6), 2412–2424. https://doi.org/10.1007/s13202-020-00942-z

Truong, D. .-N., & Chou, J. .-S. (2022). Fuzzy adaptive jellyfish search-optimized stacking machine learning for engineering planning and design. Automation in Construction, 143, Article 104579. https://doi.org/10.1016/j.autcon.2022.104579

V

Vapnik, V. (2006). Estimation of dependences based on empirical data. Springer New York. https://doi.org/10.1007/0-387-34239-5

W

Wang, X., & Han, T. (2020). Transformer fault diagnosis based on stacking ensemble learning. IEEJ Transactions on Electrical and Electronic Engineering, 15(12), 1734–1739. https://doi.org/10.1002/tee.23245

Wang, W., Jones, P., & Partridge, D. (2000). Diversity between neural networks and decision trees for building multiple classifier systems. In Multiple Classifier Systems (pp. 240–249). Springer Berlin Heidelberg. https://doi.org/10.1007/3-540-45014-9_23

Weerts, H. J. P., Mueller, A. C., & Vanschoren, J. (2020). Importance of tuning hyperparameters of machine learning algorithms. arXiv preprint arXiv:2007.07588. https://doi.org/10.48550/arXiv.2007.07588

X

Xu, Z., Liu, H., Sun, J., & ... (2022). A drilling wellbore pressure calculation model considering the effect of gas dissolution and suspension. Frontiers in Earth Science, 10, Article 1024. https://doi.org/10.3389/feart.2022.1001024

Y

Young, S., Abdou, T., & Bener, A. (2018). Deep super learner: A deep ensemble for classification problems. In E. Bagheri & J. C. Cheung (Eds.), Advances in Artificial Intelligence (pp. 84–95). Springer International Publishing. https://doi.org/10.1007/978-3-319-89656-4_8

Z

Zhang, H., Ren, Y., Zhang, Y., & Zheng, S. (2023). Intelligent prediction method for fracture pressure based on stacking ensemble algorithm. Geomechanics and Geophysics for Geo-Energy and Geo-Resources, 9(1), Article 149. https://doi.org/10.1007/s40948-023-00612-w

Zhou, X., & ... (2022). Determination of reasonable bottom-hole pressure in unconventional tight oil reservoirs: A field case investigation. Lithosphere, 2022(12), 1–15. https://doi.org/10.2113/2022/9845123

Zhu, Q. .-Y., Qin, A., Suganthan, P., & Huang, G. .-B. (2005). Evolutionary extreme learning machine. Pattern Recognition, 38(10), 1759–1763. https://doi.org/10.1016/j.patcog.2005.03.021

Zolfagharroshan, M., & Khamehchi, E. (2021). Accurate artificial intelligence-based methods in predicting bottom-hole pressure in multiphase flow wells, a comparison approach. Arabian Journal of Geosciences, 14(4), Article 284. https://doi.org/10.1007/s12517-021-06584-y

Zhou, J., Wang, Z., Zhao, M., Peng, S., Geng, S., & Hhorbani, H. (2025). Data-driven insights into climate change effects on groundwater levels using machine learning. Water Resources Management, 39(7), 3521–3536. https://doi.org/10.1007/s11269-024-03912-w

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2026-02-07

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Campos, D., Macêdo, B. da S., Ogali, O. I., Bodini, M., Martyushev, D. A., Al-Fahaidy, F. A. K., Saporetti, C. M., & Goliatt, L. (2026). Heterogeneous stacking strategy for modeling flowing bottom-hole pressure of oil wells. Emirates International University Digital Repository, 1(1). https://doi.org/10.1016/j.uncres.2026.100331

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