Variable interaction empirical relationships and machine learning provide complementary insight to experimental horizontal wellbore cleaning results

David A. Wood

Abstract view|20|times       PDF download|12|times


Long horizontal wellbore sections are now a key requirement of oil and gas drilling, particularly for tight reservoirs. However, such sections pose a unique set of borehole-cleaning challenges which are quite distinct from those associated with less inclined wellbores. Experimental studies provide essential insight into the downhole variables that influence borehole cleaning in horizontal sections, typically expressing their results in multivariate empirical relationships with dimensionless cuttings bed thickness/concentration (H%). This study demonstrates how complementary empirical H% relationships focused on pairs of influential variables can be obtained from published experimental data using interpolated trends and optimizers. It also applies five machine learning algorithms to a compiled multivariate (10-variable) interpolated dataset to illustrate how reliable H% predictions can be derived based on such information. Seven optimizer-derived empirical relationships are derived using pairs of influential variables which are capable of predicting H% with root mean squared errors of less than 1.8%. The extreme gradient boosting model provides the lowest H% prediction errors from the 10-variable dataset. The results suggest that in drilling situations where sufficient, locally-specific, information for multiple influential variables is available, machine learning methods are likely to be more effective and reliable at predicting H% than empirical relationships. On the other hand, in drilling conditions where information is only available for a limited number of influential variables, empirical relationships involving pairs of influential variables can provide valuable information to assist with drilling decisions.

Document Type: Original article

Cited as: Wood, D. A. Variable interaction empirical relationships and machine learning provide complementary insight to experimental horizontal wellbore cleaning results. Advances in Geo-Energy Research, 2023, 9(3): 172-184.


Hole-cleaning factors, cuttings carrying performance, cuttings transport feature importance, optimized empirical relationships, cuttings-bed concentrations

Full Text:



Agwu, O. E., Akpabio, J. U., Dosunmu, A. Artificial neural network model for predicting drill cuttings settling velocity. Petroleum, 2020, 6(4): 340-352.

Akhshik, S., Behzad, M., Rajabi, M. CFD-DEM simulation of the hole cleaning process in a deviated well drilling: The effects of particle shape. Particuology, 2016, 25: 72-82.

Al-Azani, K. H., Elkatatny, S., Abdulraheem, A., et al. Prediction of cutting concentration in horizontal and deviated wells using support vector machine. Paper SPE 192193 Presented at SPE Kingdom of Saudi Arabia Annual Technical Symposium and Exhibition, Dammam, Saudi Arabia, 23-26 April, 2018.

Al-Azani, K. H., Elkatatny, S., Ali, A., et al. Cutting concentration prediction in horizontal and deviated wells using artificial intelligence techniques. Journal of Petroleum Exploration and Production Technology, 2019, 9: 2769-2779.

Al-Rubaii, M., Al-Shargabi, M., Al-Shehri, D., et al. A novel efficient borehole cleaning model for optimizing drilling performance in real time. Applied Sciences, 2023, 13: 7751.

Alsaihati, A., Elkatatny, S. A new method for drill cuttings size estimation based on machine learning technique. Arabian JournaI for Science and Engineering, 2023, in press,

Arévalo, P. J., Forshaw, M., Starostin, A., et al. Monitoring hole-cleaning during drilling operations: Case studies with a real-time transient model. Paper SPE 210244 Presented at SPE Annual Technical Conference and Exhibition, Houston, Texas, 3-5 October, 2022.

Awad, A. M., Hussein, I. A., Nasser, M. S., et al. CFD modeling of particle settling in drilling fluids: Impact of fluid rheology and particle characteristics. Journal of Petroleum Science and Engineering, 2021, 199: 108326.

Awojinrin, G. T. Machine learning workflow for the determination of hole cleaning conditions. Paper SPE 212381 Presented at Annual Technical Conference and Exhibition, Houston, Texas, 3-5 October, 2022.

Busch, A., Johansen, S. T. Cuttings transport: On the effect of drill pipe rotation and lateral motion on the cuttings bed. Journal of Petroleum Science and Engineering, 2020, 191: 107136.

Busch, A., Werner, B., Johansen, S. T. Cuttings transport modeling-part 2: dimensional analysis and scaling. SPE Drilling & Completion, 2020, 35(1): 69-87.

Chang, Y., Hsieh, C. J., Chang, K., et al. Training and testing low-degree polynomial data mappings via linear SVM. Journal of Machine Learning Research, 2010, 11(4): 1471-1490.

Chen, T., Guestrin, C. XGBoost: A scalable tree boosting system. Paper Presented at Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, New York, USA, 13-17 August, 2016.

Chen, F., Liu, Z., Huo, Y., et al. Mechanical mechanism and removal effect of efficient vortexing cuttings removal tool. Advances in Mechanical Engineenng, 2022, 14(12): 1-14.

Cortes, C., Vapnik, V. Support-vector networks. Machine Learning, 1995, 120 (3): 273-297.

Epelle, E. I., Gerogiorgis, D. I. Drill cuttings transport and deposition in complex annular geometries of deviated oil and gas wells: A multiphase flow analysis of positional variability. Chemical Engineering Research and Design, 2019, 151: 214-230.

Epelle, E. I., Obande, W., Okolie, J. A., et al. CFD modelling and simulation of drill cuttings transport efficiency in annular bends: Effect of particle size polydispersity. Journal of Petroleum Science and Engineering, 2022, 208: 109795.

Fix, E., Hodges, J. L. Discriminatory analysis, nonparametric discrimination: Consistency properties. Technical Report, USAF School of Aviation Medicine, 1951.

Forshaw, M. J., Qahtani, Y. S., Aramco, S., et al. Validation of full transient hole cleaning model, with at-scale datasets, implementation into an automated advisory system. Paper SPE 32081 Presented at SPE Offshore Technology Conference, Houston, Texas, 2-5 May, 2022.

Frontline Solvers. Excel Solver–non-linear optimization methods 2023.

Hajipour, M. CFD simulation of turbulent flow of drill cuttings and parametric studies in a horizontal annulus. SN Applied Sciences, 2020, 2: 1146.

Han, Y., Zhang, X., Xu, Z., et al. Cuttings bed height prediction in microhole horizontal wells with artificial intelligence models. Energies, 2022, 15: 8389.

Harrell, F. E. Regression Modeling Strategies (second edition). Cham, Switzerland, Springer, 2015.

Hastie, T. Ridge regularization: An essential concept in data science. Technometrics, 2020, 62(4): 426-433.

Hemphill, T., Larsen, T. I. Hole-cleaning capabilities of water- and oil-based drilling fluids: a comparative experimental study. SPE Drilling & Completion, 1996, 11(4): 201-207.

Ho, T. K. The random subspace method for constructing decision forests. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1998, 20(8): 832-844.

Hopkin, E. A. Factors affecting cuttings removal during rotary Drilling. Journal of Petroleum Technology, 1967, 19(6): 807-814.

Jimmy, D., Wami, E., Ogba, M. I. Cuttings lifting coefficient model: A criteria for cuttings lifting and hole cleaning quality of mud in drilling optimization. Paper SPE 212004 Presented at SPE Nigeria Annual International Conference and Exhibition, Lagos, Nigeria, 1-3 August, 2022.

Lasdon, L. S., Waren, A. D., Jain, A., et al. Design and testing of a generalized reduced gradient code for nonlinear programming. ACM Transactions on Mathematical Software, 1978, 4 (1): 34-50.

Leporini, M., Marchetti, B., Corvaro, F., et al. Sand transport in multiphase flow mixtures in a horizontal pipeline: An experimental investigation. Petroleum, 2019, 5: 161-170.

Li, J., Luft, B. Overview of solids transport studies and applications in oil and gas industry-experimental work. Paper SPE 171285 Presented at SPE Russian Oil and Gas Exploration & Production Technical Conference and Exhibition, Moscow, Russia, 14-16 October, 2014.

Li, J., Walker, S. Sensitivity analysis of hole cleaning parameters in directional wells. SPE Journal, 2001, 6(4): 356-363.

Lin, T., Wei, C., Zhang, Q., et al. Calculation of equivalent circulating density and solids concentration in the annular space when reaming the hole in deepwater drilling. Chemistry and Technology of Fuels and Oils, 2016, 52: 70-75.

Loureiro, B. V., Paula, R. S., Serafim, M., et al. Experimental evaluation of the effect of drill string rotation in the suspension of a cuttings bed. Paper SPE 122071 Presented at SPE Latin American and Caribbean Petroleum Engineering Conference, Lima, Peru, 1-3 December, 2010.

Ma, Y., Yang, C., Liu, X. On hole cleaning evaluation method in highly deviated/horizontal well sections. Journal of Physics: Conference Series, 2023, 2442: 012037.

Mahmoud, A. A., Elzenary, M., Elkatatny, S. New hybrid hole cleaning model for vertical and deviated wells. JournaI of Energy Resources TechnoIogy, 2020a, 142(3): 034501.

Mahmoud, H., Hamza, A., Nasser, M. S., et al. Hole cleaning and drilling fluid sweeps in horizontal and deviated wells: Comprehensive review. Journal of Petroleum Science and Engineering, 2020b, 186: 106748.

Moroni, N., Ravi, K., Hemphill, T., et al. Pipe rotation improves hole cleaning and cement-slurry placement: mathematical modeling and field validation. Paper SPE 124726 Presented at SPE Offshore Europe Oil and Gas Conference and Exhibition, Aberdeen, UK, 8-11 September, 2009.

Nazari, T., Hareland, G., Azar, J. J. Review of cuttings transport in directional well drilling: Systematic approach. Paper SPE 132372 Presented at SPE Western Regional Meeting, Anaheim, California, 27-29 May, 2010.

Olukoga, T. A., Feng, Y. Practical machine-learning applications in well-drilling operations. SPE Drilling & Completion, 2021, 36(4): 849-867.

Ozbayoglu, E. M., Miska, S. Z., Reed, T., et al. Analysis of bed height in horizontal and highly-inclined wellbores by using artificial neural networks. Paper SPE 78939 Presented at SPE International Thermal Operations and Heavy Oil Symposium and International Horizontal Well Technology Conference, Calgary, Alberta, 4-7 November, 2002.

Pandya, S., Ahmed, R., Shah, S. Effects of particle density on hole cleanout operation in horizontal and inclined wellbores. Paper SPE 194240 Presented at SPE/ICoTA Well Intervention Conference and Exhibition, The Woodlands, Texas, 26-27 March, 2019.

Piroozian, A., Ismail, I., Yaacob, Z., et al. Impact of drilling fluid viscosity, velocity and hole inclination on cuttings transport in horizontal and highly deviated wells. Journal of Petroleum Exploration and Production Technology, 2012, 2: 149-156.

Power, D. J., Hight, C., Weisinger, D., et al. Drilling practices and sweep selection for efficient hole cleaning in deviated wellbores. Paper SPE 627794 Presented at IADC/ SPE Asia Pacific Drilling Technology, Kuala Lumpur, Malaysia, 11-13 September, 2000.

Rooki, R., Ardejani, F. D., Moradzadeh, A. Hole cleaning prediction in foam drilling using artificial neural network and multiple linear regression. Geomaterials, 2014, 4(1): 47-53.

Rooki, R., Rakhshkhorshid, M. Cuttings transport modeling in underbalanced oil drilling operation using radial basis neural network. Egyptian Journal of Petroleum, 2017, 26(2): 541-546.

Scikit Learn. Supervised and unsupervised machine learning models in Python, 2023a. Scikit Learn. RandomizedSearchCV function for control parameters, 2023b.

Scikit Learn. MinMaxScaler function for data pre-processing, 2023c.

Scikit Learn. Cross-validation: evaluating estimator performance, 2023d.

Shahid, R., Bertazzon, S., Knudtson, M. L., et al. Comparison of distance measures in spatial analytical modeling for health service planning. BMC Health Services Research, 2009, 9: 200.

Song, X., Xu, Z., Wang, M., et al. Experimental study on the wellbore-cleaning efficiency of microhole-horizontal-well drilling. SPE Journal, 2017, 22(4): 1189-1200.

Sun, X., Tao, L., Zhao, Y., et al. Numerical simulation of hole cleaning of a horizontal wellbore model with breakout enlargement section. Mathematics, 2023, 11(14): 3070.

Sun, X., Wang, K., Yan, T., et al. Review of hole cleaning in complex structural wells. The Open Petroleum Engineering Journal, 2013, 6: 25-32.

Tomren, P. H., Iyoho, A. W., Azar, J. J. Experimental study of cuttings transport in directional wells. SPE Drilling Engineering, 1986, 1(1): 43-56.

Ulker, E., Sorgun, M. Comparison of computational intelligence models for cuttings transport in horizontal and deviated wells. Journal of Petroleum Science and Engineering, 2016, 146: 832-837.

Vaziri, E., Simjoo, M., Chahardowli, M. Application of foam as drilling fluid for cuttings transport in horizontal and inclined wells: A numerical study using computational fluid dynamics. Journal of Petroleum Science and Engineering, 2020, 194: 107325.

Wang, K., Yan, T., Sun, X., et al. Review and analysis of cuttings transport in complex structural wells. The Open Fuels & Energy Science Journal, 2013, 6: 9-17.

Williams, C. E., Bruce, G. H. Carrying capacity of drilling muds. Journal of Petroleum Technology, 1951, 3(4): 111-120.

Wood, D. A. Dataset insight and variable influences established using correlations, regressions, and transparent customized formula optimization, in Sustainable Geoscience for Natural Gas Sub-surface Systems, edited by D. A. Wood and J. Cai, Elsevier (Gulf Professional Publishing), Amsterdam, pp. 383-408, 2022.

Wood, D. A. Predicting total organic carbon from few well logs aided by well-log attributes. Petroleum, 2023, 9: 166-182.

Xu, J., Ozbayoglu, E., Miska, S. Z., et al. Cuttings transport with foam in highly inclined wells at simulated downhole conditions. Archives of Mining Sciences, 2013, 58: 481-494.

Yeo, L., Feng, Y., Seibi, A., et al. Optimization of hole cleaning in horizontal and inclined wellbores: A study with computational fluid dynamics. Journal of Petroleum Science and Engineering, 2021, 205: 108993.

Zakerian, A., Sarafraz, S., Tabzar, A., et al. Numerical modeling and simulation of drilling cutting transport in horizontal wells. Journal of Petroleum Exploration and Production Technology, 2018, 8: 455-474.

Zhu, N., Ding, S., Shi, X., et al. Cuttings transport: Back reaming analysis based on a coupled layering-sliding mesh method via CFD. Petroleum Science, 2023, in press,

Zhu, N., Huang, W., Gao, D. Dynamic wavy distribution of cuttings bed in extended reach drilling. Journal of Petroleum Science and Engineering, 2021, 198: 108171.

Zico, M. N. A., Rahman, M. A., Yusuf, H. B., et al. CFD modeling of drill cuttings transport efficiency in annular bends: Effect of hole eccentricity and rotation. Geoenergy Science and Engineering, 2023, 221: 211380.



  • There are currently no refbacks.

Copyright (c) 2023 The Author(s)

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Copyright ©2018. All Rights Reserved