{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:48:02Z","timestamp":1760028482688,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,2,5]],"date-time":"2025-02-05T00:00:00Z","timestamp":1738713600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100005710","name":"Universiti Teknologi PETRONAS","doi-asserted-by":"publisher","award":["RG2024-1969"],"award-info":[{"award-number":["RG2024-1969"]}],"id":[{"id":"10.13039\/501100005710","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>One of the significant challenges during wellbore drilling is accurately predicting frictional pressure losses in symmetrical drill pipes. In this work, a Bayesian regularized neural network (BRANN) and multivariate adaptive regression splines (MARS) are employed to develop accurate and interpretable models for predicting frictional pressure losses during drilling. Utilizing data of frictional pressure loss collected through experimentation, the models are created. The model inputs include mud flow rate, mud density, pipe diameter (inside and outside diameters), and viscometer dial readings, while pressure loss is the output. Statistical comparisons between the model predictions and the actual values demonstrate the models\u2019 ability to reasonably forecast frictional pressure losses in wells. The performance of the models, as measured by error metrics, is as follows: BRANN (0.999, 0.076, 16.76, and 11.67) and MARS (0.998, 0.0989, 21.32, and 16.499) with respect to the coefficient of determination, average absolute percentage error, root mean square error, and mean absolute error, respectively. Additionally, a parametric importance study reveals that, among the input variables, internal and external pipe diameters are the top predictors, with a relevancy factor of \u22120.784 for each, followed by the mud flow rate, with a relevancy factor of 0.553. The trend analysis further confirms the physical validity of the proposed models. The explicit nature of the models, together with their physical validation through trend analysis and interpretability via a sensitivity analysis, adds to the novelty of this study. The precise and robust estimations provided by the models make them valuable virtual tools for the development of drilling hydraulics simulators for frictional pressure loss estimations in the field.<\/jats:p>","DOI":"10.3390\/sym17020228","type":"journal-article","created":{"date-parts":[[2025,2,5]],"date-time":"2025-02-05T05:50:36Z","timestamp":1738734636000},"page":"228","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Frictional Pressure Loss Prediction in Symmetrical Pipes During Drilling Using Soft Computing Algorithms"],"prefix":"10.3390","volume":"17","author":[{"given":"Okorie Ekwe","family":"Agwu","sequence":"first","affiliation":[{"name":"Petroleum Engineering Department, Universiti Teknologi PETRONAS, Seri Iskandar 32610, Perak Darul Ridzuan, Malaysia"},{"name":"Center of Reservoir Dynamics (CORED), Institute of Sustainable Energy, Universiti Teknologi PETRONAS, Seri Iskandar 32610, Perak Darul Ridzuan, Malaysia"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-5337-3180","authenticated-orcid":false,"given":"Sia Chee","family":"Wee","sequence":"additional","affiliation":[{"name":"Petroleum Engineering Department, Universiti Teknologi PETRONAS, Seri Iskandar 32610, Perak Darul Ridzuan, Malaysia"}]},{"given":"Moses Gideon","family":"Akpabio","sequence":"additional","affiliation":[{"name":"Department of Petroleum Engineering, University of Uyo, Uyo 52001, Akwa Ibom State, Nigeria"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,5]]},"reference":[{"key":"ref_1","unstructured":"Skalle, P. (2011). Drilling Fluid Engineering, Bookboon Publishers."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1016\/j.petlm.2021.04.003","article-title":"New model for standpipe pressure prediction while drilling using Group Method of Data Handling","volume":"8","author":"Youcefi","year":"2022","journal-title":"Petroleum"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1080\/01932691.2014.904793","article-title":"Estimation of Pressure Loss of Herschel\u2013Bulkley Drilling Fluids During Horizontal Annulus Using Artificial Neural Network","volume":"36","author":"Rooki","year":"2015","journal-title":"J. Dispers. Sci. Technol."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Gul, S., Johnson, M.D., Vajargah, A.K., Ma, Z., Hoxha, B.B., and van Oort, E. (2019, January 5\u20137). A Data Driven Approach to Predict Frictional Pressure Losses in Polymer-Based Fluids. Proceedings of the SPE\/IADC International Drilling Conference and Exhibition, The Hague, The Netherlands.","DOI":"10.2118\/194132-MS"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1016\/j.measurement.2016.02.037","article-title":"Application of general regression neural network (GRNN) for indirect measuring pressure loss of Herschel\u2013Bulkley drilling fluids in oil drilling","volume":"85","author":"Rooki","year":"2016","journal-title":"Measurement"},{"key":"ref_6","unstructured":"Drilling Formulas (2024, September 09). Equivalent Circulating Density (ECD) Using Yield Point for MW Less than 13 ppg. Available online: https:\/\/www.drillingformulas.com\/equivalent-circulating-density-ecd-using-yield-point-for-mw-less-than-13-ppg\/."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1016\/j.petrol.2011.06.013","article-title":"Friction factors for hydraulic calculations considering presence of cuttings and pipe rotation in horizontal\/highly-inclined wellbores","volume":"78","author":"Sorgun","year":"2011","journal-title":"J. Pet. Sci. Eng."},{"key":"ref_8","first-page":"272","article-title":"Annular Pressure Loss while Drilling Prediction with Artificial Neural Network Modeling","volume":"95","author":"Razi","year":"2013","journal-title":"Eur. J. Sci. Res."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1016\/j.jngse.2018.05.028","article-title":"Predicting the pressure losses while the drillstring is buckled and rotating using artificial intelligence methods","volume":"56","author":"Ozbayoglu","year":"2018","journal-title":"J. Nat. Gas Sci. Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"57","DOI":"10.2118\/141518-PA","article-title":"Frictional Pressure Loss Estimation of Non-Newtonian Fluids in Realistic Annulus with Pipe Rotation","volume":"49","author":"Ozbayoglu","year":"2010","journal-title":"J. Can. Pet. Technol."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Kumar, A., Ridha, S., Ganet, T., Vasant, P., and Ilyas, S.U. (2020). Machine Learning Methods for Herschel\u2013Bulkley Fluids in Annulus: Pressure Drop Predictions and Algorithm Performance Evaluation. Appl. Sci., 10.","DOI":"10.3390\/app10072588"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Ozbayoglu, M., Ozbayoglu, E., Ozdilli, B.G., and Erge, O. (2021, January 21\u201330). Estimation of Cuttings Concentration and Frictional Pressure Losses During Drilling Using Data-Driven Models. Proceedings of the ASME 2021 40th International Conference on Ocean, Offshore and Arctic Engineering, OMAE202, Virtual.","DOI":"10.1115\/OMAE2021-63653"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"022902","DOI":"10.1115\/1.4031743","article-title":"Modeling and Experimental Study of Solid\u2013Liquid Two-Phase Pressure Drop in Horizontal Wellbores With Pipe Rotation","volume":"138","author":"Sorgun","year":"2015","journal-title":"J. Energy Resour. Technol."},{"key":"ref_14","unstructured":"Haykin, S. (2009). Neural Networks and Learning Machines, Pearson Education, Inc., McMaster University. [3rd ed.]. Available online: http:\/\/dai.fmph.uniba.sk\/courses\/NN\/haykin.neural-networks.3ed.2009.pdf."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1081\/LFT-120002082","article-title":"Artificial neural network model for accurate prediction of pressure drop in horizontal and near-horizontal-multiphase flow","volume":"20","author":"Osman","year":"2002","journal-title":"Pet. Sci. Technol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1080\/10916460701700203","article-title":"Estimating flow patterns and frictional pressure losses of two-phase fluids in horizontal wellbores using artificial neural networks","volume":"27","author":"Ozbayoglu","year":"2009","journal-title":"Pet. Sci. Technol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/j.petrol.2010.02.001","article-title":"Prediction of Pressure Drop Using Artificial Neural Network for Non-Newtonian Liquid Flow Through Piping Components","volume":"71","author":"Bar","year":"2010","journal-title":"J. Pet. Sci. Eng."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Shahdi, A., and Arabloo, M. (2014). Application of SVM Algorithm for Frictional Pressure Loss Calculation of Three Phase Flow in Inclined Annuli. J. Pet. Environ. Biotechnol., 5.","DOI":"10.4172\/2157-7463.1000179"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"032901","DOI":"10.1115\/1.4028694","article-title":"Support Vector Regression and Computational Fluid Dynamics Modeling of Newtonian and Non-Newtonian Fluids in Annulus with Pipe Rotation","volume":"137","author":"Sorgun","year":"2014","journal-title":"J. Energy Resour. Technol."},{"key":"ref_20","first-page":"275","article-title":"Prediction of frictional pressure loss for multiphase flow in inclined annuli during Underbalanced Drilling operations","volume":"3","author":"Ali","year":"2016","journal-title":"Nat. Gas Ind. B"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"112110","DOI":"10.1115\/1.4047593","article-title":"Estimation of Pressure Drop of Two-Phase Flow in Horizontal Long Pipes Using Artificial Neural Networks","volume":"142","author":"Shadloo","year":"2020","journal-title":"J. Energy Resour. Technol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"110203","DOI":"10.1016\/j.petrol.2022.110203","article-title":"Rigorous modeling of frictional pressure loss in inclined annuli using artificial intelligence methods","volume":"211","author":"Bemani","year":"2022","journal-title":"J. Pet. Sci. Eng."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"104348","DOI":"10.1016\/j.jngse.2021.104348","article-title":"Combining physics-based and data-driven modeling in well construction: Hybrid fluid dynamics modelling","volume":"97","author":"Erge","year":"2021","journal-title":"J. Nat. Gas Sci. Eng."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Elmgerbi, A., Chuykov, E., Thonhauser, G., and Nascimento, A. (2022, January 21\u201323). Machine Learning Techniques Application for Real-Time Drilling Hydraulic Optimization. Proceedings of the International Petroleum Technology Conference, Riyadh, Saudi Arabia.","DOI":"10.2523\/IPTC-22662-MS"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"16125","DOI":"10.1007\/s00500-023-07986-4","article-title":"Application of soft computing approaches for modeling annular pressure loss of slim-hole wells in one of Iranian central oil fields","volume":"27","author":"Jafarifar","year":"2023","journal-title":"Soft Comput."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"131361","DOI":"10.1016\/j.conbuildmat.2023.131361","article-title":"Development of Bayesian regularized artificial neural network for airborne chlorides estimation","volume":"383","author":"Kim","year":"2023","journal-title":"Constr. Build. Mater."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Kayri, M. (2016). Predictive Abilities of Bayesian Regularization and Levenberg\u2013Marquardt Algorithms in Artificial Neural Networks: A Comparative Empirical Study on Social Data. Math. Comput. Appl., 21.","DOI":"10.3390\/mca21020020"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Livingstone, D.J. (2008). Bayesian Regularization of Neural Networks. Artificial Neural Networks. Methods in Molecular Biology, Humana Press.","DOI":"10.1007\/978-1-60327-101-1"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"382","DOI":"10.1111\/aogs.12344","article-title":"Multivariate adaptive regression splines analysis to predict biomarkers of spontaneous preterm birth","volume":"93","author":"Menon","year":"2014","journal-title":"Acta Obstet. Gynecol. Scand."},{"key":"ref_30","first-page":"1","article-title":"Multivariate adaptive regression splines","volume":"19","author":"Friedman","year":"1991","journal-title":"Ann. Statist."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"212584","DOI":"10.1016\/j.geoen.2023.212584","article-title":"Mathematical modelling of drilling mud plastic viscosity at downhole conditions using multivariate adaptive regression splines","volume":"233","author":"Agwu","year":"2023","journal-title":"Geoenergy Sci. Eng."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"234","DOI":"10.1016\/j.procs.2018.07.257","article-title":"Analysing Neural Network Topologies: A Game Theoretic Approach","volume":"126","author":"Stier","year":"2018","journal-title":"Procedia Comput. Sci."},{"key":"ref_33","first-page":"15","article-title":"Improving Bingham Plastic Frictional Pressure-Loss Predictions for Oil Wells","volume":"11","author":"Muherei","year":"2022","journal-title":"Am. J. Eng. Res."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1016\/j.ecolmodel.2006.11.005","article-title":"A methodology for developing simulation models of complex systems","volume":"202","author":"Aumann","year":"2007","journal-title":"Ecol. Model."},{"key":"ref_35","first-page":"157","article-title":"Research on measurement method of drilling fluid rheological parameters based on helical pipe","volume":"1","author":"Zhao","year":"2023","journal-title":"Int. J. Comput. Sci. Inf. Technol."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Mahmoudzadeh, A., Amiri-Ramsheh, B., Atashrouz, S., Abedi, A., Abuswer, M.A., Ostadhassan, M., Mohaddespour, A., and Hemmati-Sarapardeh, A. (2024). Modeling CO2 solubility in water using gradient boosting and light gradient boosting machine. Sci. Rep., 14.","DOI":"10.1038\/s41598-024-63159-9"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Aadnoy, B.S., Cooper, I., Miska, S.Z., Mitchell, R.F., and Payne, M.L. (2009). Advanced Wellbore Hydraulics. Advanced Drilling and Well Technology, Society of Petroleum Engineers.","DOI":"10.2118\/9781555631451"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/2\/228\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:27:13Z","timestamp":1760027233000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/2\/228"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,5]]},"references-count":37,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2025,2]]}},"alternative-id":["sym17020228"],"URL":"https:\/\/doi.org\/10.3390\/sym17020228","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2025,2,5]]}}}