{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T00:03:09Z","timestamp":1773273789481,"version":"3.50.1"},"reference-count":73,"publisher":"MDPI AG","issue":"14","license":[{"start":{"date-parts":[[2023,7,21]],"date-time":"2023-07-21T00:00:00Z","timestamp":1689897600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"College of Petroleum and Geo-sciences at King Fahd University of Petroleum and Minerals"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>When drilling deep wells, it is important to regulate the formation pressure and prevent kicks. This is achieved by controlling the equivalent circulation density (ECD), which becomes crucial in high-pressure and high-temperature wells. ECD is particularly important in formations where the pore pressure and fracture pressure are close to each other (narrow windows). However, the current methods for measuring ECD using downhole sensors can be expensive and limited by operational constraints such as high pressure and temperature. Therefore, to overcome this challenge, two novel models named ECDeffc.m and MWeffc.m were developed to predict ECD and mud weight (MW) from surface-drilling parameters, including standpipe pressure, rate of penetration, drill string rotation, and mud properties. In addition, by utilizing an artificial neural network (ANN) and a support vector machine (SVM), ECD was estimated with a correlation coefficient of 0.9947 and an average absolute percentage error of 0.23%. Meanwhile, a decision tree (DT) was employed to estimate MW with a correlation coefficient of 0.9353 and an average absolute percentage error of 1.66%. The two novel models were compared with artificial intelligence (AI) techniques to evaluate the developed models. The results proved that the two novel models were more accurate with the value obtained from pressure-while-drilling (PWD) tools. These models can be utilized during well design and while drilling operations are in progress to evaluate and monitor the appropriate mud weight and equivalent circulation density to save time and money, by eliminating the need for expensive downhole equipment and commercial software.<\/jats:p>","DOI":"10.3390\/s23146594","type":"journal-article","created":{"date-parts":[[2023,7,24]],"date-time":"2023-07-24T03:03:25Z","timestamp":1690167805000},"page":"6594","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["A Developed Robust Model and Artificial Intelligence Techniques to Predict Drilling Fluid Density and Equivalent Circulation Density in Real Time"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-6140-6553","authenticated-orcid":false,"given":"Mohammed","family":"Al-Rubaii","sequence":"first","affiliation":[{"name":"Department of Petroleum Engineering, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1342-9212","authenticated-orcid":false,"given":"Mohammed","family":"Al-Shargabi","sequence":"additional","affiliation":[{"name":"School of Earth Sciences & Engineering, Tomsk Polytechnic University, Lenin Avenue, Tomsk 634050, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-9781-0279","authenticated-orcid":false,"given":"Bayan","family":"Aldahlawi","sequence":"additional","affiliation":[{"name":"Department of Petroleum Engineering, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7032-5199","authenticated-orcid":false,"given":"Dhafer","family":"Al-Shehri","sequence":"additional","affiliation":[{"name":"Department of Petroleum Engineering, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia"}]},{"given":"Konstantin M.","family":"Minaev","sequence":"additional","affiliation":[{"name":"School of Earth Sciences & Engineering, Tomsk Polytechnic University, Lenin Avenue, Tomsk 634050, Russia"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Al-Rubaii, M.M., Gajbhiye, R.N., Al-Yami, A., Alshalan, M., and Al-Awami, M.B. (2020, January 13\u201315). Automated Evaluation of Hole Cleaning Efficiency While Drilling Improves Rate of Penetration. Proceedings of the International Petroleum Technology Conference 2020, Dhahran, Saudi Arabia.","DOI":"10.2523\/IPTC-19809-MS"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Al Rubaii, M.M. (2018, January 23\u201326). A New Robust Approach for Hole Cleaning to Improve Rate of Penetration. Proceedings of the SPE Kingdom of Saudi Arabia Annual Technical Symposium and Exhibition, Dammam, Saudi Arabia.","DOI":"10.2118\/192223-MS"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"118725","DOI":"10.1016\/j.molliq.2022.118725","article-title":"Nanoparticle Applications as Beneficial Oil and Gas Drilling Fluid Additives: A Review","volume":"352","author":"Davoodi","year":"2022","journal-title":"J. Mol. Liq."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"121117","DOI":"10.1016\/j.molliq.2022.121117","article-title":"Thermally Stable and Salt-Resistant Synthetic Polymers as Drilling Fluid Additives for Deployment in Harsh Sub-Surface Conditions: A Review","volume":"371","author":"Davoodi","year":"2022","journal-title":"J. Mol. Liq."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Al-Rubaii, M., Al-Shargabi, M., and Al-Shehri, D. (2023). A Novel Model for the Real-Time Evaluation of Hole-Cleaning Conditions with Case Studies. Energies, 16.","DOI":"10.20944\/preprints202304.0779.v1"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1569","DOI":"10.1007\/s13202-018-0572-y","article-title":"New Approach to Evaluate the Equivalent Circulating Density (ECD) Using Artificial Intelligence Techniques","volume":"9","author":"Abdelgawad","year":"2019","journal-title":"J. Pet. Explor. Prod. Technol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"103224","DOI":"10.1016\/j.jngse.2020.103224","article-title":"Real-Time Determination of Rheological Properties of High over-Balanced Drilling Fluid Used for Drilling Ultra-Deep Gas Wells Using Artificial Neural Network","volume":"77","author":"Gomaa","year":"2020","journal-title":"J. Nat. Gas Sci. Eng."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Al-Rubaii, M., Al-Shargabi, M., and Al-Shehri, D.A. (2023). A Novel Automated Model for Evaluation of the Efficiency of Hole Cleaning Conditions during Drilling Operations. Appl. Sci., 13.","DOI":"10.3390\/app13116464"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"503","DOI":"10.2118\/191060-PA","article-title":"A Field Case Study of Managed Pressure Drilling in Offshore Ultra High-Pressure High-Temperature Exploration Well in the South China Sea","volume":"35","author":"Yin","year":"2020","journal-title":"SPE Drill. Complet."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"101678","DOI":"10.1016\/j.asej.2021.101678","article-title":"Determining the Difference of Kick Tolerance with Single Bubble and Dynamic Multiphase Models: Evaluation of Well-Control with Water\/synthetic Based Muds","volume":"13","author":"Khan","year":"2022","journal-title":"Ain Shams Eng. J."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Ameen Rostami, S., Gumus, F., Simpkins, D., Pobedinski, I., Kinik, K., and Mir Rajabi, M. (2016, January 26\u201328). New Generation of MPD Drilling Software-From Quantifying to Control. Proceedings of the SPE Annual Technical Conference and Exhibition, Dubai, United Arab Emirates.","DOI":"10.2118\/181694-MS"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"AlBahrani, H., Alsheikh, M., Wagle, V., and Alshakhouri, A. (2022, January 8\u201310). Designing Drilling Fluids Rheological Properties with a Numerical Geomechanics Model for the Purpose of Improving Wellbore Stability. Proceedings of the IADC\/SPE International Drilling Conference and Exhibition, Galveston, TX, USA.","DOI":"10.2118\/208753-MS"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"82","DOI":"10.11648\/j.ogce.20200804.12","article-title":"Contributory Influence of Drill Cuttings on Equivalent Circulation Density Model in Deviated Wellbores","volume":"8","author":"Kerunwa","year":"2020","journal-title":"Int. J. Oil Gas Coal Eng."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Diaz, H., Miska, S., Takach, N., and Yu, M. (2004, January 2\u20134). Modeling of ECD in Casing Drilling Operations and Comparison with Experimental and Field Data. Proceedings of the IADC\/SPE Drilling Conference, Dallas TX, USA.","DOI":"10.2118\/87149-MS"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Liu, N., Zhang, D., Gao, H., Hu, Y., and Duan, L. (2021). Real-Time Measurement of Drilling Fluid Rheological Properties: A Review. Sensors, 21.","DOI":"10.3390\/s21113592"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Roy, S., Kamal, S.Z., Frazier, R., Bruns, R., and Hamlat, Y.A. (2021, January 15\u201318). Inline Drilling Fluid Property Measurement, Integration, and Modeling to Enhance Drilling Practice and Support Drilling Automation. Proceedings of the Abu Dhabi International Petroleum Exhibition & Conference, Dubai, United Arab Emirates.","DOI":"10.2118\/208064-MS"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Abdelaal, A., Ibrahim, A., and Elkatatny, S. (2022, January 26\u201329). Rheological Properties Prediction of Flat Rheology Drilling Fluids. Proceedings of the 56th U.S. Rock Mechanics\/Geomechanics Symposium, Santa Fe, NM, USA.","DOI":"10.56952\/ARMA-2022-0822"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Zuo, J.Y., Creek, J., Mullins, O.C., Chen, L., Zhang, D., Pang, J., and Jia, N. (2013, January 26\u201328). A New Method for OBM Decontamination in Downhole Fluid Analysis. Proceedings of the International Petroleum Technology Conference, Beijing, China.","DOI":"10.2523\/IPTC-16524-MS"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"804","DOI":"10.1109\/TIM.2017.2761218","article-title":"Viscosity and Density Measurements Using Mechanical Oscillators in Oil and Gas Applications","volume":"67","author":"Gonzalez","year":"2018","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"574","DOI":"10.1190\/1.1766238","article-title":"An Enhanced Approach to Real-Time Pore Pressure Prediction for Optimized Pressure Management While Drilling","volume":"23","author":"Freitag","year":"2012","journal-title":"Lead. Edge"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Gao, Y., Chen, M., Du, C., Wang, S., Sun, D., Liu, P., and Chen, Y. (2019, January 26\u201328). Integrated Real-Time Pressure Monitoring Enabled the Success of Drilling a HTHP Offshore Well: A Casing Study in Ledong Area of Yinggehai Basin, South China Sea. Proceedings of the International Petroleum Technology Conference, Beijing, China.","DOI":"10.2523\/IPTC-19313-MS"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1016\/j.ejpe.2019.12.003","article-title":"Application of Artificial Neural Networks in the Drilling Processes: Can Equivalent Circulation Density Be Estimated prior to Drilling?","volume":"29","author":"Alkinani","year":"2020","journal-title":"Egypt. J. Pet."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"109132","DOI":"10.1016\/j.petrol.2021.109132","article-title":"Experimental Measurement and Modeling of Water-Based Drilling Mud Density Using Adaptive Boosting Decision Tree, Support Vector Machine, and K-Nearest Neighbors: A Case Study from the South Pars Gas Field","volume":"207","author":"Hashemizadeh","year":"2021","journal-title":"J. Pet. Sci. Eng."},{"key":"ref_24","first-page":"1216002","article-title":"EGBM: An Ensemble Gradient Boost Machine for Lost Circulation Prediction","volume":"12160","author":"Wang","year":"2022","journal-title":"Int. Conf. Comput. Model. Simul. Data Anal."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"100","DOI":"10.2118\/78288-PA","article-title":"Pressure-While-Drilling Measurements To Solve Extended-Reach Drilling Problems on Alaska\u2019s North Slope","volume":"17","author":"Mallary","year":"2002","journal-title":"SPE Drill. Complet."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"141","DOI":"10.3189\/172756407786857712","article-title":"Viscosity and Density of a Two-Phase Drilling Fluid","volume":"47","author":"Alemany","year":"2007","journal-title":"Ann. Glaciol."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Naganawa, S., and Okatsu, K. (2008, January 25\u201327). Fluctuation of Equivalent Circulating Density in Extended Reach Drilling with Repeated Formation and Erosion of Cuttings Bed. Proceedings of the IADC\/SPE Asia Pacific Drilling Technology Conference and Exhibition, Jakarta, Indonesia.","DOI":"10.2118\/115149-MS"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"3230","DOI":"10.19026\/rjaset.5.4562","article-title":"Prediction Method of Safety Mud Density in Depleted Oilfields","volume":"5","author":"Kai","year":"2013","journal-title":"Res. J. Appl. Sci. Eng. Technol."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Zheng, X., Duan, C., Yan, Z., Ye, H., Wang, Z., and Xia, B. (2017). Equivalent Circulation Density Analysis of Geothermal Well by Coupling Temperature. Energies, 10.","DOI":"10.20944\/preprints201701.0125.v1"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"181","DOI":"10.7494\/drill.2017.34.1.181","article-title":"Wellbore Trajectory Impact on Equivalent Circulating Density","volume":"34","author":"Skrzypaszek","year":"2017","journal-title":"AGH Drill. Oil Gas"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Khalid, A., Ashraf, Q., Luqman, K., Hadj-Moussa, A., Sheikh, D., and Zafar, S. (2019, January 11\u201314). Reaching Target Depth with Zero NPT in an HPHT Tight Gas Well: A Case for Automated Managed Pressure Drilling. Proceedings of the Abu Dhabi International Petroleum Exhibition & Conference, Dubai, United Arab Emirates.","DOI":"10.2118\/197565-MS"},{"key":"ref_32","unstructured":"Kananithikorn, N., and Songsaeng, T. (April, January 23). Pre-Drilled ECD Design by Using Fracture Pressure Model in Satun-Funan Fields, Pattani Basin, Gulf of Thailand. Proceedings of the International Petroleum Technology Conference, Virtual."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"19","DOI":"10.2118\/37588-PA","article-title":"Pressure-While-Drilling Data Improve Reservoir Drilling Performance","volume":"13","author":"Ward","year":"1998","journal-title":"SPE Drill. Complet."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"7033","DOI":"10.1038\/s41598-021-86264-5","article-title":"An Insight into the Estimation of Drilling Fluid Density at HPHT Condition Using PSO-, ICA-, and GA-LSSVM Strategies","volume":"11","author":"Alizadeh","year":"2021","journal-title":"Sci. Rep."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1202","DOI":"10.1016\/j.petrol.2016.08.021","article-title":"Real Time Prediction of Drilling Fluid Rheological Properties Using Artificial Neural Networks Visible Mathematical Model (White Box)","volume":"146","author":"Elkatatny","year":"2016","journal-title":"J. Pet. Sci. Eng."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1655","DOI":"10.1007\/s13369-016-2409-7","article-title":"Real-Time Prediction of Rheological Parameters of KCl Water-Based Drilling Fluid Using Artificial Neural Networks","volume":"42","author":"Elkatatny","year":"2017","journal-title":"Arab. J. Sci. Eng."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Alkinani, H.H., Al-Hameedi, A.T.T., Dunn-Norman, S., Al-Alwani, M.A., Mutar, R.A., and Al-Bazzaz, W.H. (2019, January 21\u201323). Data-Driven Neural Network Model to Predict Equivalent Circulation Density ECD. Proceedings of the SPE Gas & Oil Technology Showcase and Conference, Dubai, United Arab Emirates.","DOI":"10.2118\/198612-MS"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"27430","DOI":"10.1021\/acsomega.1c04363","article-title":"Machine Learning Models for Equivalent Circulating Density Prediction from Drilling Data","volume":"6","author":"Gamal","year":"2021","journal-title":"ACS Omega"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/j.neucom.2016.01.106","article-title":"Toward Reliable Model for Prediction Drilling Fluid Density at Wellbore Conditions: A LSSVM Model","volume":"211","author":"Ahmadi","year":"2016","journal-title":"Neurocomputing"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"934","DOI":"10.1021\/acsomega.0c05570","article-title":"Real-Time Prediction of Equivalent Circulation Density for Horizontal Wells Using Intelligent Machines","volume":"6","author":"Alsaihati","year":"2021","journal-title":"ACS Omega"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"50","DOI":"10.2516\/ogst\/2019021","article-title":"Application of Radial Basis Function (RBF) Neural Networks to Estimate Oil Field Drilling Fluid Density at Elevated Pressures and Temperatures","volume":"74","author":"Rahmati","year":"2019","journal-title":"Oil Gas Sci. Technol.\u2013Rev. d\u2019IFP Energ. Nouv."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"32","DOI":"10.11648\/j.sd.20190701.18","article-title":"Study on the Dynamic Prediction Method of ECD in Horizontal Well Drilling","volume":"7","author":"Xianming","year":"2019","journal-title":"Sci. Discov."},{"key":"ref_43","first-page":"129","article-title":"Effect of Drilling Fluid Properties on Rate of Penetration","volume":"60","author":"Paiaman","year":"2009","journal-title":"Nafta"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"835","DOI":"10.1007\/s13762-020-02880-0","article-title":"Insights into Application of Acorn Shell Powder in Drilling Fluid as Environmentally Friendly Additive: Filtration and Rheology","volume":"18","author":"Davoodi","year":"2021","journal-title":"Int. J. Environ. Sci. Technol."},{"key":"ref_45","first-page":"523","article-title":"Smart Sensors Measurement and Instrumentation","volume":"Volume 957","author":"Chokkadi","year":"2023","journal-title":"Proceedings of the CISCON 2021"},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Bout, G., Brito, D., G\u00f3mez, R., Carvajal, G., and Ram\u00edrez, G. (2022). Physics-Based Observers for Measurement-While-Drilling System in Down-the-Hole Drills. Mathematics, 10.","DOI":"10.3390\/math10244814"},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Jimmy, D., Wami, E., and Ogba, M.I. (2022, January 1\u20133). Cuttings Lifting Coefficient Model: A Criteria for Cuttings Lifting and Hole Cleaning Quality of Mud in Drilling Optimization. Proceedings of the SPE Nigeria Annual International Conference and Exhibition, Lagos, Nigeria.","DOI":"10.2118\/212004-MS"},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Rathgeber, D., Johnson, E., Lucon, P., Anderson, R., Todd, B., Downey, J., and Richards, L. (2023, January 22\u201325). A Novel Approach to Determining Carrying Capacity Index Through Incorporation of Hole Size and Pipe Rotation. Proceedings of the SPE Western Regional Meeting, Anchorage, AK, USA.","DOI":"10.2118\/212985-MS"},{"key":"ref_49","unstructured":"Fausett, L. (1994). Fundamentals of Neural Network: Architectures, Fundamentals, and Applications, Prentice-Hall, Inc."},{"key":"ref_50","first-page":"155","article-title":"Support Vector Regression Machines","volume":"Volume 9","author":"Drucker","year":"1996","journal-title":"Advances in Neural Information Processing Systems"},{"key":"ref_51","unstructured":"Bishop, C.M. (2006). Pattern Recognition and Machine Learning, Springer."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"123807","DOI":"10.1016\/j.seppur.2023.123807","article-title":"Machine-Learning Models to Predict Hydrogen Uptake of Porous Carbon Materials from Influential Variables","volume":"316","author":"Davoodi","year":"2023","journal-title":"Sep. Purif. Technol."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"106459","DOI":"10.1016\/j.engappai.2023.106459","article-title":"Hybridized Machine-Learning for Prompt Prediction of Rheology and Filtration Properties of Water-Based Drilling Fluids","volume":"123","author":"Davoodi","year":"2023","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"6551","DOI":"10.1016\/j.egyr.2022.04.073","article-title":"Data Driven Models to Predict Pore Pressure Using Drilling and Petrophysical Data","volume":"8","author":"Jafarizadeh","year":"2022","journal-title":"Energy Rep."},{"key":"ref_55","unstructured":"Von Winterfeldt, D., and Edwards, W. (1986). Decision Analysis and Behavioral Research, Cambridge University Press."},{"key":"ref_56","first-page":"975","article-title":"Study of Various Decision Tree Pruning Methods with Their Empirical Comparison in WEKA Saurabh Upadhyay","volume":"60","author":"Patel","year":"2012","journal-title":"Int. J. Comput. Appl."},{"key":"ref_57","unstructured":"(2023, May 08). Sklearn Library. Available online: https:\/\/scikit-learn.org\/stable\/."},{"key":"ref_58","unstructured":"(2023, May 08). Tensorflow Library. Available online: https:\/\/www.tensorflow.org\/resources\/libraries-extensions?hl=ru."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"1024","DOI":"10.1061\/41073(361)109","article-title":"Quality Assurance\/Quality Control Measures in Horizontal Directional Drilling","volume":"361","author":"Ariaratnam","year":"2009","journal-title":"ICPTT 2009: Advances and Experiences with Pipelines and Trenchless Technology for Water, Sewer, Gas, and Oil Applications"},{"key":"ref_60","doi-asserted-by":"crossref","unstructured":"Al-Rubaii, M., Al-shargabi, M., Al-shehri, D., Alyami, A., and Minaev, K.M. (2023). A Novel Efficient Borehole Cleaning Model for Optimizing Drilling Performance in Real Time. Appl. Sci., 13.","DOI":"10.3390\/app13137751"},{"key":"ref_61","unstructured":"Mitchell, B. (1992). Advanced Oilwell Drilling Engineering Handbook, Society of Petroleum Engineers of the AIME."},{"key":"ref_62","doi-asserted-by":"crossref","unstructured":"Lyons, W.C., Carter, T., and Lapeyrouse, N.J. (2015). Formulas and Calculations for Drilling, Production, and Workover: All the Formulas You Need to Solve Drilling and Production Problems, Elsevier.","DOI":"10.1016\/B978-0-12-803417-0.00008-1"},{"key":"ref_63","unstructured":"Guo, B., and Liu, G. (2011). Applied Drilling Circulation Systems: Hydraulics, Calculations and Models, Gulf Professional Publishing an Imprint of Elsevier. Calculations, and Models."},{"key":"ref_64","doi-asserted-by":"crossref","unstructured":"Chen, Y., Wang, L., Chang, H., and Zhang, Q. (2023). A Review of Drag Coefficient Models in Gas-Liquid Two-Phase Flow. ChemBioEng Rev.","DOI":"10.1002\/cben.202200034"},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"115","DOI":"10.2118\/20422-PA","article-title":"Hole Cleaning in Full-Scale Inclined Wellbores","volume":"7","author":"Sifferman","year":"1992","journal-title":"SPE Drill. Eng."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"11","DOI":"10.2118\/10674-PA","article-title":"Experimental Study of Drilled Cuttings Transport Using Common Drilling Muds","volume":"23","author":"Hussaini","year":"1983","journal-title":"Soc. Pet. Eng. J."},{"key":"ref_67","unstructured":"Robello Samuel (2009). Advanced Drilling Engineering: Principles and Designs, Gulf Publishing Company Elsevier Science & Technology."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"3","DOI":"10.25079\/ukhjse.v2n2y2018.pp3-13","article-title":"Transportation of Cuttings in Inclined Wells","volume":"2","author":"Hamoudi","year":"2018","journal-title":"UKH J. Sci. Eng."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1016\/0148-9062(72)90005-8","article-title":"Annular Velocity for Rotary Drilling Operations","volume":"9","author":"Chien","year":"1972","journal-title":"Int. J. Rock Mech. Min. Sci. Geomech. Abstr."},{"key":"ref_70","doi-asserted-by":"crossref","unstructured":"Bizhani, M., Rodriguez-Corredor, F.E., and Kuru, E. (2015, January 9\u201311). Hole Cleaning Performance of Water vs. Polymer-Based Fluids under Turbulent Flow Conditions. Proceedings of the SPE Canada Heavy Oil Technical Conference, Calgary, AB, Canada.","DOI":"10.2118\/174404-MS"},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"807","DOI":"10.2118\/1697-PA","article-title":"Factors Affecting Cuttings Removal During Rotary Drilling","volume":"19","author":"Hopkin","year":"1967","journal-title":"J. Pet. Technol."},{"key":"ref_72","unstructured":"Whittaker, A. (2011). Theory and Applications of Drilling Fluid Hydraulics, Springer."},{"key":"ref_73","unstructured":"Saudi Arabian Oil Company (2018). Well Control Manual: 6th Edition Drilling and Workover, Saudi Arabian Oil Company."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/14\/6594\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:16:50Z","timestamp":1760127410000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/14\/6594"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,21]]},"references-count":73,"journal-issue":{"issue":"14","published-online":{"date-parts":[[2023,7]]}},"alternative-id":["s23146594"],"URL":"https:\/\/doi.org\/10.3390\/s23146594","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,7,21]]}}}