Predicting drilling mud equivalent circulating density with precision: A critical review of modern approaches

Abstract

Equivalent circulating density (ECD) denotes the density of drilling mud during circulation within a well. It is determined by integrating the equivalent static density with the pressure loss attributable to friction between the flowing mud and the geological formation. The effective management of ECD is imperative during drilling operations, as it plays a critical role in preventing kicks and minimising mud losses. Mud ECD has undergone extensive investigation through laboratory experiments, field measurements, and predictive modelling. Nevertheless, a comprehensive review of the various predictive models associated with ECD remains absent. The objective of this study is to review and critique existing correlations for estimating ECD. To accomplish this, a thorough bibliometric analysis was performed, focusing on peer-reviewed journals, mud manuals, and oil and gas conference papers. For the sake of clarity, existing models were categorized into tables, with their principal features highlighted. A critique of each model was subsequently provided. In total, 45 models related to ECD were identified ed, reviewed, and critiqued. The findings reveal that over 44% of the models are based on machine learning (ML), 27% are analytical models, 16% are regression based models, and 13% are simulator-related. Although there is no universally accepted model for ECD, there is an observable trend towards the utilization of ML algorithms for ECD estimation due to their predictive capabilities. However, the interpretability of these ML-based models remains a significa cant concern. This review serves as a comprehensive source of information on ECD for both readers and industry practitioners. Additionally, it directs researchers towards areas requiring further exploration and aids drilling professionals in selecting appropriate ECD models.

Keywords

Equivalent circulating density / Modelling / Machine learning / Drilling mud

CRediT authorship contribution statement

Okorie Ekwe Agwu: Writing-review & editing, Writing-original draft, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. Saad Alatefi: Writing-review & editing, Writing-original draft, Visualization, Validation, Supervision, Software, Resources, Data curation, Conceptualization. Muhammad Aslam Md Yusof: Writing-original draft, Visualization, Validation, Supervision, Resources, Formal analysis. Cosmas Brendan Orun: Visualization, Supervision, Project administration, Methodology, Formal analysis, Data curation.

Availability of data and materials

No data was used for this study.

Funding

This research received no funding from any organization.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influe uence the work reported in this paper.

Acknowledgements

The authors would like to thank Universiti Teknologi PETRONAS, Malaysia and the College of Technological Studies, PAAET, Kuwait for permitting the use of its resources in conducting this work.

References

[1] A. Alsaihati, S. Elkatatny, A. Abdulraheem, Real-time prediction of equivalent circulation density for horizontal wells using intelligent machines, ACS Omega 6 (1) (2021) 934-942, https://doi.org/10.1021/acsomega.0c05570.

[2] F. Kernche, D. Hannegan, E. Sammat, M. Arnone,Managed pressure drilling enables drilling beyond the conventional limit on an HP/HT deepwater well, in:Paper SPE-142312 presented at the SPE Offshore Europe Oil and Gas Conference and Exhibition, 2011, pp. 6-8, https://doi.org/10.2118/142310-MS. Aberdeen,UK.

[3] F. Badrouchi, V. Rasouli, N. Badrouchi, Impact of hole cleaning and drilling performance on the equivalent circulating density, J. Petrol. Sci. Eng. 211 (2022) 1-14, https://doi.org/10.1016/j.petrol.2022.110150.

[4] M. Haciislamoglu, U. Cartalos,Practical pressure loss predictions in realistic annular geometries, in:Paper SPE-28304-MS presented at the SPE Annual Technical Conference and Exhibition, 1994, https://doi.org/10.2118/28304-MS. NewOrleans,Louisiana.

[5] S. Davoodi, M. Mehrad, D.A. Wood, H. Ghorbani, V.S. Rukavishnikov, Hybridized machine learning for prompt prediction of rheology and filtration properties of water-based drilling fluids, Eng. Appl. Artif. Intell. 123 (2023) 1-29, https://doi.org/10.1016/j.engappai.2023.106459.

[6] M.A. El-Reedy, Offshore Structures: Design, Construction and Maintenance, second ed., Gulf Professional Publishing, Waltham, USA, 2020 https://doi.org/10.1016/C2017-0-03037-9.

[7] A.K. Vajargah, F.N. Fard, M. Parsi, B.B. Hoxha, Investigating the impact of the ‘Tool Joint Effect’ on equivalent circulating density in deep-water wells, in:Paper SPE-170294-MS presented at the SPE Deepwater Drilling and Completions Conference, 2014, https://doi.org/10.2118/170294-MS. Galveston, Texas, USA.

[8] R. Rommetveit, K.S. Bjorkevoll,Temperature and pressure effects on drilling fluid rheology and ECD in very deep wells, in:Paper SPE-39282-MS presented at the SPE/IADC Middle East Drilling Technology Conference, 1997, pp. 23-25, https://doi.org/10.2118/39282-MS.Bahrain.

[9] K.Z. Abdelgawad, M. Elzenary, S. Elkatatny, M. Mahmoud, A. Abdulraheem, S. Patil, New approach to evaluate the equivalent circulating density (ECD) using artificial intelligence techniques, J. Pet. Explor. Prod. Technol. 9 (2019) 1569-1578, https://doi.org/10.1007/s13202-018-0572-y.

[10] S. Lapierre, G. Courville, J. Song, Achieving technical limits: expanded application of real-time pressure-while-drilling data helps optimize ROP and hole cleaning in large-diameter, directional intervals, in: Paper SPE-99142-MS presented at the IADC/SPE Drilling Conference, 2006, pp. 21-23, https://doi.org/10.2118/99142-MS. Miami,Florida,USA.

[11] M. Al-Rubaii, M. Al-Shargabi, B. Aldahlawi, D. Al-Shehri, K.M. Minaev, A developed robust model and artificial intelligence techniques to predict drilling fluid density and equivalent circulation density in real time, Sensors 23 (14) (2023) 1-28, https://doi.org/10.3390/s23146594.

[12] V. Roy, A. Pandey, A. Saxena, S. Sharma, Assessment of machine learning techniques for real-time prediction of equivalent circulating density, in:Paper OTC-31523-MS presented at the Offshore Technology Conference Asia, 2022, https://doi.org/10.4043/31523-MS. KualaLumpur,Malaysia.

[13] H. Gamal, A. Abdelaal, S. Elkatatny, Machine learning models for equivalent circulating density prediction from drilling data, ACS Omega 6 (41) (2021) 27430-27442, https://doi.org/10.1021/acsomega.1c04363.

[14] R. Maglione, G. Robotti, R. Romagnoli,A computer program to predict stand pipe pressure while drilling using the drilling well as viscometer, in:Paper SPE-35994-MS presented at the Petroleum Computer Conference, 1996, https://doi.org/10.2118/35994-MS. Dallas,Texas.

[15] H.H. Alkinani, A. Al-Hameedi, S. Dunn-Noman, M.A. Al-Alwani, R.A. Mutar, W.H. Al-Bazzaz, Data-driven neural network model to predict equivalent circulation density (ECD),in: Paper SPE-198612-MS presented at the SPE Gas and Oil Technology Showcase and Conference, 2019, pp. 21-23, https://doi.org/10.2118/198612-MS. Dubai,UAE.

[16] M. Aljubran, J. Ramasamy, M. Albassam, A. Magana-Mora, Deep learning and time-series analysis for the early detection of lost circulation incidents during drilling operations, IEEE Access 9 (2021) 76833-76846, https://doi.org/10.1109/ACCESS.2021.3082557.

[17] B. Rehm, A. Haghshenas, A.S. Paknejad, J. Schubert,Situational problems in MPD, in: Rehm, et al. (Eds.), Managed Pressure Drilling, Gulf Publishing Company, USA, 2008, pp. 39-80, https://doi.org/10.1016/C2013-0-15524-9.

[18] G. Raabe, S. Jortner, Universal Well Control, first ed., Gulf Professional Publishing, USA, 2021 https://doi.org/10.1016/C2020-0-03930-7.

[19] A. Kandil, S. Khaled, T. Elfakharany, Prediction of the equivalent circulation density using machine learning algorithms based on real-time data, AIMS Energy 11 (3) (2023) 425-453, https://doi.org/10.3934/energy.2023023.

[20] W.J. Bailey,An Evaluation of Calculation Procedures Affecting the Constituent Factors of Equivalent Circulating Density for Drilling Hydraulics, Norwegian University of Science and Technology, 1996. Dissertation.

[21] M.A. Sarbini, Determining well control issues in HTHP Wells by predicting equivalent circulating density, Universiti Teknologi PETRONAS, 2012. Dissertation.

[22] R.G. Samuel, Formulas and Calculations for Drilling Operations, Scrivener Publishing LLC, Texas, 2010.

[23] R.D. Grace, Blowout and Well Control Handbook, second ed., Gulf Professional Publishing, Texas, 2017 https://doi.org/10.1016/B978-0-7506-7708-0.X5000-2.

[24] S.O. Osisanya, O.O. Harris, Evaluation of equivalent circulating density of drilling fluids under high pressure/high temperature conditions, in:Paper SPE-97018-MS presented at the SPE Annual Technical Conference and Exhibition, 2005, pp. 9-12, https://doi.org/10.2118/97018-MS. Dallas,Texas,USA.

[25] W.C. Lyons, T. Carter, N.J. Lapeyrouse, in: Formulas and Calculations for Drilling, Production, and Workover, fourth ed., Elsevier, Amsterdam, 2016 https://doi.org/10.1016/C2014-0-04165-2.

[26] J. Sun, F. Yang, B. Qi, Z. Li, J. Li, A new calculation model for equivalent circulating density considering interface effect between various fluids during cementing process, SPE J. (2024) 1-15, https://doi.org/10.2118/219481-PA.

[27] T. Robinson, D. Gomes, M.M. Hashim, M.H. Yusoff, M.F. Arriffin n, A. Mohamad, T. Ezharuddin, E. Othman, Real-time estimation of downhole equivalent circulating density (ECD) using machine learning and applications, in:Paper SPE-208675-MS presented at the IADC/SPE International Drilling Conference and Exhibition, 2022, https://doi.org/10.2118/208675-MS. Galveston,Texas,USA.

[28] V. Dokhani, Y. Ma, M. Yu, Determination of equivalent circulating density of drilling fluids in deep water drilling, J. Nat. Gas Sci. Eng. 34 (2016) 1096-1105, https://doi.org/10.1016/j.jngse.2016.08.009.

[29] M. Elzenary, S. Elkatatny, K.Z. Abdelgawad, A. Abdulraheem, M. Mahmoud, D. Al-Shehri,New technology to evaluate equivalent circulating density while drilling using artificial intelligence, in:Paper SPE-192282-MS presented at the SPE Kingdom of Saudi Arabia Annual Technical Symposium and Exhibition, 2018, https://doi.org/10.2118/192282-MS. Dammam,SaudiArabia.

[30] R. Arab, Z. Toktabolat, M.E. Anderson, M.M. Nasef, Realtime open hole modelling of equivalent circulating density using high frequency pressure sensors across the drillstring to maximize horizontal drilling capability, in:Paper IPTC-24340-EA presented at the International Petroleum Technology Conference, 2024, https://doi.org/10.2523/IPTC-24340-EA. Dhahran,SaudiArabia.

[31] A.T. Al-Hameedi, H.H. Alkinani, S. Dunn-Norman, A.S. Amer,Insights into the relationship between equivalent circulation density and drilling fluid rheological properties, in:Paper SPE-194623-MS presented at the SPE Oil and Gas India Conference and Exhibition, 2019, pp. 9-11, https://doi.org/10.2118/194623-MS.

[32] B.S. Grigoriev, A.A. Eliseev, T.A. Pogarskaya, E.E. Toropov, Mathematical modeling of rock crushing and multiphase flow of drilling fluid in well drilling, J. Min. Inst. 235 (2019) 16-23, https://doi.org/10.31897/PMI.2019.1.16.

[33] Z. Hui, D. Chesnee, D. Jay, S. Bill, S. Ryan, T. Tim, V. Rob, D. Carbajal,Hydraulic modelling helps designing ultralow ECD nonaqueous fluids to meet narrow ECD windows, in:Paper SPE-192951-MS presented at the Abu Dhabi International Petroleum Exhibition & Conference, 2018, https://doi.org/10.2118/192951-MS. AbuDhabi,UAE.

[34] S. Gul, M.D. Johnson, A.K. Vajargah, Z. Ma, B.B. Hoxha, E. van Oort,A data driven approach to predict frictional pressure losses in polymer-based fluids, in:Paper SPE/IADC-194132-MS presented at the SPE/IADC Drilling International Conference and Exhibition, 2019, pp. 5-7, https://doi.org/10.2118/194132-MS. TheHague,TheNetherlands.

[35] X. Jiang, Z. Lei, Q. Meng, Evaluation of equivalent circulating density in deep water dynamic kill drilling, Appl. Mech. Mater. 121-126 (2011) 3048-3052, https://doi.org/10.4028/www.scientific.net/AMM.121-126.3048.

[36] Drilling Formulas, Equivalent circulating density (ECD) using yield point for MW less than 13 ppg. https://www.drillingformulas.com/equivalent-circulating-density-ecd-using-yield-point-for-mw-less-than-13-ppg/,2012. (Accessed9 April 2024).

[37] R.A. Delwiche, M.W. Lejune, P.F. Mawet, R. Vighetto,Slimhole drilling hydraulics, in:Paper SPE-24596-MS presented at the SPE Annual Technical Conference and Exhibition, 1992, https://doi.org/10.2118/24596-MS. Washington,D.C.

[38] S. Simoes, M. Yu, S. Miska, N.E. Takach, The effect of tool joints on ECD while drilling, in:Paper SPE-106647-MS presented at the Production and Operations Symposium, 2007, https://doi.org/10.2118/106647-MS. OklahomaCity,Oklahoma,USA.

[39] R. Wisniowski, K. Skrzypaszek, P. Kiebzak, M. Kanski, Wellbore trajectory impact on equivalent circulating density, AGH Drill. Oil Gas 34 (1) (2017) 181-202, https://doi.org/10.7494/drill.2017.34.1.181.

[40] X. Zheng, C. Duan, Z. Yan, H. Ye, Z. Wang, B. Xia, Equivalent circulation density analysis of geothermal well by coupling temperature, Energies 10 (3) (2017) 1-18, https://doi.org/10.3390/en10030268.

[41] A. Kerunwa, J.U. Obibuike, U.I. Duru, S.T. Ekwueme, The effects of fluid rheology and drillstring eccentricity on drilling hydraulics, Open J. Yangtze Oil Gas 6 (4) (2021) 129-145, https://doi.org/10.4236/ojogas.2021.64012.

[42] M. Albassam,Effect of Cuttings on Annular Pressure Loss, University of Texas at Austin, 2020. Dissertation.

[43] W. Haige, S. Yinao, High temperature & high pressure (HTHP) mud P-V-T behaviour and its effect on wellbore pressure calculations,in: Paper SPE-59266-MS presented at the IADC/SPE Drilling Conference, 2000, https://doi.org/10.2118/59266-MS. NewOrleans,Louisiana.

[44] M.M. Al-Rubaii, F.Y. Al-Nassar, S. Al-Harbi, A new real-time prediction of equivalent circulation density from drilling surface parameters without using PWD tool, in: Paper SPE-209945-MS presented at the SPE Symposium: Unconventionals in the Middle East, 2022, pp. 23-24, https://doi.org/10.2118/209945-MS. Manama,Bahrain.

[45] M.A. Ahmadi, S.R. Shadizadeh, K. Shah, A. Bahadori, An accurate model to predict drilling fluid density at wellbore conditions, Egypt. J. Pet. 27 (1) (2018) 1-10, https://doi.org/10.1016/j.ejpe.2016.12.002.

[46] P. Skalle, in: Drilling Fluid Engineering, first ed., Ventus Publishing ApS, 2011.

[47] H. Wang, Y. Su, High temperature and high pressure (HTHP) mud P-D-T behavior and its effect on wellbore pressure calculations, in: Paper IADC/SPE-59266-MS presented at the 2000 IADC/SPE Drilling Conference, 2000, pp. 23-25, https://doi.org/10.2118/59266-MS. New Orleans, Louisiana.

[48] K.C. Igwilo, E.E. Okoro, O.E. Agwu, C. Onedibe, S.I. Ibeneme, N. Okoli, Experimental analysis of Persea Americana as filtration loss control additive for non-aqueous drilling fluid, J. Eng. Res. Appl. 44 (2019) 8-21, https://doi.org/10.4028/www.scientific.net/jera.44.8.

[49] O.E. Agwu, A.N. Okon, F.D. Udoh, A review of Nigerian bentonitic clays as drilling mud, in:Paper SPE-178264-MS presented at the SPE Nigeria Annual International Conference and Exhibition, 2015, https://doi.org/10.2118/178264-MS. Lagos,Nigeria.

[50] K. Taugbol, G. Fimreite, O.I. Prebensen, K. Svanes, T.H. Omland, P.E. Svela, D.H. Breivik, Development and field testing of a unique high-temperature/high-pressure oil-based drilling fluid with minimum rheology and maximum sag stability, in:Paper SPE-96285-MS presented at the SPE Offshore Europe Oil and Gas Exhibition and Conference, 2005, pp. 6-9, https://doi.org/10.2118/96285-MS. Aberdeen,UK.

[51] D. Power, M. Zamora, Drilling fluid yield stress: measurement techniques for improved understanding of critical drilling fluid parameters,in:Paper AADE-03-NTCE-35 presented at the AADE 2003 National Technology Conference, 2003, pp. 1-3. Houston, Texas, https://www.aade.org/application/files/7515/7304/4604/AADE-03-NTCE-35-Power.pdf.

[52] S.D. Kulkarni, J. Singh, V.L. Pereira, A. Porter,Real-time ECD management by accounting for effects of drillpipe rotation and eccentricity in the wellbore, in:Paper AADE-17-NTCE-097 presented at the 2017 AADE National Technical Conference and Exhibition, 2017, pp. 11-12. Houston, Texas, https://www.aade.org/application/fileles/4915/7132/1742/AADE-17-NTCE-097_-_Kulkarni.pdf.

[53] S.A. Hansen, N. Sterri,Drill pipe rotation effects on frictional pressure losses in slim annuli, in:Paper SPE-30488-MS presented at the SPE Annual Technical Conference and Exhibition, 1995, pp. 22-25, https://doi.org/10.2118/30488-MS. Dallas,Texas.

[54] T. Hemphill, K. Ravi,Improved prediction of ECD with drill pipe rotation, in:Paper IPTC-15424-MS presented at the International Petroleum Technology Conference, 2011, pp. 15-17, https://doi.org/10.2523/IPTC-15424-MS. Bangkok,Thailand.

[55] A.V. Ganea, A. Lazar, M. Stan, Smart ultra-inhibitive ecological drilling fluid — an engineered proposal to drill in narrow window offshore environments, Int. J. Eng. Res. Technol. 4 (9) (2015) 982-984.

[56] E. Kusrini, B. Suseno, M. Khalil, A. Usman, Study of the use of nanomaterials as drilling mud additives, E3S Web Conf. 67 (2018) 02007, https://doi.org/10.1051/e3sconf/20186702007.

[57] C. Baranthol, J. Alfenore, M.D. Cotterill, G. Poux-Guillaume,Determination of hydrostatic pressure and dynamic ECD by computer models and field measurements on the directional HPHT well 22130C-13, in:Paper SPE/IADC-29430-MS presented at the SPE/IADC Drilling Conference, 1995, https://doi.org/10.2118/29430-MS. Amsterdam,28February-2March.

[58] O.O. Harris, S.O. Osisanya,Evaluation of equivalent circulating density of drilling fluids under high pressure high temperature conditions, in:Paper SPE-97018-MS presented at the SPE Annual Technical Conference and Exhibition, 2005, pp. 9-12, https://doi.org/10.2118/97018-MS. Dallas,Texas,USA.

[59] E. Ataga, J. Ogbonna, B. Oriji, Accurate estimation of equivalent circulating density during high pressure high temperature (HPHT) drilling operations,in: Paper SPE-162972-MS presented at the SPE Nigerian Annual International Conference and Exhibition, 2012, pp. 6-8, https://doi.org/10.2118/162972-MS. Abuja,Nigeria.

[60] W. Panichaporn, R. Prurapark, K. Siemanond, Simulation of drilling pressure profile in directional drilling and user program development, Int. J. Mater. Mech. Manufact. 3 (4) (2015) 255-260, https://doi.org/10.7763/IJMMM.2015.V3.206.

[61] J. Skenderija, A. Koulidis, V. Kelessidis, S. Ahmed, Application of a drilling simulator for real-time drilling hydraulics training and research available, in:Paper SPE-204579-MS presented at the SPE Middle East Oil & Gas Show and Conference, November 2021, https://doi.org/10.2118/204579-MS.

[62] C. Ward, E. Andreassen, Pressure-while-drilling data improve reservoir drilling performance, SPE Drill. Complet. 13 (1) (1998) 19-24, https://doi.org/10.2118/37588-PA.

[63] C.R. Mallary, M. Varco, D. Quinn,Using pressure-while-drilling measurements to solve extended-reach drilling problems on Alaska’s North slope, in:Paper SPE-54592-MS presented at the SPE Western Regional Meeting, 1999, https://doi.org/10.2118/54592-MS. Anchorage,Alaska,May.

[64] A.W. Iyoho, J.R. Kunning, R.T. Oskarsen, Combining SBM modeling and drilling data to elucidate GOM well problems, in:Paper SPE-90047-MS presented at the SPE Annual Technical Conference and Exhibition, 2004, https://doi.org/10.2118/90047-MS. Houston,Texas,September.

[65] H. Zhang, T. Sun, D. Gao, H. Tang, A new method for calculating the equivalent circulating density of drilling fluid in deepwater drilling for oil and gas, Chem. Technol. Fuels Oils 49 (5) (2013) 430-438, https://doi.org/10.1007/s10553-013-0466-0.

[66] A.A. Keller, K. Garner, N. Rao, E. Knipping, J. Thomas, Hydrological models for climate-based assessments at the watershed scale: a critical review of existing hydrologic and water quality models, Sci. Total Environ. 867 (2023) 1-10, https://doi.org/10.1016/j.scitotenv.2022.161209.

[67] R.E. Baker, J. Peña, J. Jayamohan, A. Jerusalem, Mechanistic models versus machine learning, a fight worth fighting for the biological community? Biol. Lett. 14 (5) (2018) 1-4, https://doi.org/10.1098/rsbl.2017.0660.

[68] S. Friedenthal, A. Moore, R. Steiner, in: A Practical Guide to Sysml, third ed., MK/OMG Press, 2015 https://doi.org/10.1016/C2013-0-14457-1.

[69] R. Ahmed, M. Enfis s, H. Miftah-El-Kheir, M. Laget, A. Saasen, The effect of drillstring rotation on equivalent circulation density: modeling and analysis of field measurements,in: Paper SPE-135587-MS presented at the SPE Annual Technical Conference and Exhibition, 2010, https://doi.org/10.2118/135587-MS. Florence,Italy,September.

[70] Q. Yin, J. Yang, B. Zhou, M. Luo, W. Li, Y. Huang, T. Sun, X. Hou, X. Wu, J. Wang,Operational designs and applications of MPD in offshore ultra-HTHP exploration wells, in:Paper IADC/SPE-191060-MS presented at the IADC/SPE Asia Pacific Drilling Technology Conference, 2018, pp. 27-29, https://doi.org/10.2118/191060-MS. Bangkok,Thailand.

[71] B. Li, X. Wang, F. Zhang, X. Wang, Y. Wang, Y. Wang, A mechanistic model for minimizing pressure loss in the wellbore during drilling by considering the effects of cuttings, Front. Earth Sci. 10 (2023) 1-13, https://doi.org/10.3389/feart.2022.1036281.

[72] T. Hemphill, K. Ravi, P.A. Bern, J. Rojas,A simplified method for prediction of ECD increase with drillpipe rotation, in:Paper SPE-115378-MS presented at the SPE Annual Technical Conference and Exhibition, 2008, https://doi.org/10.2118/115378-MS. Denver,Colorado,USA,September.

[73] O. Erge, A.K. Vajargah, M.E. Ozbayoglu, E. van Oort,Improved ECD prediction and management in horizontal and extended reach wells with eccentric drillstrings, in:Paper IADC/SPE-178785-MS presented at the IADC/SPE Drilling Conference and Exhibition, 2016, pp. 1-3, https://doi.org/10.2118/178785-MS. FortWorth,Texas,USA.

[74] E. van Oort, J. Lee, J. Friedheim, B. Toups, New flat-rheology synthetic-based mud for improved deepwater drilling, in:Paper SPE-90987-MS presented at the SPE Annual Technical Conference and Exhibition, 2004, https://doi.org/10.2118/90987-MS. Houston,Texas,September.

[75] Y. Xiang, G. Liu,Impact of cuttings concentration on ECD during drilling, in:Paper AADE-12-FTCE-7 presented at the 2012 AADE Fluids Technical Conference and Exhibition, 2012, pp. 10-11. Houston, Texas.

[76] E.I. Epelle, D.I. Gerogiorgis, Transient and steady state analysis of drill cuttings transport phenomena under turbulent conditions, Chem. Eng. Res. Des. 131 (2018) 520-544, https://doi.org/10.1016/j.cherd.2017.11.023.

[77] R. Wisniowski, K. Skrzypaszek, P. Kiebzak, Drillstring rotary speed influence on equivalent circulating density value, AGH Drill. Oil Gas 35 (1) (2018) 283-294, https://doi.org/10.7494/drill.2018.35.1.283.

[78] X. Sun, K. Wang, T. Yan, S. Shao, J. Jiao, Effect of drillpipe rotation on cuttings transport using computational fluid dynamics (CFD) in complex structure wells, J. Pet. Explor. Prod. Technol. 4 (2014) 255-261, https://doi.org/10.1007/s13202-014-0118-x.

[79] B. Pang, Z. Liu, X. Liu, X. Wang, F. Wang, K. Li, H. Lu, Effect of crooked drill pipe rotation on cuttings transport in horizontal directional drilling using kinetic theory of granular flow-a numerical perspective, Tunn. Undergr. Space Technol. 128 (2022) 1-14, https://doi.org/10.1016/j.tust.2022.104665.

[80] W.L. Yoong,Calculations of Equivalent Circulating Densities (Ecds) in Underbalanced Drilling Using Landmark WELLPLAN, Universiti Teknologi PETRONAS, 2012. Dissertation.

[81] F. Xiao, Z. Guan, R. Pan, P. Li, C. Han, S. Hu, Research on ECD distribution law under managed pressure, J. Phys. Conf. Ser. 1757 (1) (2021) 1-8, https://doi.org/10.1088/1742-6596/1757/1/012189.

[82] G.K.Uyanik, N. Guler, A study on multiple linear regression analysis, Proced. Soc. Behav. Sci. 106 (2013) 234-240, https://doi.org/10.1016/j.sbspro.2013.12.027.

[83] B.G. Tabachnick, S.L. Fidell, in: Using Multivariate Statistics, third ed., Harper Collins College Publishers, New York, 1996.

[84] A.T. Al-Hameedi, S. Dunn-Norman, H.H. Alkinani, R.E. Flori, S.A. Hilgedick, Limiting drilling parameters to control mud losses in the Shuaiba Formation, South Rumaila Field, Iraq, in:Paper AADE-17-NTCE-45 presented at the 2017 AADE National Technical Conference and Exhibition, 2017, pp. 11-12. Houston, Texas.

[85] A.T. Al-Hameedi, H.H. Alkinani, S. Dunn-Norman, R.E. Flori, S.A. Hilgedick, A.S. Amer, Limiting key drilling parameters to avoid or mitigate mud losses in the Hartha Formation, Rumaila Field, Iraq, J. Petrol Environ. Biotechnol. 8 (2017) 1-8, https://doi.org/10.4172/2157-7463.1000345.

[86] A.T. Al-Hameedi, S. Dunn-Norman, H.H. Alkinani, R.E. Flori, S.A. Hilgedick,Limiting drilling parameters to control mud losses in the Dammam Formation, South Rumaila Field, Iraq, in:Paper ARMA-2017- 0930 presented at the 51st U.S. Rock Mechanics/Geomechanics Symposium, 2017. San Francisco, California, USA, June, https://onepetro.org/ARMAUSRMS/proceedings/ARMA17/All-ARMA17/ARMA-2017-0930/124538.

[87] A.T. Al-Hameedi, H.H. Alkinani, S. Dunn-Norman, R.E. Flori, S.A. Hilgedick, M.T. Alsaba, A.S. Amer,Mud losses estimation using partial least squares algorithm, in:Paper SPE-193266-MS presented at the Abu Dhabi International Petroleum Exhibition & Conference, 2018, pp. 12-15, https://doi.org/10.2118/193266-MS. AbuDhabi,UAE.

[88] M.P. Vega, F.B. Vieira, D. Fernandes, M.G. Freitas, E. Russano, A.L. Martins, Smart monitoring and decision making for regulating annulus bottom hole pressure while drilling oil wells, Braz. J. Chem. Eng. 33 (4) (2016) 969-983, https://doi.org/10.1590/0104-6632.20160334s20140163.

[89] E.M. Ozbayoglu, O. Erge, M.A. Ozbayoglu, Predicting the pressure losses while the drillstring is buckled and rotating using artificial intelligence methods, J. Nat. Gas Sci. Eng. 56 (2018) 72-80, https://doi.org/10.1016/j.jngse.2018.05.028.

[90] C. Han, Z. Guan, J. Li, H. Hu, Y. Xu,Equivalent circulating density prediction using a hybrid ARIMA and BP neural network model, in:Paper SPE-197495-MS presented at the Abu Dhabi International Petroleum Exhibition & Conference, 2019, pp. 11-14, https://doi.org/10.2118/197495-MS. AbuDhabi,UAE.

[91] A. Alsaihati, S. Elkatatny, H. Gamal, A. Abdulraheem, A statistical machine learning model to predict equivalent circulation density (ECD) while drilling, based on principal components analysis,in: Paper SPE/IADC-202101-MS presented at the SPE/IADC Middle East Drilling Technology Conference and Exhibition, 2021, pp. 25-27, https://doi.org/10.2118/202101-MS. AbuDhabi,UAE.

[92] A. Abdelaal, S. Elkatatny, H. Gamal, W. Ziadat, Drilling data-based approach for equivalent circulation density prediction while drilling, in: Paper ARMA-2023-0722 presented at the 57th U.S. Rock Mechanics/Geomechanics Symposium, 2023, https://doi.org/10.56952/ARMA-2023-0722. Atlanta,Georgia,USA,June.

[93] S.I. Okonkwo, O.F. Joel, Modelling the effects of temperature and pressure on equivalent circulating density (ECD) during drilling operations using artificial neural networks, J. Eng. Res. Rep. 25 (9) (2023) 70-82, https://doi.org/10.9734/jerr/2023/v25i9982.

[94] G. Ekechukwu, A. Adejumo, Explainable machine-learning-based prediction of equivalent circulating density using surface-based drilling data, Sci. Rep. 14 (2024) 1-9, https://doi.org/10.1038/s41598-024-66702-w.

[95] T.M. Adegoke, J.O. Adeleye, A.M. Morakinyo, Prediction of equivalent circulation density of drilling fluids using machine learning, in:Paper SPE-221595-MS presented at the SPE Nigeria Annual International Conference and Exhibition, 2024, https://doi.org/10.2118/221595-MS. Lagos,Nigeria,August.

[96] X. Gao, H. Fan, Equivalent circulation density prediction using random forest model, Trends Pet. Eng. 4 (2) (2024) 1-8, https://doi.org/10.53902/TPE.2024.04.000541.

[97] N.H. Truong,The equivalent circulating density prediction from drilling parameters while drilling wells, in:Paper ISRM-VIETROCK-2024- 018 presented at the ISRM VietRock-Vietnamese National Congress of Rock Mechanics and Rock Engineering, 2024, 26 October.

[98] M.S. Dabiri, R.H. Hashemi, A. Hemmati-Sarapardeh, R. Zabihi, M.R. Mohammadi, M. Mahin Schaffie, e, M. Ostadhassan, Artificial intelligence approaches to modelling equivalent circulating density for improved drilling mud management, ACS Omega 10 (18) (2025) 19157-19174, https://doi.org/10.1021/acsomega.5c02050.

[99] S. Alatefi, R.A. Azim, A. Alkouh, G. Hamada, Integration of multiple Bayesian optimized machine learning techniques and conventional well logs for accurate prediction of porosity in carbonate reservoirs, Processes 11 (5) (2023) 1339, https://doi.org/10.3390/pr11051339.

[100] O.E. Agwu, K.A. Elraies, A. Alkouh, S. Alatefi, R. Ferhadi, Utilization of machine learning for the estimation of production rates in wells operated by electrical submersible pumps, J. Pet. Explor. Prod. Technol. (2024), https://doi.org/10.1007/s13202-024-01761-3.

[101] O.E. Agwu, K.A. Elraies, A. Alkouh, S. Alatefi, Mathematical modelling of drilling mud plastic viscosity at downhole conditions using multivariate adaptive regression splines, Geoenergy Sci. Eng. 233 (2024) 1-11, https://doi.org/10.1016/j.geoen.2023.212584.

[102] S. Alatefi, O.E. Agwu, R.A. Azim, A. Alkouh, I. Dzulkarnain, Development of multiple explicit data-driven models for accurate prediction of CO₂ minimum miscibility pressure, Chem. Eng. Res. Des. 205 (2024) 672-694, https://doi.org/10.1016/j.cherd.2024.04.033.

[103] E.E. Okoro, O.E. Agwu, D. Olatunji, O.D. Orodu, Artificial Bee Colony (ABC) a potential for optimizing well placement-a review,in: Paper SPE-198729-MS presented at the SPE Nigeria Annual International Conference and Exhibition, 2019, https://doi.org/10.2118/198729-MS. Lagos,Nigeria,August.

[104] J. Park,Hybrid Machine Learning and Physics-based Modelling Approaches for Process Control and Optimization, Brigham Young University, 2022. PhD Thesis, https://scholarsarchive.byu.edu/etd/9759.

[105] O. Erge, E. van Oort, Combining physics-based and data-driven modelling in well construction: hybrid fluid dynamics modelling, J. Nat. Gas Sci. Eng. 97 (2022) 1-14, https://doi.org/10.1016/j.jngse.2021.104348.

[106] Y. Meng, J. Jiang, J. Wu, D. Wang, Transformer-based deep learning models for predicting permeability of porous media, Adv. Water Resour. 179 (2023) 1-12, https://doi.org/10.1016/j.advwatres.2023.104520.

[107] R. Johnson, Data science: back to basics-it’s about being flexible. https://spr.com/data-science-back-basics-flexible/, 2017. (Accessed12 December 2023).