An adaptive neuro-fuzzy inference system white-box model for real-time multiphase flowing bottom-hole pressure prediction in wellbores

Abstract

The majority of published empirical correlations and mechanistic models are unable to provide accurate flowing bottom-hole pressure (FBHP) predictions when real-time field well data are used. This is because the empirical correlations and the empirical closure correlations for the mechanistic models were developed with experimental datasets. In addition, most machine learning (ML) FBHP prediction models were constructed with real-time well data points and published without any visible mathematical equation. This makes it difficult for other readers to use these ML models since the datasets used in their development are not open-source. This study presents a white-box adaptive neuro-fuzzy inference system (ANFIS) model for real-time prediction of multiphase FBHP in wellbores. 1001 real well data points and 1001 normalized well data points were used in constructing twenty-eight different Takagi-Sugeno fuzzy inference systems (FIS) structures. The dataset was divided into two sets; 80% for training and 20% for testing. Statistical performance analysis showed that a FIS with a 0.3 range of influence and trained with a normalized dataset achieved the best FBHP prediction performance. The optimal ANFIS black-box model was then translated into the ANFIS white-box model with the Gaussian input and the linear output membership functions and the extracted tuned premise and consequence parameter sets. Trend analysis revealed that the novel ANFIS model correctly simulates the anticipated effect of input parameters on FBHP. In addition, graphical and statistical error analyses revealed that the novel ANFIS model performed better than published mechanistic models, empirical correlations, and machine learning models. New training datasets covering wider input parameter ranges should be added to the original training dataset to improve the model's range of applicability and accuracy.

Keywords

Machine learning models / Empirical correlations / Mechanistic models / Multiphase flowing bottom-hole pressure / Adaptive neuro-fuzzy inference system / White-box model

References

[1] E.A. Kanin, A.A. Osiptsov, A.L. Vainshtein, E.V. Burnaev, A predictive model for steady-state multiphase pipe flow: machine learning on lab data, J. Petrol. Sci. Eng. 180 (May) (2019) 727-746, https://doi.org/10.1016/j.petrol.2019.05.055.

[2] A.M. Ansari, N.D. Sylvester, U. Akron, C. Sarica, O. Shoham, A comprehensive mechanistic model for upward two-phase flow in wellbores, SPE Prod. Facil. 9 (2) (1994) 143-152, https://doi.org/10.2118/20630-PA.

[3] A.S. Kaya, C. Sarica, J.P. Brill, Comprehensive Mechanistic Modeling of Twophase Flow in Deviated Wells, SPE Annual Technical Conference and Exhibition, Houston, Texas, 1999, pp. 3-6, https://doi.org/10.2118/56522-MS.

[4] A.S. Kaya, C. Sarica, J.P. Brill, Mechanistic modeling of two-phase flow in deviated wells, SPE Prod. Facil. 16 (3) (2001) 156-165, https://doi.org/10.2118/72998-PA.

[5] E. Eltahan, R. Ganjdanesh, W. Yu, K. Sepehrnoori, R. Williams, J. Nohavitsa,Machine learning approach to improve calculated bottom-hole pressure, in:SPE/AAPG/SEG Unconventional Resources Technology Conference, 1-21, 2021, https://doi.org/10.15530/urtec-2021-5645.

[6] A.E. Dukler, M.G. Hubbard, A model for gaseliquid slug flow in horizontal and near horizontal tubes, Ind. Eng. Chem. Fundam. 14 (4) (1975) 337-347, https://doi.org/10.1021/i160056a011.

[7] A. Olufemi, F.A.S. Adesina, F. Olugbenga, Predictive tool for bottom-hole pressure in multiphase flowing wells, Petrol. Coal 50 (3) (2008) 67-73.

[8] A. Al-Shammari,Accurate prediction of pressure drop in two-phase vertical flow systems using artificial intelligence, in:SPE/DGS Saudi Arabia Section Technical Symposium and Exhibition, 2011, https://doi.org/10.2118/149035-ms.

[9] M. Awadalla, H. Yousef, A. Al-Shidani, A. Al-Hinai, Artificial intelligent techniques for flow bottom hole pressure prediction, Int. J. Comput. Inf. Technol. Eng. 15 (12) (2016) 7263-7283.

[10] J.V. Vogel, Inflow performance relationships for solution-gas drive wells, J. Petrol. Technol. 243 (1968) 83-92.

[11] U.I. Duru, O.I. Nwanwe, C.C. Nwanwe, A.O. Arinkola, A.O. Chikwe, Evaluating lift systems for oil wells using integrated production modeling : a case study of A Niger delta, J. Petrol. Eng. Technol. 11 (3) (2021) 32-48, https://doi.org/10.37591/jopet.v11i3.6057.

[12] C.C. Nwanwe, U.I. Duru, O.I. Nwanwe, A.O. Chikwe, K.T. Ojiabo, C.T. Umeojiakor, Optimum tubing size prediction model for vertical multiphase flow during flow production period of oil wells, J. Pet. Explor. Prod. Technol. 10 (7) (2020) 2989-3005, https://doi.org/10.1007/s13202-020-00964-8.

[13] F.H. Poettmann, P.G. Carpenter, The multiphase flow of gas, oil, and water through vertical flow strings with application to the design of gas-lift installations, API Drill. Prod. Pract. (1952) 257-317.

[14] B.C. Craft, M.F. Hawkins, Applied Petroleum Reservoir Engineering, second ed., Prentice Hall PTR, 1991.

[15] J.S. Kim, L.W. Lake, T.F. Edgar,Integrated capacitance-resistance model for characterizing waterflooded reservoirs, IFAC Proc. Vol. 1 (PART 1) (2012) 19-24, https://doi.org/10.3182/20120531-2-NO-4020.00009.

[16] S.H. Yousefi, F. Rashidi, M. Sharifi, M. Soroush, Prediction of immiscible gas flooding performance: a modified capacitanceeresistance model and sensitivity analysis, Petrol. Sci. 16 (5) (2019) 1086-1104, https://doi.org/10.1007/s12182-019-0342-6.

[17] A.A. Yousef, P. Gentil, J.L. Jensen, L.W. Lake, A capacitance model to infer interwell connectivity from production-and injection-rate fluctuations, SPE Reservoir Eval. Eng. 9 (6) (2006) 630-646, https://doi.org/10.2118/95322-pa.

[18] M. Sayarpour, E. Zuluaga, C.S. Kabir, L.W. Lake, The use of capacitanceresistance models for rapid estimation of waterflood performance and optimization, J. Petrol. Sci. Eng. 69 (3-4) (2009) 227-238, https://doi.org/10.1016/j.petrol.2009.09.006.

[19] D. Weber, T.F. Edgar, L.W. Lake, L. Lasdon, S. Kawas, M. Sayarpour,Improvements in capacitance-resistive modeling and optimization of large scale reservoirs, in:SPE Western Regional Meeting 2009 -Proceedings, 2009, pp. 369-385, https://doi.org/10.2118/121299-ms.

[20] A.P. Nguyen, J.S. Kim, L.W. Lake, T.F. Edgar, B. Haynes,Integrated capacitance resistive model for reservoir characterization in primary and secondary recovery, in:Proceedings -SPE Annual Technical Conference and Exhibition, 5(2006), 2011, pp. 4162-4181, https://doi.org/10.2118/147344-ms.

[21] D. Wang, Y. Li, J. Zhang, C. Wei, Y. Jiao, Q. Wang, Improved CRM model for inter-well connectivity estimation and production optimization: case study for karst reservoirs, Energies 12 (5) (2019), https://doi.org/10.3390/en12050816.

[22] R. W. d Holanda, E. Gildin, J.L. Jensen, L.W. Lake, C.S. Kabir, A state-of-the-art literature review on capacitance resistance models for reservoir characterization and performance forecasting, Energies 11 (12) (2018), https://doi.org/10.3390/en11123368.

[23] X. Wang, J. Wang, Z. Xia, Improved capacitance model considering bottom-hole flowing pressure and interference between oil wells, Energy Explor. Exploit. 38 (6) (2020) 2277-2295, https://doi.org/10.1177/0144598720918401.

[24] J.P. Brill, H. Mukherjee, Multiphase Flow in Wells, Society of Petroleum Engineers, Richardson, TX, 1999.

[25] P.B. Baxendell, R. Thomas, The calculation of pressure gradients in high-rate flowing wells, J. Petrol. Technol. 13 (10) (1961) 1023-1028, https://doi.org/10.2118/2-pa.

[26] G.H. Fancher, K.E. Brown, Prediction of pressure gradients for multiphase flow in tubing, Soc. Petrol. Eng. J. 3 (1) (1963) 59-69, https://doi.org/10.2118/440-pa.

[27] H. Asheim, Mona, an accurate two-phase well flow model based on phase slippage, SPE Prod. Eng. 1 (3) (1986) 221-230, https://doi.org/10.2118/12989-PA.

[28] A.R. Hagedorn, K.E. Brown, Experimental study of pressure gradients occurring during continuous two-phase flow in small-diameter vertical conduits, J. Petrol. Technol. 17 (4) (1965) 475-484, https://doi.org/10.2118/940-pa.

[29] H.D. Beggs, J.P. Brill, A Study of two-phase flow in inclined pipes, J. Petrol. Technol. 25 (5) (1973) 607-617, https://doi.org/10.2118/4007-PA.

[30] H. Duns Jr., N. C.J. Ros,Vertical flow of gas and liquid mixtures in wells, in:Proceedings of the 6th World Petroleum Congress, 19e26 June, Frankfurt Am Main, Germany, 1963, pp. 451-465.

[31] J. Orkiszewski, Predicting two-phase pressure drops in vertical pipe, J. Petrol. Technol. 19 (6) (1967) 829-838, https://doi.org/10.2118/1546-pa.

[32] A.U. Yahaya, A. Al Gahtani,A comparative study between empirical correlations & mechanistic models of vertical multiphase flow, in:SPE/DGS Saudi Arabia Section Technical Symposium and Exhibition, 2010, https://doi.org/10.2118/136931-ms.

[33] L.E. Gomez, O. Shoham, Z. Schmidt, R.N. Chokshi, T. Northug, Unified mechanistic model for steady-state two-phase flow: horizontal to vertical upward flow, SPE J. 5 (3) (2000) 339-350, https://doi.org/10.2118/65705-PA.

[34] L.B. Ouyang, K. Aziz, A mechanistic model for gas-liquid flow in horizontal wells with radial influx or outflux, Petrol. Sci. Technol. 20 (1-2) (2002) 191-222, https://doi.org/10.1081/LFT-120002095.

[35] J.J. Xiao, O. Shoham, J.P. Brill, Comprehensive mechanistic model for twophase flow in pipelines, in: 65th SPE Annual Technical Conference and Exhibition, New Orleans, LA, September 23-26, 1990, 1990, pp. 167-180, https://doi.org/10.2118/20631-MS.

[36] A.R. Hasan, C.S. Kabir, A study of multiphase flow behavior in vertical wells, SPE Prod. Eng. 3 (2) (1988a) 263-272, https://doi.org/10.2118/15138-pa.

[37] A.R. Hasan, C.S. Kabir, Predicting multiphase flow behavior in a deviated well, SPE Prod. Eng. 3 (4) (1988b) 474-482, https://doi.org/10.2118/15449-PA.

[38] P.M. Ozon, G. Ferschneider, A. Chwetzoff, A new multiphase flow model predicts pressure and temperature profiles in wells, SPE Offshore Eur. 87 (1987) 8-11, https://doi.org/10.2118/16535-ms. Aberdeen.

[39] N. Petalas, K. Aziz, Mechanistic model for multiphase flow in pipes, J. Can. Petrol. Technol. 39 (6) (2000) 43-55, https://doi.org/10.2118/00-06-04.

[40] H.Q. Zhang, C. Sarica, Unified modeling of gas/Oil/Water-Pipe flow-basic approaches and preliminary validation, SPE Proj. Facil. Constr. 1 (2) (2006) 1-7, https://doi.org/10.2118/95749-PA.

[41] H.Q. Zhang, Q. Wang, C. Sarica, J.P. Brill, Unified model for gas-liquid pipe flow via slug dynamics -Part 1: model development, J. Energy Resour. Technol. 125 (58) (2003) 266-273, https://doi.org/10.1115/1.1615246.

[42] I. Jahanandish, B. Salimifard, H. Jalalifar, Predicting bottomhole pressure in vertical multiphase flowing wells using artificial neural networks, J. Petrol. Sci. Eng. 75 (3-4) (2011) 336-342, https://doi.org/10.1016/j.petrol.2010.11.019.

[43] G. Takacs,Considerations on the selection of an optimum vertical multiphase pressure drop prediction model for oil wells, in:Proceedings -SPE Production Operations Symposium, 2001, pp. 663-672, https://doi.org/10.2118/68361-ms.

[44] C.C. Nwanwe, U.I. Duru, Comparison and performance analysis of models for predicting multiphase flow behaviours in wellbores, Int. J. Petrol. Geosci. Eng. 2022 (2022) 1-20.

[45] E.A. Osman, M.A. Ayoub, M.A. Aggour,Artificial Neural Network Model for Predicting Bottomhole Flowing Pressure in Vertical Multiphase Flow, in:SPE Middle East Oil and Gas Show and Conference, 2005, pp. 1-11, https://doi.org/10.2118/93632-ms.

[46] X. Li, J.L. Miskimins, B.T. Hoffman,A combined bottom-hole pressure calculation procedure using multiphase correlations and artificial neural network models, in:SPE Annual Technical Conference and Exhibition, 1-12, 2014, https://doi.org/10.2118/170683-ms.

[47] C.C. Nwanwe, U.I. Duru, C. Anyadiegwu, A.I.B. Ekejuba, An artificial neural network visible mathematical model for real-time prediction of multiphase flowing bottom-hole pressure in wellbores, Petrol. Res. xxxx (2022), https://doi.org/10.1016/j.ptlrs.2022.10.004.

[48] N.A. Sami, D.S. Ibrahim, Forecasting multiphase flowing bottom-hole pressure of vertical oil wells using three machine learning techniques, Petrol. Res. xxxx (2021), https://doi.org/10.1016/j.ptlrs.2021.05.004.

[49] D. Karaboga, E. Kaya, Adaptive network based fuzzy inference system (ANFIS) training approaches: a comprehensive survey, Artificial Intelligence Review (2018), https://doi.org/10.1007/s10462-017-9610-2.

[50] F. Agin, R. Khosravanian, M. Karimifard, A. Jahanshahi, Application of Adaptive Neuro-Fuzzy Inference System and Data Mining Approach to Predict Lost Circulation Using DOE Technique (Case Study: Maroon Oilfield), Petroleum 6 (4) (2020) 423-437, https://doi.org/10.1016/j.petlm.2018.07.005.

[51] P. Chen, M.M. Rahman, H.K. Sarma, A. Dhabi, Interaction between hydraulic fracture and natural fracture -a new prediction model by adaptive neurofuzzy inference system (ANFIS),in: Abu Dhabi International Petroleum Exhibition and Conference, 2014, https://doi.org/10.2118/171927-ms.

[52] M.A. Ahmadi, Z. Chen, Comparison of machine learning methods for estimating permeability and porosity of oil reservoirs via petro-physical logs, Petroleum 5 (3) (2019) 271-284, https://doi.org/10.1016/j.petlm.2018.06.002.

[53] M. Babanezhad, I. Behroyan, A.T. Nakhjiri, A. Marjani, S. Shirazian, Performance and application analysis of ANFIS artificial intelligence for pressure prediction of nanofluid convective flow in a heated pipe, Sci. Rep. (2021) 1-18, https://doi.org/10.1038/s41598-020-79628-w.

[54] H. Yavari, R. Khosravanian, D.A. Wood, B.S. Aadnoy, Application of mathematical and machine learning models to predict differential pressure of autonomous downhole inflow control devices, Adv. Geo-Energy Res. 5 (4) (2021) 386-406, https://doi.org/10.46690/ager.2021.04.05.

[55] F.S. Alakbari, M.E. Mohyaldinn, M.A. Ayoub, A.S. Muhsan, I.A. Hussein, A reservoir bubble point pressure prediction model using the Adaptive Neuro-Fuzzy Inference System (ANFIS) technique with trend analysis, PLoS One 17 (8 August) (2022) 1-19, https://doi.org/10.1371/journal.pone.0272790.

[56] A. Al-Shammari, Prediction of Pressure Drop for Two-phase Flow in Vertical Pipes Using Artificial Intelligence, M.S. Thesis. King Fahd University of Petroleum and Minerals, 2011b.

[57] R. Moazenzadeh, B. Mohammadi, M.J.S. Safari, K. wing Chau, Soil moisture estimation using novel bio-inspired soft computing approaches, Eng. Appl. Comput. Fluid Mech. 16 (1) (2022) 826-840, https://doi.org/10.1080/19942060.2022.2037467.

[58] S. Mehdizadeh, B. Mohammadi, F. Ahmadi, Establishing coupled models for estimating daily dew point temperature using nature-inspired optimization algorithms, Hydrology 9 (1) (2022), https://doi.org/10.3390/hydrology9010009.

[59] S. Mehdizadeh, B. Mohammadi, Q.B. Pham, Z. Duan, Development of boosted machine learning models for estimating daily reference evapotranspiration and comparison with empirical approaches, Water (Switzerland) 13 (24) (2021), https://doi.org/10.3390/w13243489.

[60] F. Hadadi, R. Moazenzadeh, B. Mohammadi, Estimation of actual evapotranspiration-A novel hybrid method based on remote sensing and artificial intelligence. pdf, J. Hydrol. 609 (2022), 127774, https://doi.org/10.1016/j.jhydrol.2022.127774.

[61] S. Emamgholizadeh, A. Bazoobandi, B. Mohammadi, H. Ghorbani, Prediction of soil cation exchange capacity using enhanced machine learning approaches in the southern region of the caspian sea, Ain Shams Eng. J. xxxx (2022), 101876, https://doi.org/10.1016/j.asej.2022.101876.

[62] Z. Tariq, M. Mahmoud, A. Abdulraheem, Real-time prognosis of flowing bottom-hole pressure in a vertical well for a multiphase flow using computational intelligence techniques, J. Pet. Explor. Prod. Technol. 10 (4) (2020) 1411-1428, https://doi.org/10.1007/s13202-019-0728-4.

[63] M.A. Ayoub, Development and Testing of an Artificial Neural Network Model for Predicting Bottomhole Pressure in Vertical Multiphase Flow. M.S. Thesis, King Fahd University of Petroleum and Minerals, 2004.

[64] M.A. Ahmadi, Z. Chen, Machine learning models to predict bottom hole pressure in multi-phase flow in vertical oil production wells, Can. J. Chem. Eng. (2019) 1-13, https://doi.org/10.1002/cjce.23526.

[65] O. Akinsete, B.A. Adesiji,Bottom-hole pressure estimation from wellhead data using artificial neural network, in:SPE Nigeria Annual International Conference and Exhibition, 2019, https://doi.org/10.2118/198762-ms.

[66] M.A. El-Kadi, M.A. Husien, S.M. El-Behery, H. Farouk, Prediction of two-phase pressure drop using artificial neural network, Eng. Res. J 42 (2) (2019) 99-114.

[67] E.A. Kanin, A.L. Vainshtein, A.A. Osiptsov, E.V. Burnaev,The method of calculation the pressure gradient in multiphase flow in the pipe segment based on the machine learning algorithms, IOP Conf. Ser. Earth Environ. Sci. 193 (2018), https://doi.org/10.1088/1755-1315/193/1/012028.

[68] Y. Seong, C. Park, J. Choi, I. Jang, Surrogate model with a deep neural network to evaluate gas e liquid flow in a horizontal pipe, Energies 13 (4) (2020) 1-12, https://doi.org/10.3390/en13040968.

[69] J.R. Jang, Anfis : adaptive-network-based fuzzy inference system, in: IEEE Transactions on Systems, Man, and Cybernetics, 1993, https://doi.org/10.1109/21.256541, 23(3.

[70] N. Talpur, M.N.M. Salleh, K.Hussain, Aninvestigationofmembership functions on performance ofANFIS for solving classification problems, IOP Conf. Ser.Mater. Sci. Eng. 226 (1) (2017), https://doi.org/10.1088/1757-899X/226/1/012103.

[71] S. Aminifar, G. Yosefi,Application of adaptive neuro fuzzy inference system (ANFIS) in implementing of new CMOS fuzzy logic controller (FLC) chip, AIP Conf. Proc. 936 (2007) 49-53, https://doi.org/10.1063/1.2790190.

[72] Z. Liao, F. Zhang, Identification of nonlinear system based on ANFIS with Hybrid fuzzy clustering, Inf. Technol. J. 12 (24) (2013) 8349-8353, https://doi.org/10.3923/itj.2013.8349.8353.

[73] K. Premkumar, B.V. Manikandan, Fuzzy PID supervised online ANFIS based speed controller for brushless dc motor, Neurocomputing 157 (2015) 76-90, https://doi.org/10.1016/j.neucom.2015.01.032.

[74] H. Monirvaghefi, M. Rafiee Sandgani, M. Aliyari Shoorehdeli, Interval type-2 adaptive network-based fuzzy inference system (ANFIS) with type-2 nonsingleton Fuzzification,in: 13th Iranian Conference on Fuzzy Systems, IFSC 2013, 2013, https://doi.org/10.1109/IFSC.2013.6675612.

[75] P. Hájek, V. Olej, Intuitionistic fuzzy neural network: the case of credit scoring using text information, Commun. Comput. Inf. Sci 517 (2015) 337-346, https://doi.org/10.1007/978-3-319-23983-5_31.

[76] A. Dehghanian Serej, H. Mojallali, Speed control of elliptec motor using adaptive neural-fuzzy controller with on-line learning simulated under MATLAB/SIMULINK, in: IntelliSys 2015 -Proceedings of 2015 SAI Intelligent Systems Conference, 2015, pp. 543-553, https://doi.org/10.1109/IntelliSys.2015.7361193.

[77] M. Turki, S. Bouzaida, A. Sakly, F. M'Sahli,Adaptive control of nonlinear system using neuro-fuzzy learning by PSO algorithm, in:Proceedings of the Mediterranean Electrotechnical Conference -MELECON, 2012, pp. 519-523, https://doi.org/10.1109/MELCON.2012.6196486.

[78] J.J. Cárdenas, A. García, J.L. Romeral, K. Kampouropoulos, Evolutive ANFIS training for energy load profile forecast for an IEMS in an automated factory, in: IEEE International Conference on Emerging Technologies and Factory Automation, ETFA, 1-8, 2011, https://doi.org/10.1109/ETFA.2011.6059079.

[79] D. Karaboga, E. Kaya, Training ANFIS using artificial bee colony algorithm, in: 2013 IEEE International Symposium on Innovations in Intelligent Systems and Applications, IEEE INISTA 2013, 1-5, 2013, https://doi.org/10.1109/INISTA.2013.6577625.

[80] H.N. Nhu, S. Nitsuwat, M. Sodanil,Prediction of stock price using an adaptive Neuro-fuzzy inference system trained by firefly algorithm, in:2013 International Computer Science and Engineering Conference, ICSEC 2013, 2013, pp. 302-307, https://doi.org/10.1109/ICSEC.2013.6694798.

[81] K. Hussain, M.N.M. Salleh,Optimization of fuzzy neural network using APSO for predicting strength of Malaysian SMEs, in:2015 10th Asian Control Conference: Emerging Control Techniques for a Sustainable World, ASCC 2015, 2015, https://doi.org/10.1109/ASCC.2015.7244638.

[82] O.F. Lutfy, S.B. Mohd Noor, M.H. Marhaban, A simplified adaptive neuro-fuzzy inference system (ANFIS) controller trained by genetic algorithm to control nonlinear multi-input multi-output systems, Sci. Res. Essays 6 (31) (2011) 6475-6486, https://doi.org/10.5897/sre11.1059.

[83] D. Karaboga, E. Kaya, An adaptive and hybrid artificial bee colony algorithm (aABC) for ANFIS training, Appl. Soft Comput. J. 49 (2016) 423-436, https://doi.org/10.1016/j.asoc.2016.07.039.

[84] J. Brownlee, Data preparation for machine learning-data cleaning, feature selection and data transforms in Python, Machine Learning Mastery, 2020.

[85] B. Illowsky, S. Dean, Introductory. Stat., Issue 9 53, OpenStax, 2018.

[86] O. Shoham, Mechanistic Modeling of Gas Liquid Two Phase Flow in Pipes, SPE Textbook Series, Richardson, TX, 2006.

[87] L. Márquez-Torres, J. Ochoa-Pineda, P. Pico, J.P. Valdés, D. Becerra, A. Pinilla, E. Pereyra, N. Ratkovich, Comparison of 63 different void fraction correlations for different flow patterns, pipe inclinations, and liquid viscosities, SN Appl. Sci. 2 (10) (2020) 1-24, https://doi.org/10.1007/s42452-020-03464-w.