Bottom hole pressure estimation using hybridization neural networks and grey wolves optimization

Abstract

An effective design and optimum production strategies of a well depend on the accurate prediction of its bottomhole pressure (BHP) which may be calculated or determined by several methods. However, it is not practical technically or economically to apply for a well test or to deploy a permanent pressure gauge in the bottom hole to predict the BHP. Consequently, several correlations and mechanistic models based on the known surface measurements have been developed. Unfortunately, all these tools (correlations & mechanistic models) are limited to some conditions and intervals of application. Therefore, establish a global model that ensures a large coverage of conditions with a reduced cost and high accuracy becomes a necessity.

In this study, we propose new models for estimating bottom hole pressure of vertical wells with multiphase flow. First, Artificial Neural Network (ANN) based on back propagation training (BP-ANN) with 12 neurons in its hidden layer is established using trial and error. The next methods correspond to optimized or evolved neural networks (optimize the weights and thresholds of the neural networks) with Grey Wolves Optimization (GWO), and then its accuracy to reach the global optima is compared with 2 other naturally inspired algorithms which are the most used in the optimization field: Genetic Algorithm (GA) and Particle Swarms Optimization (PSO). The models were developed and tested using 100 field data collected from Algerian fields and covering a wide range of variables.

The obtained results demonstrate the superiority of the hybridization ANN-GWO compared with the 2 other hybridizations or with the BP learning alone. Furthermore, the evolved neural networks with these global optimization algorithms are strongly shown to be highly effective to improve the performance of the neural networks to estimate flowing BHP over existing approaches and correlations.

Keywords

Flowing bottom hole pressure (BHP) / BHP correlations & mechanistic models / Artificial neural network / Neural network training / BP (back propagation) / GWO / GA / PSO

References

[1] 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 (1965) 475-484.

[2] H. Duns Jr., N. C.J. Ros, Vertical flow of gas and liquid mixtures in wells, in: 6th World Pet. Congr, 1963.

[3] J. Orkiszewski, Predicting two-phase pressure drops in vertical pipe, J. Petrol. Technol. 19 (1967) 829-838.

[4] D.H. Beggs, J.P. Brill, An experimantal study of two-phase flow in inclined pipes, J. Petrol. Technol. 25 (1973) 607-617.

[5] K. Aziz, G.W. Govier, Pressure drop in wells producing oil and gas, J. Can. Pet. Technol. 11 (1972).

[6] H. Mukherjee, J.P. Brill, Pressure drop correlations for inclined two-phase flow, J. Energy Resour. Technol. 107 (1985) 549, https://doi.org/10.1115/1.3231233.

[7] A.M. Ansari, N.D. Sylvester, O. Shoham, J.P. Brill, A comprehensive mechanistic model for upward two-phase flow in wellbores, in: SPE Annu. Tech. Conf. Exhib, 1990.

[8] R.N. Chokshi, Z. Schmidt, D.R. Doty, Experimental study and the development of a mechanistic model for two-phase flow through vertical tubing, in: SPE West. Reg. Meet, 1996.

[9] 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 (2000) 339-350.

[10] H.E. Gray,Vertical flow correlation in gas wells, User Man. API14B, in: Subsurf. Control. Saf. Valve Sizing Comput. Progr, 1974.

[11] R.B.C. Gharbi, G.A. Mansoori, An introduction to artificial intelligence applications in petroleum exploration and production, J. Petrol. Sci. Eng. 49 (2005) 93-96, https://doi.org/10.1016/j.petrol.2005.09.001.

[12] X. Li, J. Miskimins, B.T. Hoffman, A combined bottom-hole pressure calculation procedure using multiphase correlations and artificial neural network models, in: SPE Annu. Tech. Conf. Exhib, 2014.

[13] Z. Li, N. Hovakimyan, G.-O. Kaasa, Bottom hole pressure estimation and L 1 adaptive control in managed pressure drilling system, Int. J. Adapt. Contr. Signal Process. 31 (2017) 545-561.

[14] R. Ashena, J. Moghadasi, Bottom hole pressure estimation using evolved neural networks by real coded ant colony optimization and genetic algorithm, J. Petrol. Sci. Eng. 77 (2011) 375-385.

[15] N. Ghaffarian, R. Eslamloueyan, B. Vaferi, Model identification for gas condensate reservoirs by using ANN method based on well test data, J. Petrol. Sci. Eng. 123 (2014) 20-29.

[16] B. Vaferi, R. Eslamloueyan, S. Ayatollahi, Automatic recognition of oil reservoir models from well testing data by using multi-layer perceptron networks, J. Petrol. Sci. Eng. 77 (2011) 254-262.

[17] Z. Jeirani, A. Mohebbi, Estimating the initial pressure, permeability and skin factor of oil reservoirs using artificial neural networks, J. Petrol. Sci. Eng. 50 (2006) 11-20.

[18] B. Vaferi, R. Eslamloueyan, Hydrocarbon reservoirs characterization by cointerpretation of pressure and flow rate data of the multi-rate well testing, J. Petrol. Sci. Eng. 135 (2015) 59-72.

[19] B. Vaferi, R. Eslamloueyan, Characterization of gas/gas condensate reservoirs by deconvolution of multirate well test data, J. Porous Media 19 (2016).

[20] B. Vaferi, R. Eslamloueyan, N. Ghaffarian, Hydrocarbon reservoir model detection from pressure transient data using coupled artificial neural networkdwavelet transform approach, Appl. Soft Comput. 47 (2016) 63-75.

[21] E.-S.A. Osman, M.A. Ayoub, M.A. Aggour, An artificial neural network model for predicting bottomhole flowing pressure in vertical multiphase flow, in: SPE Middle East Oil Gas Show Conf, 2005.

[22] G. Takacs, Considerations on the selection of an optimum vertical multiphase pressure drop prediction model for oil wells, in: SPE/ICoTA Coiled Tubing Roundtable, 2001.

[23] A. Witek-Krowiak, K. Chojnacka, D. Podstawczyk, A. Dawiec, K. Pokomeda, Application of response surface methodology and artificial neural network methods in modelling and optimization of biosorption process, Bioresour. Technol. 160 (2014) 150-160.

[24] O. Ronneberger, P. Fischer, T. Brox, U-net: convolutional networks for biomedical image segmentation, in: Int. Conf. Med. Image Comput. Comput. Interv, 2015, pp. 234-241.

[25] F. Amato, A. López, E.M. Pe-na-Méndez, P. Va\vnhara, A. Hampl, J. Havel, Artificial Neural Networks in Medical Diagnosis, 2013.

[26] W. Huang, K.K. Lai, Y. Nakamori, S. Wang, L. Yu, Neural networks in finance and economics forecasting, Int. J. Inf. Technol. Decis. Making 6 (2007) 113-140.

[27] M. Aiken, J. Krosp, M. Vanjani, C. Govindarajulu, A neural network for predicting total industrial production, J. End User Comput. 7 (1995) 19.

[28] Y. Tighilt, F. Bouttout, A. Khellaf, Modeling and design of printed antennas using neural networks, Int. J. RF Microw. Comput. Eng 21 (2011) 228-233.

[29] A.H. Zaabab, Q.-J. Zhang, M. Nakhla, A neural network modeling approach to circuit optimization and statistical design, IEEE Trans. Microw. Theor. Tech. 43 (1995) 1349-1358.

[30] J.E. Rayas-Sánchez, EM-based optimization of microwave circuits using artificial neural networks: the state-of-the-art, IEEE Trans. Microw. Theor. Tech. 52 (2004) 420-435.

[31] B. Vaferi, R. Eslamloueyan, S. Ayatollahi, Application of recurrent networks to classification of oil reservoir models in well-testing analysis, Energy Sources, Part A Recover. Util. Environ. Eff 37 (2015) 174-180.

[32] M. Nait Amar, N. Zeraibi, K. Redouane, Optimization of WAG process using dynamic proxy, genetic algorithm and ant colony optimization, Arabian J. Sci. Eng. (2018) 1-14, https://doi.org/10.1007/s13369-018-3173-7.

[33] B. Malakooti, Y. Zhou, Approximating polynomial functions by feedforward artificial neural networks: capacity analysis and design, Appl. Math. Comput. 90 (1998) 27-51.

[34] Y.-W. Huang, Neural Networks for Chemical Engineers Edited by AB Bulsari (Lappeenranta University of Technology, Finland), Elsevier, Amsterdam, 1996, 1995. ix+ 680 pp. $285.25. ISBN 0-444-820970-3.

[35] K. Hornik, M. Stinchcombe, H. White, Multilayer feedforward networks are universal approximators, Neural Network. 2 (1989) 359-366, https://doi.org/10.1016/0893-6080(89)90020-8.

[36] J.-R. Zhang, J. Zhang, T.-M. Lok, M.R. Lyu, A hybrid particle swarm optimizationeback-propagation algorithm for feedforward neural network training, Appl. Math. Comput. 185 (2007) 1026-1037.

[37] S. Mirjalili, S.Z. Mohd Hashim, H. Moradian Sardroudi, Training feedforward neural networks using hybrid particle swarm optimization and gravitational search algorithm, Appl. Math. Comput. 218 (2012) 11125-11137.

[38] S.N. Sivanandam, S.N. Deepa, Introduction to Genetic Algorithms, Springer, 2007.

[39] J. Kennedy, R. Eberhart, PSO optimization, in: Proc. IEEE Int. Conf. Neural Networks, 1995, pp. 1941-1948.

[40] Y. Shi, R.C. Eberhart, Empirical study of particle swarm optimization, in: Evol. Comput, 1999, pp. 1945-1950. CEC 99. Proc. 1999 Congr., 1999.

[41] Y. Shi, R. Eberhart, A modified particle swarm optimizer, in: Evol. Comput. Proceedings, 1998. IEEE World Congr. Comput. Intell. 1998 IEEE Int. Conf, 1998, pp. 69-73.

[42] M. Clerc,The swarm and the queen: towards a deterministic and adaptive particle swarm optimization,in:Evol. Comput. 1999. CEC 99. Proc. 1999 Congr, 1999, pp. 1951-1957.

[43] S. Mirjalili, S.M. Mirjalili, A. Lewis, Grey wolf optimizer, Adv. Eng. Software 69 (2014) 46-61.

[44] N. Samani, M. Gohari-Moghadam, A.A. Safavi, A simple neural network model for the determination of aquifer parameters, J. Hydrol 340 (2007) 1-11, https://doi.org/10.1016/j.jhydrol.2007.03.017.

[45] B. Vaferi, F. Samimi, E. Pakgohar, D. Mowla, Artificial neural network approach for prediction of thermal behavior of nanofluids flowing through circular tubes, Powder Technol. 267 (2014) 1-10.

[46] G. Cybenko, Approximation by superpositions of a sigmoidal function, Math. Control. Signals Syst 2 (1989) 303-314.

[47] X.-Q. Bian, B. Han, Z.-M. Du, J.-N. Jaubert, M.-J. Li, Integrating support vector regression with genetic algorithm for CO2-oil minimum miscibility pressure (MMP) in pure and impure CO₂ streams, Fuel 182 (2016) 550-557.

[48] P.J. Rousseeuw, A.M. Leroy, Robust Regression and Outlier Detection, John wiley & sons, 2005.

[49] C.R. Goodall, 13 Computation using the QR decomposition, Handb. Stat. 9 (1993) 467-508, https://doi.org/10.1016/S0169-7161(05)80137-3.

[50] P. Gramatica, Principles of QSAR models validation: internal and external, Mol. Inform 26 (2007) 694-701.

[51] MATLAB -MathWorks, 2016.