Production optimization under waterflooding with long short-term memory and metaheuristic algorithm

Abstract

In petroleum domain, optimizing hydrocarbon production is essential because it does not only ensure the economic prospects of the petroleum companies, but also fulfills the increasing global demand of energy. However, applying numerical reservoir simulation (NRS) to optimize production can induce high computational footprint. Proxy models are suggested to alleviate this challenge because they are computationally less demanding and able to yield reasonably accurate results. In this paper, we demonstrated how a machine learning technique, namely long short-term memory (LSTM), was applied to develop proxies of a 3D reservoir model. Sampling techniques were employed to create numerous simulation cases which served as the training database to establish the proxies. Upon blind validating the trained proxies, we coupled these proxies with particle swarm optimization to conduct production optimization. Both training and blind validation results illustrated that the proxies had been excellently developed with coefficient of determination, R² of 0.99. We also compared the optimization results produced by NRS and the proxies. The comparison recorded a good level of accuracy that was within 3% error. The proxies were also computationally 3 times faster than NRS. Hence, the proxies have served their practical purposes in this study.

Declaration of interest statement

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

Acknowledgement

This research is a part of BRU21 -NTNU Research and Innovation Program on Digital Automation Solutions for the Oil and Gas Industry (www.ntnu.edu/bru21).

References

[1] M.L. Wiggins, R.A. Startzman, An approach to reservoir management, SPE Repr. Ser. (1998), https://doi.org/10.2118/20747-ms.

[2] L.W. Lake, R. Johns, B. Rossen, G.A. Pope, Fundamentals of Enhanced Oil Recovery, others, 2014.

[3] B. Guyaguler, R.N. Horne, L. Rogers, J.J. Rosenzweig, Optimization of well placement in a gulf of Mexico waterflooding project, SPE Reservoir Eval. Eng. (2002), https://doi.org/10.2118/78266-PA.

[4] A. Mamghaderi, A. Bastami, P. Pourafshary, Optimization of waterflooding performance in a layered reservoir using a combination of capacitanceresistive model and genetic algorithm method, J. Energy Resour. Technol. (2013), https://doi.org/10.1115/1.4007767.

[5] J.L. Mogollón, T.M. Lokhandwala, E. Tillero,New trends in waterflooding project optimization, SPE Lat. Am. Caribb. Pet. Eng. Conf. Proc. (2017), https://doi.org/10.2118/185472-ms.

[6] A.J. Hong, R.B. Bratvold, G. Nævdal, Robust production optimization with capacitance-resistance model as precursor, Comput. Geosci. (2017), https://doi.org/10.1007/s10596-017-9666-8.

[7] P. Ogbeiwi, Y. Aladeitan, D. Udebhulu, An approach to waterflood optimization: case study of the reservoir X, J. Pet. Explor. Prod. Technol. (2018), https://doi.org/10.1007/s13202-017-0368-5.

[8] S.S. Rao, Engineering optimization: theory and practice. https://doi.org/10.1002/9781119454816, 2019.

[9] M.C. Bellout, D. Echeverría Ciaurri, L.J. Durlofsky, B. Foss, J. Kleppe, Joint optimization of oil well placement and controls, Comput. Geosci. (2012), https://doi.org/10.1007/s10596-012-9303-5.

[10] X. Liu, A.C. Reynolds, Gradient-based multi-objective optimization with applications to waterflooding optimization, Comput. Geosci. 20 (2016), https://doi.org/10.1007/s10596-015-9523-6.

[11] M. Al-Aghbari, M. Al-Wadhahi, A.M. Gujarathi, Multi-objective optimization of Brugge field for short-term and long-term waterflood management, Arabian J. Sci. Eng. (2021), https://doi.org/10.1007/s13369-021-05614-7.

[12] S.D. Mohaghegh, Reservoir simulation and modeling based on artificial intelligence and data mining (AI&DM), J. Nat. Gas Sci. Eng. (2011), https://doi.org/10.1016/j.jngse.2011.08.003.

[13] S.D. Mohaghegh, Data-Driven Reservoir Modeling, 2017.

[14] S.D. Mohaghegh, S. Amini, V. Gholami, R. Gaskari, G. Bromhal, Grid-Based Surrogate Reservoir Modeling (SRM) for fast track analysis of numerical reservoir simulation models at the grid block level, Soc. Pet. Eng. West. Reg. Meet. (2012), https://doi.org/10.2118/153844-ms, 2012.

[15] S.D. Mohaghegh,Quantifying uncertainties associated with reservoir simulation studies using surrogate reservoir models, Proc. SPE Annu. Tech. Conf. Exhib. (2006), https://doi.org/10.2523/102492-ms.

[16] S.D. Mohaghegh, H. Hafez, R. Gaskari, M. Haajizadeh, M. Kenawy,Uncertainty analysis of a giant oil field in the middle east using surrogate reservoir model, in: 12th Abu Dhabi Int. Pet. Exhib. Conf. ADIPEC 2006 Meet. Increasing Oil Gas Demand through Innov, 2006, https://doi.org/10.2523/101474-ms.

[17] G. Vida, M.D. Shahab, M. Mohammad, Smart proxy modeling of SACROC CO2-EOR, Fluids (2019), https://doi.org/10.3390/fluids4020085.

[18] A. Shahkarami, S. Mohaghegh, Applications of smart proxies for subsurface modeling, Petrol. Explor. Dev. (2020), https://doi.org/10.1016/S1876-3804(20)60057-X.

[19] A. Shahkarami, S.D. Mohaghegh, V. Gholami, S.A. Haghighat, Artificial intelligence (AI) assisted history matching, in: Soc. Pet. Eng. SPE West. North Am. Rocky Mt. Jt. Meet, 2014, https://doi.org/10.2118/169507-ms.

[20] Q. He, S.D. Mohaghegh, Z. Liu, Reservoir simulation using smart proxy in SACROC unit -case study, in: SPE East. Reg. Meet, 2016, https://doi.org/10.2118/184069-MS.

[21] F. Alenezi, S. Mohaghegh,Developing a smart proxy for the SACROC waterflooding numerical reservoir simulation model, in:SPE West. Reg. Meet. Proc., 2017, https://doi.org/10.2118/185691-ms.

[22] J. Jalali, S.D. Mohaghegh, Reservoir simulation and uncertainty analysis of enhanced CBM production using artificial neural networks, in: SPE East. Reg. Meet, 2009, https://doi.org/10.2118/125959-ms.

[23] A. Kalantari-Dahaghi, S.D. Mohaghegh, A new practical approach in modelling and simulation of shale gas reservoirs: application to New Albany Shale, Int. J. Oil Gas Coal Technol. (2011), https://doi.org/10.1504/IJOGCT.2011.038925.

[24] 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), https://doi.org/10.1007/s13369-018-3173-7.

[25] N.A. Menad, Z. Noureddine, An efficient methodology for multi-objective optimization of water alternating CO₂ EOR process, J. Taiwan Inst. Chem. Eng. 99 (2019) 154-165, https://doi.org/10.1016/j.jtice.2019.03.016.

[26] J. Kim, H. Yang, J. Choe, Robust optimization of the locations and types of multiple wells using CNN based proxy models, J. Petrol. Sci. Eng. 193 (2020), 107424, https://doi.org/10.1016/j.petrol.2020.107424.

[27] J. Kim, K. Lee, J. Choe, Efficient and robust optimization for well patterns using a PSO algorithm with a CNN-based proxy model, J. Petrol. Sci. Eng. 207 (2021), 109088, https://doi.org/10.1016/j.petrol.2021.109088.

[28] L. Deng, Y. Pan, Data-driven proxy model for waterflood performance prediction and optimization using Echo State Network with Teacher Forcing in mature fields, J. Petrol. Sci. Eng. 197 (2021), 107981, https://doi.org/10.1016/j.petrol.2020.107981.

[29] C.S.W. Ng, A. Jahanbani Ghahfarokhi, M. Nait Amar, O. Torsæter, Smart proxy modeling of a fractured reservoir model for production optimization: implementation of metaheuristic algorithm and probabilistic application, Nat. Resour. Res. 30 (2021) 2431-2462, https://doi.org/10.1007/s11053-021-09844-2.

[30] M. Nait Amar, A. Jahanbani Ghahfarokhi, C.S.W. Ng, N. Zeraibi, Optimization of WAG in real geological field using rigorous soft computing techniques and nature-inspired algorithms, J. Petrol. Sci. Eng. (2021), 109038, https://doi.org/10.1016/j.petrol.2021.109038.

[31] C.S.W. Ng, A. Jahanbani Ghahfarokhi, M. Nait Amar, Application of natureinspired algorithms and artificial neural network in waterflooding well control optimization, J. Pet. Explor. Prod. Technol. (2021), https://doi.org/10.1007/s13202-021-01199-x.

[32] S.H. Yousefi, F. Rashidi, M. Sharifi, M. Soroush, A.J. Ghahfarokhi, Interwell connectivity identification in immiscible gas-oil systems using statistical method and modified capacitance-resistance model: a comparative study, J. Petrol. Sci. Eng. 198 (2021), 108175, https://doi.org/10.1016/J.PETROL.2020.108175.

[33] M. Nait Amar, N. Zeraibi, A. Jahanbani Ghahfarokhi, Applying hybrid support vector regression and genetic algorithm to water alternating CO₂ gas EOR, Greenh. Gases Sci. Technol. (2020), https://doi.org/10.1002/ghg.1982.

[34] M. Talebkeikhah, M. Nait Amar, A. Naseri, M. Humand, A. Hemmati-Sarapardeh, B. Dabir, M.E.A. Ben Seghier, Experimental measurement and compositional modeling of crude oil viscosity at reservoir conditions, J. Taiwan Inst. Chem. Eng. 109 (2020) 35-50, https://doi.org/10.1016/j.jtice.2020.03.001.

[35] M. Nait Amar, A. Jahanbani Ghahfarokhi, N. Zeraibi, Predicting thermal conductivity of carbon dioxide using group of data-driven models, J. Taiwan Inst. Chem. Eng. 113 (2020) 165-177, https://doi.org/10.1016/j.jtice.2020.08.001.

[36] H. Mehrjoo, M. Riazi, M. Nait Amar, A. Hemmati-Sarapardeh, Modeling interfacial tension of methane-brine systems at high pressure and high salinity conditions, J. Taiwan Inst. Chem. Eng. 114 (2020) 125-141, https://doi.org/10.1016/j.jtice.2020.09.014.

[37] M. Nait Amar, M.A. Ghriga, A. Hemmati-Sarapardeh, Application of gene expression programming for predicting density of binary and ternary mixtures of ionic liquids and molecular solvents, J. Taiwan Inst. Chem. Eng. 117 (2020) 63-74, https://doi.org/10.1016/j.jtice.2020.11.029.

[38] M.Z. Alom, T.M. Taha, C. Yakopcic, S. Westberg, P. Sidike, M.S. Nasrin, M. Hasan, B.C. Van Essen, A.A.S. Awwal, V.K. Asari, A state-of-the-art survey on deep learning theory and architectures, Electron 8 (2019), https://doi.org/10.3390/electronics8030292.

[39] S. Hochreiter, J. Schmidhuber, Long short-term memory, Neural Comput. 9 (1997) 1735-1780. http://direct.mit.edu/neco/article-pdf/9/8/1735/813796/neco.1997.9.8.1735.pdf.

[40] J. Kennedy, R. Eberhart, Particle swarm optimization, in: IEEE Int. Conf. Neural Networks Conf. Proc, 1995, https://doi.org/10.4018/ijmfmp.2015010104.

[41] Y. Shi, R. Eberhart, Modified particle swarm optimizer, in: Proc. IEEE Conf. Evol. Comput. ICEC, 1998, https://doi.org/10.1109/icec.1998.699146.

[42] K.L. Du, M.N.S. Swamy, Search and Optimization by Metaheuristics:Techniques and Algorithms Inspired by Nature, Springer International Publishing, 2016, https://doi.org/10.1007/978-3-319-41192-7.

[43] A.E. Ezugwu, O.J. Adeleke, A.A. Akinyelu, S. Viriri, A conceptual comparison of several metaheuristic algorithms on continuous optimisation problems, Neural Comput. Appl. 32 (2020), https://doi.org/10.1007/s00521-019-04132-w.

[44] C.S.W. Ng, A. Jahanbani Ghahfarokhi, M. Nait Amar, Well production forecast in Volve field: application of rigorous machine learning techniques and metaheuristic algorithm, J. Petrol. Sci. Eng. 208 (2022), 109468, https://doi.org/10.1016/J.PETROL.2021.109468.

[45] J.D. Jansen, R.M. Fonseca, S. Kahrobaei, M.M. Siraj, G.M. Van Essen, P.M.J. Van den Hof, The egg model -a geological ensemble for reservoir simulation, Geosci. Data J. (2014), https://doi.org/10.1002/gdj3.21.

[46] M.D. McKay, R.J. Beckman, W.J. Conover, A comparison of three methods for selecting values of input variables in the analysis of output from a computer code, Technometrics (1979), https://doi.org/10.2307/1268522.

[47] J.M. Hammersley, D.C. Handscomb, Monte Carlo methods. https://doi.org/10.1007/978-94-009-5819-7, 1964.

[48] I.M. Sobol, On the distribution of points in a cube and the approximate evaluation of integrals, USSR Comput. Math. Math. Phys. (1967), https://doi.org/10.1016/0041-5553(67)90144-9.

[49] D.P. Kingma, J.L. Ba,Adam: a method for stochastic optimization,in:3rd Int. Conf. Learn. Represent. ICLR 2015 -Conf, Track Proc., 2015.