Efficient Optimization and Robust Value Quantification of Enhanced Oil Recovery Strategies
Keywords:Enhanced Oil Recovery, EOR
With an increasing demand for hydrocarbon reservoir produces such as oil, etc., and difficulties in finding green oil fields, the use of Enhanced Oil Recovery (EOR) methods such as polymer, Smart water, and solvent flooding for further develop- ment of existing fields can not be overemphasized. For reservoir profitability and reduced environmental impact, it is crucial to consider appropriate well control settings of EOR methods for given reservoir characterization. Moreover, finding appropriate well settings requires solving a constrained optimization problem with suitable numerical solution methods. Conventionally, the solution method requires many iterations involving several computationally demanding function evaluations before convergence to the appropriate near optimum. The major subject of this thesis is to develop an efficient and accurate solution method for constrained op- timization problems associated with EOR methods for their value quantifications and ranking in the face of reservoir uncertainties.
The first contribution of the thesis develops a solution method based on the inexact line search method (with Ensemble Based Optimization (EnOpt) for approximate gradient computation) for robust constrained optimization problems associated with polymer, Smart water, and solvent flooding. Here, the objective function is the expectation of the Net Present Value (NPV) function over given geological realizations. For a given set of well settings, the NPV function is defined based on the EOR simulation model, which follows from an appropriate extension of the black-oil model. The developed solution method is used to find the economic benefits and also the ranking of EOR methods for different oil reservoirs developed to mimic North Sea reservoirs.
Performing the entire optimization routine in a transformed domain along with truncations has been a common practice for handling simple linear constraints in reservoir optimization. Aside from the fact that this method has a negative impact on the quality of gradient computation, it is complicated to use for non-linear constraints. The second contribution of this thesis proposes a technique based on the exterior penalty method for handling general linear and non-linear constraints in reservoir optimization problems to improve gradient computation quality by the EnOpt method for efficient and improved optimization algorithm.
Because of the computationally expensive NPV function due to the costly reservoir simulation of EOR methods, the solution method for the underlying EOR optimization problem becomes inefficient, especially for large reservoir problems. To speedup the overall computation of the solution method, this thesis introduces a novel full order model (FOM)-based certified adaptive machine learning optimiza- tion procedures to locally approximate the expensive NPV function. A supervised feedforward deep neural network (DNN) algorithm is employed to locally create surrogate model. In the FOM-based optimization algorithm of this study, several FOM NPV function evaluations are required by the EnOpt method to approximate the gradient function at each (outer) iteration until convergence. To limit the number FOM-based evaluations, we consider building surrogate models locally to replace the FOM based NPV function at each outer iteration and proceed with an inner optimization routine until convergence. We adapt the surrogate model using some FOM-based criterion where necessary until convergence. The demonstration of methodology for polymer optimization problem on a benchmark model results in an improved optimum and found to be more efficient compared to using the full order model optimization procedures.
Ahmadi, M. A. (2015). Developing a robust surrogate model of chemical flooding based on the artificial neural network for enhanced oil recovery implications. Mathematical Problems in Engineering 2015.
Alfazazi, U., W. AlAmeri, and M. R. Hashmet (2019). Experimental investigation of polymer flooding with low-salinity preconditioning of high temperature-high- salinity carbonate reservoir. Journal of Petroleum Exploration and Production Technology 9(2), 1517-1530.
Alizadeh Nomeli, M. and A. Riaz (2013). Reactive transport modeling of CO2 inside a fractured rock: Implications of mass transfer and storage capacity. In APS Division of Fluid Dynamics Meeting Abstracts, pp. M26-004.
Amini, S., S. Mohaghegh, R. Gaskari, and G. Bromhal (2012). Uncertainty analysis of a CO2 sequestration project using surrogate reservoir modeling technique. In SPE Western Regional Meeting. OnePetro.
Arouri, Y. and M. Sayyafzadeh (2020). An accelerated gradient algorithm for well control optimization. Journal of Petroleum Science and Engineering 190, 106872.
Astrid, P., G. Papaioannou, J. C. Vink, and J. Jansen (2011). Pressure precondi- tioning using proper orthogonal decomposition. In SPE Reservoir Simulation Symposium. OnePetro.
Baker, R. (1998). A primer of offshore operations. University of Texas at Austin Petroleum.
Bao, K., K.-A. Lie, O. Møyner, and M. Liu (2017). Fully implicit simulation of polymer flooding with mrst. Computational Geosciences 21(5), 1219-1244.
Baxendale, D., A. F. Rasmussen, A. B. Rustad, T. Skille, and T. H. Sandve (2021). Opm flow documentation manual manual. Open Porous Media Initiative.
Brouwer, D. R. and J. Jansen (2002). Dynamic optimization of water flooding with smart wells using optimal control theory. In European Petroleum Conference. Society of Petroleum Engineers.
Cardoso, M. A. and L. J. Durlofsky (2010). Linearized reduced-order models for subsurface flow simulation. Journal of Computational Physics 229(3), 681-700.
Cardoso, M. A., L. J. Durlofsky, and P. Sarma (2009). Development and appli- cation of reduced-order modeling procedures for subsurface flow simulation. International journal for numerical methods in engineering 77(9), 1322-1350.
Chakraverty, S. and S. K. Jeswal (2021). Applied Artificial Neural Network Methods for Engineers and Scientists: Solving Algebraic Equations. World Scientific.
Chase, C. A. and M. R. Todd (1984). Numerical simulation of CO2 flood per- formance (includes associated papers 13950 and 13964). Society of Petroleum Engineers Journal 24(06), 597-605.
Chen, G., K. Zhang, X. Xue, L. Zhang, J. Yao, H. Sun, L. Fan, and Y. Yang (2020). Surrogate-assisted evolutionary algorithm with dimensionality reduction method for water flooding production optimization. Journal of Petroleum Science and Engineering 185, 106633.
Chen, Y. and D. S. Oliver (2010). Ensemble-based closed-loop optimization applied to brugge field. SPE Reservoir Evaluation & Engineering 13(01), 56- 71.
Chen, Y., D. S. Oliver, and D. Zhang (2009). Efficient ensemble-based closed-loop production optimization. SPE Journal 14(04), 634-645.
Chen, Z. (2007). Reservoir simulation: mathematical techniques in oil recovery. SIAM.
Cheraghi, Y., S. Kord, and V. Mashayekhizadeh (2021). Application of ma- chine learning techniques for selecting the most suitable enhanced oil recovery method; challenges and opportunities. Journal of Petroleum Science and Engi- neering 205, 108761.
Coats, K. H. (1980). An equation of state compositional model. Society of Petroleum Engineers Journal 20(05), 363-376.
Davidon, W. (1959). Variable metric method for minimization.
Do, S. T. and A. C. Reynolds (2013). Theoretical connections between opti- mization algorithms based on an approximate gradient. Computational Geo- sciences 17(6), 959-973.
Dudek, J., D. Janiga, and P. Wojnarowski (2021). Optimization of CO2-EOR process management in polish mature reservoirs using smart well technology. Journal of Petroleum Science and Engineering 197, 108060.
Durlofsky, L. (2010). Use of reduced-order modeling procedures for production optimization. SPE Journal 15(02), 426-435.
Eberhart, R. and J. Kennedy (1995). Particle swarm optimization. In Proceedings of the IEEE international conference on neural networks, Volume 4, pp. 1942- 1948. Citeseer.
Fani, M., H. Al-Hadrami, P. Pourafshary, G. Vakili-Nezhaad, and N. Mosavat (2018). Optimization of smart water flooding in carbonate reservoir. In Abu Dhabi International Petroleum Exhibition & Conference. Society of Petroleum Engineers.
Fonseca, R., E. Della Rossa, A. Emerick, R. Hanea, and J. Jansen (2018). Overview of the olympus field development optimization challenge. In EC- MOR XVI-16th European Conference on the Mathematics of Oil Recovery, Vol- ume 2018, pp. 1-10. European Association of Geoscientists & Engineers.
Fonseca, R., S. Kahrobaei, L. Van Gastel, O. Leeuwenburgh, and J. Jansen (2015). Quantification of the impact of ensemble size on the quality of an ensemble gradient using principles of hypothesis testing. In SPE Reservoir Simulation Symposium. OnePetro.
Fonseca, R., O. Leeuwenburgh, P. Van den Hof, and J.-D. Jansen (2014). Improv- ing the ensemble-optimization method through covariance-matrix adaptation. SPE Journal 20(01), 155-168.
Fonseca, R. R.-M., B. Chen, J. D. Jansen, and A. Reynolds (2017). A stochastic simplex approximate gradient (StoSAG) for optimization under uncertainty. In- ternational Journal for Numerical Methods in Engineering 109(13), 1756-1776.
Fukunaga, K. (1990). The artificial neural network book.
Goldberg, D. E. (1989). Genetic algorithms in search, optimization, and machine learning. addison. Reading.
Golzari, A., M. H. Sefat, and S. Jamshidi (2015). Development of an adaptive surrogate model for production optimization. Journal of petroleum Science and Engineering 133, 677-688.
Goodfellow, I., Y. Bengio, and A. Courville (2016). Deep Learning. MIT Press. http://www.deeplearningbook.org.
Heijn, T., R. Markovinovic, and J.-D. Jansen (2004). Generation of low-order reservoir models using system-theoretical concepts. SPE Journal 9(02), 202- 218.
Higham, N. J. (2008). Functions of matrices: theory and computation. SIAM.
Holmes, J. (1983). Enhancements to the strongly coupled, fully implicit well model: wellbore crossflow modeling and collective well control. In SPE Reser- voir Simulation Symposium. OnePetro.
Holmes, J., T. Barkve, and O. Lund (1998). Application of a multisegment well model to simulate flow in advanced wells. In European petroleum conference. OnePetro.
Holmes, P., J. L. Lumley, G. Berkooz, and C. W. Rowley (2012). Turbulence, coherent structures, dynamical systems and symmetry. Cambridge university press.
Hou, J., K. Zhou, X.-S. Zhang, X.-D. Kang, and H. Xie (2015). A review of closed-loop reservoir management. Petroleum Science 12(1), 114-128.
Islam, J., P. M. Vasant, B. M. Negash, M. B. Laruccia, M. Myint, and J. Watada (2020). A holistic review on artificial intelligence techniques for well placement optimization problem. Advances in Engineering Software 141, 102767.
Jain, M. K. (2003). Numerical methods for scientific and engineering computation. New Age International.
Jakupsstovu, S., D. Zhou, J. Kamath, L. Durlofsky, and E. H. Stenby (2001). Upscaling of miscible displacement processes. In Proceedings of the 6th Nordic Symposium on Petrophysics, pp. 15-16.
Janiga, D., R. Czarnota, E. Kuk, J. Stopa, and P. Wojnarowski (2020). Measure- ment of oil-CO2 diffusion coefficient using pulse-echo method for pressure- volume decay approach under reservoir conditions. Journal of Petroleum Science and Engineering 185, 106636.
Jansen, J. (2011a). Adjoint-based optimization of multi-phase flow through porous media - a review. Computers & Fluids 46(1), 40 - 51. 10th ICFD Conference Series on Numerical Methods for Fluid Dynamics (ICFD 2010).
Jansen, J. D. (2011b). Adjoint-based optimization of multi-phase flow through porous media-a review. Computers & Fluids 46(1), 40-51.
Jansen, J.-D., O. H. Bosgra, and P. M. Van den Hof (2008). Model-based control of multiphase flow in subsurface oil reservoirs. Journal of Process Control 18(9), 846-855.
Jansen, J.-D., R. Brouwer, and S. G. Douma (2009). Closed loop reservoir management. In SPE reservoir simulation symposium. Society of Petroleum Engineers.
Jesmani, M., B. Jafarpour, M. C. Bellout, and B. Foss (2020). A reduced ran- dom sampling strategy for fast robust well placement optimization. Journal of Petroleum Science and Engineering 184, 106414.
Jia, X., K. Ma, Y. Liu, B. Liu, J. Zhang, and Y. Li (2013). Enhance heavy oil recovery by in-situ carbon dioxide generation and application in china offshore oilfield. In SPE Enhanced Oil Recovery Conference. Society of Petroleum Engineers.
Jung, S., K. Lee, C. Park, and J. Choe (2018). Ensemble-based data assimilation in reservoir characterization: A review. Energies 11(2), 445.
Kaleta, M. P., R. G. Hanea, A. W. Heemink, and J.-D. Jansen (2011). Model- reduced gradient-based history matching. Computational Geosciences 15(1), 135-153.
Kiefer, J. (1957). Optimum sequential search and approximation methods under minimum regularity assumptions. Journal of the Society for Industrial and Applied Mathematics 5(3), 105-136.
Kraaijevanger, J., P. Egberts, J. Valstar, and H. Buurman (2007). Optimal water- flood design using the adjoint method. In SPE Reservoir Simulation Symposium. OnePetro.
Lee, A. and J. Aronofsky (1958). A linear programming model for scheduling crude oil production. Journal of Petroleum Technology 10(07), 51-54.
Lei, Y., S. Li, X. Zhang, Q. Zhang, and L. Guo (2012). Optimal control of polymer flooding based on maximum principle. Journal of Applied Mathematics 2012.
Li, G. and A. C. Reynolds (2011). Uncertainty quantification of reservoir per- formance predictions using a stochastic optimization algorithm. Computational Geosciences 15(3), 451-462.
Li-xin, G. X.-j. W. and Y. Jian-jun (2005). Optimization of operation plan for water injection system in oilfield using hybrid genetic algorithm [j]. Acta Petrolei Sinica 3.
Liu, D. C. and J. Nocedal (1989). On the limited memory bfgs method for large scale optimization. Mathematical programming 45(1), 503-528.
Liu, X. and A. C. Reynolds (2014). Gradient-based multiobjective optimization with applications to waterflooding optimization. In ECMOR XIV-14th Euro- pean Conference on the Mathematics of Oil Recovery, Volume 2014, pp. 1-21. European Association of Geoscientists & Engineers.
Lorentzen, R. J., A. Berg, G. Nævdal, and E. H. Vefring (2006). A new approach for dynamic optimization of water flooding problems. In Intelligent Energy Conference and Exhibition. Society of Petroleum Engineers.
Lu, R., F. Forouzanfar, and A. C. Reynolds (2017). Bi-objective optimization of well placement and controls using StoSAG. In SPE reservoir simulation conference. OnePetro.
Lyons, W. (2009). Working guide to reservoir engineering. Gulf professional publishing.
Mehos, G. J. and W. F. Ramirez (1989). Use of optimal control theory to optimize carbon dioxide miscible-flooding enhanced oil recovery. Journal of Petroleum Science and Engineering 2(4), 247-260.
Memon, P. Q., S.-P. Yong, W. Pao, and P. J. Sean (2014). Surrogate reservoir modeling-prediction of bottom-hole flowing pressure using radial basis neural network. In 2014 Science and Information Conference, pp. 499-504. IEEE.
Milk, R., S. Rave, and F. Schindler (2016). pyMOR-generic algorithms and inter- faces for model order reduction. SIAM Journal on Scientific Computing 38(5), S194-S216.
Muggeridge, A., A. Cockin, K. Webb, H. Frampton, I. Collins, T. Moulds, and P. Salino (2014). Recovery rates, enhanced oil recovery and technological limits. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 372(2006), 20120320.
Nævdal, G., D. R. Brouwer, and J.-D. Jansen (2006). Waterflooding using closed- loop control. Computational Geosciences 10(1), 37-60.
Neumann, A. W., R. David, and Y. Zuo (2010). Applied surface thermodynamics, Volume 151. CRC press.
Niu, J., Q. Liu, J. Lv, and B. Peng (2020). Review on microbial enhanced oil recovery: Mechanisms, modeling and field trials. Journal of Petroleum Science and Engineering, 107350.
Nocedal, J. and S. J. Wright (2006). Numerical Optimization (Second ed.). Springer.
Norwegian-Petroleum-Directorate (2019). Petroleum reources report on the nor- wegian continental shelf. https://www.npd.no/en/facts/publications/ reports2/resource-report/resourc-report-2019/fields/.
Nwachukwu, A., H. Jeong, M. Pyrcz, and L. W. Lake (2018). Fast evaluation of well placements in heterogeneous reservoir models using machine learning. Journal of Petroleum Science and Engineering 163, 463-475.
Nwachukwu, C. (2018). Machine learning solutions for reservoir characterization, management, and optimization. Ph. D. thesis.
Ogbeiwi, P., Y. Aladeitan, and D. Udebhulu (2018). An approach to waterflood optimization: case study of the reservoir x. Journal of Petroleum Exploration and Production Technology 8(1), 271-289.
Patelli, E. and H. J. Pradlwarter (2010). Monte carlo gradient estimation in high dimensions. International journal for numerical methods in engineering 81(2), 172-188.
Powell, M. J. (1964). An efficient method for finding the minimum of a function of several variables without calculating derivatives. The computer journal 7(2), 155-162.
Rao, S. S. (2019). Engineering optimization: theory and practice. John Wiley & Sons.
Rasmussen, A. F., T. H. Sandve, K. Bao, A. Lauser, J. Hove, B. Skaflestad, R. Klöfkorn, M. Blatt, A. B. Rustad, and O. Sævareid (2021). The open porous media flow reservoir simulator. Computers & Mathematics with Applications 81, 159-185.
Rewienski, M. and J. White (2003). A trajectory piecewise-linear approach to model order reduction and fast simulation of nonlinear circuits and micro- machined devices. IEEE Transactions on computer-aided design of integrated circuits and systems 22(2), 155-170.
Ridwan, M. G., M. I. Kamil, M. Sanmurjana, A. M. Dehgati, P. Permadi, T. Marhaendrajana, and F. Hakiki (2020). Low salinity waterflooding: Sur- face roughening and pore size alteration implications. Journal of Petroleum Science and Engineering 195, 107868.
Saberi, H., E. Esmaeilnezhad, and H. J. Choi (2021). Artificial neural network to forecast enhanced oil recovery using hydrolyzed polyacrylamide in sandstone and carbonate reservoirs. Polymers 13(16), 2606.
Sadeed, A., Z. Tariq, A. N. Janjua, A. Asad, and M. E. Hossain (2018). Smart water flooding: an economic evaluation and optimization. In SPE Kingdom of Saudi Arabia Annual Technical Symposium and Exhibition. Society of Petroleum Engineers.
Sampaio, T. P., V. J. M. Ferreira Filho, and A. D. S. Neto (2009). An application of feed forward neural network as nonlinear proxies for use during the his- tory matching phase. In Latin American and Caribbean Petroleum Engineering Conference. OnePetro.
Sarma, P., K. Aziz, and L. J. Durlofsky (2005). Implementation of adjoint solution for optimal control of smart wells. In SPE reservoir simulation symposium. Society of Petroleum Engineers.
Sarma, P. and W. Chen (2014). Improved estimation of the stochastic gradient with quasi-monte carlo methods. In ECMOR XIV-14th European Conference on the Mathematics of Oil Recovery, Volume 2014, pp. 1-25. European Association of Geoscientists & Engineers.
Sarma, P. and W. H. Chen (2008). Efficient well placement optimization with gradient-based algorithms and adjoint models. In Intelligent energy conference and exhibition. Society of Petroleum Engineers.
Sarma, P., W. H. Chen, L. J. Durlofsky, and K. Aziz (2006). Production opti- mization with adjoint models under nonlinear control-state path inequality con- straints. In Intelligent Energy Conference and Exhibition. Society of Petroleum Engineers.
Schlegel, M. and B. R. Noack (2015). On long-term boundedness of galerkin models. Journal of Fluid Mechanics 765, 325-352.
Schlumberger, A. (2010). Eclipse technical description. Schlumberger Information Solutions.
Sehbi, B. S., S. M. Frailey, and A. S. Lawal (2001). Analysis of factors affecting microscopic displacement efficiency in CO2 floods. In SPE Permian Basin Oil and Gas Recovery Conference. Society of Petroleum Engineers.
Semnani, A., M. Ostadhassan, Y. Xu, M. Sharifi, and B. Liu (2021). Joint optimization of constrained well placement and control parameters using teaching-learning based optimization and an inter-distance algorithm. Journal of Petroleum Science and Engineering 203, 108652.
Shirangi, M. G. (2012). Applying machine learning algorithms to oil reservoir production optimization. In Tech. Rep. Machine Learning Course Project Report. Stanford University.
Snyman, J. A. and D. N. Wilke (2005). Practical mathematical optimization. Springer.
Stengel, R. F. (1994). Optimal control and estimation. Courier Corporation.
Sun, X.-h. and M.-h. Xu (2017). Optimal control of water flooding reservoir using proper orthogonal decomposition. Journal of Computational and Applied Mathematics 320, 120-137.
Svein, M. S. and J. Kleppe (1992). Recent advances in improved oil recovery methods for north sea sandstone reservoirs. SPOR Monograph.
Todd, M. and W. Longstaff (1972). The development, testing, and application of a numerical simulator for predicting miscible flood performance. Journal of Petroleum Technology 24(07), 874-882.
Van Doren, J., S. G. Douma, L. B. M. Wassing, J. Kraaijevanger, and A. H. De Zwart (2011). Adjoint-based optimization of polymer flooding. In SPE Enhanced Oil Recovery Conference. Society of Petroleum Engineers.
Van Doren, J. F., R. Markovinović, and J.-D. Jansen (2006). Reduced-order opti- mal control of water flooding using proper orthogonal decomposition. Compu- tational Geosciences 10(1), 137-158.
Van Essen, G., M. Zandvliet, P. Van den Hof, O. Bosgra, and J.-D. Jansen (2009). Robust waterflooding optimization of multiple geological scenarios. SPE Journal 14(01), 202-210.
Völcker, C. (2011). Production optimization of oil reservoirs. Kongens Lyngby, Denmark: Department of Informatics and Mathematical Modelling-Technical, University of Denmark.
Walton, S., O. Hassan, and K. Morgan (2013). Reduced order modelling for unsteady fluid flow using proper orthogonal decomposition and radial basis functions. Applied Mathematical Modelling 37(20-21), 8930-8945.
Wang, G. C. (1980). Microscopic study of oil recovery by carbon dioxide. final report, october 1, 1978-august 31, 1980. Technical report, Alabama Univ., Tuscaloosa (USA). Dept. of Mineral Engineering.
Wang, Y., C. Liu, Y. Wang, and S. Zhou (2010). Optimization in oilfield water injection system based on algorithm of ant colony-particle swarm method. J. Daqing Pet. Inst 2, 014.
Xiangguo, L., C. Bao, X. Kun, C. Weijia, L. Yigang, Y. ZHANG, W. Xiaoyan, and J. ZHANG (2021). Enhanced oil recovery mechanisms of polymer flooding in a heterogeneous oil reservoir. Petroleum Exploration and Development 48(1), 169-178.
Xiao, D., F. Fang, C. Pain, I. Navon, and A. Muggeridge (2016). Non-intrusive reduced order modelling of waterflooding in geologically heterogeneous reser- voirs. In ECMOR XV-15th European conference on the mathematics of oil recovery, pp. cp-494. European Association of Geoscientists & Engineers.
Xu, L., H. Zhao, Y. Li, L. Cao, X. Xie, X. Zhang, and Y. Li (2018). Pro- duction optimization of polymer flooding using improved monte carlo gradient approximation algorithm with constraints. Journal of Circuits, Systems and Computers 27(11), 1850167.
Yang, C. and X. Wang (2021). A steam injection distribution optimization method for sagd oil field using lstm and dynamic programming. ISA transactions 110, 198-212.
Yeten, B. (2003). Optimum deployment of nonconventional wells. Stanford Uni- versity.
Yousef, A. and S. Ayirala (2014). Optimization study of a novel water-ionic technology for smart-waterflooding application in carbonate reservoirs. Oil and Gas Facilities 3(05), 72-82.
Yousef, A. A., S. Al-Saleh, and M. Al-Jawfi (2012). The impact of the injec- tion water chemistry on oil recovery from carbonate reservoirs. In SPE EOR Conference at Oil and Gas West Asia. OnePetro.
Yousef, A. A., S. Al-Saleh, A. Al-Kaabi, and M. Al-Jawfi (2011). Laboratory investigation of the impact of injection-water salinity and ionic content on oil recovery from carbonate reservoirs. SPE Reservoir Evaluation & Engineer- ing 14(05), 578-593.
Zandvliet, M., M. Handels, G. van Essen, R. Brouwer, and J.-D. Jansen (2008). Adjoint-based well-placement optimization under production constraints. SPE Journal 13(04), 392-399.
Zerkalov, G. (2015). Polymer flooding for enhanced oil recovery. Stanford Uni- versity, 1-4.
Zhang, K., X. Zhang, W. Ni, L. Zhang, J. Yao, L. Li, and X. Yan (2016). Nonlinear constrained production optimization based on augmented lagrangian function and stochastic gradient. Journal of Petroleum Science and Engineering 146, 418-431.
Zhong, Z., A. Y. Sun, Y. Wang, and B. Ren (2020). Predicting field production rates for waterflooding using a machine learning-based proxy model. Journal of Petroleum Science and Engineering 194, 107574.
Zhou, K., J. Hou, X. Zhang, Q. Du, X. Kang, and S. Jiang (2013). Optimal control of polymer flooding based on simultaneous perturbation stochastic ap- proximation method guided by finite difference gradient. Computers & chemical engineering 55, 40-49.
Zurada, J. (1992). Introduction to artificial neural systems. West Publishing Co.
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