Global and Local Surrogate-Model-Assisted Differential Evolution for Waterflooding Production Optimization
- Guodong Chen (China University of Petroleum (East China)) | Kai Zhang (China University of Petroleum (East China)) | Liming Zhang (China University of Petroleum (East China)) | Xiaoming Xue (China University of Petroleum (East China)) | Dezhuang Ji (China University of Petroleum (East China)) | Chuanjin Yao (China University of Petroleum (East China)) | Jun Yao (China University of Petroleum (East China)) | Yongfei Yang (China University of Petroleum (East China))
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- February 2020
- Document Type
- Journal Paper
- 105 - 118
- 2020.Society of Petroleum Engineers
- differential evolution, radial basis function, RBF, production optimization, surrogate
- 13 in the last 30 days
- 139 since 2007
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Surrogate models, which have become a popular approach to oil-reservoir production-optimization problems, use a computationally inexpensive approximation function to replace the computationally expensive objective function computed by a numerical simulator. In this paper, a new optimization algorithm called global and local surrogate-model-assisted differential evolution (GLSADE) is introduced for waterflooding production-optimization problems. The proposed method consists of two parts: (1) a global surrogate-model-assisted differential-evolution (DE) part, in which DE is used to generate multiple offspring, and (2) a local surrogate-model-assisted DE part, in which DE is used to search for the optimum of the surrogate. The cooperation between global optimization and local search helps the production-optimization process become more efficient and more effective. Compared with the conventional one-shot surrogate-based approach, the developed method iteratively selects data points to enhance the accuracy of the promising area of the surrogate model, which can substantially improve the optimization process. To the best of our knowledge, the proposed method uses a state-of-the-art surrogate framework for production-optimization problems. The approach is tested on two 100-dimensional benchmark functions, a three-channel model, and the egg model. The results show that the proposed method can achieve higher net present value (NPV) and better convergence speed in comparison with the traditional evolutionary algorithm and other surrogate-assisted optimization methods for production-optimization problems.
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Babaei, M. and Pan, I. 2016. Performance Comparison of Several Response Surface Surrogate Models and Ensemble Methods for Water Injection Optimization under Uncertainty. Comput Geosci 91: 19–32. https://doi.org/10.1016/j.cageo.2016.02.022.
Balabanov, V., Haftka, R. T., Grossman, B. et al. 2007. Multifidelity Response Surface Model for HSCT Wing Bending Material Weight. Paper Presented at the 7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, St. Louis, Missouri, USA, 2 September–4 September. https://doi.org/10.2514/6.1998-4804.
Cai, X., Gao, L., and Li, X. 2019. Efficient Generalized Surrogate-Assisted Evolutionary Algorithm for High-Dimensional Expensive Problems. IEEE Trans Evol Comput (early access; posted online 31 May 2019). https://doi.org/10.1109/TEVC.2019.2919762.
Cao, F., Luo, H., and Lake, L. W. 2015. Oil-Rate Forecast by Inferring Fractional-Flow Models from Field Data with Koval Method Combined with the Capacitance/Resistance Model. SPE Res Eval & Eng 18 (4): 534–553. SPE-173315-PA. https://doi.org/10.2118/173315-PA.
Chen, B., He, J., Wen, X. H. et al. 2017. Uncertainty Quantification and Value of Information Assessment Using Proxies and Markov Chain Monte Carlo Method for a Pilot Project. J Pet Sci Eng 157: 328–339. https://doi.org/10.1016/j.petrol.2017.07.039.
Chen, C., Jin, L., Gao, G. et al. 2012a. Assisted History Matching Using Three Derivative-Free Optimization Algorithms. Paper presented at the SPE Europec/EAGE Annual Conference, Copenhagen, Denmark, 4–7 June. SPE-154112-MS. https://doi.org/10.2118/154112-MS.
Chen, C., Li, G., and Reynolds, A. 2012b. Robust Constrained Optimization of Short- and Long-Term Net Present Value for Closed-Loop Reservoir Management. SPE J. 17 (3): 849–864. SPE-141314-PA. https://doi.org/10.2118/141314-PA.
Chen, C., Wang, Y., Li, G. et al. 2010. Closed-Loop Reservoir Management on the Brugge Test Case. Comput Geosci 14 (4): 691–703. https://doi.org/10.1007/s10596-010-9181-7.
Chen, Y., Oliver, D. S., and Zhang, D. 2009. Efficient Ensemble-Based Closed-Loop Production Optimization. SPE J. 14 (4): 634–645. SPE-112873-PA. https://doi.org/10.2118/112873-PA.
Das, S. and Suganthan, P. 2011. Differential Evolution: A Survey of the State-of-the-Art. IEEE Trans Evol Comput 15 (1): 4–31. https://doi.org/10.1109/TEVC.2010.2059031.
Ebrahimi, A. and Khamehchi, E. 2016. Sperm Whale Algorithm: An Effective Metaheuristic Algorithm for Production Optimization Problems. J Nat Gas Sci Eng 29: 211–222. https://doi.org/10.1016/j.jngse.2016.01.001.
Fonseca, R. M., Chen, B., Jansen, J. D. et al. 2016. A Stochastic Simplex Approximate Gradient (StoSAG) for Optimization Under Uncertainty. Int J Numer Methods Eng 109 (13): 1756–1776. https://doi.org/10.1002/nme.5342.
Foroud, T., Baradaran, A., and Seifi, A. 2018. A Comparative Evaluation of Global Search Algorithms in Black Box Optimization of Oil Production: A Case Study on Brugge Field. J Pet Sci Eng 167: 131–151. https://doi.org/10.1016/j.petrol.2018.03.028.
Foroud, T., Seifi, A., and Aminshahidi, B. 2014. Assisted History Matching Using Artificial Neural Network Based Global Optimization Method—Applications to Brugge Field and a Fractured Iranian Reservoir. J Pet Sci Eng 123: 46–61. https://doi.org/10.1016/j.petrol.2014.07.034.
Forrester, A. I. J., and Keane, A. J. 2009. Recent Advances in Surrogate-Based Optimization. Prog Aerosp Sci 45 (1): 50–79. https://doi.org/10.1016/j.paerosci.2008.11.001.
Golzari, A., Sefat, M. H., and Jamshidi, S. 2015. Development of an Adaptive Surrogate Model for Production Optimization. J Pet Sci Eng 133 (6): 677–688. https://doi.org/10.1016/j.petrol.2015.07.012.
Guo, Z., Chen, C., Gao, G. et al. 2018a. Integration of Support Vector Regression with Distributed Gauss-Newton Optimization Method and Its Applications to the Uncertainty Assessment of Unconventional Assets. SPE Res Eval & Eng 21 (4): 1007–1026. SPE-191373-PA. https://doi.org/10.2118/191373-PA.
Guo, Z., Chen, C., Gao, G. et al. 2018b. Enhancing the Performance of the Distributed Gauss-Newton Optimization Method by Reducing the Effect of Numerical Noise and Truncation Error with Support-Vector Regression. SPE J. 23 (6): 2428–2443. SPE-187430-PA. https://doi.org/10.2118/187430-PA.
Guo, Z. and Reynolds, A. C. 2018. Robust Life-Cycle Production Optimization with a Support-Vector-Regression Proxy. SPE J. (6): 2409–2427. SPE-191378-PA. https://doi.org/10.2118/191378-PA.
Hajizadeh, Y., Christie, M. A., and Demyanov, V. 2010. Comparative Study of Novel Population-Based Optimization Algorithms for History Matching and Uncertainty Quantification: PUNQ-S3 Revisited. Paper presented at the Abu Dhabi International Petroleum Exhibition and Conference, Abu Dhabi, UAE, 1–4 November. SPE-136861-MS. https://doi.org/10.2118/136861-MS.
Hanssen, K. G., Codas, A., and Foss, B. 2017. Closed-Loop Predictions in Reservoir Management Under Uncertainty. SPE J. 22 (5): 1585–1595. SPE-185956-PA. https://doi.org/10.2118/185956-PA.
He, J., Xie, J., Sarma, P. et al. 2016. Proxy-Based Work Flow for a Priori Evaluation of Data-Acquisition Programs. SPE J. 21 (4): 1400–1412. SPE-173229-PA. https://doi.org/10.2118/173229-PA.
He, J., Xie, J., Wen, X.-H. et al. 2015. Improved Proxy for History Matching Using Proxy-for-Data Approach and Reduced Order Modeling. Paper presented at the SPE Western Regional Meeting, Garden Grove, California, USA. SPE-174055-MS. https://doi.org/10.2118/174055-MS.
Horowitz, B., Afonso, S. M. B., and Mendonça, C. V. P. D. 2013. Surrogate Based Optimal Waterflooding Management. J Pet Sci Eng 112 (3): 206–219. https://doi.org/10.1016/j.petrol.2013.11.006.
Jansen, J. D., Fonseca, R. M., Kahrobaei, S. et al. 2015. The Egg Model—A Geological Ensemble for Reservoir Simulation. Geosci Data J 1 (2): 192–195. https://doi.org/10.1002/gdj3.21.
Jin, Y., Wang, H., Chugh, T. et al. 2018. Data-Driven Evolutionary Optimization: An Overview and Case Studies. IEEE Trans Evol Comput 23 (3): 442–458. https://doi.org/10.1109/TEVC.2018.2869001.
Joo, E. M., Shiqian, W., Juwei, L. et al. 2002. Face Recognition with Radial Basis Function (RBF) Neural Networks. IEEE Trans Neural Netw 13 (3): 697–710. https://doi.org/10.1109/TNN.2002.1000134.
Kai, Z., Zhang, L. M., Yao, J. et al. 2014. Water Flooding Optimization with Adjoint Model Under Control Constraints. J Hydrodyn Ser B 26 (1): 75–85. https://doi.org/10.1016/S1001-6058(14)60009-3.
Liming, Z., Saisai, W., Kai, Z. et al. 2018. Cooperative Artificial Bee Colony Algorithm with Multiple Populations for Interval Multi-Objective Optimization Problems. IEEE Trans Fuzzy Systems 27 (5): 1052–1065.
Liu, B., Grout, V., and Nikolaeva, A. 2017. Efficient Global Optimization of Actuator Based on a Surrogate Model Assisted Hybrid Algorithm. IEEE Trans Ind Elec 65 (7): 5712–5721. https://doi.org/10.1109/TIE.2017.2782203.
Liu, B., Zhang, Q., and Gielen, G. G. E. 2014. A Gaussian Process Surrogate Model Assisted Evolutionary Algorithm for Medium Scale Expensive Optimization Problems. IEEE Trans Evol Comput 18 (2): 180–192. https://doi.org/10.1109/TEVC.2013.2248012.
Liu, Z., Forouzanfar, F., and Zhao, Y. 2018. Comparison of SQP and AL Algorithms for Deterministic Constrained Production Optimization of Hydrocarbon Reservoirs. J Pet Sci Eng 171: 542–557. https://doi.org/10.1016/j.petrol.2018.06.063.
Liu, Z. and Reynolds, A. C. 2019. An SQP-Filter Algorithm with an Improved Stochastic Gradient for Robust Life-Cycle Optimization Problems with Nonlinear Constraints. Paper presented at the SPE Reservoir Simulation Conference, Galveston, Texas, USA, 10–11 April. SPE-193925-MS. https://doi.org/10.2118/193925-MS.
Loshchilov, I., Schoenauer, M., and Sebag, M. 2010. Comparison-Based Optimizers Need Comparison-Based Surrogates. Proceedings of the 11th International Conference on Parallel Problem Solving from Nature, 11–15 September, Kraków, Poland.
Moraes, R., Rodrigues, J. R. P., Hajibeygi, H. et al. 2017. Multiscale Gradient Computation for Multiphase Flow in Porous Media. Paper presented at the SPE Reservoir Simulation Conference, Montgomery, Texas, USA, 20–22 February. SPE-182625-MS. https://doi.org/10.2118/182625-MS.
Park, J. and W. Sandberg, I. (1993). Approximation and Radial-Basis-Function Networks. Neural Comput 5 (2): 305–316. https://doi.org/10.1162/neco.19220.127.116.115.
Plaksina, T. and Gildin, E. 2018. Applied Method for Production Design Optimization Under Geologic and Economic Uncertainties in Shale Gas Reservoirs. Int J Modell Simul 38 (2): 67–82. https://doi.org/10.1080/02286203.2017.1393712.
Pope, G. A., Delshad, M., Edgar, T. F. et al. 2008. Development and Application of Capacitance-Resistive Models to Water/CO2 Floods. PhD dissertation, University of Texas at Austin, Austin, Texas, USA (August 2008).
Qing, A. 2009. Advances in Differential Evolution, 61–88. Springer-Verlag Berlin Heidelberg.
Regis, R. G. 2013. An Initialization Strategy for High-Dimensional Surrogate-Based Expensive Black-Box Optimization. In Modeling and Optimization: Theory and Applications, ed. Zuluaga, L. and Terlaky, T., Vol. 62. New York, New York, USA: Springer.
Sefat, M. H., Salahshoor, K., Jamialahmadi, M. et al. 2012. A New Approach for the Development of Fast-Analysis Proxies for Petroleum Reservoir Simulation. Pet Sci Technol 30 (18): 1920–1930. https://doi.org/10.1080/10916466.2010.512885.
Stein, M. 1987. Large Sample Properties of Simulations Using Latin Hypercube Sampling. Technometrics 29 (2): 143–151. https://doi.org/10.2307/1269769.
Sun, C., Jin, Y., Cheng, R. et al. 2017. Surrogate-Assisted Cooperative Swarm Optimization of High-Dimensional Expensive Problems. IEEE Trans Evol Comput 21 (4): 644–660. https://doi.org/10.1109/TEVC.2017.2675628.
Wang, C., Li, G., and Reynolds, A. C. 2009. Production Optimization in Closed-Loop Reservoir Management. SPE J. 14 (3): 506–523. SPE-109805-PA. https://doi.org/10.2118/109805-PA.
Wang, X., Wang, G. G., Song, B. et al. 2019. A Novel Evolutionary Sampling Assisted Optimization Method for High Dimensional Expensive Problems. IEEE Trans Evol Comput 23 (5): 815–827. https://doi.org/10.1109/TEVC.2019.2890818.
Wang, Y., Yin, D. Q., Yang, S. et al. 2018. Global and Local Surrogate-Assisted Differential Evolution for Expensive Constrained Optimization. IEEE Trans Cybern 49 (5): 1642–1656. https://doi.org/10.1109/TCYB.2018.2809430.
Weber, D. B. 2009. The Use of Capacitance-Resistance Models to Optimize Injection Allocation and Well Location in Water Floods. PhD dissertation, University of Texas at Austin, Austin, Texas, USA (August 2009).
Xu, X.-F., Hao, J., Deng, Y.-R. et al. 2017. Design Optimization of Resource Combination for Collaborative Logistics Network Under Uncertainty. Appl Soft Comput 56: 684–691. https://doi.org/10.1016/j.asoc.2016.07.036.
Xu, X., Hao, J., Yu, L. et al. 2018. Fuzzy Optimal Allocation Model for Task–Resource Assignment Problem in a Collaborative Logistics Network. IEEE Trans Fuzzy Syst 27 (5): 1112–1125. https://doi.org/10.1109/TFUZZ.2018.2826479.
Yan, X. and Reynolds, A. C. 2013. An Optimization Algorithm Based on Combining Finite-Difference Approximations and Stochastic Gradients. Paper presented at the SPE Reservoir Simulation Symposium, The Woodlands, Texas, USA. 18–20 February. SPE-163613-MS. https://doi.org/10.2118/163613-MS.
Yeten, B., Castellini, A., Guyaguler, B. et al. 2005. A Comparison Study on Experimental Design and Response Surface Methodologies. Paper presented at the SPE Reservoir Simulation Symposium, The Woodlands, Texas, USA, 31 January–2 February. SPE-93347-MS. https://doi.org/10.2118/93347-MS.
Yousef, A. A., Gentil, P. H., Jensen, J. L. et al. 2006. A Capacitance Model to Infer Interwell Connectivity from Production and Injection Rate Fluctuations. SPE Res Eval & Eng 9 (6): 630–646. SPE-95322-PA. https://doi.org/10.2118/95322-PA.
Yu, H., Tan, Y., Sun, C. et al. 2019. A Generation-Based Optimal Restart Strategy for Surrogate-Assisted Social Learning Particle Swarm Optimization. Knowl Based Syst 163: 14–25. https://doi.org/10.1016/j.knosys.2018.08.010.
Yu, H., Ying, T., Zeng, J. et al. 2018. Surrogate-Assisted Hierarchical Particle Swarm Optimization. Inf Sci 454–455. https://doi.org/10.1016/j.ins.2018.04.062.
Zakirov, I., Aanonsen, S. I., Zakirov, E. S. et al. 1996. Optimizing Reservoir Performance by Automatic Allocation of Well Rates. Paper presented at the ECMOR V—5th European Conference on the Mathematics of Oil Recovery, Leoben, Austria, 3–6 September. https://doi.org/10.3997/2214-4609.201406895.
Zangl, G., Graf, T., and Al-Kinani, A. 2006. Proxy Modeling in Production Optimization. Paper presented at the SPE Europec/EAGE Annual Conference and Exhibition, Vienna, Austria. 12–15 June. SPE-100131-MS. https://doi.org/10.2118/100131-MS.
Zhang, K., Ma, X., Li, Y. et al. 2018. Parameter Prediction of Hydraulic Fracture for Tight Reservoir Based on Micro-Seismic and History Matching. Fractals 26 (2): 1840009, 17 pages. https://doi.org/10.1142/S0218348X18400091.
Zhang, K., Zhang, X., Ni, W. et al. 2016. Nonlinear Constrained Production Optimization Based on Augmented Lagrangian Function and Stochastic Gradient. J Pet Sci Eng 146: 418–431. https://doi.org/10.1016/j.petrol.2016.06.007.
Zhang, K., Zhang, X., Zhang, L. et al. 2017. A Novel Approach for Optimization of Polymer-Surfactant Flooding Based on Simultaneous Perturbation Stochastic Approximation Algorithm. J China Univ Pet (Edition of Natural Science) 41 (5): 102–109.
Zhang, L., Cui, C., Ma, X. et al. 2019. A Fractal Discrete Fracture Network Model for History Matching of Naturally Fractured Reservoirs. Fractals 27 (1): 1940008, 15 pages. https://doi.org/10.1142/S0218348X19400085.
Zhou, Z., Ong, Y. S., Nair, P. B. et al. 2006. Combining Global and Local Surrogate Models to Accelerate Evolutionary Optimization. IEEE Trans Syst Man Cybern Part C 37 (1): 66–76. https://doi.org/10.1109/TSMCC.2005.855506.
Zhu, Y. and Zabaras, N. 2018. Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantification. J Comput Phys 366: 415–447. https://doi.org/10.1016/j.jcp.2018.04.018.