Gradient-free strategies to robust well control optimization.

*(English)*Zbl 1452.86013Summary: In this work, the well control optimization of the Olympus challenge is solved by two non-intrusive strategies that use the simulator as a black box. This reservoir model contains uncertainties on geological scenarios, in which the optimal management process is conducted through robust optimization, which can use a set of representative realizations to honor the statistics of the geological properties. The statistic considered here is the mean of the net present value (NPV). Control variables are flow rates and bottom hole pressures (BHP) of each well completion. The first strategy used here is the sequential approximate optimization (SAO) with variable reparameterization that uses polynomial control trajectories. In order to reduce the computational cost of the overall process, this strategy builds surrogate models to be used in the several function calls required in the optimization process. The other strategy is the refined ensemble-based (REB) method that computes the approximate gradient of the expected NPV as a sum of the columns of a refined sensitivity matrix obtained from ensemble-based covariance matrices of controls and cross-covariance between well NPVs and controls. The use of small-sized ensembles introduces spurious correlations that degrade gradient quality. Non-distance-based localization and competitiveness coefficients between producer wells and smoothing control trajectories are used to reduce spurious correlations. Both strategies use approximate derivatives and they are able to include any general nonlinear constraints. The SQP (sequential quadratic programming) is the algorithm used in both methodologies. The strategies produced similar results, are close to the reactive control solution, and are viable alternatives for robust optimization problem and the choice depends mostly on the number of control variables.

##### MSC:

86A20 | Potentials, prospecting |

65K05 | Numerical mathematical programming methods |

86-08 | Computational methods for problems pertaining to geophysics |

##### Keywords:

robust optimization; sequential approximate method; large-scale algorithms; ensemble-based method; waterflooding optimization; sequential quadratic programming; refined sensitivity matrix; constrained optimization; polynomial trajectories
PDF
BibTeX
XML
Cite

\textit{J. W. O. Pinto} et al., Comput. Geosci. 24, No. 6, 1959--1978 (2020; Zbl 1452.86013)

Full Text:
DOI

##### References:

[1] | Afonso, S.M.B., Horowitz, B., Wilmersdorf, R.B.: Comparative Study of Surrogate Models for Engineering Problems. ASMO-UK (Association for Structural and Multidisciplinary Optimization in the UK), Bath, UK (2008) |

[2] | Albertoni, A.; Lake, L., Inferring interwell connectivity only from well-rate fluctuations in waterfloods, SPE Reserv. Eval. Eng., 6, 1, 6-16 (2003) |

[3] | Alexandrov, N.; Dennis, JJ; Lewisand, R.; Torczon, V., A trust region framework for managing the use of approximation models in optimization, Struct. Optim, 15, 1, 16-23 (1998) |

[4] | Alhuthali, AH; Datta-Gupta, A.; Yuen, B.; Fontanilla, JP, Optimizing smart well controls under geologic uncertainty, J. Pet. Sci. Eng., 73, 1-2, 107-121 (2010) |

[5] | Alim, M.: Constraint Handling in Life-Cycle Optimization Using Ensemble Gradients, MSc Thesis Report, Delft University of Technology, The Netherlands (2013) |

[6] | Awotunde, A.A.: On the joint optimization of well placement and control. In SPE Saudi Arabia Section Technical Symposium and Exhibition. Society of Petroleum Engineers (2014) |

[7] | Bahagio, D.N.T.: Ensemble Optimization of CO2 WAG EOR. MS Thesis Report, Delft University of Technology, The Netherlands (2013) |

[8] | Bigler, LT, Nonlinear Programming: Concepts, Algorithms, and Applications to Chemical Processes (2010), Philadelphia: SIAM - Society for Industrial and Applied Mathematics, Philadelphia · Zbl 1207.90004 |

[9] | Biniaz, DE; Pishvaie, MR; Bozorgmehry, BR, Distance dependent localization approach in oil reservoir history matching: a comparative study, Iranian Journal of Chemistry & Chemical Engineering (IJCCE), 33, 1, 75-91 (2014) |

[10] | Brouwer, D.; Jansen, J., Dynamic optimization of waterflooding with smart wells using optimal control theory. SPE 78278-PA, SPE J., 9, 4, 391-402 (2004) |

[11] | Buhmann, M.D.: Radial basis functions: theory and implementations (vol. 12). Cambridge University Press (2003) · Zbl 1038.41001 |

[12] | Capolei, A.; Suwartadi, E.; Foss, B.; Jørgensen, JB, A mean-variance objective for robust production optimization in uncertain geological scenarios, J. Pet. Sci. Eng., 125, 23-37 (2015) |

[13] | Chen, Y.; Oliver, DS, Localization of ensemble-based control-setting updates for production optimization, SPE J., 17, 1, 122-136 (2012) |

[14] | Chen, B.; Reynolds, AC, Ensemble-based optimization of the water alternating-gas-injection process, SPE J., 21, 3, 786-798 (2016) |

[15] | Chen, B., and Xu, J.: Stochastic simplex approximate gradient for robust life-cycle production optimization: applied to Brugge field. United States (2019). doi:10.1115/1.4043244 |

[16] | Chen, Y.; Oliver, DS; Zhang, D., Efficient ensemble-based closed-loop production optimization, SPE J., 14, 4, 634-645 (2009) |

[17] | Computer Modeling Group LTD.: IMEX: User’s Guide. Calgary - Canada (2017) |

[18] | Dehdari, V.; Oliver, DS; Deutsch, CV, Comparison of optimization algorithms for reservoir management with constraints—a case study, J. Pet. Sci. Eng., 100, 41-49 (2012) |

[19] | Dehdari, V.; Oliver, DS, Sequential quadratic programming for solving constrained production optimization—case study from Brugge field, SPE J., 17, 874-884 (2012) |

[20] | Deutsch, C., Srinivasan, S.: Improved reservoir management through ranking stochastic reservoir models. SPE/DOE Improved Oil Recovery Symposium. SPE, 105-113 (1996) |

[21] | Do, ST; Reynolds, AC, Theoretical connections between optimization algorithms based on an approximate gradient, Comput. Geosci., 17, 6, 959-973 (2013) · Zbl 1393.90137 |

[22] | Eldred, M.S., Giunta, A.A., Collis, S.S.: Second-order corrections for surrogate-based optimization with model hierarchies. In 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference (p 4457) (2004) |

[23] | Elsayed, K., Vucinic, D., d’Ippolito, R., Lacor, C.: Comparison between RBF and Kriging surrogates in design optimization of high dimensional problems. Proceeding of 3rd international conference on engineering optimization conference, Rio de Janeiro, Brazil, (pp. 1-5) (2012) |

[24] | Fedutenko, E., Yang, C., Card, C., Nghiem, L.: Optimization of SAGD process accounting for geological uncertainties using proxy models. Proceedings of CSPG/CSEG/CWLS GeoConvention. (6-12 May), Calgary, AB, Canada (2013) |

[25] | Fenik, D.R., Nouri, A., Deutsch, C.V.: Criteria for ranking realizations in the investigation of SAGD reservoir performance. In Canadian International Petroleum Conference. Petroleum Society of Canada (2009) |

[26] | Fonseca, R.M., Kahrobaei, S., Van Gastel, L.J.T., Leeuwenburgh, O., Jansen, J.D.: Quantification of the impact of ensemble size on the quality of an ensemble gradient using principles of hypothesis testing. Paper 173236-MS presented at the 2015 SPE Reservoir Simulation Symposium, Houston, USA; 22-25 (2015) |

[27] | Fonseca, RM; Leeuwenburgh, O.; Della Rossa, ED; Van den Hof, PMJ; Jansen, JD, Ensemble-based multi-objective optimization of on-off control devices under geological uncertainty, SPE Reserv. Eval. Eng., 18, 554-563 (2015) |

[28] | Fonseca, R.M., Geel, C.R., Leeuwenburgh, O.: Description of OLYMPUS reservoir model for optimization challenge. Integrated Systems Approach to Petroleum Production. Netherlands (2017) |

[29] | Fonseca, RM; Chen, B.; Jansen, JD; Reynolds, A., A stochastic simplex approximate gradient (stoSAG) for optimization under uncertainty, Int. J. Numer. Methods Eng., 109, 13, 1756-1776 (2017) · Zbl 1365.90177 |

[30] | Forrester, A., Sobester, A., Keane, A.: Engineering Design via Surrogate Modelling: a Practical Guide. 228 p. Chichester: Wiley (2008) |

[31] | Fu, J.; Wen, XH, A regularized production-optimization method for improved reservoir management, SPE J., 23, 2, 467-481 (2018) |

[32] | Gill, P., Murray, W., Saunders, M.: User’s Guide for SNOPT Version 7: Software for Large-Scale Nonlinear Programming. Stanford University (2008) |

[33] | Giunta, A.: Use of Data Sampling, Surrogate Models, and Numerical Optimization in Engineering Design. Paper AIAA-2002-0538 in Proceedings of the 40th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV (2002) |

[34] | Giunta, A., Eldred, M.: Implementation of a trust region model management strategy in the DAKOTA optimization toolkit. 8th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization. AIAA-2000-4935. Long Beach, CA (2000) |

[35] | Giunta, A., Wojtkiewicz, S., Eldred, M.: Overview of Modern Design of Experiments Methods for Computational Simulations. Proceedings of the 41st AIAA Aerospace Sciences Meeting and Exhibit. Reno, NV: AIAA-2003-0649 (2003) |

[36] | Gutmann, H.M.: A radial basis function method for global optimization. J. Glob. Optim., 201-227 (2001) · Zbl 0972.90055 |

[37] | Haghighat Sefat, M.; Muradov, KM; Elsheikh, AH; Davies, DR, Proactive optimization of intelligent-well production using stochastic gradient-based algorithms, SPE Reserv. Eval. Eng., 19, 2, 239-252 (2016) |

[38] | Hewson, C.W., Leeuwenburgh, O.: CO2 Water-Alternating-Gas Flooding Optimization of the Chigwell Viking I Pool in the Western Canadian Sedimentary Basin. SPE Reservoir Simulation Conference. Society of Petroleum Engineers (2017). doi:10.2118/182597-MS |

[39] | Holanda, R.W., Gildin, E., Jensen, J.L.: Improved Waterflood Analysis Using the Capacitance-Resistance Model within a Control Systems Framework. SPE Latin American and Caribbean Petroleum Engineering Conference. Society of Petroleum Engineers (2015). doi:10.2118/177106-MS |

[40] | Horowitz, B.; Afonso, SMB; Mendonça, CVP, Surrogate based optimal waterflooding management, J. Pet. Sci. Eng., 112, 206-219 (2013) |

[41] | Katz, H., Horowitz, B., Tueros, J.A.R.: Numerical experience using capacitance resistance multilayered models. CILAMCE 2017, Ibero-latin American Congress in Computational Methods in Engineering. Florianópolis, Brazil (2017). doi:10.20906/CPS/CILAMCE2017-0282 (in Portuguese) |

[42] | Lajevardi, S.: Improved Probabilistic Representation of Facies Through Developments in Geostatistical Practice. Doctoral dissertation. University of Alberta (2015) |

[43] | Liu, Z., Reynolds, A.C.: An SQP-Filter Algorithm with an Improved Stochastic Gradient for Robust Life-Cycle Optimization Problems with Nonlinear Constraints. Society of Petroleum Engineers (2019). doi:10.2118/193925-MS |

[44] | McLennan, J.A.: Local ranking of geostatistical realizations for flow simulation. University of Alberta, Edmonton, AB.: Technical Report 114, CCG Annual Report 7 (2005) |

[45] | Naidu, S.L.: Neural Network Surrogate Model for Multidisciplinary Design Optimization. M. Tech. Dissertation, Indian Institute of Technology (2004) |

[46] | Perrone, A., Rossa, E.D.: Optimizing reservoir life-cycle production under uncertainty: a robust ensemble-based methodology. SPE Reservoir Characterisation and Simulation Conference and Exhibition (2015). doi:10.2118/175570-MS |

[47] | Pinto, J.W.O., Tueros, J.A.R., Horowitz, B., Silva, S.M.B., Willmersdorf, R. B.: Gradient-free strategies to robust well control optimization. In EAGE/TNO Workshop on OLYMPUS Field Development Optimization (2018). doi:10.3997/2214-4609.201802299 |

[48] | Powel, M.J.D.: Algorithms for Nonlinear Constraints That Use Lagrangian Function. Math. Programming, vol. 14, Heidelberg, Germany, pp. 224-248 (1978) |

[49] | Moraes, RJ; Fonseca, RM; Helici, MA; Heemink, AW; Jansen, JD, An efficient robust optimization workflow using multiscale simulation and stochastic gradients, J. Pet. Sci. Eng., 172, 247-258, 0920-4105 (2019) |

[50] | Sayarpour, M.; Zuluaga, E.; Kabir, CS; Lake, LW, The use of capacitance-resistive models for rapid estimation of waterflood performance and optimization, J. Pet. Sci. Eng., 69, 3-4, 227-238 (2009) |

[51] | Sorek, N.; Gildin, E.; Boukouvala, F.; Beykal, B.; Floudas, CA, Dimensionality reduction for production optimization using polynomial approximations, Comput. Geosci., 21, 2, 247-266 (2017) |

[52] | Tueros, JAR; Horowitz, B.; Willmersdorf, R.; Oliveira, D., Non-distance-based localization techniques for ensemble-based waterflooding optimization, J. Pet. Sci. Eng., 170, 440-452 (2018) |

[53] | Tueros, J.A.R., Horowitz, B., Willmersdorf, R., Oliveira, D.: Refined Ensemble-Based Waterflooding Optimization Subject to Field-Wide Constraints. Presented at 16th European Conference on the Mathematics of Oil Recovery (ECMOR XVI). Barcelona (2018). doi:10.3997/2214-4609.201802210 · Zbl 1434.86008 |

[54] | Van Essen, G., Zandvliet, M., Van den Hof, P., Bosgra, O., Jansen, J. D.: Robust waterflooding optimization of multiple geological scenarios. SPE J., 14(01), 202-210 (2009) |

[55] | Vanderplaats, G.N.: Numerical optimization techniques for engineering design. Vanderplaats Research and Development, Incorporated (2001) · Zbl 0613.90062 |

[56] | Weber, D.: The Use of Capacitance-Resistance Models to Optimize Injection Allocation and Well Location in Water Floods. The University of Texas at Austin Ph. D dissertation (2009) |

[57] | Wild, SM; Regis, RG; Shoemaker, CA, ORBIT: optimization by radial basis function interpolation in trust-regions, SIAM J. Sci. Comput., 30, 6, 3197-3219 (2008) · Zbl 1178.65065 |

[58] | Yang, C., Card, C., Nghiem, L.X., Fedutenko, E.: Robust optimization of SAGD operations under geological uncertainties. SPE Reservoir Simulation Symposium (2011) |

[59] | Yasari, E.; Pishvaie, MR; Khorasheh, F.; Salahshoor, K.; Kharrat, R., Application of multi-criterion robust optimization in water-flooding of oil reservoir, J. Pet. Sci. Eng., 109, 1-11 (2013) |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.