Abstract
A Derivative-Free Trust-Region (DFTR) algorithm is proposed to solve the robust well control optimization problem under geological uncertainty. Derivative-Free (DF) methods are often a practical alternative when gradients are not available or are unreliable due to cost function discontinuities, e.g., caused by enforcement of simulation-based constraints. However, the effectiveness of DF methods for solving realistic cases is heavily dependent on an efficient sampling strategy since cost function calculations often involve time-consuming reservoir simulations. The DFTR algorithm samples the cost function space around an incumbent solution and builds a quadratic polynomial model, valid within a bounded region (the trust-region). A minimization of the quadratic model guides the method in its search for descent. Because of the curvature information provided by the model-based routine, the trust-region approach is able to conduct a more efficient search compared to other sampling methods, e.g., direct-search approaches. DFTR is implemented within FieldOpt, an open-source framework for field development optimization, and is tested in the Olympus benchmark against two other types of methods commonly applied to production optimization: a direct-search (Asynchronous Parallel Pattern Search) and a population-based (Particle Swarm Optimization). Current results show that DFTR has improved performance compared to the model-free approaches. In particular, the method presented improved convergence, being capable to reach solutions with higher NPV requiring comparatively fewer iterations. This feature can be particularly attractive for practitioners who seek ways to improve production strategies while using an ensemble of full-fledged models, where good convergence properties are even more relevant.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Baumann, E.J., Dale, S.I., Bellout, M.C.: FieldOpt: A powerful and effective programming framework tailored for field development optimization. Comput. Geosci. 135(104), 379 (2020)
Brouwer, D.R., Jansen, J.D.: Dynamic optimization of waterflooding with smart wells using optimal control theory. SPE J. 9(04), 391–402 (2004)
Bukshtynov, V., Volkov, O., Durlofsky, L.J., Aziz, K.: Comprehensive framework for gradient-based optimization in closed-loop reservoir management. Comput. Geosci. 19(4), 877–897 (2015)
Capolei, A., Suwartadi, E., Foss, B., Jørgensen, J.B.: Waterflooding optimization in uncertain geological scenarios. Comput. Geosci. 17(6), 991–1013 (2013)
Chen, C., Li, G., Reynolds, A.: Robust constrained optimization of short- and long-term net present value for closed-loop reservoir management. SPE J. 17(3) (2012)
Codas, A., Foss, B., Camponogara, E.: Output-constraint handling and parallelization for oil-reservoir control optimization by means of multiple shooting. SPE J. 20(4), 856–871 (2015)
Conn, A.R., Gould, N.I.M., Toint, P.L.: Trust Region Methods. Society for Industrial and Applied Mathematics (SIAM) and Mathematical Programming Society (MPS) (2000)
Conn, A.R., Scheinberg, K., Toint, P.L.: Recent progress in unconstrained nonlinear optimization without derivatives. Math. Program. 79(1-3), 397–414 (1997)
Conn, A.R., Scheinberg, K., Vicente, L.N.: Geometry of interpolation sets in derivative free optimization. Math. Program. 111(1-2), 141–172 (2008)
Conn, A.R., Scheinberg, K., Vicente, L.N.: Introduction to Derivative-Free Optimization. Society for Industrial and Applied Mathematics (SIAM) and Mathematical Programming Society (MPS) (2009)
Datta-Gupta, A., Alhuthali, A.H.H., Yuen, B., Fontanilla, J.: Field applications of waterflood optimization via optimal rate control with smart wells. SPE Reserv. Eval. Eng. 13(03), 406–422 (2010)
Dehdari, V., Oliver, D.S.: Sequential quadratic programming for solving constrained production optimization–case study from brugge field. SPE J. 17(03), 874–884 (2012)
Echeverría Ciaurri, D., Isebor, O., Durlofsky, L.: Application of derivative-free methodologies to generally constrained oil production optimization problems. Procedia Comput. Sci. 1(1), 1301–1310 (2010)
van Essen, G., Van den Hof, P., Jansen, J.D.: Hierarchical long-term and short-term production optimization. SPE J. 16(01), 191–199 (2011)
Fonseca, R., Rossa, E.D., Emerick, A., Hanea, R., Jansen, J.: Overview of the olympus field development optimization challenge. In: ECMOR XVI - 16th European Conference on the Mathematics of Oil Recovery, EAGE, pp 1–10 (2018)
G., K.T., Michael, L.R., Virginia, T.: Optimization by direct search: New perspectives on some classical and modern methods. SIAM Rev. 45(3), 385–482 (2003)
GeoQuest, S.: Eclipse reservoir simulator. Man. Tech. Descr. Houston TX (2014)
Giuliani, C.M.: Contributions to derivative-free optimization: an exact-penalty method and decompositions for distributed control. Ph.D. thesis, Universidade Federal de Santa Catarina. https://bu.ufsc.br/teses/PEAS0331-T.pdf(2019)
Giuliani, C.M., Camponogara, E., Conn, A.R.: A derivative-free exact penalty algorithm: Basic ideas, convergence theory and computational studies. To appear in Computational and Applied Mathematics (2021)
Hasan, A., Gunnerud, V., Foss, B., Teixeira, A.F., Krogstad, S.: Decision analysis for long-term and short-term production optimization applied to the voador field. In: Proc. of SPE Reservoir Characterization and Simulation Conference and Exhibition. Society of Petroleum Engineers, pp 16–18 (2013)
Hough, P.D., Kolda, T.G., Torczon, V.J.: Asynchronous parallel pattern search for nonlinear optimization. SIAM J. Sci. Comput. 23(1), 134–156 (2001)
Isebor, O.J., Echeverría Ciaurri, D., Durlofsky, L.J.: Generalized field-development optimization with derivative-free procedures. SPE J. 19(5) (2014)
Jansen, J.D.: Adjoint-based optimization of multi-phase flow through porous media - a review. Comput. Fluids 46(1), 40–51 (2011)
Jansen, J.D., Brouwer, R., Douma, S.G.: Closed loop reservoir management. In: SPE Reservoir Simulation Symposium. Society of Petroleum Engineers (2009)
Kourounis, D., Durlofsky, L.J., Jansen, J.D., Aziz, K.: Adjoint formulation and constraint handling for gradient-based optimization of compositional reservoir flow. Comput. Geosci. 18(2), 117–137 (2014)
Kraaijevanger, J.F.B.M., Egberts, P.J.P., Valstar, J.R., Buurman, H.W.: Optimal waterflood design using the adjoint method. SPE Reservoir Simulation Symposium p. 15. SPE-105764-MS (2007)
Nocedal, J., Wright, S.: Numerical Optimization. Springer, New York (2006). https://doi.org/10.1007/978-0-387-40065-5
Nwankwor, E., Nagar, A.K., Reid, D.: Hybrid differential evolution and particle swarm optimization for optimal well placement. Comput. Geosci. 17(2), 249–268 (2013)
Pardalos, P.M., Vavasis, S.A.: Quadratic programming with one negative eigenvalue is NP-hard. J. Glob. Optim. 1(1), 15–22 (1991)
Powell, M.J.D.: Least frobenius norm updating of quadratic models that satisfy interpolation conditions. Math. Program. 100(1), 183–215 (2004)
Sampaio, P.R., Toint, P.L.: Numerical experience with a derivative-free trust-funnel method for nonlinear optimization problems with general nonlinear constraints. Optim. Methods Softw. 31(3), 511–534 (2016)
Sarma, P., Durlofsky, L.J., Aziz, K., Chen, W.H.: Efficient real-time reservoir management using adjoint-based optimal control and model updating. Comput. Geosci. 10(1), 3–36 (2006)
Scheinberg, K., Toint, P.L.: Self-correcting geometry in model-based algorithms for derivative-free unconstrained optimization. SIAM J. Optim. 20(6), 3512–3532 (2010)
Silva, T.L., Codas, A., Stanko, M., Camponogara, E., Foss, B., et al: Network-constrained production optimization by means of multiple shooting. SPE Reserv. Eval. Eng. 22(2), 709–733 (2019)
Suwartadi, E., Krogstad, S., Foss, B.: Nonlinear output constraints handling for production optimization of oil reservoirs. Comput. Geosci. 16(2), 499–517 (2011)
Volkov, O., Bellout, M.C.: Gradient-based production optimization with simulation-based economic constraints. Comput. Geosci. 21(5), 1385–1402 (2017)
Volkov, O., Voskov, D.V.: Effect of time stepping strategy on adjoint-based production optimization. Comput. Geosci. 20(3), 707–722 (2016)
Wang, C., Li, G., Reynolds, A.C.: Production optimization in closed-loop reservoir management. SPE J. 14(3), 506–523 (2010)
Yan, X., Reynolds, A.C.: Optimization algorithms based on combining FD approximations and stochastic gradients compared with methods based only on a stochastic gradient. SPE J. 19(5) (2014)
Acknowledgements
This research is a part of BRU21 – NTNU Research and Innovation Program on Digital and Automation Solutions for the Oil and Gas Industry (www.ntnu.edu/bru21). The authors acknowledge funding from the Research Council of Norway (INTPART – Brazil-Norway Production Optimization Consortium - Phase 2, project number 286801).
Funding
Open access funding provided by NTNU Norwegian University of Science and Technology (incl St. Olavs Hospital - Trondheim University Hospital).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Silva, T.L., Bellout, M.C., Giuliani, C. et al. Derivative-free trust region optimization for robust well control under geological uncertainty. Comput Geosci 26, 329–349 (2022). https://doi.org/10.1007/s10596-022-10132-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10596-022-10132-y