Computational Geosciences

, Volume 18, Issue 3–4, pp 449–461 | Cite as

Ensemble-based hierarchical multi-objective production optimization of smart wells

  • R. M. Fonseca
  • O. Leeuwenburgh
  • P. M. J. Van den Hof
  • J. D. Jansen
ORIGINAL PAPER
First Online:
Received:
Accepted:

Abstract

In an earlier study, two hierarchical multi-objective methods were suggested to include short-term targets in life-cycle production optimization. However, this earlier study has two limitations: (1) the adjoint formulation is used to obtain gradient information, requiring simulator source code access and an extensive implementation effort, and (2) one of the two proposed methods relies on the Hessian matrix which is obtained by a computationally expensive method. In order to overcome the first of these limitations, we used ensemble-based optimization (EnOpt). EnOpt does not require source code access and is relatively easy to implement. To address the second limitation, we used the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm to obtain an approximation of the Hessian matrix. We performed experiments in which water flood was optimized in a geologically realistic multilayer sector model. The controls were inflow control valve settings at predefined time intervals. Undiscounted net present value (NPV) and highly discounted NPV were the long-term and short-term objective functions used. We obtained an increase of approximately 14 % in the secondary objective for a decrease of only 0.2–0.5 % in the primary objective. The study demonstrates that ensemble-based hierarchical multi-objective optimization can achieve results of practical value in a computationally efficient manner.

Keywords

Ensemble optimization Multi-objective optimization Smart wells Hierarchical optimization Null-space BFGS 
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Brouwer, D.R., Jansen, J.D.: Dynamic optimization of water flooding with smart wells using optimal control theory. SPE J 9(4), 391–402 (2004)CrossRefGoogle Scholar
  2. 2.
    Chen, C., Li, G., Reynolds, A.C.: Robust constrained optimization of short- and long-term net present value for closed-loop reservoir management. SPE J 17(3), 849–864 (2012)CrossRefGoogle Scholar
  3. 3.
    Chen, Y.: Efficient ensemble based reservoir management. PhD thesis, University of Oklahoma (2008)Google Scholar
  4. 4.
    Chen, Y., Oliver, D.S., Zhang, D.: Efficient ensemble-based closed-loop production optimization. SPE J 14(4), 634–645 (2009)CrossRefGoogle Scholar
  5. 5.
    Dehdari, V., Oliver, D.S.: Sequential quadratic programming for solving constrained production optimization—case study from Brugge field. SPE J 17(3), 874–884 (2012)CrossRefGoogle Scholar
  6. 6.
  7. 7.
    Hansen, N.: The CMA evolution strategy: a comparing review. In: Lozano, J. A., Larranaga, P., Inza, I., Bengoetxea, E. (eds.) Towards a new evolutionary computation. Advances on estimation of distribution algorithms, pp 75–102. Springer, Berlin (2006)Google Scholar
  8. 8.
    Jansen, J.D., Douma, S.G., Brouwer, D.R., Van den Hof, P.M.J., Bosgra, O.H., Heemink, A.W.: Closed-loop reservoir management. Paper SPE 119098 presented at 2009 SPE Reservoir Simulation Symposium. The Woodlands, Texas (2009)Google Scholar
  9. 9.
    Jansen, J.D.: Adjoint-based optimization of multiphase flow through porous media—a review. Comput. Fluids 46(1), 40–51 (2011)CrossRefGoogle Scholar
  10. 10.
    Lorentzen, R.J., Berg, A.M., Naevdal, G., Vefring, E.H.: A new approach for dynamic optimization of waterflooding problems. Paper SPE 99690 Presented at the SPE Intelligent Energy Conference and Exhibition, Amsterdam (2006)Google Scholar
  11. 11.
    Nocedal, J., Wright, S.J.: Numerical optimization. 2nd edn. Springer, New York (2006)Google Scholar
  12. 12.
    Oliver, D.S., Reynolds, A.C., Liu, N.: Inverse theory for petroleum reservoir characterization and history matching. Cambridge University Press, Cambridge (2008)CrossRefGoogle Scholar
  13. 13.
    Sarma, P., Aziz, K., Durlofsky, L.J.: Implementation of adjoint solution for optimal control of smart wells. Paper SPE 92864 Presented at the SPE Reservoir Simulation Symposium, The Woodlands, Texas (2005)Google Scholar
  14. 14.
    Sarma, P., Chen, W.H., Durlofsky, L.J., Aziz, K.: Production optimization with adjoint models under nonlinear control-state path inequality constraints. SPE Reserv. Eng. Eval 11(2), 326–339 (2006)CrossRefGoogle Scholar
  15. 15.
    Spall, J.C.: Implementation of the simultaneous perturbation algorithm for stochastic optimization. IEEE Trans. Aerosp. Electron. Syst 34(3), 817–823 (1998)CrossRefGoogle Scholar
  16. 16.
    Strang, G.: Linear algebra and its applications. 4th edn. Thomson Brooks/Cole, Pacific Grove (2006)Google Scholar
  17. 17.
    Suwartadi, E., Krogstad, S., Foss, B.: Nonlinear output constraints handling for production optimization of oil reservoirs. Comput. Geosci 16(2), 499–517 (2012)CrossRefGoogle Scholar
  18. 18.
    Van Essen, G.M., Van den Hof, P.M.J., Jansen, J.D.: Hierarchical long and short-term production optimization. SPE J 16(1), 191–199 (2011)CrossRefGoogle Scholar
  19. 19.
    Van Essen, G.M., Van den Hof, P.M.J., Jansen, J.D.: Determination of lower and upper bounds of predicted production from history-matched models. In: Proceedings of 12th European Conference on the Mathematics of Oil Recovery ECMOR XII, Oxford (2010)Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • R. M. Fonseca
    • 1
  • O. Leeuwenburgh
    • 2
  • P. M. J. Van den Hof
    • 3
  • J. D. Jansen
    • 1
  1. 1.Department of Geoscience and EngineeringDelft University of TechnologyDelftThe Netherlands
  2. 2.TNOUtrechtThe Netherlands
  3. 3.Department of Electrical EngineeringEindhoven University of TechnologyEindhovenThe Netherlands

Personalised recommendations