1887

Abstract

Summary

We consider life-cycle production optimization with the aid of the Ensemble Optimization (EnOpt) technique. Although the number of applications of EnOpt has increased, and the theoretical understanding, which is based on strong assumptions, has recently significantly improved, there is still ample room for further development of the underlying theory. Here we study the mathematics (or statistics) of EnOpt and show that it is a version of an already well-defined natural evolution strategy known as Gaussian Mutation. With increased focus on ensemble-based methods in reservoir history matching over the last decade, a natural description of uncertainty arises from the use of multiple realizations. Thus it is a logical step to incorporate this ensemble-based uncertainty description in life-cycle production optimization through defining the expected objective function value as the mean over all geological realizations. We show that the frequently advocated strategy of applying a different control parameter to each reservoir realization, as a means to incorporate geological uncertainty in optimization, delivers an unbiased estimate. However, it is more variance prone than the deterministic strategy of applying the entire ensemble of control parameters to each realization of reservoir models.

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2014-09-08
2024-03-28
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References

  1. Akimoto, Y., Nagata, Y., Ono, I. and Kobayashi, S.
    [2010] Biderectional relation between CMS evolution strategies and natural evolution strategies. PPSN XI, Part I, LNCS 6238, 154–163.
    [Google Scholar]
  2. Amari, S.I.
    [1998] Natural gradients works efficiently in learning. Neural Computation, 10(2), 333–339.
    [Google Scholar]
  3. Bouzarkouna, Z., Ding, D. and Auger, A.
    [2011] Well placement optimization with the covariance matrix adaptation evolution strategy and meta-models. Computational Geosciences, 1–18.
    [Google Scholar]
  4. Brouwer, D.R., Naevdal, G., Jansen, J.D., Vefring, E.H. and van Kruijsdijk, C.P.J.W.
    [2004] Improved reservoir management through optimal control and continuous model updating. SPE Annual Technical Conference and Exhibition, Houston, Texas, SPE90149.
    [Google Scholar]
  5. Chen, Y.
    [2008] Efficient Ensemble based Reservoir Management. Phd thesis, University of Oklahoma.
    [Google Scholar]
  6. Chen, Y., Oliver, D.S. and Zhang, D.
    [2009] Efficient ensemble-based closed-loop production optimization. SPE Journal, 14(4), 634–645.
    [Google Scholar]
  7. Chen, Y. and Oliver, D.S.
    [2012] Localization of ensemble-based control-setting updates for production optimization. SPE Journal, 17(1), pp. 122–136.
    [Google Scholar]
  8. Ding, Y.D.
    [2008] Optimization of well placement using evolutionary algorithms. Europec/EAGE Conference and Exhibition.
    [Google Scholar]
  9. Do, S.T. and Reynolds, A.C.
    [2013] Theoretical connections between optimization algorithms based on an approximate gradient. Computational Geosciences, 17(6), 959–973.
    [Google Scholar]
  10. Fonseca, R.M., Leeuwenburgh, O., Hof, P.V.d. and Jansen, J.D.
    [2013] Improving the ensemble optimization method through covariance matrix adaptation (cma-enopt). SPE Reservoir Simulation Symposium.
    [Google Scholar]
  11. Hansen, N. and Ostermeier, A.
    [1996] Adapting arbitrary normal mutation distributions in evolution strategies: The covariance matrix adaptation. 1996 IEEE International Conference on Evolutionary Computation, IEEE, 312–317.
    [Google Scholar]
  12. [2001] Completely derandomized self-adaptation in evolution strategies. Evolutionary computation, 9(2), 159–195.
    [Google Scholar]
  13. Hasan, A., Foss, B. and Sagatun, S.
    [2013] Optimization of oil production under gas coning conditions. Journal of Petroleum Science and Engineering, 105, 33–.
    [Google Scholar]
  14. Jansen, J.D., Brouwer, D.R., Naevdal, G. and van Kruijsdijk, C.P.J.W.
    [2004] Closed-loop reservoir management. EAGE 66th Conference & Exhibition, Paris, France, presented at Workshop “Uncertainties in production forecasts and history matching”.
    [Google Scholar]
  15. Jansen, J.
    [2011] Adjoint-based optimization of multi-phase flow through porous media-A review. Computers and Fluids, 46, 51–.
    [Google Scholar]
  16. Leeuwenburgh, O., Egberts, P.J. and Abbink, O.A.
    [2010] Ensemble methods for reservoir life-cycle optimization and well placement. SPE/DGS Saudi Arabia Section Technical Symposium and Exhibition.
    [Google Scholar]
  17. Lorentzen, R.J., Berg, A.M., Nævdal, G. and Vefring, E.H.
    [2006] A new approach for dynamic optimization of water flooding problems. SPE Intelligent Energy Conference and Exhibition, Amsterdam, The Netherlands, sPE99690.
    [Google Scholar]
  18. Lozano, J., Larranaga, P., Inza, I. and Bengoetxea, E.
    (Eds.) [2006] The CMA Evolution Strategy: A Comparing Review, Springer. 75–102.
    [Google Scholar]
  19. Nwaozo, J.
    [2006] Dynamic optimization of a water flood reservoir. Ph.D. thesis, University of Oklahoma.
    [Google Scholar]
  20. Pajonk, O., Schulze-Riegert, R., Krosche, M., Hassan, M. and Nwakile, M.M.
    [2011] Ensemble-based water flooding optimization applied to mature fields. SPE Middle East Oil and Gas Show and Conference.
    [Google Scholar]
  21. Raniolo, S., Dovera, L., Cominelli, A., Callegaro, C. and Masserano, F.
    [2013] History match and polymer injection optimization in a mature field using the ensemble kalman filter. 17th European Symposium on Improved Oil Recovery, St. Petersburg, Russia, 16–18 April2013.
    [Google Scholar]
  22. Rosenbrock, H.
    [1960] An automatic method for finding the greatest or least value of a function. The Computer Journal, 3(3), 175–184.
    [Google Scholar]
  23. Sarma, P., Durlofsky, L.J., Aziz, K. and Chen, W.H.
    [2006] Efficient real-time reservoir management using adjoint-based optimal control and model based updating. Computational Geosciences, 10, 36–.
    [Google Scholar]
  24. Schulze-Riegert, R., Bagheri, M., Krosche, M., Kueck, N. and Ma, D.
    [2011] Multiple-objective optimization applied to well path design under geological uncertainty. SPE Reservoir Simulation Symposium.
    [Google Scholar]
  25. Su, H.J. and Oliver, D.S.
    [2010] Smart well production optimization using an ensemble-based method. SPE Reservoir Evaluation & Engineering, 13(6), pp. 884–892.
    [Google Scholar]
  26. Sun, Y., Wierstra, D., Schaul, T. and Schmidhuber, J.
    [2009] Efficient natural evolution strategies. Proceedings of GECCO, 539–545.
    [Google Scholar]
  27. Tarantola, A.
    [2005] Inverse Problem Theory: Methods for Data Fit-ting and Model Parameter Estimation.
    [Google Scholar]
  28. van Essen, G.M., Zandvliet, M.J., van den Hof, P.M.J., Bosgra, O.H. and Jansen, J.D.
    [2006] Robust water-flooding optimization of multiple geological scenarios. SPE Annual Technical Conference and Exhibition, Society of Petroleum Engineers, San Antonio, Texas, USA, SPE102913.
    [Google Scholar]
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