1887

Abstract

Summary

Incorporating uncertainty in reservoir life-cycle optimization has been shown to achieve results of significant practical value. We introduce an automated technique for scenario reduction using clustering techniques to accelerate robust life-cycle optimization. The technique determines, based on a statistical metric, a representative subset of model realizations that correlates with the cumulative distribution function (CDF) of a quantity of interest of the full ensemble. More specifically, the proposed approach addresses the automatic determination of the appropriate number of clusters. A database of clustering results is generated by repeating the inexpensive clustering procedure with different number of clusters. This allows for the construction of a “distance” curve, which is then used to determine the appropriate number of clusters. We have applied the workflow to waterflooding optimization in two synthetic cases where geological uncertainty is characterized through an ensemble of equiprobable model realizations. The optimization based on the subset of representative model realizations obtained from the newly introduced workflow lead to almost the same objective function values compared to the optimization of the full ensemble using approximately 70% fewer simulations. Our results indicate that the proposed automated workflow provides a computationally efficient scheme for optimization under uncertainty.

Loading

Article metrics loading...

/content/papers/10.3997/2214-4609.201802179
2018-09-03
2024-04-24
Loading full text...

Full text loading...

References

  1. Armstrong, M., Ndiaye, A., Razanatsimba, R. and Galli, A.
    [2013] Scenario reduction applied to geostatistical simulations. Mathematical Geosciences, 45, 165–182.
    [Google Scholar]
  2. Barros, E., Yap, F., Insuasty, E., Van den Hof, P. and Jansen, J.
    [2016] Clustering Techniques for Value-of-information Assessment in Closed-loop Reservoir Management. In: ECMOR XV-15th European Conference on the Mathematics of Oil Recovery.
    [Google Scholar]
  3. Carreira-Perpinan, M.A.
    [2015] A review of mean-shift algorithms for clustering. arXiv 1503.00687.
    [Google Scholar]
  4. Chen, B., Reynolds, A.C. et al.
    [2016] Ensemble-based optimization of the water-alternating-gas-injection process. SPE Journal, 21(03), 786–798.
    [Google Scholar]
  5. Chen, Y., Oliver, D.S. and Zhang, D.
    [2009] Efficient Ensemble-Based Closed-Coop Production Optimization. SPEJ, 14(04), 634–645. SPE-112873-PA. doi:10.2118/112873-PA.
    [Google Scholar]
  6. Dubes, R.
    [1987] How many clusters are best? An experiment. Pattern Recognition, 20(6), 645–663.
    [Google Scholar]
  7. Fonseca, R., Stordal, A., Leeuwenburgh, O., Van den Hof, P. and Jansen, J.
    [2014] Robust ensemble-based multi-objective optimization. In: ECMOR XIV-14th European Conference on the mathematics of oil recovery.Sicily, Italy, 8–11 September.
    [Google Scholar]
  8. Fonseca, R.M., Chen, B., Jansen, J.D. and Reynolds, A.C.
    [2017] A stochastic simplex approximate gradient (StoSAG) for optimization under uncertainty. nternational Journal for Numerical Methods in Engineering, 109, 1756–1776. doi:10.1002/nme.5342.
    [Google Scholar]
  9. Fonseca, R.M., Kahrobaei, S.S., Van Gastel, L.J.T., Leeuwenburgh, O. and Jansen, J.D.
    [2015] Quantification of the impact of ensemble size on the quality of an ensemble gradient using principles of hypothesis testing. In: SPE Reservoir Simulation Symposium. Society of Petroleum Engineers. Texas, USA, 23–25 February 2015. SPE-173236-MS. doi:10.2118/173236-MS.
    [Google Scholar]
  10. Goutte, C., Hansen, L.K., Liptrot, M.G. and Rostrup, E.
    [2001] Feature-space clustering for fMRI metaanalysis. Human Brain Mapping, 13(3), 165–183.
    [Google Scholar]
  11. Hill, P.D.
    [1985] Kernel estimation of a distribution function. Communications in Statistics - Theory and Methods, 14(3), 605–620.
    [Google Scholar]
  12. Jansen, J.D., Bosgra, O.H. and Van den Hof, P.M.
    [2008] Model-based control of multiphase flow in subsurface oil reservoirs. Journal of Process Control, 18(9), 846–855. doi:10.1016/j.jprocont.2008.06.011.
    [Google Scholar]
  13. Jansen, J.D., Fonseca, R., Kahrobaei, S., Siraj, M., Van Essen, G. and Van den Hof, P.
    [2014] The egg model–a geological ensemble for reservoir simulation. Geoscience Data Journal, 1(2), 192–195.
    [Google Scholar]
  14. Jones, M.C., Marron, J.S. and Sheather, S.J.
    [1996] A brief survey of bandwidth selection for density estimation. Journal of the American Statistical Association, 91(433), 401–407.
    [Google Scholar]
  15. Kawamoto, T. and Kabashima, Y.
    [2017] Cross-validation estimate of the number of clusters in a network. Scientific Reports, 7(1), 1–17.
    [Google Scholar]
  16. Li, L., Jafarpour, B. and Mohammad-Khaninezhad, M.
    [2012] A simultaneous perturbation stochastic approximation algorithm for coupled well placement and control optimization under geologic uncertainty. Computational Geosciences, 17(1), 167–188.
    [Google Scholar]
  17. Liu, Z. and Forouzanfar, F.
    [2017] Ensemble clustering for efficient robust optimization of naturally fractured reservoirs. Computational Geosciences, 1–14.
    [Google Scholar]
  18. Lu, R., Forouzanfar, F. and Reynolds, A.
    [2017] An efficient adaptive algorithm for robust control optimization using StoSAG. Journal ofPetroleum Science and Engineering, 159, 314–330.
    [Google Scholar]
  19. Massey, F.J.
    [1951] The Kolgomorov-Smirnov test for goodness of fit. Journal of the American Statistical Association, 46(253), 68–78.
    [Google Scholar]
  20. Moraes, R., Fonseca, R.M., Helici, M., Heemink, A.W. and Jansen, J.D.
    [2017] Improving the computational efficiency of approximate gradients using a multiscale reservoir simulation framework. In: SPE Reservoir Simulation Conference. Society of Petroleum Engineers. Montgomery, Texas, USA, 20–22 February. SPE-182620-MS.
    [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. In: Proceedings of the 17th European Symposium on Improved Oil Recovery. St. Petersburg, Russia, 16 April-18 April.
    [Google Scholar]
  22. Rodrigues, J.R.P.
    [2006] Calculating derivatives for automatic history matching. Computational Geosciences, 10(1), 119–136.
    [Google Scholar]
  23. Rousseeuw, P.J.
    [1987] Silhouettes: A graphical aid to the interpretation and validation of cluster analysis. Journal of Computational and Applied Mathematics, 20, 53–65.
    [Google Scholar]
  24. Shirangi, M. and Durlofsky, L.
    [2015] Closed-loop field development under uncertainty by use of optimization with sample validation. SPE Journal, 20, 908–922.
    [Google Scholar]
  25. [2016] A general method to select representative models for decision making and optimization under uncertainty. Computers and Geosciences, 96, 109–123.
    [Google Scholar]
  26. Silverman, B.
    [1986] Density estimation for statistics and data analysis. Chapman and Hall.
    [Google Scholar]
  27. Stordal, A.S., Szklarz, S.P. and Leeuwenburgh, O.
    [2016] A theoretical look at Ensemble-based optimization in reservoir management. Mathematical Geosciences, 48(4), 399–417. doi:10.1007/s11004-015-9598-6.
    [Google Scholar]
  28. Strang, G.
    [1993] Introduction to linear algebra. Wellesley-Cambridge PressWellesley, MA.
    [Google Scholar]
  29. The MathWorks Inc
    . [2017] MATLAB Optimization Toolbox. The MathWorks Inc., Natick, MA, USA.
    [Google Scholar]
  30. The Open Porous Media Initiative
    [2017] Open Porous Media – OPM.
    [Google Scholar]
  31. Theodoridis, S. and Koutroumbas, K.
    [2009] Pattern Recognition. Academic Press Elsevier, San Diego, USA.
    [Google Scholar]
  32. Van Essen, G., Zandvliet, M., Van den Hof, P., Bosgra, O., Jansen, J.D. et al.
    [2009] Robust water-flooding optimization of multiple geological scenarios. SPEJ, 14(01), 202–210. SPE-102913-PA. doi:10.2118/102913-PA.
    [Google Scholar]
  33. Yang, C., Card, C., Nghiem, L. and Fedutenko, E.
    [2011] Robust Optimization of SAGD Operations under Geological Uncertainties. In: SPE Reservoir Simulation Symposium. Society of Petroleum Engineers. The Woodlands, USA, 21–23 February. SPE-141676-MS.
    [Google Scholar]
http://instance.metastore.ingenta.com/content/papers/10.3997/2214-4609.201802179
Loading
/content/papers/10.3997/2214-4609.201802179
Loading

Data & Media loading...

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error