1887

Abstract

Summary

A systematic framework, involving flow simulation and model selection at many fidelity (resolution) levels, is introduced to accurately quantify the impact of geological xincertainty on output quantities of interest (Qols). The methodology considers large numbers of realizations (0(1000) in the cases presented), though very few (0(10)) simulations are performed at the highest resolutions. We proceed from coarser to finer resolution levels, and at each stage simulation results are used to select a subset of realizations to simulate at the next (higher) fidelity level. Models are constructed at all resolution levels through upscaling of the underlying fine-scale realizations. A global transmissibility upscaling procedure is applied for this purpose. Approximate cumulative distribution functions (CDFs) are constructed for all Qols considered. The Qol values themselves are always computed at the finest scale, but corresponding percentile values are determined using results at a ‘rank-preserving’ fidelity level. Detailed results are presented for oil-water flow in a channelized system. Simulations at seven different fidelity levels are used, and eight Qols are evaluated. Results for the example considered demonstrate accurate reconstruction of fine-scale CDFs for all Qols. with a speedup factor of 12 relative to performing all simulations on the fine scale.

Loading

Article metrics loading...

/content/papers/10.3997/2214-4609.201802224
2018-09-03
2025-01-23
Loading full text...

Full text loading...

References

  1. Aliyev, E.
    [2015] Multilevel field development optimization under uncertainty using a sequence of up-scaled models. Ph.D. thesis, Stanford University.
    [Google Scholar]
  2. Aliyev, E. and Durlofsky, L.J.
    [2015] Multilevel field-development optimization using a sequence of up-scaled models. Paper SPE-173198-MS, presented at SPE Reservoir Simulation Symposium, Houston, Texas, 23–25 February.
    [Google Scholar]
  3. [2017] Multilevel field development optimization under uncertainty using a sequence of upscaled models. Mathematical Geosciences, 49(3), 307–339.
    [Google Scholar]
  4. Ballin, P.R., Journel, A.G. and Aziz, K.
    [1992] Prediction of uncertainty in reservoir performance forecast. Journal of Canadian Petroleum Technology, 31(4), 52–62.
    [Google Scholar]
  5. Castro, S.A.
    [2007] A probabilistic approach to jointly integrate 3D/4D seismic, production data and geological information for building reservoir models. Ph.D. thesis, Stanford University.
    [Google Scholar]
  6. Chen, Y. and Durlofsky, L.J.
    [2008] Ensemble-level upscaling for efficient estimation of fine-scale pro-duction statistics. SPE Journal, 13(4), 26–28.
    [Google Scholar]
  7. Chen, Y., Mallison, B.T. and Durlofsky, L.J.
    [2008] Nonlinear two-point flux approximation for modeling full-tensor effects in subsurface flow simulations. Computational Geosciences, 12, 317–335.
    [Google Scholar]
  8. Durlofsky, L.J. and Chen, Y.
    [2012] Uncertainty quantification for subsurface flow problems using coarse-scale models. In: Numerical Analysis of Multiscale Problems, Lecture Notes in Computational Science and Engineering, Springer, 163–202.
    [Google Scholar]
  9. Giles, M.B.
    [2008] Multilevel Monte Carlo path simulation. Operations Research, 56(3), 607–617.
    [Google Scholar]
  10. Giles, M.B., Nagapetyan, T. and Ritter, K.
    [2015] Multilevel Monte Carlo approximation of distribution functions and densities. Journal of Uncertainty Quantification, 3(1), 267–295.
    [Google Scholar]
  11. Gilman, J.R., Meng, H.Z., Uland, M.J., Dzurman, P.J. and Cosic, S.
    [2013] Statistical ranking of stochastic geomodels using streamline simulation: A field application. Paper SPE-77374-MS, presented at SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 29 September-2 October.
    [Google Scholar]
  12. Grujic, O., Menafoglio, A., Yang, G. and Caers, J.
    [2018] Cokriging for multivariate Hilbert space valued random fields: application to multi-fidelity computer code emulation. Stochastic Environmental Research and Risk Assessment, 32(7), 1955–1971.
    [Google Scholar]
  13. Li, H. and Durlofsky, L.J.
    [2016] Ensemble level upscaling for compositional flow simulation. Computational Geosciences, 20(3), 525–540.
    [Google Scholar]
  14. McLennan, J. and Deutsch, C.
    [2005] Selecting geostatistical realizations by measures of connectivity. Paper SPE-98168-MS, presented at SPE International Thermal Operations and Heavy Oil Symposium, Calgary, Alberta, Canada, 1–3 November.
    [Google Scholar]
  15. Müller, F., Jenny, P. and Meyer, D.W.
    [2013] Multilevel Monte Carlo for two phase flow and Buckley-Leverett transport in random heterogeneous porous media. Journal of Computational Physics, 250, 685–702.
    [Google Scholar]
  16. [2016] Parallel multilevel Monte Carlo for two-phase flow and transport in random heterogeneous porous media with sampling error and discretization error balancing. SPE Journal, 21(6), 2027–2037.
    [Google Scholar]
  17. Remy, N., Boucher, A. and Wu, J.
    [2009] Applied Geostatistics with SGeMS: A User’s Guide.Cambridge University Press.
    [Google Scholar]
  18. Sarma, P., Chen, W.H. and Xie, J.
    [2013] Selecting representative models from a large set of models. Paper SPE-163671-MS, presented at SPE Reservoir Simulation Symposium, The Woodlands, Texas, 18-20 February.
    [Google Scholar]
  19. Scheidt, C., Caers, J., Chen, Y. and Durlofsky, L.J.
    [2011] A multi-resolution workflow to generate high-resolution models constrained to dynamic data. Computational Geosciences, 15(3), 545–563.
    [Google Scholar]
  20. Strebelle, S.
    [2002] Conditional simulation of complex geological structures using multiple-point statistics. Mathematical Geology, 34(1), 1–21.
    [Google Scholar]
  21. Trehan, S. and Durlofsky, L.J.
    [2018] Machine-learning-based modeling of coarse-scale error, with application to uncertainty quantification. Computational Geosciences, to appear.
    [Google Scholar]
  22. Zhang, P., Pickup, G. and Christie, M.
    [2008] A new practical method for upscaling in highly heterogeneous reservoir models. SPE Journal, 13(1), 68–76.
    [Google Scholar]
  23. Zhou, Y.
    [2012] Parallel general-purpose reservoir simulation with coupled reservoir models and mul-tisegment wells. Ph.D. thesis, Stanford University.
    [Google Scholar]
/content/papers/10.3997/2214-4609.201802224
Loading
/content/papers/10.3997/2214-4609.201802224
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