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Abstract

Summary

Prior to any estimation process of channelized reservoirs, in the context of an Assisted History Matching method, the parameterization of facies fields is a necessary task. The parameterization of channelized reservoirs consists of defining a numerical field (parameter field) so that a projection function recovers the facies field from the parameter field. Mostly, the dimension of parameter field is equal to the dimension of reservoir domain. The issue of dimensionality is becoming relevant when the history matching method is applied, especially due to the tremendous number of parameters involved in the estimation process of the channelized reservoirs. In addition, one of the most important issue encountered is the loss of the multi-point geostatistical properties in the updates (channel continuity). In this study, we start from an initial parameterization of the channelized fields and infer from it a low-dimensional parameterization obtained after a high order singular value decomposition of a tensor built with the parameter fields. We show how the facies fields are fully characterized by a linear combination of a small number of coefficients with “basis functions”. The decomposition is followed by a truncation so that we keep the relevant information from the channel continuity perspective. This new parameterization is further introduced in the estimation process of facies fields, using the ensemble smoother with multiple data assimilation (ES-MDA), updating the coefficients of decomposition. For a fair assessment of the parameterization, we perform a comparison of the results with those obtained by applying the traditional singular value decomposition and the original parameterization. The comparison is done from the perspective of multipoint geostatistical characteristics of the updates and predictions (oil and water rates). We show that the new parameterization is able to better keep the multipoint geostatistical structure in the updates than the other two parameterizations, while the prediction capabilities are the same.

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/content/papers/10.3997/2214-4609.201802236
2018-09-03
2024-04-24

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References

  1. Afra, S. and Gildin, E.
    [2016] Tensor based geology preserving reservoir parameterization with Higher Order Singular Value Decomposition (HOSVD).Computers & Geosciences, 94, 110 – 120.
     [Google Scholar]
  2. Bergqvist, G. and Larsson, E.
    [2010] Higher-Order Singular Value Decomposition: Theory and an Application.IEEE SIGNAL PROCESSING MAGAZINE, 27(3), 151–154.
     [Google Scholar]
  3. Caers, J. and Zhang, T.
    [2004] Multiple-point geostatistics: a quantitative vehicle forintegrating geologic analogs into multiple reservoir models.
     [Google Scholar]
  4. De Lathauwer, L., De Moor, B. and Vandewalle, J.
    [2000] A Multilinear Singular Value Decomposition.SIAM Journal on Matrix Analisys and Applications, 21(4), 1253 – 1278.
     [Google Scholar]
  5. Deutsch, C.V. and Wang, L.
    [1996] Hierarchical object-based stochastic modeling of fluvial reservoirs.Mathematical Geology, 28(7), 857–880.
     [Google Scholar]
  6. Emerick, A.A.
    [2017] Investigation on Principal Component Analysis Parameterizations for History Matching Channelized Facies Models with Ensemble-Based Data Assimilation.Mathematical Geo-sciences, 49(1), 85–120. 10.1007/s11004‑016‑9659‑5.
     https://doi.org/10.1007/s11004-016-9659-5 [Google Scholar]
  7. Emerick, A.A. and Reynolds, A.C.
    [2013] Ensemble smoother with multiple data assimilation.Computers & Geosciences, 55, 3 – 15. Http://dx.doi.org/10.1016/j.cageo.2012.03.011.
     [Google Scholar]
  8. Evensen, G.
    [2003] The ensemble Kalman filter: Theoretical formulation and practical implementation.Ocean dynamics, 53(4), 343–367.
     [Google Scholar]
  9. Golmohammadia, A., Khaninezhad, M.R. and Jafarpour, B.
    [2018] Pattern-Based Calibration of Complex Subsurface Flow Models against Dynamic Response Data.Advances in Water Resources.https://doi.org/10.1016/j.advwatres.2018.04.007.
     [Google Scholar]
  10. Hanea, R., Ek, T. and Sebacher, B.
    [2015] Consistent Joint Updates of Facies and Petrophysical Heterogeneities Using an Ensemble Based Assisted History Matching. In: Petroleum Geostatistics, 2015.EAGE. Doi:10.3997/2214‑4609.201413598.
     https://doi.org/10.3997/2214-4609.201413598 [Google Scholar]
  11. Insuasty, E., Van den Hof, P., Weiland, S. and Jansen, J.
    [2017] Low-Dimensional Tensor Representations for the Estimation of Petrophysical Reservoir Parameters. In: SPE Reservoir Simulation Conference, SPE-182707-MS. SPE, Society of Petroleum Engineers. https://doi.org/10.2118/182707-MS.
     [Google Scholar]
  12. Jafarpour, B.
    [2011] Wavelet reconstruction of geologic facies from nonlinear dynamic flow measurements.Geoscience and Remote Sensing, IEEE Transactions on, 49(5), 1520–1535.
     [Google Scholar]
  13. Jafarpour, B. and McLaughlin, D.B.
    [2008] History matching with an ensemble Kalman filter and discrete cosine parameterization.Computational Geosciences, 12(2), 227–244.
     [Google Scholar]
  14. Khaninezhad, M., Golmohammadi, A. and Jafarpour, B.
    [2018] Discrete Regularization for Calibration of Geologic Facies Against Dynamic Flow Data.Water Resources Research.Https://doi.org/10.1002/2017WR022284.
     [Google Scholar]
  15. Khaninezhad, M.M., Jafarpour, B. and Li, L.
    [2012] Sparse geologic dictionaries for subsurface flow model calibration: Part I. Inversion formulation.Advances in Water Resources, 39, 106 – 121.
     [Google Scholar]
  16. Remy, N.
    [2005] SGeMS: the stanford geostatistical modeling software, a tool for new algorithms development.Geostatistics Banff 2004, 865–871.
     [Google Scholar]
  17. Sarma, P., Chen, W.H. et al.
    [2009] Generalization of the Ensemble Kalman Filter using kernels for non-gaussian Random Fields. In: SPE Reservoir Simulation Symposium.Society of Petroleum Engineers.
     [Google Scholar]
  18. Sarma, P., Durlofsky, L.J. and Aziz, K.
    [2008] Kernel principal component analysis for efficient, differentiate parameterization of multipoint geostatistics.Mathematical Geosciences, 40(1), 3–32.
     [Google Scholar]
  19. Sebacher, B., Stordal, A. and Hanea, R.
    [2015] Bridging Multi Point Statistics and Truncated Gaussian Fields for Improved Estimation of Channelized Reservoirs with Ensemble Methods.Computational Geosciences, DOI:10.1007/s10596‑014‑9466‑3, 19(2), 341–369.
     https://doi.org/10.1007/s10596-014-9466-3 [Google Scholar]
  20. [2016] Complex geology estimation using the iterative adaptive Gaussian mixture filter.Computational Geosciences, DOI 10.1007/s10596‑015‑9553‑0, 20(1), 133–148.
     https://doi.org/10.1007/s10596-015-9553-0 [Google Scholar]
  21. Strebelle, S.
    [2002] Conditional simulation of complex geological structures using multiple-point statistics.Mathematical Geology, 34(1), 1–21.
     [Google Scholar]
  22. Tahmasebi, P., Sahimi, M. and Shirangi, M.
    [2018] Rapid Learning-Based and Geologically Consistent History Matching.Transport in Porous Media, 122(2), 279 – 304.
     [Google Scholar]
  23. Tavakoli, R. and Reynolds, A.C.
    [2011] Monte Carlo simulation of permeability fields and reservoir performance predictions with SVD parameterization in RML compared with EnKF.Computational Geosciences, 15(1), 99–116. 10.1007/s10596‑010‑9200‑8.
     https://doi.org/10.1007/s10596-010-9200-8 [Google Scholar]
  24. Tene, M.
    [2013] Ensemble-Based History Matching forcChannelized Petroleum Reservoirs.MSc Thesis Applied Mathematics, Delft University of Technology.
     [Google Scholar]
  25. Vo, H.X. and Durlofsky, L.J.
    [2014] A New Differentiable Parameterization Based on Principal Component Analysis for the Low-Dimensional Representation of Complex Geological Models.Mathematical Geosciences, 46(7), 775–813.
     [Google Scholar]
  26. [2016] Regularized kernel PCA for the efficient parameterization of complex geological models.Journal of Computational Physics, 322, 859 – 881.
     [Google Scholar]
  27. Zhang, Y., Oliver, D., Chen, Y. and Skaug, H.
    [2015] Data Assimilation by Use of the Iterative Ensemble Smoother for 2D Facies Models.SPE Journal, 20(1), 169–185.
     [Google Scholar]
  28. Zhao, Y., Forouzanfar, F. and . Reynold, A.C.
    [2016] History matching of multi-facies channelized reservoirs using ES-MDA with common basis DCT.Computational Geosciences, 1–22. 10.1007/s10596‑016‑9604‑1.
     https://doi.org/10.1007/s10596-016-9604-1 [Google Scholar]
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Channelized Reservoir Estimation Using A Low Dimensional Parameterization Based On High Order Singular Value Decomposition
Conference Proceedings 2018, 1 (2018); https://doi.org/10.3997/2214-4609.201802236
/content/papers/10.3997/2214-4609.201802236
/content/papers/10.3997/2214-4609.201802236
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