1887

Abstract

Summary

We propose an ensemble based seismic inversion framework to estimate static and dynamic reservoir parameters such as saturation, pressure and porosity fields using seismic data. The proposed method has certain novelties, in terms of the choice of seismic data, as well as uncertainty quantification of the estimates. Further, the method uses reservoir-engineering data as the prior information (such as pressure-saturation data) from reservoir simulation model to constrain the inversion process.

Many conventional seismic inversion algorithms are deterministic in nature, and thus they pay less attention to uncertainty quantification. To quantify the uncertainties in the estimates, we adopt an iterative ensemble smoother as the inversion algorithm. Compared to the conventional deterministic inversion algorithms, this ensemble-based method is a derivative-free and non-intrusive approach, and has better capacity of uncertainty quantification. On the other hand, inverted seismic parameters, such as acoustic impedance, are often adopted as the data in inversion. In doing so, extra uncertainties may arise during the inversion processes. Here, we avoid such intermediate inversion processes by adopting amplitude versus angle (AVA) data.

To handle the big-data problem in the AVA inversion process, we adopt a wavelet based sparse representation procedure ( ). Precisely, we apply a discrete wavelet transform to the AVA data, and estimate noise in the resulting wavelet coefficients. We then use the leading wavelet coefficients above a certain threshold value as the data in inversion.

We apply the proposed framework to a 2D synthetic model for a proof-of-concept study. This reservoir model consists of three phases (water, oil and gas), and is a vertical section of a 3D Norne field model. We also test the performance of the framework in the 3D Brugge benchmark case that consists of two phases (water and oil). The numerical results from both cases indicate that the proposed framework can integrate the reservoir-engineering data as prior knowledge with seismic data, while achieving reasonably good estimates of both static and dynamic reservoir variables.

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2017-04-24
2024-04-25
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References

  1. Aanonsen, S., Nœvdal, G., Oliver, D., Reynolds, A. and Vallès, B.
    [2009] The Ensemble Kalman Filter in Reservoir Engineering: a Review. SPE Journal, 14, 393–412. SPE-117274-PA.
    [Google Scholar]
  2. Bhakta, T.
    [2015] Better estimation of pressure-saturation changes from time-lapse PP-AVO data by using non-linear optimization method. In: SEG Technical Program Expanded Abstracts 2015, Society of Exploration Geophysicists, 5456–5460.
    [Google Scholar]
  3. Bhakta, T. and Landrø, M.
    [2013] Discrimination between pressure and fluid saturation changes in compacting reservoirs using both the time-lapse amplitudes and travel time information. 75th EAGE Conference and Exhibition incorporating SPE EUROPEC 2013, Extended Abstracts.
    [Google Scholar]
  4. Bhakta, T., Luo, X. and Nœvdal, G.
    [2016] Ensemble based 4D seismic history matching using a sparse representation of AVA data. In: SEG Technical Program Expanded Abstracts 2016, Society of Exploration Geophysicists, 2961–2966.
    [Google Scholar]
  5. Chen, Y. and Oliver, D.
    [2013] Levenberg-Marquardt forms of the iterative ensemble smoother for efficient history matching and uncertainty quantification. Computational Geosciences, 17, 689–703.
    [Google Scholar]
  6. Dadashpour, M., Ciaurri, D.E., Mukerji, T., Kleppe, J. and Landrø, M.
    [2010] A derivative-free approach for the estimation of porosity and permeability using time-lapse seismic and production data. Journal of Geophysics and Engineering, 7(4), 351.
    [Google Scholar]
  7. Dadashpour, M., Landrø, M. and Kleppe, J.
    [2008] Nonlinear inversion for estimating reservoir parameters from time-lapse seismic data. Journal of Geophysics and Engineering, 5, 54.
    [Google Scholar]
  8. Domenico, S.N.
    [1974] Effect of water saturation on seismic reflectivity of sand reservoirs encased in shale. Geophysics, 39, 759–769.
    [Google Scholar]
  9. Donoho, D.L. and Johnstone, I.M.
    [1995] Adapting to unknown smoothness via wavelet shrinkage. Journal of the American Statistical Association, 90, 1200–1224.
    [Google Scholar]
  10. Donoho, D.L. and Johnstone, J.M.
    [1994] Ideal spatial adaptation by wavelet shrinkage. Biometrika, 81, 425–455.
    [Google Scholar]
  11. Emerick, A.A.
    [2014] Estimation of pressure and saturation fields from time-lapse impedance data using the ensemble smoother. Journal of Geophysics and Engineering, 11(3), 035007.
    [Google Scholar]
  12. Emerick, A.A. and Reynolds, A.C.
    [2012a] Ensemble smoother with multiple data assimilation. Computers & Geosciences, 55, 3–15.
    [Google Scholar]
  13. [2012b] History matching time-lapse seismic data using the ensemble Kalman filter with multiple data assimilations. Computational Geosciences, 16, 639–659.
    [Google Scholar]
  14. Emerick, A.A., Reynolds, A.C. et al.
    [2013] History-matching production and seismic data in a real field case using the ensemble smoother with multiple data assimilation. In: SPE Reservoir Simulation Symposium. Society of Petroleum Engineers. SPE-163675-MS.
    [Google Scholar]
  15. Engl, H.W., Hanke, M. and Neubauer, A.
    [2000] Regularization of Inverse Problems. Springer.
    [Google Scholar]
  16. Evensen, G. and van Leeuwen, P.J.
    [2000] An Ensemble Kalman Smoother for Nonlinear Dynamics. Mon. Wea. Rev., 128, 1852–1867.
    [Google Scholar]
  17. Fahimuddin, A., Aanonsen, S. and Skjervheim, J.A.
    [2010] Ensemble Based 4D Seismic History Matching-Integration of Different Levels and Types of Seismic Data. In: 72nd EAGE Conference & Exhibition.
    [Google Scholar]
  18. Gassmann, F.
    [1951] Über die Elastizität poröser Medien. Vierteljahresschrift der Naturforschenden Gesellschaft, 96, 1–23.
    [Google Scholar]
  19. Gu, Y. and Oliver, D.
    [2007] An iterative ensemble Kalman filter for multiphase fluid flow data assimilation. SPE Journal, 12, 438–446. SPE-108438-PA.
    [Google Scholar]
  20. Jack, I.
    [2001] The coming of age for 4D seismic. First Break, 19(1), 24–28.
    [Google Scholar]
  21. Landrø, M.
    [2001] Discrimination between pressure and fluid saturation changes from time-lapse seismic data. Geophysics, 66, 836–844.
    [Google Scholar]
  22. Landrø, M., Veire, H.H., Duffaut, K. and Najjar, N.F.
    [2003] Discrimination between pressure and fluid saturation changes from marine multicomponent time-lapse seismic data. Geophysics, 68, 1592–1599.
    [Google Scholar]
  23. Li, G. and Reynolds, A.
    [2009] Iterative Ensemble Kalman Filters for Data Assimilation. SPE Journal, 14, 496–505. SPE-109808-PA.
    [Google Scholar]
  24. Luo, X., Bhakta, T., Jakobsen, M. and Nœvdal, G.
    [2016a] An Ensemble 4D Seismic History Matching Framework with Sparse Representation Based on Wavelet Multiresolution Analysis. SPE Journal, Preprint. SPE-180025-PA.
    [Google Scholar]
  25. [2016b] An Ensemble 4D Seismic History Matching Framework with Wavelet Multiresolution Analysis-A 3D Benchmark Case Study. ECMOR XV-15th European Conference on the Mathematics of Oil Recovery.
    [Google Scholar]
  26. Luo, X., Bhakta, T. and Nœvdal, G.
    [2017] Data Driven Adaptive Localization With Applications To Ensemble-Based 4D Seismic History Matching. SPE Bergen One Day Seminar, Bergen, Norway, April 5. SPE-185936-MS.
    [Google Scholar]
  27. Luo, X., Stordal, A., Lorentzen, R. and Nœvdal, G.
    [2015] Iterative ensemble smoother as an approximate solution to a regularized minimum-average-cost problem: theory and applications. SPE Journal, 20, 962–982. SPE-176023-PA.
    [Google Scholar]
  28. Mindlin, R.D.
    [1949] Compliance of elastic bodies in contact. Journal of Applied Mechanics, 16, 259– 268.
    [Google Scholar]
  29. Nœvdal, G., Johnsen, L.M., Aanonsen, S.I., Vefring, E.H. et al.
    [2005] Reservoir monitoring and continuous model updating using ensemble Kalman filter. SPE journal, 10, 66–74. SPE-84372-PA.
    [Google Scholar]
  30. Nur, A.
    [1989] Four-dimensional seismology and (true) direct detection of hydrocarbon. The Leading Edge, 8.
    [Google Scholar]
  31. Peters, L., Arts, R., Brouwer, G., Geel, C., Cullick, S., Lorentzen, R.J., Chen, Y., Dunlop, N., Vossepoel, F.C., Xu, R. et al.
    [2010] Results of the Brugge benchmark study for flooding optimization and history matching. SPE Reservoir Evaluation & Engineering, 13, 391–405.
    [Google Scholar]
  32. Røste, T. and Landrø, M.
    [2007] Discrimination between pressure and fluid saturation changes in compacting reservoirs from time-lapse seismic data. 69th EAGE Conference and Exhibition, Extended Abstracts.
    [Google Scholar]
  33. Skjervheim, J.A., Evensen, G., Aanonsen, S.I., Ruud, B.O. and Johansen, T.A.
    [2007] Incorporating 4D seismic data in reservoir simulation models using ensemble Kalman filter. SPE Journal, 12, 282– 292. SPE-95789-PA.
    [Google Scholar]
  34. Stovas, A., Landrø, M. and Arntsen, B.
    [2003] Use of PP and PS time-lapse stacks for fluid-pressure discrimination. 65th Annual Conference and Exhibition, EAGE,Extended Abstracts, A-23.
    [Google Scholar]
  35. Trani, M., Arts, R., Leeuwenburgh, O. and Brouwer, J.
    [2011] Estimation of changes in saturation and pressure from 4D seismic AVO and time-shift analysis. Geophysics, 76, P.C1–C17.
    [Google Scholar]
  36. Van Leeuwen, P.J. and Evensen, G.
    [1996] Data assimilation and inverse methods in terms of a probabilistic formulation. Mon. Wea. Rev., 124, 2898–2913.
    [Google Scholar]
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