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Facies estimation through data assimilation and structure parameterization

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Abstract

Data assimilation in a reservoir with facies description using the ensemble Kalman filter (EnKF) is challenging. An important reason is that probability density functions for pixel-based representations of facies fields seldom follow the unimodal Gaussian assumption underlying traditional EnKF implementations. Different approaches for identification of facies fields, aiming to overcome this challenge, have been proposed within the EnKF framework. Level set (LS) representations of the facies field have been reported to alleviate the problems of multimodality. Several authors have, however, pointed out that the most commonly applied LS representation suffers from topological constraints that can create difficulties in an estimation setting. An alternative LS representation, that overcomes these topological constraints, leads to instabilities in the assimilated ensemble members. To overcome topological constraints, the recently proposed hierarchical LS representation is applied in an estimation setting for the first time in this paper. To improve stability and to alleviate challenges associated with model nonlinearities, we apply regularization by reduced representation of the LS functions and adjustable smoothing of the LS representation. The resolution of the reduced LS representation is selected based on the variability of the initial ensemble, aiming at preserving enough flexibility to disclose unexpected features. 2D and 3D estimation results demonstrate that the hierarchical LS representation does avoid topological constraints and that instabilities are avoided. The results suggest that the method is capable of handling estimation of facies fields while preserving geological plausibility.

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References

  1. Aanonsen, S.I., Nævdal, G., Oliver, D.S., Reynolds, A.C., Valles, B.: The ensemble Kalman filter in reservoir engineering—a review. SPE J. 14 (3), 393–412 (2009)

    Article  Google Scholar 

  2. Agbalaka, C.C., Oliver, D.S.: Automatic history matching of production and facies data with nonstationary proportions using EnKF. SPE-118916, the Woodlands, Texas (2009)

  3. Anderson, J.L.: Exploring the need for localization in ensemble data assimilation using a hierarchical ensemble filter. Phys. D 230(1-2), 99–111 (2010)

    Article  Google Scholar 

  4. Berre, I., Lien, M., Mannseth, T.: Multi-level parameter structure identification for two-phase porous-media flow problems using flexible representations. Adv. Water Resour. 32, 1777–1788 (2009)

    Article  Google Scholar 

  5. Berre, I, Lien, M, Mannseth, T: Identification of three-dimensional electric conductivity changes from time-lapse electromagnetic observations. J. Comput. Phys. 230(10), 3915–3928 (2011)

    Article  Google Scholar 

  6. Cardiff, M., Kitanidis, P.K.: Bayesian inversion for facies detection: an extensible level set framework. Water Resour. Res. 45, W10416 (2009)

    Google Scholar 

  7. Chan, T, Tai, X-C: Level set and total variation regularization for elliptic inverse problems with discontinuous coefficients. J. Comput. Phys. 193(1), 40–66 (2003)

    Article  Google Scholar 

  8. Chang, H., Zhang, D., Lu, Z.: History matching of facies distribution with the EnKF and level set parameterization. J. Comput. Phys. 229(20), 8011–8030 (2010)

    Article  Google Scholar 

  9. Chen, Y., Oliver, D.S.: Cross-covariances and localization for EnKF in multiphase flow data assimilation. Comput. Geosci. 14(4), 579–601 (2010)

    Article  Google Scholar 

  10. Deutsch, C.V., Journel, A.G.: Gslib: Geostatistical Software Library and Users Guide. Oxford University Press, New York (1998)

    Google Scholar 

  11. Dorn, O., Villegas, R.: History matching of petroleum reservoirs using a level set technique. Inverse Probl. 24(3), 03501 (2008)

    Article  Google Scholar 

  12. Dovera, L., Della Rossa, E.: Multimodal ensemble Kalman filter using Gaussian mixture models. Comput. Geosci. 15(2), 307–323 (2011)

    Article  Google Scholar 

  13. Emerick, A.A., Reynolds, A.C.: Investigation of the sampling performance of ensemble-based methods with a simple reservoir model. Comput. Geosci. 17(2), 325–350 (2013)

    Article  Google Scholar 

  14. Evensen, G.: Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J. Geophys. Res. 99, 10143–10162 (1994)

    Article  Google Scholar 

  15. Evensen, G.: Data Assimilation: The Ensemble Kalman Filter. Springer, New York (2007)

    Google Scholar 

  16. Evensen, G., van Leeuwen, P.J.: An ensemble Kalman smoother for nonlinear dynamics. Mon. Weather Rev. 128(6), 1852–1867 (2000)

    Article  Google Scholar 

  17. Gaspari, G., Cohn, S.E.: Construction of correlation functions in two and three dimensions. Quart. J. Roy. Meteor. Soc. 125, 723–757 (1999)

    Article  Google Scholar 

  18. Jafarpour, B., Khodabakhshi, M.: A probability conditioning method (pcm) for nonlinear flow data integration into multipoint statistical facies simulation. Math. Geosci. 43(2), 133–164 (2011)

    Article  Google Scholar 

  19. Jafarpour, B., McLaughlin, D.B.: History matching with an ensemble Kalman filter and discrete cosine parameterization. Comput. Geosci. 12(2), 227–244 (2008)

    Article  Google Scholar 

  20. Kalman, R.E.: A new approach to linear filtering and prediction problems. Trans.of the ASME-J. Basic Eng. 82(Series D), 35–45 (1960)

    Article  Google Scholar 

  21. Kitanidis, P.K.: Quasi-linear geostatistical theory for inversing. Water Resour. Res. 31 (10), 2411–2419 (1995)

    Article  Google Scholar 

  22. Lien, M., Berre, I., Mannseth, T.: Combined adaptive multiscale and level-set parameter estimation. Multiscale Model. Simul. 4(4), 1349–1372 (electronic) (2005) MR2203856

    Article  Google Scholar 

  23. Liu, N., Oliver, D.S.: Critical evaluation of the ensemble Kalman filter on history matching of geological facies. SPE Res. Eval. & Eng. 8(6), 470–477 (2005)

    Google Scholar 

  24. Liu, N., Oliver, D.S.: Ensemble Kalman filter for automatic history matching of geologic facies. J. Pet. Sci. Eng. 47 (3-4), 147–161 (2005)

    Article  Google Scholar 

  25. Lorentzen, R.J., Flornes, K. M., Nævdal, G.: History matching of channelized reservoirs using the ensemble Kalman filter. SPE J. 17(1), 137–151 (2012)

    Article  Google Scholar 

  26. Lorentzen, R.J., Nævdal, G., Shafieirad, A.: Estimating facies fields by use of the ensemble Kalman filter and distance functions–applied to shallow-marine environments. SPE J. 18 (1), 146–158 (2013)

    Article  Google Scholar 

  27. Mannseth, T.: Relation between level set and truncated pluri-gaussian methodologies for facies representation. Accepted for publication in Mathematical Geosciences (2013)

  28. Moreno, D., Aanonsen, S. I.: Continuous facies updating using the ensemble Kalman filter and the level set method. Math. Geosci. 43(8), 951–970 (2011)

    Article  Google Scholar 

  29. Oliver, D.S., He, N., Reynolds, A.C.: Conditioning Permeability Fields to Pressure Data. Leoben, Austria (1996)

  30. Peters, E., Arts, R.J., Brouwer, G.K., Geel, C.R., Cullic, S., Lorentzen, R.J., Chen, Y., Dunlop, K.N.B., Vosspoel, F.C., Xu, R., Sarma, P., Alhutali, A.N., Reynolds, A.C.: Results of the BRUGGE benchmark study for flooding optimization and history matching. SPE Reserv. Eval. & Eng. 13, 391–405 (2010)

    Article  Google Scholar 

  31. Sarma, P., Chen, W. H.: Generalization of the ensemble Kalman filter using kernels for nongaussian random fields. SPE-119177, the Woodlands, Texas (2009)

  32. Schlumberger: Software, http://www.slb.com/services/software.aspx (2011)

  33. Sun, A.Y., Morris, A.P., Mohanty, S.: Sequential updating of multimodal hydrogeologic parameter fields using localization and clustering techniques. Water Resour. Res. 45, W07424 (2009)

    Google Scholar 

  34. Vese, L.A., Chan, T.F.: A multiphase level set framework for image segmentation using the Mumford and Shah model. Int. J. Comput. Vis. 50(3), 271–293 (2002)

    Article  Google Scholar 

  35. Wang, MY, Wang, X: ‘Colour’ level sets: a multi-phase method for structural topology optimization with multiple materials. Comput. Methods Appl. Mech. Eng. 193(6–8), 469–496 (2004)

    Article  Google Scholar 

  36. Wang, Y., Li, G., Reynolds, A.C.: Estimation of depths of fluid contacts by history matching using iterative ensemble smoothers. SPE J. 15(2), 509–525 (2010)

    Article  Google Scholar 

  37. Zhao, Y., Reynolds, A.C., Li, G.: Generating facies maps by assimilating production data and seismic data with the ensemble Kalman filter. SPE-113990, Tulsa, Oklahoma (2008)

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Author notes

  1. Martha Lien

    Present address: Octio AS, Bøhmergaten 44, 5057, Bergen, Norway

Authors and Affiliations

  1. Uni Research CIPR, P O Box 7800, 5020, Bergen, Norway

    Martha Lien & Trond Mannseth

  2. Department of Mathematics, University of Bergen, P O Box 7800, 5020, Bergen, Norway

    Trond Mannseth

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  1. Martha Lien
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  2. Trond Mannseth
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Correspondence to Trond Mannseth.

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Lien, M., Mannseth, T. Facies estimation through data assimilation and structure parameterization. Comput Geosci 18, 869–882 (2014). https://doi.org/10.1007/s10596-014-9431-1

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  • DOI: https://doi.org/10.1007/s10596-014-9431-1

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