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Deterministic ensemble smoother with multiple data assimilation as an alternative for history-matching seismic data. (English) Zbl 1406.86021
Summary: This paper reports the results of an investigation on the use of a deterministic analysis scheme combined with the method ensemble smoother with multiple data assimilation (ES-MDA) for the problem of assimilating a large number of correlated data points. This is the typical case when history-matching time-lapse seismic data in petroleum reservoir models. The motivation for the use of the deterministic analysis is twofold. First, it tends to result in a smaller underestimation of the ensemble variance after data assimilation. This is particularly important for problems with a large number of measurements. Second, the deterministic analysis avoids the factorization of a large covariance matrix required in the standard implementation of ES-MDA with the perturbed observations scheme. The deterministic analysis is tested in a synthetic history-matching problem to assimilate production and seismic data.

86A22 Inverse problems in geophysics
86A32 Geostatistics
86A15 Seismology (including tsunami modeling), earthquakes
62M20 Inference from stochastic processes and prediction
65C05 Monte Carlo methods
Full Text: DOI
[1] Abadpour, A., Bergey, P., Piasecki, R.: 4D seismic history matching with ensemble Kalman filter-assimilation on hausdorff distance to saturation front. In: Proceedings of the SPE Reservoir Simulation Symposium. The Woodlands, Texas, USA, 18-20 February, number SPE-163635-MS. https://doi.org/10.2118/163635-MS (2013)
[2] Anderson, JL, An ensemble adjustment Kalman filter for data assimilation, Mon. Weather Rev., 129, 2884-2903, (2001)
[3] Avansi, GD; Schiozer, DJ, UNISIM-I: synthetic model for reservoir development and management applications, Int. J Model. Simul. Pet. Ind., 9, 21-30, (2015)
[4] Bishop, CH; Etherton, BJ; Majumdar, SJ, Adaptive sampling with the ensemble transform Kalman filter. Part I: Theoretical aspects, Mon. Weather Rev., 129, 420-436, (2001)
[5] Burgers, G.; Leeuwen, P.; Evensen, G., Analysis scheme in the ensemble Kalman filter, Mon. Weather Rev., 126, 1719-1724, (1998)
[6] Chen, Y.; Oliver, DS, Ensemble-based closed-loop optimization applied to Brugge field, SPE Reserv. Eval. Eng., 13, 56-71, (2010)
[7] Chen, Y., Oliver, D.S.: History matching of the Norne full-field model with an iterative ensemble smoother. SPE Reserv. Eval. Eng. 17(2). https://doi.org/10.2118/164902-PA (2014)
[8] Deutsch, C.V., Journel, A.G.: GSLIB Geostatistical Software Library And User’s Guide, 2nd edition. Oxford University Press, New York (1998)
[9] Emerick, AA, Analysis of the performance of ensemble-based assimilation of production and seismic data, J. Pet. Sci. Eng., 139, 219-239, (2016)
[10] Emerick, AA; Reynolds, AC, Combining sensitivities and prior information for covariance localization in the ensemble Kalman filter for petroleum reservoir applications, Comput. Geosci., 15, 251-269, (2011) · Zbl 1213.86009
[11] Emerick, AA; Reynolds, AC, History matching time-lapse seismic data using the ensemble Kalman filter with multiple data assimilations, Comput. Geosci., 16, 639-659, (2012)
[12] Emerick, AA; Reynolds, AC, Investigation on the sampling performance of ensemble-based methods with a simple reservoir model, Comput. Geosci., 17, 325-350, (2013) · Zbl 1382.86018
[13] Emerick, AA; Reynolds, AC, Ensemble smoother with multiple data assimilation, Comput. Geosci., 55, 3-15, (2013)
[14] Emerick, A.A., Reynolds, A.C.: History matching of production and seismic data for a real field case using the ensemble smoother with multiple data assimilation. In: Proceedings of the SPE Reservoir Simulation Symposium. The Woodlands, Texas, USA, 18-20 February, number SPE-163675-MS. https://doi.org/10.2118/163675-MS (2013)
[15] Evensen, G., Sampling strategies and square root analysis schemes for the enKF, Ocean Dyn., 54, 539-560, (2004)
[16] Evensen, G.: The ensemble Kalman filter for combined state and parameter estimation. IEEE Control. Syst. Mag., 83-104. https://doi.org/10.1109/MCS.2009.932223 (2009) · Zbl 1395.93534
[17] Gaspari, G.; Cohn, SE, Construction of correlation functions in two and three dimensions, Q. J. Roy. Meteorol. Soc., 125, 723-757, (1999)
[18] Golub, G.H., van Loan, C.F.: Matrix Computations, 2nd edn. The Johns Hopkins University Press, Baltimore (1989) · Zbl 0733.65016
[19] Hoteit, I.; Pham, D-T; Gharamti, ME; Luo, X., Mitigating observation perturbation sampling errors in the stochastic enKF, Mon. Weather. Rev., 143, 2918-2936, (2015)
[20] Houtekamer, PL; Mitchell, HL, A sequential ensemble Kalman filter for atmospheric data assimilation, Mon. Weather Rev., 129, 123-137, (2001)
[21] Kalman, RE, A new approach to linear filtering prediction problems, Trans. ASME J. Basic Eng., 82, 35-45, (1960)
[22] Le, DH; Emerick, AA; Reynolds, AC, An adaptive ensemble smoother with multiple data assimilation for assisted history matching, SPE J., 21, 2195-2207, (2016)
[23] Leeuwenburgh, O.; Arts, R., Distance parameterization for efficient seismic history matching with the ensemble Kalman filter, Comput. Geosci., 18, 535-548, (2014)
[24] Maschio, C., Avansi, G.D., Santos, A.A., Schiozer, D.J.: UNISIM-I-H case study for history matching. Dataset. www.unisim.cepetro.unicamp.br/benchmarks/br/unisim-i/unisim-i-h (2013)
[25] Oliver, DS, Moving averages for Gaussian simulation in two and three dimensions, Math. Geol., 27, 939-960, (1995) · Zbl 0970.86549
[26] Oliver, D.S., Reynolds, A.C., Liu, N.: Inverse Theory for Petroleum Reservoir Characterization and History Matching. Cambridge University Press, Cambridge (2008)
[27] Rafiee, J., Reynolds, A.C.: Theoretical and Efficient Practical Procedures for the Generation of Inflation Factors for ES-MDA. Inverse Problems. https://doi.org/10.1088/1361-6420/aa8cb2 (2017) · Zbl 1379.65033
[28] Sakov, P.; Bertino, L., Relation between two common localisation methods for the enKF, Comput. Geosci., 15, 225-237, (2011) · Zbl 1213.62150
[29] Sakov, P.; Oke, PR, Implications of the form of the ensemble transformation in the ensemble square root filters, Mon. Weather. Rev., 136, 1042-1053, (2008)
[30] Sakov, P.; Oke, PR, A deterministic formulation of the ensemble Kalman filter: an alternative to ensemble square root filters, Tellus A, 60, 361-371, (2008)
[31] Skjervheim, J-A; Evensen, G.; Aanonsen, SI; Ruud, BO; Johansen, T-A, Incorporating 4D seismic data in reservoir simulation models using ensemble Kalman filter, SPE J., 12, 282-292, (2007)
[32] Sun, AY; Morris, A.; Mohanty, S., Comparison of deterministic ensemble Kalman filters for assimilating hydrogeological data, Adv. Water Resour., 32, 280-292, (2009)
[33] Tarantola, A.: Inverse problem theory methods for model parameter estimation. SIAM, Philadelphia (2005) · Zbl 1074.65013
[34] Tippett, MK; Anderson, JL; Bishop, CH; Hamill, TM; Whitaker, JS, Ensemble square-root filters, Mon. Weather Rev., 131, 1485-1490, (2003)
[35] Trani, M., Arts, R., Leeuwenburgh, O.: Seismic history matching of fluid fronts using the ensemble Kalman filter. SPE J. 18(1). https://doi.org/10.2118/163043-PA (2012)
[36] Leeuwen, PJ, An ensemble smoother with error estimates, Mon. Weather Rev., 129, 709-728, (2001)
[37] van Leeuwen, P.J.: Nonlinear data assimilation for high-dimensional systems—with geophysical applications, volume 2 of nonlinear data assimilation. In: Frontiers in Applied Dynamical Systems: Reviews and Tutorials, pp 1-73. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-18347-3_1
[38] Whitaker, JS; Hamill, TM, Ensemble data assimilation without perturbed observations, Mon. Weather Rev., 130, 1913-1924, (2002)
[39] Zhang, Y.; Liu, N.; Oliver, DS, Ensemble filter methods with perturbed observations applied to nonlinear problems, Comput. Geosci., 14, 249-261, (2010) · Zbl 1425.65015
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