Abstract
While 3D seismic has been the basis for geological model building for a long time, time-lapse seismic has primarily been used in a qualitative manner to assist in monitoring reservoir behavior. With the growing acceptance of assisted history matching methods has come an equally rising interest in incorporating 3D or time-lapse seismic data into the history matching process in a more quantitative manner. The common approach in recent studies has been to invert the seismic data to elastic or to dynamic reservoir properties, typically acoustic impedance or saturation changes. Here we consider the use of both 3D and time-lapse seismic amplitude data based on a forward modeling approach that does not require any inversion in the traditional sense. Advantages of such an approach may be better estimation and treatment of model and measurement errors, the combination of two inversion steps into one by removing the explicit inversion to state space variables, and more consistent dependence on the validity of assumptions underlying the inversion process. In this paper, we introduce this approach with the use of an assisted history matching method in mind. Two ensemble-based methods, the ensemble Kalman filter and the ensemble randomized maximum likelihood method, are used to investigate issues arising from the use of seismic amplitude data, and possible solutions are presented. Experiments with a 3D synthetic reservoir model show that additional information on the distribution of reservoir fluids, and on rock properties such as porosity and permeability, can be extracted from the seismic data. The role for localization and iterative methods are discussed in detail.
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References
Anderson, J.L.: An adaptive covariance inflation error correction algorithm for ensemble filters. Tellus 59A, 210–224 (2007)
Burgers, G., van Leeuwen, P.J., Evensen, G.: Analysis scheme in the Ensemble Kalman Filter. Mon. Weather Rev. 126, 1719–1724 (1998)
Chen, Y., Oliver, D.S.: Cross-covariances and localization for EnKF in multiphase flow data assimilation. Comput. Geosci. (2009). doi:10.1007/210596-009-9174-6
Dadashpour, M., Landrø, M., Kleppe, J.: Nonlinear inversion for estimating reservoir parameters from time-lapse seismic data. J. Geophys. Eng. 5, 54–66 (2008)
Dadashpour, M., Echeverria-Ciaurri, D., Kleppe, J., Landrø, J.: Porosity and permeability estimation by integration of production and time-lapse near and far offset seismic data. J. Geophys. Eng. 6, 325–344 (2009)
Devegowda, D., Arroyo-Negrete, E., Datta-Gupta, A., Douma, S.G.: Efficient and robust reservoir model updating using Ensemble Kalman Filter with sensitivity-based covariance localization. SPE Reservoir Simulation Symposium, SPE, vol. 106144 (2007)
de Marseilly, G., Levendam, G., Boucher, M., Fasanino, G.: Interpretation of interference tests in a well field using geostatistical techniques to fit the permeability distributions in a reservoir model. In: Verly, G., David, M., Journel, A.G., Marechal, A. (eds.) Geostatistics for natural resource characterisation, Proc. NATO Advanced Study Inst. 831–849 (1984)
Dong, Y., Oliver, D.S.: Quantitative use of 4D seismic data for reservoir description. SPE J. SPE 84571, 91–99 (2005)
Dong, Y., Gu, Y., Oliver, D.S.: Sequential assimilation of 4D seismic data for reservoir description using the ensemble Kalman filter. J. Pet. Sci. Eng. 53, 83–99 (2006). doi:10.1016/j.petrol.2006.03.028
Evensen, G.: Sequential data assimilation with a nonlinear quasigeostrophic model using Monte Carlo methods to do forecast error statistics. J. Geophys. Res. 99(5), 10143–10162 (1994)
Evensen, G.: Using the EnKF for assisted history matching of a North Sea reservoir model. SPE Reservoir Simulation Symposium, SPE, vol. 106184 (2007)
Evensen, G.: Ensemble Kalman Filters for large geophysical applications. IEEE Control Systems Magazine (2009). doi:10.1109/MCS.2009.932222
Fahimuddin, A., Aanonsen, S.I., Skjervheim, J.-A.: Ensemble based 4D seismic history matching: integration of different levels and types of seismic data. SPE EUROPEC/EAGE Annual Conference and Exhibition, SPE, vol. 131453 (2010)
Furrer, R., Bengtsson, T.: Estimation of high-dimensional prior and posterior covariance matrices in Kalman filter variants. J. Multivar. Anal. 98, 227–255 (2007)
Gassmann, F.: Über die Elastizität poroser Medien. Vierteljahrsschr. Nat.forsch. Ges. Zür. 96, 251–262 (1951)
Gaspari, G., Cohn, S.E.: Construction of correlation functions in two and three dimensions. Q. J. R. Meteorol. Soc. 125(554), 723–757 (1999)
Gu, Y., Oliver, D.S.: An iterative Ensemble Kalman Filter for multiphase fluid flow data assimilation. SPE J. SPE 108438, 438–446 (2007)
Hammill, T.M., Whitaker, J.S., Snyder, C.: Distance-dependent filtering of background error covariance estimates in an Ensemble Kalman Filter. Mon. Weather Rev. 129, 2776–2790 (2001)
Hashin, Z., Shtrikman, S.: A variational approach to the elastic behavior of multiphase material. J. Mech. Phys. Solids 11, 127–140 (1963)
Haverl, M.C., Skjervheim, J.-A., Landrø, M.: 4D seismic modeling integrated with the Ensemble Kalman Filter method for history matching of reservoir simulations models. European Conference on the Mathematics of Oil Recovery (2008)
Houtekamer, P., Mitchell, H.: A sequential Ensemble Kalman Filter for atmospheric data assimilation. Mon. Weather Rev. 129, 123–137 (2001)
Jazwinski, A.H.: Stochastic processes and filtering theory. Academic, San Diego (1970)
Jin, L., Sen, M.K., Stoffa, P.L., Seif, R.K.: Optimal model parameterization in stochastic inversion for reservoir properties using time-lapse seismic and production data. SEG/San Antionio 2007 Annual Meeting, pp 1805–1809 (2007)
Landrø, M.: Discrimination between pressure and fluid saturation from time-lapse seismic data. Geophysics 66(3), 836–844 (2001)
Mindlin, R.D.: Compliance of elastic bodies in contact. J. Appl. Mech. 16, 259–268 (1949)
Naevdal, G., Johnsen, L.M., Aanonsen, S.I., Vefring, E.H.: Reservoir monitoring and continuous updating using Ensemble Kalma Filter. SPE Annual Technical Conference and Exhibition, SPE, vol. 84372 (2003)
Reynolds, A.C., Zafari, M., Li, G.: Iterative forms of the Ensemble Kalman Filter. In: Proceedings of the 10th European Conference on the Mathematics of Oil Recovery, Amsterdam, A030 (2006)
Sakov, P., Oke, P.R.: A deterministic formulation of the ensemble Kalman filter: an alternative to ensemble square-root filters. Tellus 60A, 361–371 (2008)
Sambridge, M.S.: Geopgysical inversion with a neighbourhood algorithm—I. Searching a parameter space. Geophys. J. Int. 138, 479–494 (1999)
Sakov, P., Evensen, G., Bertino, L.: Asynchronous data assimilation with the EnKF. Tellus 62A, 24–29 (2010). doi:10.1111/j.1600-0870.2009.00417.x
Sarma, P., Durlofsky, L.J., Aziz, K., Chen, W.H. : A new approach to automatic history matching using kernel PCA. SPE Reservoir Simulation Symposium, SPE, vol. 106176 (2007)
Skjervheim, J.-A., Evensen, G., Aanonsen, S.I., Ruud, B.O., Johansen, T.A.: Incorporating 4D seismic data in reservoir simulation models using ensemble Kalman filter. SPE Annual Technical Conference and Exhibition, SPE, vol. 95789 (2005)
Skjervheim, J.-A., Ruud, B.O.: Combined inversion of 4D seismic waveform data and production data using ensemble Kalman filter. SEG Expanded Abstracts 25, 1776 (2006). doi:10.1190/1.2369868
Stephen, K.D., Soldo, J., MacBeth, C., Christie, M.: Multiple-model seismic and production history matching: a case study. SPE Europec/EAGE Annual Conference, SPE, vol. 94173 (2006)
Stephen, K.D., Shams, A., MacBeth, C.: Faster seismic history matching in a UKCS reservoir. SPE Europec/EAGE Annual Conference, SPE, vol. 107147 (2007)
Tippett, M., Anderson, J.L., Bishop, C.H., Hamill, T.M., Whitaker, J.S.: Ensemble square-root filters. Month. Weather Rev. 131, 1485–1490 (2003)
Trani, M., Arts, R., Leeuwenburgh, O., Brouwer, J., Douma, S.: The importance of localization for the assimilation of 4D seismic data using the EnKF. SEG Expanded Abstracts 28, 3835 (2009). doi:10.1190/1.3255667
Trani, M., Arts, R., Leeuwenburgh, O., Brouwer, J.: Estimation of changes in saturation and pressure from 4D seismic AVO and time-shift analysis. Geophysics (2010, accepted)
van Leeuwen, P.J.: Comment on data assimilation using an Ensemble Kalman Filter technique. Mon. Weather Rev. 127, 1374–1379 (1999)
Wang, Y., Li, G., Reynolds, A.C.: Estimation of depths of fluid contacts by history matching using iterative Ensemble Kalman Smoothers. SPE Reservoir Simulation Symposium, SPE, vol. 119056 (2009)
Wen, X.-H., Chen, W.H.: Real-time reservoir model updating using Ensemble Kalman Filter. SPE Reservoir Simulation Symposium, SPE, vol. 92991 (2005)
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Leeuwenburgh, O., Brouwer, J. & Trani, M. Ensemble-based conditioning of reservoir models to seismic data. Comput Geosci 15, 359–378 (2011). https://doi.org/10.1007/s10596-010-9209-z
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DOI: https://doi.org/10.1007/s10596-010-9209-z