Multiscale ensemble filtering for reservoir engineering applications
Tóm tắt
Reservoir management requires periodic updates of the simulation models using the production data available over time. Traditionally, validation of reservoir models with production data is done using a history matching process. Uncertainties in the data, as well as in the model, lead to a nonunique history matching inverse problem. It has been shown that the ensemble Kalman filter (EnKF) is an adequate method for predicting the dynamics of the reservoir. The EnKF is a sequential Monte-Carlo approach that uses an ensemble of reservoir models. For realistic, large-scale applications, the ensemble size needs to be kept small due to computational inefficiency. Consequently, the error space is not well covered (poor cross-correlation matrix approximations) and the updated parameter field becomes scattered and loses important geological features (for example, the contact between high- and low-permeability values). The prior geological knowledge present in the initial time is not found anymore in the final updated parameter. We propose a new approach to overcome some of the EnKF limitations. This paper shows the specifications and results of the ensemble multiscale filter (EnMSF) for automatic history matching. EnMSF replaces, at each update time, the prior sample covariance with a multiscale tree. The global dependence is preserved via the parent–child relation in the tree (nodes at the adjacent scales). After constructing the tree, the Kalman update is performed. The properties of the EnMSF are presented here with a 2D, two-phase (oil and water) small twin experiment, and the results are compared to the EnKF. The advantages of using EnMSF are localization in space and scale, adaptability to prior information, and efficiency in case many measurements are available. These advantages make the EnMSF a practical tool for many data assimilation problems.
Tài liệu tham khảo
Caers, J.: Petroleum Geostatistics. Society of Petroleum Engineers, Richardson (2005)
Courtier, P., Derber, J., Errico, R., Louis, J.-F., Vukicevic, T.: Important literature on the use of adjoint, variational methods and the kalman filter in meteorology. Tellus 45A, 342 (1993)
Dee, D.P.: Simplification of the kalman filter for meteorological data assimilation. Q. J. R. Meteorol. Soc. 117, 365–384 (1991)
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)
Evensen, G.: Sampling strategies and square root analysis schemes for the enkf. Ocean Dyn. 54, 539–560 (2004)
Evensen, G., van Leeuwen, P.: Assimilation of geosat altimeter data for the agulhas current using ensemble kalman filter with quasi-geostrophic model. Mon. Weather Rev. 124, 85–96 (1996)
Frakt, A., Willsky, A.: Computationally efficient stochastic realization for internal multiscale autoregressive models. Multidimens. Syst. Signal Process. 12, 109–142 (2001)
Gao, G., Reynolds, A.: Quantifying uncertainty for the punq-s3 problem in a bayesian settings with rml and enkf. In: SPE Reservoir simulation symposium, SPE 93324, SPE 93324, The Woodlands, 31 January–2 Feburary 2005
Ghil, M., Malanotte-Rizzoli, P.: Data assimilation in meteorology and oceanography. Adv. Geophys. 33, 141–266 (1991)
Gu, Y., Oliver, D.: History matching of the punq-s3 reservoir model using te ensemble kalman filter. In: SPE Annual Technical Conference and Exhibition, SPE 89942, Houston, 26–29 September 2004
Hamill, T., Whitaker, J., Snyder, C.: Distance-dependent filtering of background error covariance estimates in an ensemble kalman filter. Mon. Weather Rev. 129, 2884–2903 (2001)
Hanea, R., Velders, G., Heemink, A.: Data assimilation of ground level ozone in Europe with a kalman filter and chemistry transport model. J. Geophys. Res. 109, 1–19 (2004)
Houtekamer, P., Mitchell, H.L.: Data assimilation using an ensemble kalman filter technique. Mon. Weather Rev. 126, 796–811 (1998)
Houtekamer, P., Mitchell, H.L.: A sequential ensemble kalman filter for atmospheric data assimilation. Mon. Weather Rev. 129, 123–137 (2001)
Liu, N., Oliver, D.: Critical evaluation of the ensemble kalman filter on history matching of geoogical facies. In: SPE Reservoir Simulation Symposium, SPE 92867, The Woodlands, 31 January–2 Feburary 2005
Lorenc, A.: The potential for the ensemble kalman filter for nwp: a comparison with 4dvar. Q. J. R. Meteorol. Soc. 129, 3183–3203 (2003)
Margulis, S., McLaughlin, D., Entekhabi, D., Dune, S.: Land data assimilation and estimation of soil moisture using measurements from the southern great plains 1997 field experiment. Water Resour. Res. 38, 1299 (2002)
Mitchell, H.L., Houtekamer, P., Pellerin, G.: Ensemble size, balance, and model-error representation in an ensemble kalman filter. Mon. Weather Rev. 130, 2791–2808 (2002)
Nævdal, G., Johnson, L., Aanonsen, S., Vefring, E.: Reservoir monitoring and continuos model updating using ensemble kalam filter. In: SPE Annual Technical Conference and Exhibition, Houston, 26–29 September 2004
Nævdal, G., Mannset, T., Vefring, E.: Instrumented wells and near well reservoir monitoring through ensemble kalman filter. In: 8th European Conference on the Mathematics of Oil Recovery (2002a)
Nævdal, G., Mannset, T., Vefring, E.: Near well reservoir monitoring through ensemble kalman filter. In: SPE 75235 (2002b)
Ott, E., Hunt, B., Szunyogh, I., Zimin, A., Kostelich, E., Corazo, M., Kalnay, E.D.P., Yorke, J.: A local ensemble kalman filter for atmospheric data assimilation. Tellus A, 56, 415–428 (2004)
Segers, A., Heemink, A., M.Verlaan, van Loon, M.: A modified rrsqrt-filter for assimilating data in atmospheric chemistry models. Environ. Model. Softw. 15, 663–671 (2000)
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. In: SPE Annual Technical Conference and Exhibition, SPE 95789 (2005)
Verlaan, M., Heemink, A.: Tidal flow forecasting using reduced-rank square root filters. Stoch. Hydrol. Hydraul. 11, 349–368 (1997)
Wang, K., Lary, D., Shallcross, D., Hall, S., Pyle, J.: A review on the use of the adjoint method in four-dimensional atmospheric-chemistry data assimilation. Q. J. R. Meteorol. Soc. 127, 2181–2204 (2001)
Wen, X.H., Chen, W.H.: Real-time reservoir model updating using ensemble kalman filter. In: SPE Reservoir Simulation Symposium, SPE 92991 (2005)
Willsky, A.: Multiresolution markov models for signal and image processing. Proc. I. E. E. E. 90, 1396–1458 (2002)
Zhou, Y., McLaughlin, D., Entekhabi, D., Ng, G.: An ensemble multiscale filter for large nonlinear data assimilation problems. Mon. Weather. Rev. 136, 678–698 (2008)