Some Practical Issues on Real-Time Reservoir Model Updating Using Ensemble Kalman Filter
- Xian-Huan Wen (Chevron Corp.) | Wen H. Chen (Chevron Corp.)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- June 2007
- Document Type
- Journal Paper
- 156 - 166
- 2007. Society of Petroleum Engineers
- 5.5.8 History Matching, 5.6.9 Production Forecasting, 3.3 Well & Reservoir Surveillance and Monitoring, 4.3.4 Scale, 5.1 Reservoir Characterisation, 5.5 Reservoir Simulation, 5.6.4 Drillstem/Well Testing, 5.1.5 Geologic Modeling, 7.2.3 Decision-making Processes
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The concept of "closed-loop" reservoir management is currently receiving considerable attention in the petroleum industry. A "real-time" or "continuous" reservoir model updating technique is a critical component for the feasible application of any closed-loop, model-based reservoir management process. This technique should be able to rapidly and continuously update reservoir models assimilating the up-to-date observations of production data so that the performance predictions and the associated uncertainty are up-to-date for optimization of future development/operations. The ensemble Kalman filter (EnKF) method has been shown to be quite efficient for this purpose in large-scale nonlinear systems.
Previous studies show that a relatively large ensemble size is required for EnKF to reliably assess the uncertainty, and a confirming step is recommended to ensure the consistency of the updated static and dynamic variables with the flow equations. In this paper, we further explore the capability of EnKF, focusing on some practical issues including the correction of the linear and Gaussian assumptions during filter updating with iteration, the reduction of ensemble size with a resampling scheme, and the impact of data assimilation time interval.
Results from the example in this paper demonstrate that the proposed iterative EnKF performs better with more accurate predictions and less uncertainty than the traditional noniterative EnKF. The use of iteration reduces the impact of nonlinearity and non-Gaussianity. Results also show that iteration may only be required when predictions are considerably deviated from the observations. The proposed resampling scheme can significantly reduce the ensemble size necessary for reliable assessment of uncertainty with improved accuracy. Finally, we show that the noniterative EnKF is sensitive to the size of time interval between the assimilation steps. Using the proposed iterative EnKF, results are more stable, more accurate reservoir models and predictions can be obtained even when a large time interval is used. This also indicates that iteration within the EnKF updating serves as a process that corrects the stronger nonlinear and non-Gaussian behaviors when larger time interval is used.
Reservoir models have become an important part of day-to-day decision analysis related to management of oil/gas fields. The closed-loop reservoir management concept (Jansen et al. 2005) allows real-time decisions to be made that maximize the production potential of a reservoir. These decisions are based on the most current information available about the reservoir model and the associated uncertainty of the information. One critical requirement in this real-time, model-based reservoir management process is the ability to rapidly estimate the reservoir models and the associated uncertainty reflecting the most current production data in a real-time fashion. Based on a number of studies, the EnKF method was shown to be well-suited for such applications compared to the traditional history-matching (HM) methods (Evensen 1999; Gu and Oliver 2006; Wen and Chen 2006).
|File Size||3 MB||Number of Pages||11|
Burgers, G., van Leeuwen, P.J., and Evensen, G. 1998. Analysis scheme in theensemble Kalman filter. Monthly Weather Review 126:1719-1724.
Deutsch, C.V. and Journel, A.G. 1998. GSLIB: Geostatistical SoftwareLibrary and User's Guide. 2nd edition. New York City: Oxford UniversityPress.
Dong, Y., Gu, Y., and Oliver, D.S. Quantitative use of 4D seismic data forreservoir description: the ensemble Kalman filter approach. Submitted toJournal of Petroleum Science & Engineering.
Evensen, G. 1999. Sequential data assimilation with a nonlinearquasi-geostrophic model using Monte Carlo methods to forecast error statistics.Monthly Weather Review 127 (12): 2741-2758.
Evensen, G. 2003. The ensemble Kalman filter: Theoretical formulation andpractical implementation. Ocean Dynamics 53 (4): 343-367.
Evensen, G. 2004. Sampling strategies and square root analysis schemes forthe EnKF. Ocean Dynamics 54: 539-560.
Evensen, G. 2005. The combined parameter and state estimation problem.Submitted to Computational Geosciences.
Gu, Y. and Oliver, D.S. 2005. History Matching of the PUNQ-S3Reservoir Model Using the Ensemble Kalman Filter. SPEJ 10(2): 217-224. SPE-89942-PA. DOI: 10.2118/89942-PA.
Gu, Y. and Oliver, D.S. 2006. The ensemble Kalman filter for continuousupdating of reservoir simulation models. Journal of Energy ResourcesTechnology—Transactions of the ASME 128 (1): 79-87.
Houtekamer, P.L. and Mitchell, H.L. 1998. Data assimilation using anensemble Kalman filter technique. Monthly Weather Review 126 (3):796-811.
Jansen, J.D., Brouwer, D.R., Naevdal, G., and van Kruijsdiik, J.W. 2005.Closed-loop reservoir management. First Break 23: 43-48.
Liu, N. and Oliver, D.S. 2005a. Critical Evaluation of the EnsembleKalman Filter on History Matching of Geological Facies. Paper SPE 92867presented at the SPE Reservoir Simulation Symposium, Houston, 31 January-2February. DOI: 10.2118/92867-MS.
Liu, N. and Oliver, D.S. 2005b. Critical evaluation of the ensemble Kalmanfilter on history matching of geological facies. J. Petroleum Science &Engineering 47 (3-4): 147-161.
Lorentzen, R.J., Naevdal, G., Valles, B., Berg, A.M., and Grimstad, A.A.2005. Analysis of the EnsembleKalman Filter for Estimation of Permeability and Porosity in ReservoirModels. Paper SPE 96375 presented at the SPE Annual Technical Conferenceand Exhibition, Dallas, 9-12 October. DOI: 10.2118/96375-MS.
Moradkhani, H., Sorooshian, S., Gupta, H.V., and Houser, P.R. 2005. Dualstate-parameter estimation of hydrological models using ensemble Kalman filter.Advances in Water Resources 28: 135-147.
Nævdal, G., Mannseth, T., and Vefring, E.H. 2002. Near-Well Reservoir MonitoringThrough Ensemble Kalman Filter. Paper SPE 75235 presented at the SPE/DOEImproved Oil Recovery Symposium, Tulsa, 13-17 April. DOI: 10.2118/75235-MS.
Nævdal, G., Johnsen, L.M., Aanonsen, S.I., and Vefring, E.H. 2005. Reservoir Monitoring and ContinuousModel Updating Using Ensemble Kalman Filter. SPEJ 10 (1):66-74. SPE-84372-PA. DOI: 10.2118/84372-PA.
Reichle, R.H., McLaughlin, D.B., and Entekhabi, D. 2002. Hydrologic dataassimilation with the ensemble Kalman filter. Monthly Weather Review130 (1): 103-114.
Reynolds, A.C., He, N., Chu, L., and Oliver, D.S. 1996. Reparameterization Techniques forGenerating Reservoir Descriptions Conditioned to Variograms and Well-TestPressure Data. SPEJ 1 (4): 413-426. SPE-30588-PA. DOI:10.2118/30588-PA.
Sarma, P., Durlofsky, L.J., Aziz, K., and Chen, W.H. 2005. Efficientreal-time reservoir management using adjoint-based optimal control and modelupdating. Submitted to Computational Geosciences.
Sun N.-Z. 1994. Inverse Problem in Groundwater Modeling. Boston:Kluwer Academic Publishers.
Tarantola, H. 1987. Inverse Problem Theory: Methods for Data Fitting andModel Parameter Estimation. Amsterdam: Elsevier.
Van Leeuwen, P.J. 1999. Comment on ‘Data assimilation using an ensembleKalman filter technique.' Monthly Weather Review 127 (6):1374-1377.
Van Leeuwen, P.J. and Evensen, G. 1996. Data assimilation and inversemethods in terms of probabilities formulation. Monthly Weather Review124: 2898-2913.
Wen, X.-H. and Chen, W.H. 2006. Real-Time Reservoir Model UpdatingUsing Ensemble Kalman Filter With Confirming Option. SPEJ 11(4): 431-442. SPE-92991-PA. DOI: 10.2118/92991-PA.
Xiu, D. and Karniadaskis, G.E. 2003. Modeling uncertainty in flowsimulations via generalized polynomial chaos. Journal of ComputationalPhysics 187: 137-167.
Zafari, M. and Reynolds, A.C. 2005. Assessing the Uncertainty inReservoir Description and Performance Predictions With the Ensemble KalmanFilter. Paper SPE 95750 presented at the SPE Annual Technical Conferenceand Exhibition, Dallas, 9-12 October.DOI: 10.2118/95750-MS.
Zhang, D., Lu, Z., and Chen, Y. 2007. Dynamic Reservoir Data AssimilationWith an Efficient, Dimension-Reduced Kalman Filter. SPEJ 12(1): 108-117. SPE-95277-PA. DOI: 10.2118/95277-PA.brary/servlet/spepreview?id=95277-PA">DynamicReservoir Data Assimilation With an Efficient, Dimension-Reduced KalmanFilter. SPEJ 12 (1): 108-117. SPE-95277-PA. DOI:10.2118/95277-PA.