Incorporating 4D Seismic Data in Reservoir Simulation Models Using Ensemble Kalman Filter
- Jan-Arild Skjervheim (University of Bergen) | Geir Evensen (Norsk Hydro) | Sigurd Ivar Aanonsen (U. of Bergen) | Bent Ole Ruud (U. of Bergen) | Tor-Arne Johansen (U. of Bergen)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- September 2007
- Document Type
- Journal Paper
- 282 - 292
- 2007. Society of Petroleum Engineers
- 3.3 Well & Reservoir Surveillance and Monitoring, 5.5 Reservoir Simulation, 7.2.2 Risk Management Systems, 5.1.8 Seismic Modelling, 4.1.5 Processing Equipment, 5.1.5 Geologic Modeling, 5.1.9 Four-Dimensional and Four-Component Seismic, 4.3.4 Scale, 5.2.1 Phase Behavior and PVT Measurements, 1.2.3 Rock properties, 5.1.2 Faults and Fracture Characterisation, 5.6.1 Open hole/cased hole log analysis, 4.1.2 Separation and Treating, 5.5.8 History Matching
- 0 in the last 30 days
- 775 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 10.00|
|SPE Non-Member Price:||USD 30.00|
A method based on the ensemble Kalman filter (EnKF) for continuous model updating with respect to the combination of production data and 4D seismic data is presented. When the seismic data are given as a difference between two surveys, a combination of the ensemble Kalman filter and the ensemble Kalman smoother has to be applied. Also, special care has to be taken because of the large amount of data assimilated. Still, the method is completely recursive, with little additional cost compared to the traditional EnKF. The model system consists of a commercial reservoir simulator coupled with a rock physics and seismic modeling software. Both static variables (porosity, permeability, and rock physic parameters) and dynamic variables (saturations and pressures) may be updated continuously with time based on the information contained in the assimilated measurements. The method is applied to a synthetic model and a real field case from the North Sea. In both cases, the 4D seismic data are different variations of inverted seismic. For the synthetic case, it is shown that the introduction of seismic data gives a much better estimate of reservoir permeability. For the field case, the introduction of seismic data gives a very different permeability field than using only production data, while retaining the production match.
The Kalman filter was originally developed to update the states of linear systems (Kalman 1960). For a presentation of this method in a probabilistic, linear least-squares setting, see Tarantola (2005). However, this method is not suitable for nonlinear models, and the ensemble Kalman filter (EnKF) method was introduced in 1994 by Geir Evensen for updating nonlinear ocean models (Evensen 1994). The method may also be applied to a combined state and parameter estimation problem (Evensen 2006; Lorentzen 2001; Anderson 1998). Several recent investigations have shown the potential of the EnKF for continuous updating of reservoir simulation models, as an alternative to traditional history matching (Nævdal et al. 2002a, b; Nævdal et al. 2005; Gu and Oliver 2004; Gao and Reynolds 2005; Wen and Chen 2005). The EnKF method is a Monte Carlo type sequential Bayesian inversion, and provides an approximate solution to the combined parameter and state-estimation problem. The result is an ensemble of solutions approximating the posterior probability density function for the model input parameters (e.g., permeability and porosity), state variables (pressures and saturations), and other output data (e.g., well production history) conditioned to measured, dynamic data.
Conditioning reservoir simulation models to seismic data is a difficult task (Gosselin et al. 2003). In this paper, we show how the ensemble Kalman filter method can be used to update a combined reservoir simulation/seismic model using the combination of production data and inverted 4D seismic data. There are special challenges involved in the assimilation of the large amount of data available with 4D seismic, and the present work is based on the work presented by Evensen (2006, 2004) and Evensen and van Leeuwen (2000). In the following, the combined state and parameter estimation problem is described in a Bayesian framework, and it is shown how this problem is solved using the EnKF method, with emphasis on the application to 4D seismic data. When the seismic data are given as a difference between two surveys, a combination of the ensemble Kalman filter and the ensemble Kalman smoother has to be applied. Special challenges involved when the amount of data is very large are discussed. The validity of the method is examined using a synthetic model, and finally, a real case from the North Sea is presented.
|File Size||5 MB||Number of Pages||11|
Aanonsen, S.I. et al. 2003. Effect of Scale Dependent DataCorrelations in an Integrated History Matching Loop Combining Production Dataand 4D Seismic Data. Paper SPE 79665 presented at the SPE ReservoirSimulation Symposium, Houston, 3-5 February. DOI: 10.2118/79665-MS.
Anderson, J.L. 1998. An Ensemble Adjustment Kalman Filter. MonthlyWeather Review 126: 1719-1724.
Cressie, N.A.C. 1991. Statistics for Spatial Data. New York City:Wiley.
Evensen, G. 1994. Sequential data assimilation with a nonlinearquasi-geostrophic model using Monte Carlo methods to forecast error statistics.J. Geophys. Res. 99: 10,143-10,162.
Evensen, G. 2004. Sampling strategies and square root analysis schemes forthe EnKF. Ocean Dynamics 54: 539-560.
Evensen, G. 2006. Data Assimilation: The Ensemble Kalman Filter.Berlin: Springer-Verlag.
Evensen, G. and van Leeuwen, P.J. 2000. An Ensemble Kalman Smoother forNonlinear Dynamics. Monthly Weather Review 128: 1852-1867.
Gao, G., Zafari, M., and Reynolds, A.C. 2006. Quantifying Uncertainty for thePUNQ-S3 Problem in a Bayesian Setting With RML and EnKF. SPEJ11 (4): 506-515. SPE-93324-PA. DOI: 10.2118/93324-PA.
Gosselin, O. et al. 2003. History Matching Using Time-LapseSeismic (HUTS). Paper SPE 84464 presented at the SPE Annual TechnicalConference and Exhibition, Denver, 5-8 October. DOI: 10.2118/84464-MS.
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.
Haverl, M.C., Aga, M., and Reiso, E. 2005. Integrated Workflow for QuantitativeUse of Time-Lapse Seismic Data in History Matching: A North Sea Field Case.Paper SPE 94453 presented at the SPE Europec/EAGE Annual Conference, Madrid,13-16 June. DOI: 10.2118/94453-MS.
Kalman, R.E. 1960. A New Approach to Linear Filtering and PredictionProblems. Trans. ASME, J. Basic Eng. 3: 33-45.
Keepert, J.D. 2004. On Ensemble Representation of the Observation ErrorCovariance in the Ensemble Kalman Filter. Ocean Dynamics 6:539-560.
Lecomte, I., Gjøystdal, H., and Drottning, Å. 2003. Simulated Prestack LocalImaging: A robust and efficient interpretation tool to control illumination,resolution, and time-lapse properties of reservoirs. Proc., SEGInternational Exposition and Seventy-Third Annual Meeting, Dallas, 26-31October, 1529-1532.
Lorentzen, R. J. et al. 2001. Underbalanced and Low-Head DrillingOperations: Real Time Interpretation of Measured Data and OperationalSupport. Paper SPE 71384 presented at the SPE Annual Technical Conferenceand Exhibition, New Orleans, 30 September-3 October. DOI: 10.2118/71384-MS.
Nævdal, G., Mannseth, T., and Vefring, E. H. 2002a. 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., Mannseth, T., and Vefring, E. H. 2002b. Instrumented wells andnear-well reservoir monitoring through ensemble Kalman filter. Proc.,European Conference on the Mathematics of Oil Recovery VIII, Freiberg, Germany,3-6 September.
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.
http://www.nersc.no/~geir/EnKF. EnKF Home Page. Geir Evensen, ed.
Tarantola, A. 2005. Inverse Problem Theory and Methods for ModelParameter Estimation. Philadelphia: The Society for Industrial and AppliedMathematics.
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.