History Matching Using the Ensemble Kalman Filter on a North Sea Field Case
- Vibeke Eilwn J. Haugen (StatoilHydro) | Geir Naevdal (Intl Research Inst of Stavanger) | Lars-Joergen Natvik (Statoil ASA) | Geir Evensen (StatoilHydro) | Aina M. Berg (IRIS) | Kristin M. Flornes (IRIS)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- December 2008
- Document Type
- Journal Paper
- 382 - 391
- 2008. Society of Petroleum Engineers
- 4.2 Pipelines, Flowlines and Risers, 1.6 Drilling Operations, 4.3.4 Scale, 5.1.5 Geologic Modeling, 5.5.8 History Matching, 4.1.5 Processing Equipment, 5.3.2 Multiphase Flow, 5.6.9 Production Forecasting, 5.6.4 Drillstem/Well Testing, 5.5.3 Scaling Methods, 5.5 Reservoir Simulation, 2.2.2 Perforating, 5.2.1 Phase Behavior and PVT Measurements, 4.1.2 Separation and Treating, 3.3 Well & Reservoir Surveillance and Monitoring
- 1 in the last 30 days
- 638 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 5.00|
|SPE Non-Member Price:||USD 35.00|
This paper applies the ensemble Kalman filter (EnKF) to history match a North Sea field model. This is, as far as we know, one of the first published studies in which the EnKF is applied in a realistic setting using real production data. The reservoir-simulation model has approximately 45,000 active grid cells, and 5 years of production data are assimilated. The estimated parameters consist of the permeability and porosity fields, and the results are compared with a model previously established using a manual history-matching procedure. It was found that the EnKF estimate improved the match to the production data. This study, therefore, supported previous findings when using synthetic models that the EnKF may provide a useful tool for history matching reservoir parameters such as the permeability and porosity fields.
The EnKF developed by Evensen (1994, 2003, 2007) is a statistical method suitable for data assimilation in large-scale nonlinear models. It is a Monte Carlo method, where model uncertainty is represented by an ensemble of realizations. The prediction of the estimate and uncertainty is performed by ensemble integration using the reservoir-simulation model. The method provides error estimates at any time based on information from the ensemble. When production data are available, a variance-minimizing scheme is used to update the realizations. The EnKF provides a general and model-independent formulation and can be used to improve the estimates of both the parameters and variables in the model. The method has previously been applied in a number of applications [e.g., in dynamical ocean models (Haugen and Evensen 2002), in model systems describing the ocean ecosystems (Natvik and Evensen 2003a, 2003b), and in applications within meteorology (Houtekamer et al. 2005)]. This shows that the EnKF is capable of handling different types of complex- and nonlinear-model systems.
The method was first introduced into the petroleum industry in studies related to well-flow modeling (Lorentzen et al. 2001, 2003). Nævdal et al. (2002) used the EnKF in a reservoir application to estimate model permeability focusing on a near-well reservoir model. They showed that there could be a great benefit from using the EnKF to improve the model through parameter estimation, and that this could lead to improved predictions. Nævdal et al. (2005) showed promising results estimating the permeability as a continuous field variable in a 2D field-like example. Gu and Oliver (2005) examined the EnKF for combined parameter and state estimation in a standardized reservoir test case. Gao et al. (2006) compared the EnKF with the randomized-maximum-likelihood method and pointed out several similarities between the methods. Liu and Oliver (2005a, 2005b) examined the EnKF for facies estimation in a reservoir-simulation model. This is a highly nonlinear problem where the probability-density function for the petrophysical properties becomes multimodal, and it is not clear how the EnKF can best handle this. A method was proposed in which the facies distribution for each ensemble member is represented by two normal distributed Gaussian fields using a method called truncated pluri-Gaussian simulation (Lantuéjoul 2002). Wen and Chen (2006) provided another discussion on the EnKF for estimation of the permeability field in a 2D reservoir-simulation model and examined the effect of the ensemble size. Lorentzen et al. (2005) focused on the sensitivity of the results with respect to the choice of initial ensemble using the PUNQ-S3. Skjervheim et al. (2007) used the EnKF to assimilate seismic 4D data. It was shown that the EnKF can handle these large data sets and that a positive impact could be found despite the high noise level in the data.
The EnKF has some important advantages when compared to traditional assisted history-matching methods; the result is an ensemble of history-matched models that are all possible model realizations. The data are processed sequentially in time, meaning that new data are easily accounted for when they arrive. The method allows for simultaneous estimation of a huge number of poorly known parameters such as fields of properties defined in each grid cell.
By analyzing the EnKF update equations, it is seen that the actual degrees of freedom in the estimation problem are limited equal to the ensemble size. One is still able to update the most important features of large-scale models. A limitation of the EnKF is the fact that its computations are based on first- and second-order moments, and there are problems that are difficult to handle, particularly when the probability distributions are multimodal (e.g., when representing a bimodal channel facies distribution).
This paper considers the use of the EnKF for estimating dynamic and static parameters, focusing on permeability and porosity, in a field model of a StatoilHydro-operated field in the North Sea. The largest uncertainty in the model is expected to be related to the permeability values, especially in the upper part of the reservoir where the uncertainty may be as large as 30%.
|File Size||6 MB||Number of Pages||10|
Bennett, A.F. 1992. Inverse Methods in Physical Oceanography.Cambridge, UK: Cambridge University Press.
Bianco, A., Cominelli, A., Dovera, L., Naevdal, G., and Vallès, B. 2007. History Matching and ProductionForecast Uncertainty by Means of the Ensemble Kalman Filter: A Real FieldApplication. Paper SPE 107161 presented at the Europec/EAGE Conference andExhibition, London, 11-14 June. doi: 10.2118/107161-MS.
Evensen, G. 1992. Using theextended Kalman filter with a multilayer quasi-geostrophic ocean model.J. Geophys. Res. 97 (C11): 17905-17924.doi:10.1029/92JC01972.
Evensen, G. 1994. Sequentialdata assimilation with a nonlinear quasi-geostrophic model using Monte Carlomethods to forecast error statistics. J. Geophys. Res. 99(C5): 10,143-10,162. doi:10.1029/94JC00572.
Evensen, G. 2003. Theensemble Kalman filter: Theoretical formulation and practicalimplementation. Ocean Dynamics 53 (4): 343-367.doi:10.1007/s10236-003-0036-9.
Evensen, G. 2007. Data Assimilation: The Ensemble Kalman Filter.Heidelberg, Germany: Springer-Verlag.
Evensen, G., Hove, J., Meisingset, H.C., Reiso, E., Seim, K.S., and Espelid,O. 2007. Using the EnKF forAssisted History Matching of a North Sea Reservoir Model. Paper SPE 106184presented at the SPE Reservoir Simulation Symposium, Houston, 26-28 February.doi: 10.2118/106184-MS.
Gao, G., Zafari, M., and Reynolds, A.C. 2006. Quantifying the 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.
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.
Haugen, V.E.J. and Evensen, G. 2002. Assimilation of SST and SLAdata into an OGCM for the Indian Ocean. Ocean Dynamics 52(3): 133-151. doi:10.1007/s10236-002-0014-7.
Houtekamer, P.L., Mitchell, H.L., Pellerin, G., Buehner, M., Charron, M.,Spacek, L., and Hansen, B. 2005. Atmospheric data assimilation withan ensemble Kalman filter: Results with real observations. MonthlyWeather Review 133 (3): 604-620. doi:10.1175/MWR-2864.1.
Jazwinski, A.H. 1970. Stochastic Processes and Filtering Theory, Vol.68. New York City: Mathematics in Science & Engineering series, AcademicPress.
Kalman, R.E. 1960. A new approach to linear filter and prediction problems.Transactions of the ASME--Journal of Basic Engineering 82 (SeriesD): 35-45.
Lantuéjoul, C. 2002. Geostatistical Simulation: Models andAlgorithms. Heidelberg, Germany: Springer-Verlag.
Liu, N. and Oliver, D.S. 2005a. Critical Evaluation of the EnsembleKalman Filter on History Matching of Geologic Facies. SPEREE8 (6): 470-477. SPE-92867-PA. doi: 10.2118/92867-PA.
Liu, N. and Oliver, D.S. 2005b. Ensemble Kalman filterfor automatic history matching of geologic facies. J. Pet. Sci. Eng.47 (3-4): 147-161. doi:10.1016/j.petrol.2005.03.006.
Lorentzen, R.J., Fjelde, K.K., Frøyen, J., Lage, A.C.V.M., Nævdal, G., andVefring, E.H. 2001. Underbalancedand Low-head Drilling Operations: Real Time Interpretation of Measured Data andOperational Support. Paper SPE 71384 presented at the SPE Annual TechnicalConference and Exhibition, New Orleans, 30 September-3 October. doi:10.2118/71384-MS.
Lorentzen, R.J., Nævdal, G., and Lage, A.C.V.M. 2003. Tuning of parameters ina two-phase flow model using ensemble Kalman filter. Int. J. MultiphaseFlow 29 (8): 1283-1309. doi:10.1016/S0301-9322(03)00088-0.
Lorentzen, R.J., Nævdal, G., Vallès, 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.
Nævdal, G., Johnsen, L.M., Aanonsen, S.I., and Vefring, E. 2005. Reservoir Monitoring and ContinuousModel Updating Using Ensemble Kalman Filter. SPEJ 10 (1):66-74. SPE-84372-PA. doi: 10.2118/84372-PA.
Nævdal, G., Mannseth, T., and Vefring, E. 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.
Natvik, L.-J. and Evensen, G. 2003a. Assimilation of oceancolour data into a biochemical model of the North Atlantic. Part 1. Dataassimilation experiments. J. of Marine Systems 40-41 (April2003): 127-153. doi:10.1016/S0924-7963(03)00016-2.
Natvik, L.-J. and Evensen, G. 2003b. Assimilation of oceancolour data into a biochemical model of the North Atlantic. Part 2. Statisticalanalysis. J. of Marine Systems 40-41 (April 2003): 155-169.doi:10.1016/S0924-7963(03)00017-4.
Skjervheim, J.-A., Evensen, G., Aanonsen, S.I., Ruud, B.O., and Johansen,T.A. 2007. Incorporating 4DSeismic Data in Reservoir Simulation Models Using Ensemble Kalman Filter.SPEJ 12 (3): 282-292. SPE-95789-PA. doi: 10.2118/95789-PA.
Thulin, K. and Nævdal, G. 2006. Ensemble Kalman filter for fieldestimation--Investigations on the effect of the ensemble size. Paper presentedat the 10th European Conference on the Mathematics of Oil Recovery, Amsterdam,4-7 September.
Wen, X.-H. and Chen, W.H. 2006. Real Time Reservoir Model UpdatingUsing the Ensemble Kalman Filter With Confirming Opinion. SPEJ11 (4): 431-442. SPE-92991-PA. doi: 10.2118/92991-PA.