Structural Surface Uncertainty Modeling and Updating Using the Ensemble Kalman Filter
- Alexandra Seiler (Nansen Environmental and Remote Sensing Center) | Sigurd I. Aanonsen (Center for Integrated Petroleum Research) | Geir Evensen (Statoil) | Jan C. Rivenæs (Statoil)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- December 2010
- Document Type
- Journal Paper
- 1,062 - 1,076
- 2010. Society of Petroleum Engineers
- 5.1.5 Geologic Modeling, 5.1 Reservoir Characterisation, 5.1.7 Seismic Processing and Interpretation, 1.1 Well Planning, 5.1.8 Seismic Modelling, 5.5.8 History Matching, 5.1.1 Exploration, Development, Structural Geology
- Grid deformation, horizon uncertainty, Structural uncertainties, EnKF, grid updating
- 1 in the last 30 days
- 435 since 2007
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Although typically large uncertainties are associated with reservoir structure, the reservoir geometry is usually fixed to a single interpretation in history-matching workflows, and focus is on the estimation of geological properties such as facies location, porosity, and permeability fields. Structural uncertainties can have significant effects on the bulk reservoir volume, well planning, and predictions of future production.
In this paper, we consider an integrated reservoir-characterization workflow for structural-uncertainty assessment and continuous updating of the structural reservoir model by assimilation of production data. We address some of the challenges linked to structural-surface updating with the ensemble Kalman filter (EnKF).
An ensemble of reservoir models, expressing explicitly the uncertainty resulting from seismic interpretation and time-to-depth conversion, is created. The top and bottom reservoir-horizon uncertainties are considered as a parameter for assisted history matching and are updated by sequential assimilation of production data using the EnKF. To avoid modifications in the grid architecture and thus to ensure a fixed dimension of the state vector, an elastic-grid approach is proposed. The geometry of a base-case simulation grid is deformed to match the realizations of the top and bottom reservoir horizons.
The method is applied to a synthetic example, and promising results are obtained. The result is an ensemble of history-matched structural models with reduced and quantified uncertainty. The updated ensemble of structures provides a more reliable characterization of the reservoir architecture and a better estimate of the field oil in place.
|File Size||1 MB||Number of Pages||15|
Aanonsen, S.I., Nævdal, G., Oliver, D.S., Reynolds, A.C., and Vallès, B.2009. The Ensemble Kalman Filterin Reservoir Engineering--a Review. SPE J. 14 (3):393-412. SPE-117274-PA. doi: 10.2118/117274-PA.
Abrahamsen, P. 1993. Bayesian Kriging for Seismic Depth Conversion of aMulti-Layer Reservoir. In Geostatistics Tria ‘92, ed. A. Soares,385-398. Dordrecht, The Netherlands: Kluwer Academic Publishing.
Agbalaka, C. and Oliver, D.S. 2008. Application of the EnKF andLocalization to Automatic History Matching of Facies Distribution andProduction Data. Mathematical Geosciences 40 (4):353-374. doi: 10.1007/s11004-008-9155-7.
Caumon, G., Tertois, A.-L., and Zhang, L. 2007. Elements for StochasticStructural Perturbation of Stratigraphic Models. Proc., EAGE PetroleumGeostatistics, Cascais, Portugal, 10-14 September, Paper A02.
Chen, Y., Oliver, D.S., and Zhang, D. 2008. Data Assimilation forNonlinear Problems by Ensemble Kalman Filter With Reparameterization. J.Pet. Sci. Eng. 66 (1-2): 1-14. doi:10.1016/j.petrol.2008.12.002.
Evensen, G. 1994. SequentialData Assimilation With a Nonlinear Quasi-Geostrophic Model Using Monte CarloMethods to Forecast Error Statistics. J. of Geophysical Research 99 (C5): 10143-10162. 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. 2009a. Data Assimilation: The Ensemble Kalman Filter,second edition. Berlin: Springer Verlag.
Evensen, G. 2009b. TheEnsemble Kalman Filter for Combined State and Parameter Estimation. IEEEControl Systems Magazine 29 (3): 83-104. doi:10.1109/MCS.2009.932223.
Evensen, G. and van Leeuwen, P.J. 2000. AnEnsemble Kalman Smoother for Nonlinear Dynamics. Monthly WeatherReview 128 (6): 1852-1867. doi:10.1175/1520-0493(2000)128<1852:AEKSFN>2.0.CO;2.
Evensen, G., Hove, J., Meisingset, H.C., Reiso, E., Seim, K.S., and Espelid,S.O. 2007. Using the EnKF forAssisted History Matching of a North Sea Reservoir. Paper SPE 106184presented at the SPE Reservoir Simulation Symposium, Houston, 26-28 February.doi: 10.2118/106184-MS.
Fahimuddin, A., Aanonsen, S.I., and Mannseth, T. 2008. Effect of LargeNumber of Measurements on the Performance of EnKF Model Updating. Proc.,11th European Conference on the Mathematics of Oil Recovery (ECMOR XI), Bergen,Norway, 8-11 September.
Gu, Y. and Oliver, D.S. 2007. An Iterative Ensemble Kalman Filterfor Multiphase Fluid Flow Data Assimilation. SPE J. 12(4): 438-446. SPE-108438-PA. doi: 10.2118/108438-PA.
Holden, L., Mostad, P., Nielsen, B.F., Gjerde, J., Townsend, C., andOttesen, S. 2003. StochasticStructural Modeling. Mathematical Geology 35 (8):899-914. doi: 10.1023/B:MATG.0000011584.51162.69.
Jafarpour, B. and McLaughlin, D. 2009. EstimatingChannelized Reservoirs Permeabilities With the Ensemble Kalman Filter: TheImportance of Ensemble Design. SPE J. 14 (2): 374-388.SPE-108941-PA. doi: 10.2118/108941-PA.
Li, G. and Reynolds, A.C. 2007. An Iterative Ensemble Kalman Filterfor Data Assimilation. Paper SPE 109808 presented at the SPE AnnualTechnical Conference and Exhibition, Anaheim, California, USA, 11-14 November.doi: 10.2118/109808-MS.
Palatnik, B. M., Aanonsen, S.I., Zakirov, I.S., and Zakirov, E.S. 1994. NewTechnique To Improve Efficiency of History Matching of Full-Field Models.Proc., 4th European Conference on the Mathematics of Oil Recovery (ECMORIV), Røros, Norway, 7-10 June.
Reynolds, A.C., Zafari, M., and Li, G. 2006. Iterative Forms of the EnsembleKalman Filter. Proc., 10th European Conference on the Mathematics of OilRecovery (ECMOR X), Amsterdam, 4-7 September, Paper A030.
Rivenæs, J., Otterlei, C., Zachariassen, E., Dart, C., and Sjøholm, J. 2005.A 3D Stochastic ModelIntegrating Depth, Fault and Property Uncertainty for Planning Robust Wells,Njord Field, offshore Norway. Petroleum Geoscience 11(1): 57-65. doi: 10.1144/1354-079303-612.
Schaaf, T., Coureaud, B., and Labaune, F. 2009. Joint Structural and PetrophysicalHistory Matching Leads to Global Geological Stochastic Reservoir Models.Paper SPE 121899 presented at the EUROPEC/EAGE Conference and Exhibition,Amsterdam, 8-11 June. doi: 10.2118/121899-MS.
Seiler, A., Evensen, G., Skjervheim, J.-A., and Vabø, J.G. 2009. Advanced Reservoir ManagementWorkflow Using an EnKF Based Assisted History Matching Method. Paper SPE118906 presented at the SPE Reservoir Simulation Symposium, The Woodlands,Texas, USA, 2-4 February. doi: 10.2118/118906-MS.
Suzuki, S. and Caers, J. 2006. History Matching With an UncertainGeological Scenario. Paper SPE 102154 presented at the SPE Annual TechnicalConference and Exhibition, San Antonio, Texas, USA, 24-27 September. doi:10.2118/102154-MS.
Suzuki, S. Caumon, G., and Caers, J. 2008. Dynamic Data Integration forStructural Modeling: Model Screening Approach Using a Distance-Based ModelParameterization. Computational Geosciences 12 (1):105-119. doi: 10.1007/s10596-007-9063-9.
Thore, P. and Shtuka, A. 2008. Integration of Structural Uncertainties IntoReservoir Grid Construction. Paper I022 presented at the 70th EAGE Conferenceand Exhibition, Rome, 9-12 June.
Thore, P., Shtuka, A., Lecour, M., Ait-Ettajer, T., and Cognot, R. 2002. Structural Uncertainties:Determination, Management, and Applications. Geophysics 67 (3): 840-852. doi: 10.1190/1.1484528.
Wang, Y., Li, G., and Reynolds, A.C. 2009. Estimation of Depths of FluidContacts by History Matching Using Iterative Ensemble Kalman Smoothers.Paper SPE 119056 presented at the SPE Reservoir Simulation Symposium, TheWoodlands, Texas, USA, 2-4 February. doi: 10.2118/119056-MS.
Zhang, Y. and Oliver, D.S. 2009. History Matching Using aHierarchical Stochastic Model With the Ensemble Kalman Filter: A Field CaseStudy. Paper SPE 118879 presented at the SPE Reservoir SimulationSymposium, The Woodlands, Texas, USA, 2-4 February. doi:10.21188/118879-MS.
Zhao, Y., Reynolds, A.C., and Li, G. 2008. Generating Facies Maps byAssimilating Production Data and Seismic Data With the Ensemble KalmanFilter. Paper SPE 113990. Paper SPE 113990 presented at the SPE/DOESymposium on Improved Oil Recovery, Tulsa, 20-23 April. doi:10.2118/113990-MS.