Generating Multiple History-Matched Reservoir-Model Realizations Using Wavelets
- Isha Sahni (Stanford University) | Roland N. Horne (Stanford University)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- June 2006
- Document Type
- Journal Paper
- 217 - 226
- 2006. Society of Petroleum Engineers
- 5.6.1 Open hole/cased hole log analysis, 4.1.5 Processing Equipment, 4.3.4 Scale, 7.6.2 Data Integration, 4.1.2 Separation and Treating, 7.2.1 Risk, Uncertainty and Risk Assessment, 5.6.5 Tracers, 5.5.8 History Matching, 5.5 Reservoir Simulation, 5.6.4 Drillstem/Well Testing, 5.1 Reservoir Characterisation, 5.1.5 Geologic Modeling
- 1 in the last 30 days
- 521 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 10.00|
|SPE Non-Member Price:||USD 30.00|
This paper focuses on an automated way to generate multiple history-matched reservoir models with the inclusion of both geological uncertainty and varying levels of trust in the production data, using wavelet methods. As opposed to previously developed automated history-matching algorithms, this methodology not only ensures geological consistency in the final models but also includes uncertainty in the production data.
A data distribution, such as a permeability field, can be (reversibly) transformed into wavelet space in which it is fully described by a set of wavelet coefficients. It was found that different subsets of the collection of wavelet coefficients can be constrained separately to (a) the production history and (b) the geological constraints. This means that the history match need be performed only once, after which multiple realizations can be generated by adjusting only the second subset of coefficients.
The ability to include both geological and production-data uncertainty into the reservoir model automatically is of great consequence to reservoir modeling and, hence, to reservoir management, risk analysis, and making key economic decisions. A more complete and realistic reservoir model will lead to better reservoir production and development decisions.
Reservoir modeling is an important step in forecasting the performance of a reservoir, forming the basis for reservoir management, risk analysis, and making key economic decisions. A history match, however, is not a sufficient condition for a reservoir to make better predictions for future production. The model should at least conform to all the available data and the geologist's prior conception of the reservoir. Thus, the purpose of reservoir modeling is to use all available sources of information to develop such a reservoir model. This model then can be used to forecast future performance and optimize reservoir-management decisions.
It is essential to integrate all the different sources of data to provide the most complete reservoir model or models (Landa and Horne 1997; Landa 1997; Wang 2001). Our model certainty is always limited by the data available to us. As such, it is never possible to infer or develop a reservoir model with full certainty. However, the optimal use of all consistent data available will yield reservoir models that are less and less uncertain. Herein lies the significance of methodologies that can realistically and efficiently integrate different sources of reservoir information.
Reservoir data are, generally speaking, divided into two categories: production data (e.g., pressure and water-cut histories from wells) and all other sources of data (e.g., core samples, seismic, and well logs). This second category of data depends on reservoir properties like porosity and permeability in a relatively direct way. Core samples can be used to provide porosity and permeability measurements at specific locations (well locations); semivariograms (Deutsch and Journel 1998; Isaaks and Srivastava 1989) obtained from outcrops, for example, act as spatial statistics information, and seismic surveys may provide 3D impedance distributions that can be inverted and used as "soft-conditioning data?? at the corresponding locations. These different sources of data can be combined together with different approaches (e.g., Bayesian probability techniques) to give a single set of probabilities.
|File Size||2 MB||Number of Pages||10|
Anterion, F., Eymard, R., and Karcher, B. 1989. Use of Parameter Gradients forReservoir History Matching. Paper SPE 18433 presented at the SPE Symposiumon Reservoir Simulation, Houston, 6-8 February.
Bissel, R. 1996. History Matching a Reservoir Model by the Positioning ofGeological Objects. Paper presented at the 5th European Conference on theMathematics of Oil Recovery, Leoben, Austria, 3-6 September.
Boggess, A. and Narcowich, F.J. 2001. A First Course in Wavelets WithFourier Analysis. Upper Saddle River, New Jersey: Prentice-Hall.
Carter, R.D., Kemp, L.F. Jr., Pierce, A.C., and Williams, D.L. 1974. Performance Matching WithConstraints. SPEJ 14 (2): 187-196; Trans., AIME, 257. SPE-4260-PA.
Chen, W.H., Gavalas, G.R., Seinfeld, J.H., and Wasserman, M.L. 1974. A New Algorithm for Automatic HistoryMatching. SPEJ 14 (6): 593-608; Trans., AIME, 257. SPE-4545-PA.
Chu, L., Reynolds, A.C., and Oliver, D.S. 1995. Computation of SensitivityCoefficients for Conditioning the Permeability Field to Well-Test PressureData. In Situ 19 (2): 179-223.
Datta-Gupta, A., Vasco, D.W., and Long, J.C.S. 1997. On the Sensitivity and SpatialResolution of Transient Pressure and Tracer Data For HeterogeneityCharacterization. SPEFE 12 (2): 137-144. SPE-30589-PA.
Daubechies, I. 1988. Orthonormal Bases of Compactly Supported Wavelets.Comm. On Pure and Appl. Math. 41 (7): 909-996.
Daubechies, I. 1992. Ten Lectures on Wavelets. CBMS-NSF Regional ConferenceSeries in Applied Mathematics, Soc. for Industrial and Applied Mathematics(SIAM) 61: 115-137.
de Marsily, G., Lavedan, G., Boucher, M., and Fasanino, G. 1984.Interpretation of Interference Tests in a Well Field Using GeostatisticalTechniques to Fit the Permeability Distribution in a Reservoir Model. InGeostatistics for Natural Resources Characterization, Part 2: 831-849.
Deutsch, C.V. and Journel, A.G. 1998. GSLIB: Geostatistical Software Libraryand Users Guide, second edition. New York City: Oxford U. Press.
Gill, P.E., Murray W., and Wright, M.H. 1981. Practical Optimization. NewYork City: Academic Press.
Isaaks, E. and Srivastava, M. 1989. An Introduction toAppliedGeostatistics. New York City: Oxford U. Press.
Jacquard, P. and Jain, C. 1965. Permeability Distribution From FieldPressure Data. SPEJ 5 (4): 281-294; Trans., AIME, 234. SPE-1307-PA.
Jaffard, S. and Meyer, Y. 2001. Wavelets: Tools for Science and Technology.Philadelphia, Pennsylvania: Soc. for Industrial and Applied Mathematics(SIAM).
Landa, J.L. 1997. Reservoir Parameter Estimation Constrained to PressureTransients, Performance History and Distributed Saturation Data. PhDdissertation, Stanford U., Stanford, California.
Landa, J.L. and Horne, R.N. 1997. A Procedure to Integrate Well TestData, Reservoir Performance History and 4D Seismic Data Into a ReservoirDescription. Paper SPE 38653 presented at the SPE Annual TechnicalConference and Exhibition, San Antonio, Texas, 5-8 October.
Lu, P. 2001. Reservoir Parameter Estimation Using Wavelet Analysis. PhDdissertation, Stanford U., Stanford, California.
Lu, P. and Horne, R.N. 2000. AMultiresolution Approach to Reservoir Parameter Estimation Using WaveletAnalysis. Paper SPE 62985 presented at the SPE Annual Technical Conferenceand Exhibition, Dallas, 1-4 October.
Mallat, S. 1987. An Efficient Image Representation for Multiscale Analysis.Paper presented at the Machine Vision Conference, Lake Tahoe, February.
Sahni, I. 2003. Multiresolution Wavelet Analysis for Improved ReservoirDescription. MS report, Stanford U., Stanford, California.
Sahni, I. and Horne, R.N. 2005. Multiresolution Wavelet Analysis forImproved Reservoir Description. SPEREE 8 (1): 53-69. SPE-87820-PA.
Tarantola, A. 2003. Inverse Problem Theory and Methods for Model ParameterEstimation. Philadelphia, Pennsylvania: Soc. for Industrial and AppliedMathematics (SIAM).
Wang, Y. 2001. Streamline Approaches for Integrating Production History WithGeologic Information in Reservoir Models. PhD dissertation, Stanford U.,Stanford, California.
Wickerhauser, M.V. 1994. Adapted Wavelet Analysis From Theory to Software.Wellesley, Massachusetts: A.K. Peters.