Systematic Uncertainty Reduction for Petroleum Reservoirs Combining Reservoir Simulation and Bayesian Emulation Techniques
- Helena Nandi Formentin (Durham University and University of Campinas) | Ian Vernon (Durham University) | Guilherme Daniel Avansi (University of Campinas) | Camila Caiado (Durham University) | Célio Maschio (University of Campinas) | Michael Goldstein (Durham University) | Denis José Schiozer (University of Campinas)
- Document ID
- Society of Petroleum Engineers
- SPE Europec featured at 81st EAGE Conference and Exhibition, 3-6 June, London, England, UK
- Publication Date
- Document Type
- Conference Paper
- 2019. Society of Petroleum Engineers
- Uncertainty Reduction, Simulation target, Emulation, Bayesian History Matching, Systematic procedure
- 10 in the last 30 days
- 57 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 9.50|
|SPE Non-Member Price:||USD 28.00|
Reservoir simulation models incorporate physical laws and reservoir characteristics. They represent our understanding of sub-surface structures based on the available information. Emulators are statistical representations of simulation models, offering fast evaluations of a sufficiently large number of reservoir scenarios, to enable a full uncertainty analysis. Bayesian History Matching (BHM) aims to find the range of reservoir scenarios that are consistent with the historical data, in order to provide comprehensive evaluation of reservoir performance and consistent, unbiased predictions incorporating realistic levels of uncertainty, required for full asset management. We describe a systematic approach for uncertainty quantification that combines reservoir simulation and emulation techniques within a coherent Bayesian framework for uncertainty quantification.
Our systematic procedure is an alternative and more rigorous tool for reservoir studies dealing with probabilistic uncertainty reduction. It comprises the design of sets of simulation scenarios to facilitate the construction of emulators, capable of accurately mimicking the simulator with known levels of uncertainty. Emulators can be used to accelerate the steps requiring large numbers of evaluations of the input space in order to be valid from a statistical perspective. Via implausibility measures, we compare emulated outputs with historical data incorporating major process uncertainties. Then, we iteratively identify regions of input parameter space unlikely to provide acceptable matches, performing more runs and reconstructing more accurate emulators at each wave, an approach that benefits from several efficiency improvements. We provide a workflow covering each stage of this procedure.
The procedure was applied to reduce uncertainty in a complex reservoir case study with 25 injection and production wells. The case study contains 26 uncertain attributes representing petrophysical, rock-fluid and fluid properties. We selected phases of evaluation considering specific events during the reservoir management, improving the efficiency of simulation resources use. We identified and addressed data patterns untracked in previous studies: simulator targets, e.g. liquid production, and water breakthrough lead to discontinuities in relationships between outputs and inputs. With 15 waves and 115 valid emulators, we ruled out regions of the searching space identified as implausible, and what remained was only a small proportion of the initial space judged as non-implausible (~10−11%). The systematic procedure showed that uncertainty reduction using iterative Bayesian History Matching has the potential to be used in a large class of reservoir studies with a high number of uncertain parameters.
We advance the applicability of Bayesian History Matching for reservoir studies with four deliveries: (a) a general workflow for systematic BHM, (b) the use of phases to progressively evaluate the historical data; and (c) the integration of two-class emulators in the BHM formulation. Finally, we demonstrate the internal discrepancy as a source of error in the reservoir model.
|File Size||4 MB||Number of Pages||46|
Almeida, F. L. R., Formentin, H. N., Maschio, C.. 2018. Influence of Additional Objective Functions in the History Matching and Uncertainty Reduction. Proc., SPE Europec Featured at 80th EAGE Conference and Exhibition, Copenhagen, Denmark, 11-14 June, SPE-190804-MS. https://doi.org/10.2118/190804-MS.
Almeida, F. L. R., Davolio, A., and Schiozer, D.J. 2014. A New Approach to Perform a Probabilistic and Multi-Objective History Matching. Proc., SPE Annual Technical Conference and Exhibition, Amsterdam, The Netherlands, 27-29 October, SPE-170623-MS. https://doi.org/10.2118/170623-MS.
Altman, D. G. and Bland, J. M. 1994. Diagnostic Tests 2: Predictive Values. BMJ Jul 9 309 (6947): 102. https://doi.org/10.1136/bmj.309.6947.102.
Avansi, G., Rios, V., and Schiozer, D.J. 2019. Numerical Tuning in Reservoir Simulation: it is Worth the Effort in Practical Petroleum Applications. Journal of the Brazilian Society of Mechanical Sciences and Engineering (01/2019): 41–59. https://doi.org/10.1007/s40430-018-1559-9.
Baker, R. 1998. Reservoir Management for Waterfloods - Part II. Journal of Canadian Petroleum Technology 37 (1): 12–17. https://doi.org/10.2118/98-01-DA.
Barber, D. 2012. Bayesian Reasoning and Machine Learning. Cambridge: Cambridge University Press. Available in http://www.cs.ucl.ac.uk/staff/d.barber/brml/, 10/01/2019. ISBN: 9780521518147.
Bastos, L. S. and O'Hagan, A. 2009. Diagnostics for Gaussian Process Emulators. Technometrics 51 (4): 425–438. doi:10.1198/TECH.2009.08019.
Busby, D. 2009. Hierarchical Adaptive Experimental Design for Gaussian Process Emulators. Reliability Eng. and System Safety 94 (7): 1183–93. https://doi.org/10.1016/j.ress.2008.07.007.
Busby, D., Farmer, C. L. and Iske, A. 2007. Uncertainty Evaluation in Reservoir Forecasting by Bayes Linear Methodology. Proc., 5th International Conference, Algorithms for Approximation, Chester, July 2005. https://doi.org/10.1007/978-3-540-46551-5_14
Carrassi, A., Bocquet, M., Bertino, L.. 2018. Data Assimilation in the Geosciences: An Overview of Methods, Issues, and Perspectives. Wiley Interdisciplinary Reviews: Climate Change 9 (5): 1–79. doi:10.1002/wcc.535.
Craig, P. S., Goldstein, M., Rougier, J.C.. 2011. Bayesian Forecasting for Complex Systems Using Computer Simulations. Journal of the American Statistical Association 96: 717–729. https://doi.org/10.1198/016214501753168370
Craig, P S, Goldstein M., Seheult A.H.. 1996. Bayes Linear Strategies for Matching Hydrocarbon Reservoir History. In Bayesian Statistics 5 - Proceedings of the Fifth Valencia International Meeting June 5-9, 1994, ed. J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, 69–95. Oxford University Press.
Craig, P. S., Goldstein M., Seheult A. H.. 1997. Pressure Matching for Hydrocarbon Reservoirs: A Case Study in the Use of Bayes Linear Strategies for Large Computer Experiments. In: Case Studies in Bayesian Statistics. Lecture Notes in Statistics, ed. C. Gatsonis, J.S. Hodges, R. E. Kass, R. McCulloch, P. Rossi, N.D. Singpurwalla, Vol. 121: 37–93. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2290-3_2.
Evensen, G. 2018. Introducing Stochastic Model Errors in Ensemble-Based History Matching. Proc., ECMOR XVI – 16th European Conference on the Mathematics of Oil Recovery, Barcelona, 3-6 September 2018. doi:10.3997/2214-4609.201802280.
Evensen, G. 2018. Accounting for Model Errors in Iterative Ensemble Smoothers. ArXiv preprint:1806.00237 [Physics.Data-An], 1–17. Submitted on 1 Jun 2018. http://arxiv.org/abs/1806.00237.
Evensen, G. 2009. Data Assimilation: The Ensemble Kalman Filter, second edition. Berlin: Springer-Verlag Berlin Heidelberg. doi:10.1007/978-3-642-03711-5.
Evensen, G. and Eikrem, K. S. 2018. Conditioning Reservoir Models on Rate Data Using Ensemble Smoothers. Computational Geosciences 22 (5): 1251–70. https://doi.org/10.1007/s10596-018-9750-8.
Ferreira, C. J., Vernon, I. R., Schiozer, D. J.. 2014. Use of Emulator Methodology for Uncertainty Reduction Quantification. Proc., SPE Latin America and Caribbean Petroleum Engineering Conference, Maracaibo, Venezuela, 21-23 May, SPE-169405-MS. https://doi.org/10.2118/169405-MS.
Formentin, H. N., Almeida, F. L., Avansi, G. D.. 2019. Gaining More Understanding About Reservoir Behavior Through Assimilation of Breakthrough Time and Productivity Deviation in the History Matching Process. Journal of Petroleum Science and Engineering 173 (February): 1080–96. https://doi.org/10.1016/j.petrol.2018.10.045.
Goldstein, M., Seheult, A. and Vernon, I. 2013. Assessing model adequacy. In Environmental Modelling: Finding Simplicity in Complexity, second edition, ed. J. Wainwright and M. Mulligan, Chap. 26, 435–49. Wiley-Blackwell. https://doi.org/10.1002/9781118351475.ch26.
Goldstein, M. and Rougier, J. 2006. Bayes Linear Calibrated Prediction for Complex Systems. Journal of the American Statistical Association. 101 (475): 1132–43. https://doi.org/10.1198/016214506000000203.
Lawal, K. A., Utin, E. and Langaas, K. 2007. A Didactic Analysis of Water Cut Trend During Exponential Oil-Decline. Proc., Nigeria Annual International Conference and Exhibition, Abuja, Nigeria, 6-8 August, SPE-111920-MS. https://doi.org/10.2118/111920-MS.
Maschio, C. and Schiozer, D. J. 2016. Probabilistic History Matching Using Discrete Latin Hypercube Sampling and Nonparametric Density Estimation. Journal of Petroleum Science and Engineering 147: 98–115 (November 2017). https://doi.org/10.1016/j.petrol.2016.05.011.
Moreno, R., Avansi, G. D., Schiozer, D. J.. 2018. Emulation of Reservoir Production Forecast Considering Variation in Petrophysical Properties. Journal of Petroleum Science and Engineering 165 (June 2017): 711–25. https://doi.org/10.1016/j.petrol.2018.02.056.
O'Hagan, A. 2004. Bayesian Analysis of Computer Code Outputs. Reliability Engineering & System Safety 91 (10-11): 1290–1300. http://dx.doi.org/10.1016/j.ress.2005.11.025.
Oliver, D. and Chen, Y. 2011. Recent Progress on Reservoir History Matching: A Review. Computational Geosciences 15 (1): 185–221. https://doi.org/10.1007/s10596-010-9194-2.
Oliver, D., Reynolds, A. and Liu, N. 2008. Inverse Theory for Petroleum Reservoir Characterization and History Matching. Cambridge University Press. https://doi.org/10.1017/CBO9780511535642.
Pukelsheim, F. 1994. The Three Sigma Rule. The American Statistician 48 (2): 88–91. https://www.jstor.org/stable/2684253.
Vernon, I., Goldstein, M. and Bower, R. G. 2010. Galaxy Formation: A Bayesian Uncertainty Analysis. Bayesian Analysis 5 (4): 619–70. doi:10.1214/10-BA524.
Vernon, I., Liu, J., Goldstein, M., Rowe, J.. 2018. Bayesian Uncertainty Analysis for Complex Systems Biology Models: Emulation, Global Parameter Searches and Evaluation of Gene Functions. BMC Systems Biology 12 (1). https://doi.org/10.1186/s12918-017-0484-3.
Williamson, D. B., Blaker, A. T. and Sinha, B. 2017. Tuning without Over-Tuning: Parametric Uncertainty Quantification for the NEMO Ocean Model. Geoscientific Model Development 10 (4): 1789–1816. https://doi.org/10.5194/gmd-10-1789-2017.