Quantifying Expected Uncertainty Reduction and Value of Information Using Ensemble-Variance Analysis
- Jincong He (Chevron Energy Technology Company) | Pallav Sarma (Chevron Energy Technology Company (now with Tachyus Corporation)) | Eric Bhark (Chevron Energy Technology Company (now with Chevron Asia Pacific E&P Company)) | Shusei Tanaka (Chevron Energy Technology Company) | Bailian Chen (Chevron Energy Technology Company (now with Los Alamos National Laboratory)) | Xian-Huan Wen (Chevron Energy Technology Company) | Jairam Kamath (Chevron Energy Technology Company)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- April 2018
- Document Type
- Journal Paper
- 428 - 448
- 2018.Society of Petroleum Engineers
- Data Acquisition, Pilot, Surveillance, Value of Information, Uncertainty Reduction
- 5 in the last 30 days
- 361 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 5.00|
|SPE Non-Member Price:||USD 35.00|
Data-acquisition programs, such as surveillance and pilots, play an important role in minimizing subsurface risks and improving decision quality for reservoir management. For design optimization and investment justification of these programs, it is crucial to be able to quantify the expected uncertainty reduction and the value of information (VOI) attainable from a given design. This problem is challenging because the data from the acquisition program are uncertain at the time of the analysis. In this paper, a method called ensemble-variance analysis (EVA) is proposed. Derived from a multivariate Gaussian assumption between the observation data and the objective function, the EVA method quantifies the expected uncertainty reduction from covariance information that is estimated from an ensemble of simulations. The result of EVA can then be used with a decision tree to quantify the VOI of a given data-acquisition program.
The proposed method has several novel features compared with existing methods. First, the EVA method directly considers the data/objective-function relationship. Therefore, it can handle nonlinear forward models and an arbitrary number of parameters. Second, for cases when the multivariate Gaussian assumption between the data and objective function does not hold, the EVA method still provides a lower bound on expected uncertainty reduction, which can be useful in providing a conservative estimate of the surveillance/pilot performance. Finally, EVA also provides an estimate of the shift in the mean of the objective-function distribution, which is crucial for VOI calculation. In this paper, the EVA work flow for expected-uncertainty-reduction quantification is described. The result from EVA is benchmarked with recently proposed rigorous sampling methods, and the capacity of the method for VOI quantification is demonstrated for a pilot-analysis problem using a field-scale reservoir model.
|File Size||1 MB||Number of Pages||21|
Aanonsen, S. I., Nævdal, G., Oliver, D. S. et al. 2009. The Ensemble Kalman Filter in Reservoir Engineering—A Review. SPE J. 14 (3): 393–412. SPE-117274-PA. https://doi.org/10.2118/117274-PA.
Ballin, P. R., Ward, G. S., Whorlow, C. V. et al. 2005. Value of Information for a 4D-Seismic Acquisition Project. Presented at the SPE Latin American and Caribbean Petroleum Engineering Conference, Rio de Janeiro, 20–23 June. SPE-94918-MS. https://doi.org/10.2118/94918-MS.
Barros, E. G. D., Jansen, J. D., and Van den Hof, P. M. J. 2014. Value of Information in Closed-Loop Reservoir Management. Oral presentation given at ECMOR XIV–14th European Conference on Mathematics in Oil Recovery, Catania, Italy, 8–11 September.
Barros, E. G. D., Jansen, J. D., and Van den Hof, P. M. J. 2015. Value of Information in Closed-Loop Reservoir Management. Computat. Geosci. 20 (3): 737–749. https://doi.org/10.1007/s10596-015-9509-4.
Bibby, J. and Toutenburg, H. 1977. Prediction and Improved Estimation in Linear Models. Hoboken, New Jersey: Wiley.
Cameron, D. A. 2013. Optimization and Monitoring of Geological Carbon Storage Operations. PhD dissertation, Stanford University, Stanford, California.
Castellini, A., Gross, H., Zhou, Y. et al. 2010. An Iterative Scheme to Construct Robust Proxy Models. Oral presentation given at ECMOR XII–12th European Conference on the Mathematics of Oil Recovery, Oxford, UK, 6–9 September.
Chang, C. C. and Lin, C. J. 2011. LIBSVM: A Library for Support Vector Machines. ACM Trans. Intell. Syst. Technol. 2 (3): Article No. 27. https://doi.org/10.1145/1961189.1961199.
Chen, B., He, J., Wen, X.-H. et al. 2016. Pilot Design Analysis using Proxies and Markov Chain Monte Carlo Method. Oral presentation given at ECMOR XIV–14th European Conference on Mathematics in Oil Recovery, Catania, Italy, 8–11 September.
Chen, Y. and Oliver, D. S. 2012. Ensemble Randomized Maximum Likelihood Method as an Iterative Ensemble Smoother. Math. Geosci. 44 (1): 1–26. https://doi.org/10.1007/s11004-011-9376-z.
Eaton, M. L. 1983. Multivariate Statistics: A Vector Space Approach. Hoboken, New Jersey: Wiley.
Eeckhoudt, L. and Godfroid, P. 2000. Risk Aversion and the Value of Information. J. Econ. Educ. 31 (4): 382–388. https://doi.org/10.2307/1183152.
Emerick, A. A. and Reynolds, A. C. 2013. Investigation of the Sampling Performance of Ensemble-Based Methods with a Simple Reservoir Model. Computat. Geosci. 17 (2): 325–350. https://doi.org/10.1007/s10596-012-9333-z.
Geisser, S. 1993. Predictive Inference: An Introduction. Boca Raton, Florida: CRC Press.
Gerhardt, J. H. and Haldorsen, H. H. 1989. On the Value of Information. Presented at Offshore Europe, Aberdeen, 5–8 September. SPE-19291-MS. https://doi.org/10.2118/SPE-19291-MS.
Golub, G. H. and Van Loan, C. F. 2012. Matrix Computations, third edition. Baltimore, Maryland: Johns Hopkins University Press.
Guyaguler, B. and Byer, T. J. 2008. A New Rate-Allocation-Optimization Framework. SPE Prod & Oper 23 (4): 448–457. SPE-105200-PA. https://doi.org/10.2118/105200-PA.
Harville, D. 2003. C472. The Expected Value of a Conditional Variance: An Upper Bound. J. Stat. Comput. Sim. 73 (8): 609–612. https://doi.org/10.1080/0094965031000138173c.
He, J. and Durlofsky, L. J. 2015. Constraint Reduction Procedures for Reduced-Order Subsurface Flow Models based on POD-TPWL. Int. J. Numer. Meth. Eng. 103 (1): 1–30. https://doi.org/10.1002/nme.4874.
He, J., Sarma, P., and Durlofsky, L. J. 2013. Reduced-Order Flow Modeling and Geological Parameterization for Ensemble-Based Data Assimilation. Comput. Geosci. 55 (June): 54–69. https://doi.org/10.1016/j.cageo.2012.03.027.
He, J., Sarma, P., Bhark, E. et al. 2017a. Quantifying Value of Information using Ensemble Variance Analysis. Presented at the SPE Reservoir Simulation Conference, Montgomery, Texas, 20–22 February. SPE-182609-MS. https://doi.org/10.2118/182609-MS.
He, J., Tanaka, S., Wen, X.-H. et al. 2017b. Rapid S-Curve Update Using Ensemble Variance Analysis with Model Validation. Presented at the SPE Western Regional Meeting, Bakersfield, California, 23–27 April. SPE-185630-MS. https://doi.org/10.2118/185630-MS.
He, J., Xie, J., Sarma, P. et al. 2015. Model-Based A Priori Evaluation of Surveillance Programs Effectiveness Using Proxies. Presented at the SPE Reservoir Simulation Symposium, Houston, 23–25 February. SPE-173229-MS. https://doi.org/10.2118/173229-MS.
He, J., Xie, J., Sarma, P. et al. 2016a. Proxy-Based Work flow for A Priori Evaluation of Data-Acquisition Programs. SPE J. 21 (4): 1400–1412. SPE-173229-PA. https://doi.org/10.2118/173229-PA.
He, J., Xie, J., Wen, X. H. et al. 2016b. An Alternative Proxy for History Matching Using Proxy-for-Data Approach and Reduced Order Modeling. J. Pet. Sci. Eng. 146 (October): 392–399. https://doi.org/10.1016/j.petrol.2016.05.026.
Howard, R. A. and Abbas, A. E. 2015. Foundations of Decision Analysis. Upper Saddle River, New Jersey: Prentice Hall.
Koninx, J. P. M. 2001. Value of Information: From Cost Cutting to Value Creation. J Pet Technol 53 (4): 84–92. SPE-69839-JPT. https://doi.org/10.2118/69839-JPT.
Landa, J. L. 1997. Reservoir Parameter Estimation Constrained to Pressure Transients, Performance History and Distributed Saturation Data. PhD dissertation, Stanford University, Stanford, California.
Le, D. H. and Reynolds, A. C. 2014a. Optimal Choice of a Surveillance Operation Using Information Theory. Computat. Geosci. 18 (3–4): 505–518. https://doi.org/10.1007/s10596-014-9401-7.
Le, D. H. and Reynolds, A. C. 2014b. Estimation of Mutual Information and Conditional Entropy for Surveillance Optimization. SPE J. 19 (4): 648–661. SPE-163638-PA. https://doi.org/10.2118/163638-PA.
Mian, M. A. 2011. Project Economics and Decision Analysis: Probabilistic Models, second edition. Tulsa: Pennwell Books.
Moore, C. and Doherty, J. 2005. Role of the Calibration Process in Reducing Model Predictive Error. Water Resour. Res. 41 (5): W05020. https://doi.org/10.1029/2004WR003501.
Nævdal, G., Johnsen, L. M., Aanonsen, S. I. et al. 2005. Reservoir Monitoring and Continuous Model Updating Using Ensemble Kalman Filter. SPE J. 10 (1): 66–74. SPE-84372-PA. https://doi.org/10.2118/84372-PA.
Peters, L., Arts, R., Brouwer, G. et al. 2010. Results of the Brugge Benchmark Study for Flooding Optimization and History Matching. SPE Res Eval & Eng 13 (3): 391–405. SPE-119094-PA. https://doi.org/10.2118/119094-PA.
Pratt, J. W. 1964. Risk Aversion in the Small and in the Large. Econometrica 32 (1/2): 122–136.
Sarma, P. 2015. Efficient Identification of Leading Indicators for Improved Decision Making Uncertainty. Oral presentation given at the SIAM Conference on Mathematical & Computational Issues in Geosciences, Stanford, California, 29 June–2 July.
Satija, A. and Caers, J. 2015. Direct Forecasting of Subsurface Flow Response from Non-Linear Dynamic Data by Linear Least-Squares in Canonical Functional Principal Component Space. Adv. Water Resour. 77 (March): 69–81. https://doi.org/10.1016/j.advwatres.2015.01.002.
Sun, W., Durlofsky, L., and Hui, M. 2016. Production Forecasting and Uncertainty Quantification for a Naturally Fractured Reservoir using a New Data-Space Inversion Procedure. Oral presentation given at the ECMOR XIV–15th European Conference on the Mathematics of Oil Recovery, Amsterdam, 29 August–1 September.
van Leeuwen, P. J. and Evensen, G. 1996. Data Assimilation and Inverse Methods in Terms of a Probabilistic Formulation. Mon. Weather Rev. 124 (12): 2898–2913. https://doi.org/10.1175/1520-0493(1996)124%3C2898:DAAIMI%3E2.0.CO;2.
Walker, G. J. and Lane, H. S. 2007. Assessing the Accuracy of History-Match Predictions and the Impact of Time-Lapse Seismic Data: A Case Study for the Harding Reservoir. Presented at the SPE Reservoir Simulation Symposium, Houston, 26–28 February. SPE-106019-MS. https://doi.org/10.2118/106019-MS.
Wen, X.-H. and Chen, W. H. 2006. Real-Time Reservoir Model Updating Using Ensemble Kalman Filter with Confirming Option. SPE J. 11 (4): 431–442. SPE-92991-PA. https://doi.org/10.2118/92991-PA.
Yeten, B., Castellini, A., Gu¨yagu¨ ler, B. et al. 2005. A Comparison Study on Experimental Design and Response Surface Methodologies. Presented at the SPE Reservoir Simulation Symposium, Houston, 31 January–2 February. SPE-93347-MS. https://doi.org/10.2118/93347-MS.