Uncertainty quantification of reservoir performance predictions using a stochastic optimization algorithm

Computational Geosciences

Volumn 15, Issue 3, 2011, Pages 451-462

  Li, Gaoming ^a   Reynolds, Albert C ^a  

^a The University of Tulsa   (United States)

Author keywords

History matching; Quasi Newton; RML; SGSD; SPSA; Uncertainty quantification

Indexed keywords

ALGORITHM; DEFORMATION; ESTIMATION METHOD; GAUSSIAN METHOD; HYDROCARBON EXPLORATION; HYDROCARBON RESERVOIR; MAXIMUM LIKELIHOOD ANALYSIS; OPTIMIZATION; STOCHASTICITY;

EID: 79957838364     PISSN: 14200597     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10596-010-9214-2     Document Type: Article

References (34)

1. Aanonsen, S. I., Nævdal, G., Oliver, D. S., Reynolds, A. C., Vallès, B.: Review paper: ensemble Kalman filter to petroleum engineering. SPE J. 14(3), 393-412 (2009).
2. Bangerth, W., Klie, H. Wheeler, M. Stoffa, P., Sen, M.: On optimization algorithm for the reservoir oil well placement problem. Comput. Geosci. 10(3), 303-319 (2006).
3. Barker, J. W., Cuypers, M., Holden, L.: Quantifying uncertainty in production forecasts: another look at the PUNQ-S3 problem. SPE J. 6(4), 433-441 (2001).
4. Bianco, A., Cominelli, A., Dovera, L., Nævdal, G., Vallès, B.: History matching and production forecast uncertainty by means of the ensemble Kalman filter: a real field application. In: SPE107161 in Proceedings of EAGE/EUROPEC Conference and Exhibition, London, UK (2007).
5. Evensen, G.: Data Assimilation: The Ensemble Kalman Filter. Springer, Berlin (2007).
6. Evensen, G., Hove, J., Meisingset, H. C., Reiso, E., Seim, K. S., Espelid, Ø: Using the EnKF for assisted history matching of a North Sea reservoir. In: SPE-106184 in Proceedings of the SPE Reservoir Simulation Symposium (2007).
7. Floris, F. J. T., Bush, M. D., Cuypers, M., Roggero, F., Syversveen, A.-R.: Methods for quantifying the uncertainty of production forecasts: a comparative study. Pet. Geosci. 7(SUPP), 87-96 (2001).
8. Gao, G.: Data integration and uncertainty evaluation for large scale automatic history matching problems. Ph. D. thesis, University of Tulsa (2005).
9. Gao, G., Reynolds, A. C.: An improved implementation of the LBFGS algorithm for automatic history matching. SPE J. 11(1), 5-17 (2006).
10. Gao, G., Zafari, M., Reynolds, A. C.: Quantifying uncertainty for the PUNQ-S3 problem in a Bayesian setting with RML and EnKF. SPE J. 11(4), 506-515 (2006).
11. Gao, G., Li, G., Reynolds, A. C.: A stochastic optimization algorithm for automatic history matching. SPE J. 12(2), 196-208 (2007).
12. Haugen, V., Natvik, L.-J., Evensen, G., Berg, A., Flornes, K., Nævdal, G.: History matching using the ensemble Kalman filter on a North Sea field case. In: SPE-102430 in Proceedings of the SPE Annual Technical Conference and Exhibition (2006).
13. Hu, L. Y.: Gradual deformation and iterative calibration of Gaussian-related stochastic models. Math. Geol. 32(1), 87-108 (2000).
14. Hu, L. Y., Blanc, G., Noetinger, B.: Gradual deformation and iterative calibration of sequential stochastic simulations. Math. Geol. 33(4), 475-489 (2001).
15. Kitanidis, P. K.: Parameter uncertainty in estimation of spatial functions: Bayesian estimation. Water Resour. Res. 22(4), 499-507 (1986).
16. Le Ravalec, M., Hu, L. Y., Noetinger, B.: Stochastic reservoir modeling constrained to dynamic data: local calibration and inference of the structural parameters. In: SPE-56556 in Proceedings of the SPE Annual Technical Conference and Exhibition, Houston, 3-6 October 1999.
17. Le Ravalec, M., Noeinger, B.: Optimization with the gradual deformation method. Math. Geol. 34(2), 125-142 (2002).
18. Li, R., Reynolds, A. C., Oliver, D. S.: Sensitivity coefficients for three-phase flow history matching. J. Can. Pet. Technol. 42(4), 70-77 (2003).
19. Nævdal, G., Johnsen, L. M., Aanonsen, S. I., Vefring, E. H.: Reservoir monitoring and continuous model updating using ensemble Kalman Filter. SPE J. 10(1), 66-74 (2005).
20. Oliver, D. S., He, N., Reynolds, A. C.: Conditioning permeability fields to pressure data. In: European Conference for the Mathematics of Oil Recovery V (1996).
21. Oliver, D. S., Reynolds A. C., Liu, N.: Inverse Theory for Petroleum Reservoir Characterization and History Matching. Cambridge University Press, Cambridge (2008).
22. Reynolds, A. C., He, N., Oliver, D. S.: Reducing uncertainty in geostatistical description with well testing pressure data. In: Schatzinger, R. A., Jordan J. F. (eds) Reservoir Characterization: Recent Advances, pp. 149-162. American Association of Petroleum Geologists, Tulsa (1999).
23. Reynolds, A. C., Zafari, M., Li, G.: Iterative forms of the ensemble Kalman Filter. In: Proceedings of 10th European Conference on the Mathematics of Oil Recovery, Amsterdam, 4-7 September 2006.
24. Rodrigues, J. R. P.: Calculating derivatives for automatic history matching. Comput. Geosci. 10, 119-136 (2006).
25. Spall, J. C.: A stochastic approximation technique for generating maximum likelihood parameter estimates. In: Proceedings of the American Control Conference, pp 1161-1167, Minneapolis, MN, 10-12 June 1987.
26. Spall, J. C.: Multivariate stochastic approximation using a simultaneous perturbation gradient approximation. IEEE Trans. Automat. Contr. 37, 332-341 (1992).
27. Spall, J. C.: Implementation of the simultaneous perturbation algorithm for stochastic optimization. IEEE Trans. Aerosp. Electron. Syst. 34, 817-823 (1998).
28. Tarantola, A.: Inverse Problem Theory: Methods for Data Fitting and Model Parameter Estimation. Elsevier, Amsterdam (1987).
29. Thulin, K., Li, G., Aanonsen, S. I., Reynolds, A. C.: Estimation of initial fluid contacts by assimilation of production data with EnKF. In: SPE-109975 in Proceedings of the SPE Annual Technical Conference and Exhibition (2007).
30. Wang, C., Li, G., Reynolds, A. C.: Production optimization in closed-loop reservoir management. SPE J. 14(3), 506-523 (2009).
31. Wang, Y., Li, G., Reynolds, A. C.: Estimation of depths of fluid contacts by history matching using iterative ensemble Kalman smoothers. SPE J. 15(2), 509-525 (2010).
32. Zhang, F., Reynolds, A. C.: Optimization algorithms for automatic history matching of production data. In: Proceedings of the European Conference on the Mathematics of Oil Recovery (2002).
33. Zhang, F., Skjervheim, J. A., Reynolds, A. C., Oliver, D. S.: Automatic history matching in a Bayesian framework: example applications. SPE Res. Eval. Eng. 8(3), 214-223 (2005).
34. Zhao, Y., Reynolds, A. C., Li, G.: Generating facies maps by assimilating production data and seismic data with the ensemble Kalman filter. In: SPE-113990 in Proceedings of the 2008 SPE Improved Oil Recovery Symposium, Tulsa, 20-23 April 2008.