An iterative ensemble Kalman filter for multiphase fluid flow data assimilation

SPE Journal

Volumn 12, Issue 4, 2007, Pages 438-446

  Gu, Yaqing ^b   Oliver, Deon S ^a  

^a BP AMERICA INC   (United States)

^b UNIVERSITY OF OKLAHOMA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; FLUID DYNAMICS; ITERATIVE METHODS; KALMAN FILTERS; POROUS MATERIALS;

DATA ASSIMILATION; ITERATIVE ENSEMBLE KALMAN FILTER; NONLINEAR PROBLEMS;

MULTIPHASE FLOW;

EID: 38349192524     PISSN: 1086055X     EISSN: None     Source Type: Journal    
DOI: 10.2118/108438-PA     Document Type: Article

References (45)

1. Anderson, J. L. 2001. An Ensemble Adjustment Kalman Filter for Data Assimilation. Monthly Weather Review 129 (12): 2884-2903. DOI
2. Anderson, J. L. 2003. A Local Least Squares Framework for Ensemble Filtering. Monthly Weather Review 131 (4): 634-642.
3. Anderson, J. L. and Anderson, S. L. 1999. A Monte Carlo Implementation of the Nonlinear Filtering Problem to Produce Ensemble Assimilations and Forecasts. Monthly Weather Review 127 (12): 2741-2758.
4. Bell, B. M. and Cathey, F. W. 1993. The iterated Kalman Filter Update as a Gauss-Newton Method. IEEE Transactions on Automatic Control 38 (2): 294-297.
5. Bishop, C. H., Etherton, B. J., and Majumdar, S. J. 2001. Adaptive Sampling With the Ensemble Transform Kalman Filter. Part I: Theoretical Aspects. Mon. Wea. Rev. 129: 420-436.
6. Chen, Y and Zhang, D. 2006. Data Assimilation for Transient Flow in Geologic Formations via Ensemble Kalman Filter. Advances in Water Resources 29 (8): 1107-1122.
7. Corset, G. P., Harmse, J. E., Corser, B. A., Weiss, M. W., and Whitflow, G. L. 2000. Field Test Results for a Real-Time Intelligent Drilling Monitor. Paper SPE 59227 presented at the IADC/SPE Drilling Conference, New Orleans, 23-25 February. DOI: 10.2118/59227-MS.
8. Dennis, J. E. and Schnabel, R. B. 1983. Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Prentice-Hall, Englewood Cliffs.
9. Dong, Y., Gu, Y., and Oliver, D. S. 2006. Sequential Assimilation of 4D Seismic Data for Reservoir Description Using the Ensemble Kalman Filter. Journal of Petroleum Science and Engineering 53 (1-2): 83-99.
10. Eisenmann, P., Gounot, M.-T., Juchereau, B., and Whittaker, S. J., 1994. Improved Rxo Measurements Through Semi-Active Focusing. Paper SPE 28437 presented at the SPE Annual Technical Conference and Exhibition, New Orleans, 25-28 September. DOI: 10.2118/28437-MS.
11. Evensen, G. 1994. Sequential Data Assimilation With a Nonlinear Quasi-geostrophic Model Using Monte Carlo Methods to Forecast Error Statistics. Journal of Geophysical Research 99 (C5): 10143-10162.
12. Evensen, G. 2003. The Ensemble Kalman Filter: Theoretical Formulation and Practical Implementation. Ocean Dynamics 53: 343-367.
13. Evensen, G., Hove, J., Meisingset, H. C., Reiso, E., Seim, K. S., and Espelid, O. 2007. Using the EnKF for Assisted History Matching of a North Sea Reservoir Model. Paper SPE 106184 presented at the SPE Reservoir Simulation Symposium, Houston, 26-28 February. DOI: 10.2118/ 106184-MS.
14. Gao, G., Zafari, M., and Reynolds, A. C. 2006. Quantifying Uncertainty for the PUNQ-S3 Problem in a Bayesian Setting with RML and EnKF. SPEJ 11 (4): 506-515. SPE-93324-PA. DOI: 10.2118/93324-PA.
15. Gavalas, G. R., Shah, P. C., and Seinfeld, J. H. 1976. Reservoir History Matching by Bayesian Estimation. SPEJ 16 (6): 337-350. SPE-5740-PA. DOI: 10.2118/5740-PA.
16. Golub, G. H. and van Loan, C. F. 1989. Matrix Computations. The Johns Hopkins University Press, Baltimore, second edition.
17. Gu, Y. 2006. History Matching Production Data Using the Ensemble Kalman Filter. PhD dissertation, University of Oklahoma.
18. Gu, Y. and Oliver, D. S. 2005. History Matching of the PUNQ-S3 Reservoir Model Using the Ensemble Kalman Filter. SPEJ 10 (2): 51-65. SPE-89942-PA. DOI: 10.2118/89942-PA.
19. Gu, Y. and Oliver, D. S. 2006. The Ensemble Kalman Filter for Continuous Updating of Reservoir Simulation Models. Journal of Energy Resources Technology 128 (1): 79-87.
20. Hamill, T. M., Snyder, C., Baumhefner, D. P., Toth, Z., and Mullen, S. L. 2000. Ensemble Forecasting in the Short to Medium Range: Report From a Workshop. Bull. Amer Meteor Soc. 81: 2653-2664.
21. Houtekamer, P. L. and Mitchell, H. L. 1998. Data Assimilation Using an Ensemble Kalman Filter Technique. Monthly Weather Review 126 (3): 796-811.
22. Houtekamer, P. L. and Mitchell, H. L. 2001. A Sequential Ensemble Kalman Filter for Atmospheric Data Assimilation. Monthly Weather Review 129 (1): 123-137.
23. Jazwinski, A. H. 1970. Stochastic Processes and Filtering Theory. Academic Press, New York.
24. Journel, A. and Huijbregts, C. J. 1978. Mining Geostatistics. Academic Press, New York. 600 p.
25. Kitanidis, R K. 1995. Quasi-Linear Geostatistical Theory for Inversing. Water Resour Res. 31 (10): 2411-2419.
26. Li, R., Reynolds, A. C., and Oliver, D. S. 2003. History Matching of Three-Phase Flow Production Data. SPEJ 8 (4): 328-340. SPE-87336-PA. DOI: 10.2118/87336-PA.
27. Liu, N. and Oliver, D. S. 2003. Evaluation of Monte Carlo Methods for Assessing Uncertainty. SPEJ 8 (2): 188-195. SPE-84936-PA. DOI: 10.2118/84936-PA.
28. Liu, N. and Oliver, D. S. 2005a. Critical Evaluation of the Ensemble Kalman Filter on History Matching of Geologic Facies. SPEREE 8 (6): 470-477. SPE-92867-PA. DOI: 10.2118/92867-PA.
29. Liu, N. and Oliver, D. S. 2005b. Ensemble Kalman filter for Automatic History Matching of Geologic Facies. Journal of Petroleum Science and Engineering 47 (3-4): 147-161.
30. Lorentzen, R. J., Nævdal, G., Vàdles, B., Berg, A. M., and A-A. Grimstad 2005. Analysis of the Ensemble Kalman Filter for Estimation of Permeability and Porosity in Reservoir Models. Paper SPE 96375 presented at the SPE Annual Technical Conference and Exhibition, Dallas, 9-12 October. DOI: 10.2118/96375-MS.
31. Nævdal, G., Johnsen, L. M., Aanonsen, S. I., and Vefring, E. H. 2005. Reservoir Monitoring and Continuous Model Updating Using Ensemble Kalman Filter. SPEJ 10 (1): 66-74. SPE-84372-PA. DOI: 10.2118/84372-PA.
32. Nævdal, G., Mannseth, T., and Vefring, E. H. 2002. Near-Well Reservoir Monitoring Through Ensemble Kalman Filter. Paper SPE 75235 presented at the SPE/DOE Improved Oil Recovery Symposium, Tulsa, 13-17 April. DOI: 10.211 8n5235-MS.
33. Oliver, D. S., He, N., and Reynolds, A. C. 1996. Conditioning Permeability Fields to Pressure Data. In European Conference for the Mathematics of Oil Recovery, V 1-11.
34. Reichle, R. H., McLaughlin, D. B., and Entekhabi, D. 2002. Hydrologic Data Assimilation With the Ensemble Kalman Filter. Monthly Weather Review 130 (1): 103-114.
35. Ripley, B. D. 1987. Stochastic Simulation. John Wiley & Sons, New York.
36. Skjervheim, J.-A., Evensen, G., Aanonsen, S. I., Ruud, B. O., and Johansen, T. A. 2007. Incorporating 4D Seismic Data in Reservoir Simulation Models Using Ensemble Kalman Filter. SPEJ 12 (3): 282-292. SPE-95789-PA. DOI: 10.2118/95789-PA.
37. Tan, T. B. and Kalogerakis, N. 1992. A Three-Dimensional Three-Phase Automatic History Matching Model: Reliability of Parameter Estimates. Journal of Canadian Petroleum Technology 31 (3): 34-41.
38. Tarantola, A. 1987. Inverse Problem Theory: Methods for Data Fitting and Model Parameter Estimation. Elsevier, Amsterdam, The Netherlands.
39. Thulin, K., Li, G., Aanonsen, S. I., and Reynolds, A. C. 2007. Estimation of Initial Fluid Contacts by Assimilation of Production Data With EnKF. Paper to be presented at the SPE Annual Technical Conference and Exhibition, Anaheim, California, 11-14 November.
40. Tjølsen, C. B., Damsleth, E., and Bu, T. 1994. The Effect of Stochastic Relative Permeabilities in Reservoir Simulation. Journal of Petroleum Science and Engineering 10: 273-290.
41. Wen, X.-H. and Chen, W. H. 2006. Real-time Reservoir Model Updating Using Ensemble Kalman Filter. SPEJ 11 (4): 431-442. SPE-92991-PA. DOI: 10.2118/92991-PA.
42. Wen, X.-H. and Chen, W. H. 2007. Some Practical Issues on Real-time Reservoir Model Updating Using Ensemble Kalman Filter. SPEJ 12 (2): 156-166. SPE-111571-PA. DOI: 10.2118/111571-PA.
43. Zafari, M., Li, G., and Reynolds, A. C. 2006. Iterative Forms of the Ensemble Kalman Filter. In Proceedings of the l0th European Conference on the Mathematics of Oil Recovery - Amsterdam A030.
44. Zafari, M. and Reynolds, A. C. 2007. Assessing the Uncertainty in Reservoir Description and Performance Predictions With the Ensemble Kalman Filter. SPEJ 12 (3): 378-387. SPE-95750-PA. DOI: 10.2118/95750-PA.
45. Zupanski, M. 2005. Maximum Likelihood Ensemble Filter: Theoretical Aspects. Monthly Weather Review 133 (6): 1710-1726.