Bayesian uncertainty quantification for flows in heterogeneous porous media using reversible jump Markov chain Monte Carlo methods

Advances in Water Resources

Volumn 33, Issue 3, 2010, Pages 241-256

  Mondal, A ^a   Efendiev, Y ^a   Mallick, B ^a   Datta Gupta, A ^b  

^a TEXAS A AND M UNIVERSITY   (United States)

^b Texas AandM University   (United States)

Author keywords

Facies; Level sets; MCMC; Multiscale; Porous media; Reversible jump; Upscaling

Indexed keywords

CHAINS; IMAGE SEGMENTATION; INVERSE PROBLEMS; MARKOV PROCESSES; POROUS MATERIALS; UNCERTAINTY ANALYSIS;

FACIES; LEVEL SET; MCMC; MULTISCALE; REVERSIBLE JUMP; UPSCALING;

MONTE CARLO METHODS;

ALGORITHM; BAYESIAN ANALYSIS; FLOW MODELING; HETEROGENEOUS MEDIUM; INVERSE PROBLEM; MARKOV CHAIN; MONTE CARLO ANALYSIS; POROUS MEDIUM; UNCERTAINTY ANALYSIS; UPSCALING;

EID: 77954259242     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.advwatres.2009.10.010     Document Type: Article

References (44)

1. Aarnes JE. On the use of a mixed multiscale finite element method for greater flexibility and increased speed or improved accuracy in reservoir simulation. SIAM MMS 2004;2:421-39.
2. Al-Harbi M, Cheng H, Zhong He, Datta-Gupta A. Streamline-based production data integration in naturally fractured reservoirs. SPE J 2005;10(4):426-39.
3. Arbogast T. Implementation of a locally conservative numerical subgrid upscaling scheme for two-phase Darcy flow. Comput Geosci 2002;6:453-81.
4. Barker JW, Thibeau S. A critical review of the use of pseudo-relative permeabilities for upscaling. SPE Res Eng 1997;12:138-43.
5. Bi Z, Oliver DS, Reynolds AC. Conditioning 3D stochastic channels to pressure data. Soc Petrol Eng J 2000;5(4):474-84.
6. Caers J. Petroleum geostatistics. SPE Interdisc Primer Series Soc Petrol Eng 2006:96.
7. Caumon G, Strebelle S, Caers J, Journel A. Assessment of global uncertainty for early appraisal of hydrocarbon fields. In: SPE 89943, annual technical conference and exhibition, 26-29 September, Houston, Texas; 2004.
8. Chen Z, Hou TY. A mixed multiscale finite element method for elliptic problems with oscillating coefficients. Math Comput 2002;72:541-76.
9. Christen A, Fox C. MCMC using an approximation. J Comput Graph Stat 2005; 14(4): 795-810. doi:10.1198/106186005X76983.
10. Christie M. Upscaling for reservoir simulation. J Petrol Technol 1996:1004-10.
11. Cotter SL, Dashti M, Robinson JC, Stuart AM. Data assimilation problems in fluid mechanics: Bayesian formulation on function space. Inverse Prob 2009;25(11):115008.
12. Datta-Gupta A, King MJ. Streamline simulation: theory and practice. Society of Petroleum Engineers; 2007.
13. Dubrule O. Geostatistics in petroleum geology, American association of petroleum geology. Course Note Series 1998;38.
14. Durlofsky LJ. Coarse scale models of two phase flow in heterogeneous reservoirs: volume averaged equations and their relationship to the existing upscaling techniques. Comput Geosci 1998;2:73-92.
15. Durlofsky LJ, Behrens RA, Jones RC, Bernath A. Scale up of heterogeneous three dimensional reservoir descriptions. In: SPE paper 30709; 1996.
16. Durlofsky LJ, Jones RC, Milliken WJ. A nonuniform coarsening approach for the scale up of displacement processes in heterogeneous media. Adv Water Resour 1997;20:335-47.
17. Efendiev Y, Hou T, Luo W. Preconditioning Markov chain Monte Carlo simulations using coarse-scale models. SIAM Sci 2006;28(2):776-803.
18. Efendiev Y, Datta-Gupta A, Ginting V, Ma X, Mallick B. An efficient two-stage Markov chain Monte Carlo method for dynamic data integration. Water Resour Res 2006.
19. Efendiev Y, Ma X, Datta-Gupta A, Mallick B. Multi-stage MCMC using non-parametric error estimators, Water Resour Res, in press.
20. Efendiev Y, Hou TY. Multiscale finite element methods: theory and applications. Springer; 2009.
21. Egeland T, Georgsen F, Knarud R, Omre H. Multifacies modelling of fluvial reservoirs. In: SPE 26502 proceedings of the SPE annual technical conference and exhibition, 3-6 October, Houston, Texas; 1993.
22. Galli A, Beucher H, Le Loc'h G, Doligez B. The pros and cons of the truncated Gaussian simulation. In: Armstrong M, Dowd PA, editors. Geostatistical simulations. Dordrecht, Netherlands: Kluwer Academic Publishers; 1994. p. 217-33.
23. Gelman A, Rubin B. Inference from iterative simulation using multiple sequences. Stat Sci 1992;7:457-511.
24. Glimm J, Sharp DH. Prediction and the quantification of uncertainty. Phys D 1999;133:152-70 [Predictability: quantifying uncertainty in models of complex phenomena. Los Alamos, NM; 1998].
25. Green PJ. Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 1995;82(4):732-71.
26. Haldorsen H, Damsleth E. Stochastic modeling. JPT (SPE 20321) 1990;404:412.
27. Hairer M, Stuart A, Voss J. Signal processing problems on function space: Bayesian formulation, stochastic PDEs and effective MCMC methods, preprint.
28. Hu L. Gradual deformation and iterative calibration of Gaussian-related stochastic models. Math Geol 2000;32(1):87-108.
29. Koltermann CE, Gorelick SM. Heterogeneity in sedimentary deposits: a review of structure-imitating, process-imitating, and descriptive approaches. Water Resour Res 1996;32(9):2617-58. doi:10.1029/96WR00025.
30. Landa JL, Horne RN. A procedure to integrate well test data, reservoir performance history and 4-D seismic information into a reservoir description. In: SPE 38653 presented at the 1997 SPE annual technical conference and exhibition, October 5-8, San Antonio, TX.
31. Lee H, Higdon D, Bi Z, Ferreira M, West M. Markov random field models for high-dimensional parameters in simulations of fluid flow in porous media, technometrics; 2002.
32. Liu N, Oliver Dean S. Critical evaluation of the ensemble Kalman filter on history matching of geologic facies. SPE Reserv Eval Eng 2005;8(6):470-7.
33. Lodoen O, Omre H, Durlofsky L, Chen Y. Assessment of uncertainty in reservoir production forecasts using upscaled models. In: Proceedings of seventh international geostatistics congress, Sept. 26-Oct. 1, Banff, Canada; 2004.
34. Loève M. Probability theory. 4th ed. Berlin: Springer; 1977.
35. Ma X, Al-Harbi M, Datta-Gupta A, Efendiev Y. A multistage sampling approach to quantifying uncertainty during history matching geological models. SPE 102476, SPE J; 2008.
36. Oliver DS, Reynolds AC, Bi Z, Abacioglu Y. Integration of production data into reservoir models. Petrol Geosci 2001;7:S65-73.
37. Omre H, Petter Loden O. Improved production forecasts and history matching using approximate fluid-flow simulators. SPE J 2004;9(3):339-51.
38. Osher S, Fedkiw R. Level set methods and dynamic implicit surfaces. Springer; 2002.
39. Robert C, Casella G. Monte Carlo statistical methods. New York: Springer-Verlag; 1999.
40. Sethian JA. Level set methods and fast marching methods. Cambridge University Press; 1999.
41. Waagepetersen R, Sorensen D. A tutorial on reversible jump MCMC with a view toward applications on QTL mapping. Int Stat Rev 2001;69:49-62.
42. Weber KJ. Influence of common sedimentary structures on fluid flow in reservoir models. J Petrol Technol 1990;March:665-72.
43. Wong E. Stochastic processes in information and dynamical systems. MCGraw-Hill; 1971.
44. Wu XH, Efendiev Y, Hou TY. Analysis of upscaling absolute permeability. Discrete Contin Dyn Syst Series B 2002;2:185-204.