Comparison of ensemble filtering algorithms and null-space Monte Carlo for parameter estimation and uncertainty quantification using CO2 sequestration data

Water Resources Research

Volumn 49, Issue 12, 2013, Pages 8108-8127

  Tavakoli, Reza ^a   Yoon, Hongkyu ^b   Delshad, Mojdeh ^a,c   ElSheikh, Ahmed H ^a   Wheeler, Mary F ^a   Arnold, Bill W ^b  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^b SANDIA NATIONAL LABORATORIES   (United States)

^c The University of Texas at Austin   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONALLY EFFICIENT; MULTI-PHASE FLOW MODELS; OBJECTIVE FUNCTION VALUES; PERMEABILITY AND POROSITIES; PREDICTION UNCERTAINTY; STRUCTURAL ORIENTATIONS; STRUCTURAL UNCERTAINTY; UNCERTAINTY QUANTIFICATIONS;

BOTTOM HOLE PRESSURE; CARBON DIOXIDE; COMPUTATIONAL EFFICIENCY; DATA PROCESSING; DIGITAL STORAGE; FORECASTING; HYDROGEOLOGY; INJECTION (OIL WELLS); MULTIPHASE FLOW; SIGNAL FILTERING AND PREDICTION;

MONTE CARLO METHODS;

ALGORITHM; CARBON DIOXIDE; CARBON SEQUESTRATION; COMPARATIVE STUDY; ENSEMBLE FORECASTING; GEOLOGICAL STRUCTURE; KALMAN FILTER; MONTE CARLO ANALYSIS; MULTIPHASE FLOW; PARAMETERIZATION; PERMEABILITY; PRESSURE GRADIENT; STORAGE STRUCTURE; UNCERTAINTY ANALYSIS;

EID: 84896737963     PISSN: 00431397     EISSN: 19447973     Source Type: Journal    
DOI: 10.1002/2013WR013959     Document Type: Article

References (88)

1. Aanonsen, S. I., G. Nævdal, D. S. Oliver, A. C. Reynolds, and B. Vallès (2009), The ensemble Kalman filter in reservoir engineering-A Review, SPE J., 14(3), 393-412, doi:10.2118/117274-PA.
2. Agbalaka, C., and D. S. Oliver (2008), Application of the EnKF and localization to automatic history matching of facies distribution and production data, Math. Geosci., 40(4), 353-374.
3. Alcolea, A., J. Carrera, and M. Medina (2006), Inversion of heterogeneous parabolic type equations using the pilot points method, Int. J. Numer. Methods Fluids, 51, 963-980, doi:10.1002/fld.1213. (Pubitemid 44082322)
4. Bertino, L., G. Evensen, and H. Wackernagel (2003), Sequential data assimilation techniques in oceanography, Int. Stat. Rev., 71(2), 223-241. (Pubitemid 37052980)
5. Beven, K., and A. Binley (1992), The future of distributed models: Model calibration and uncertainty prediction, Hydrol. Processes, 6(3), 279-298, doi:10.1002/hyp.3360060305.
6. Bonet-Cunha, L., D. S. Oliver, R. A. Redner, and A. C. Reynolds (1998), Hybrid Markov chain Monte Carlo method for generating permeability fields conditioned to multiwell pressure data and prior information, SPE J., 11(3), 261-271. (Pubitemid 128444683)
7. Chen, S., G. Li, and A. C. Reynolds (2006), An in situ test for the estimation of relative permeabilities: An approximate analytical solution for the wellbore pressure, in TUPREP Res. Rep. 23, The Univ. of Tulsa, Tulsa, Okla.
8. Chen, Y., and D. S. Oliver (2013), Levenberg-Marquardt forms of the iterative ensemble smoother for efficient history matching and uncertainty quantification, Comput. Geosci., 17, 689-703, doi:10.1007/s10596-013-9351-5.
9. CMG (2013), Computer Modeling Group, Calgary, Alberta, Canada. [Available at http://www.cmgl.ca/.]
10. Collins, D. A., L. X. Nghiem, Y. K. Li, and J. E. Grabonstotter (1992), An efficient approach to adaptive-implicit compositional simulation with an equation of state (SPE 15133), SPE Reservoir Eng., 7(2), 259-264. (Pubitemid 23573260)
11. Crestani, E., M. Camporese, D. Bau, and P. Salandin (2013), Ensemble Kalman filter versus ensemble smoother for assessing hydraulic conductivity via tracer test data assimilation, Hydrol. Earth Syst. Sci., 17, 1517-1531, doi:10.5194/hess-17-1517-2013.
12. de Marsily, G., G. Lavedan, M. Boucher, and G. Fasanino (1984), Interpretation of interference tests in a well field using geostatistical techniques to fit the permeability distribution in a reservoir model, in Geostatistics for Natural Resources Characterization, Part 2, pp. 831-849, D. Reidel, London.
13. de Marsily, G., J. P. Delhomme, F. Delay, and A. Buoro (1999), 40 years of inverse problems in hydrogeology, Earth Planet. Sci., 329(2), 73-87. (Pubitemid 29511155)
14. de Marsily, G., J. P. Delhomme, A. Coudrain-Ribstein, and A. M. Lavenue (2000), Four decades of inverse problems in hydrogeology, in Theory, Modeling and Field Investigation in Hydrogeology: A Special Volume in Honor of Shlomo P. Neuman's 60th Birthday, edited by D. Zhang and C. L. Winters, Geol. Soc. of Am. Spec. Pap. 348, pp. 1-17.
15. Delshad, M., X. Kong, R. Tavakoli, S. A. Hosseini, and M. F. Wheeler (2013), Modeling and simulation of carbon sequestration at Cranfield incorporating new physical models, Int. J. Greenhouse Gas Control., 18, 463-473.
16. Doherty, J. (2003), Ground water model calibration using pilot points and regularization, Ground Water, 41(2), 170-177. (Pubitemid 36280735)
17. Doherty, J. (2012), PEST: Model Independent Parameter Estimation, Watermark Numer. Comput., Corinda, Queensland, Australia. [Available at http://www.pesthomepage.org.]
18. Doherty, J., and R. J. Hunt (2010), Approaches to highly parameterized inversion: A guide to using PEST for groundwater-model calibration, Tech. Rep., U.S. Geol. Surv. Sci. Invest. Rep. 2010-5169, U.S. Geol. Surv., Middleton,Wis.
19. Doherty, J., M. N. Fienen, and R. J. Hunt (2010a), Approaches to highly parameterized inversion: Pilot-point theory, guidelines, and research directions, Tech. Rep., U.S. Geol. Surv. Sci. Invest. Rep. 2010-5168, U.S. Geol. Surv., Middleton, Wis.
20. Doherty, J., R. J. Hunt, and M. J. Tonkin (2010b), Approaches to highly parameterized inversion: A guide to using PEST for model-parameter and predictive-uncertainty analysis, Tech. Rep., U.S. Geol. Surv. Sci. Invest. Rep. 2010-5211, U.S. Geol. Surv., Middleton, Wis.
21. Doucet, A., and A. M. Johansen (2009), A tutorial on particle filtering and smoothing: Fifteen years later, in Oxford Handbook of Nonlinear Filtering, vol. 12, edited by D. Crisan and B. Rozovsky, pp. 656-704, Oxford Univ. Press.
22. Doucet, A., N. D. Freitas, and N. Gordon (2001), Sequential Monte Carlo Methods in Practice, Stat. for Eng. and Inf. Sci., Springer, New York.
23. Dovera, L., and E. D. Rossa (2011), Multimodal ensemble Kalman filtering using Gaussian mixture models, Comput. Geosci., 15(2), 307-323.
24. Elsheikh, A. H., M. D. Jackson, and T. C. Laforce (2012), Bayesian reservoir history matching considering model and parameter uncertainties, Math. Geosci., 44(5), 515-543, doi:10.1007/s11004-012-9397-2.
25. Emerick, A., and A. Reynolds (2010), Combining sensitivities and prior information for covariance localization in the ensemble Kalman filter for petroleum reservoir applications, Comput. Geosci., 15(2), 251-269.
26. Emerick, A., and A. Reynolds (2012), Ensemble smoother with multiple data assimilation, Comput. Geosci., 55, 3-15, doi:10.1016/j.cageo.2012.03.011.
27. Emerick, A., and A. Reynolds (2013), Investigation of the sampling performance of ensemble-based methods with a simple reservoir model, Comput. Geosci., 17, 1-26.
28. Espinet, A. J., and C. Shoemaker (2013), Comparison of optimization algorithms for parameter estimation of multi-phase flow models with application to geological carbon sequestration, Adv. Water Resour., 54, 133-148.
29. Evensen, G. (1994), Sequential data assimilation with a nonlinear quasigeostrophic model using Monte Carlo methods to forecast error statistics, J. Geophys. Res., 99, 10,143-10,162.
30. Evensen, G. (2004), Sampling strategies and square root analysis schemes for the EnKF, Ocean Dynamics, 54, 539-560, doi:10.1007/s10236-004-0099-2. (Pubitemid 40003080)
31. Evensen, G., and B. Laurent (2005), The combined parameter and state estimation problem, Computational Geosciences, 1-39.
32. Evensen, G., and P. J. van Leeuwen (2000), An ensemble Kalman smoother for nonlinear dynamics, Mon. Weather Rev., 128(6), 1852-1867. (Pubitemid 30464421)
33. Gilks, W. R., S. Richardson, and D. J. Spiegelhalter (Eds.) (1996), Markov Chain Monte Carlo in Practice, Chapman and Hall, New York.
34. Gómez-Hernández, J. J., A. Sahuquillo, and J. E. Capilla (1997), Stochastic simulation of transmissivity fields conditional to both transmissivity and piezometric data. 1. Theory, J. Hydrol., 203, 162-174. (Pubitemid 28118236)
35. Goovaerts, P. (1997), Geostatistics for Natural Resources Evaluation, Oxford Univ. Press, New York.
36. Gu, Y., and D. S. Oliver (2007), An iterative ensemble Kalman filter for multiphase fluid flow data assimilation, SPE J., 12(4), 438-446.
37. Harvey, C. F., and S. M. Gorelick (1995), Mapping hydraulic conductivity: Sequential conditioning with measurements of solute arrival time, hydraulic head, and local conductivity, Water Resour. Res., 31(7), 1615-1626. (Pubitemid 26443157)
38. Hastings, W. K. (1970), Monte Carlo sampling methods using Markov chains and their applications, Biometrika, 57(1), 97-109.
39. He, J., P. Sarma, and L. Durlofsky (2011), Use of reduced-order models for improved data assimilation within an EnKF context (SPE-141967), paper presented at SPE Reservoir Simulation Symposium,Woodlands, Tex.
40. Heidari, L., V. Gervais, M. L. Ravalec, and H. Wackernagel (2013), History matching of petroleum reservoir models by the ensemble Kalman filter and parameterization methods, Comput. Geosci., 55, 84-95, doi: 10.1016/j.cageo. 2012.06.006.
41. Hendricks-Franssen, H., A. Alcolea, M. Riva, M. Bakr, N. van der Wiel, F. Stauffer, and A. Guadagnini (2009), A comparison of seven methods for the inverse modelling of groundwater flow. Application to the characterisation of well catchments, Adv. Water Resour., 32(6), 851-872, doi: 10.1016/j.advwatres. 2009.02.011.
42. Hosseini, S. A., H. Lashgari, J. W. Choi, J. P. Nicot, J. Lu, and S. D. Hovorka (2012), Static and dynamic reservoir modeling for geological CO2 sequestration at Cranfield, Mississippi, U.S.A., Int. J. Greenhouse Gas Control, 18, 449-462, doi:10.1016/j.ijggc.2012.11.009.
43. Houtekamer, P. L., and H. L. Mitchell (1998), Data assimilation using an ensemble Kalman filtering technique, Mon. Weather Rev., 126, 796-811. (Pubitemid 128581567)
44. Houtekamer, P. L., H. L. Mitchell, G. Pellerin, M. Buehner, M. Charron, L. Spacek, and B. Hansen (2005), Atmospheric data assimilation with an ensemble Kalman filter: Results with real observations, Mon. Weather Rev., 133(3), 604-620.
45. Hunt, R. J., J. Luchette, W. A. Shreuder, J. Rumbaugh, J. Doherty, M. J. Tonkin, and D. Rumbaugh (2010), Using the cloud to replenish parched groundwater modeling efforts, Ground Water, 48(3), 360-365, doi: 10.1111/j.1745-6584.2010. 00699.x.
46. Jafarpour, B., and D. B. McLaughlin (2009), Estimating channelized reservoir permeabilities with the ensemble Kalman filter: The importance of ensemble design, SPE J., 14(2), 374-388.
47. Jafarpour, B., and M. Tarrahi (2011), Assessing the performance of the ensemble Kalman filter for subsurface flow data integration under variogram uncertainty, Water Resour. Res., 47, W05537, doi:10.1029/2010WR009090.
48. Kalman, R. E. (1960), A new approach to linear filtering and prediction problems, J. Basic Eng., 82, 35-45.
49. Keating, E. H., J. Doherty, and Q. Kang (2010), Optimization and uncertainty assessment of strongly non-linear groundwater models with high parameter dimensionality, Water Resour. Res., 46, W10517, doi: 10.1029/2009WR008584.
50. Keppenne, C. L. (2000), Data assimilation into a primitive-equation model with a parallel ensemble Kalman filter, Mon. Weather Rev., 128(6), 1971-1981. (Pubitemid 30464430)
51. Kitanidis, P. (1996), On the geostatistical approach to the inverse problem, Adv. Water Resour., 19(6), 333-342, doi:10.1016/0309-1708(96)00005-x.
52. Kitanidis, P. K. (1995), Quasi-linear geostatistical theory for inversing, Water Resour. Res., 31, 2411-2419. (Pubitemid 26475164)
53. Lépine, O. J., R. C. Bissell, S. I. Aanonsen, I. C. Pallister, and J. W. Barker (1999), Uncertainty analysis in predictive reservoir simulation using gradient information, SPE J., 4(3), 251-259. (Pubitemid 129513434)
54. Liu, N., and D. S. Oliver (2003), Evaluation of Monte Carlo methods for assessing uncertainty, SPE J., 8(2), 188-195.
55. Medina, A., and J. Carrera (2003), Geostatistical inversion of coupled problems: Dealing with computational burden and different types of data, J. Hydrol., 281(4), 251-264. (Pubitemid 37325624)
56. Moore, C., and J. Doherty (2005), Role of the calibration process in reducing model predictive error, Water Resour. Res., 41, 1-14, doi:10.1029/2004WR003501. (Pubitemid 40856470)
57. Moreno, D., and S. I. Aanonsen (2007), Stochastic facies modelling using the level set method, in Extended Abstracts Book of Petroleum Geostatistics 2007, vol. A18, Cascais, Portugal, EAGE Publications BV, Utrecht, Netherlands.
58. Nicot, J. P., J. Choi, T. Meckel, C. Y. Chang, S. D. Hovorka, and S. Solano (2009), Results of numerical investigations at SECARB Cranfield, MS fielt test site, in Eighth Annual Conference on Carbon Capture and Sequestration, 11 p., Dep. of Energy/Natl. Energy Technol. Lab.
59. Nowak, W. (2009), Best unbiased ensemble linearization and the quasilinear Kalman ensemble generator, Water Resour. Res., 45, W04431, doi:10.1029/2008WR007328.
60. Oladyshkin, S., C. Holger, and W. Nowak (2013), Bayesian updating via bootstrap filtering combined with data-driven polynomial chaos expansions: Methodology and application to history matching for carbon dioxide storage in geological formations, Comput. Geosci., 17(4), 671-687, doi:10.1007/s10596-013- 9350-6.
61. Oliver, D. S., and Y. Chen (2010), Recent progress on reservoir history matching: A review, Comput. Geosci., 15(1), 185-221.
62. Oliver, D. S., L. B. Cunha, and A. C. Reynolds (1997), Markov chain Monte Carlo methods for conditioning a permeability field to pressure data, Math. Geol., 29(1), 61-91.
63. Oliver, D. S., A. C. Reynolds, and N. Liu (2008), Inverse Theory for Petroleum Reservoir Characterization and History Matching, Cambridge Univ. Press, Cambridge, U. K.
64. Peng, D. Y., and D. B. Robinson (1976), A new two-constant equation of state, Ind. Eng. Chem. Fundam., 15(1), 59-64.
65. RamaRao, B. S., A. M. LaVenue, G. de Marsily, and M. G. Marietta (1995), Pilot point methodology for automated calibration of an ensemble of conditionally simulated transmissivity fields, 1. Theory and computational experiments, Water Resour. Res., 31, 475-493. (Pubitemid 26437835)
66. Reichle, R. H., D. B. McLaughlin, and D. Entekhabi (2002), Hydrologic data assimilation with the ensemble Kalman filter, Mon. Weather Rev., 130(1), 103-114. (Pubitemid 34838242)
67. Reynolds, A. C., M. Zafari, and G. Li (2006), Iterative forms of the ensemble Kalman filter, paper presented at 10th European Conference on the Mathematics of Oil Recovery, Amsterdam, .
68. Saad, G., and R. Ghanem (2009), Characterization of reservoir simulation models using a polynomial chaos-based ensemble Kalman filter, Water Resour. Res., 45,W04417, doi:10.1029/2008WR007148.
69. Sarma, P., and W. H. Chen (2009), Generalization of the ensemble Kalman filter using kernels for non-Gaussian random fields, paper presented at the SPE Reservoir Simulation Symposium, SPE 119177, Woodlands, Tex., 2-4 Feb.
70. Shah, P. C., G. R. Gavalas, and J. H. Seinfeld (1978), Error analysis in history matching: The optimum level of parameterization, Soc. Pet. Eng. J., 18(6), 219-228. (Pubitemid 8613422)
71. Skjervheim, J.-A., G. Evensen, J. Hove, and J. G. Vabo (2011), An ensemble smoother for assisted history matching, paper presented at the SPE Reservoir Simulation Symposium, SPE 141929,Woodlands, Tex., 21-23 Feb.
72. Smith, A., and A. Gefland (1992), Bayesian statistics without tears: A sampling-resampling perspective, Am. Stat., 46(2), 84-88.
73. Soave, G. (1972), Equilibrium constants from a modified Redlich-Kwong equation of state, Chem. Eng. Sci., 27(6), 1197-1203.
74. Tarantola, A. (1987), Inverse Problem Theory: Methods for Data Fitting and Model Parameter Estimation, Elsevier, Amsterdam.
75. Tavakoli, R., and A. A. Reynolds (2011), Monte Carlo simulation of permeability fields and reservoir performance predictions with SVD parameterization in RML compared with EnKF, Comput. Geosci., 15(1), 99-116.
76. Tavakoli, R., G. Pencheva, M. F. Wheeler, and B. Ganis (2012), A parallel ensemble-based framework for reservoir history matching and uncertainty characterization, Comput. Geosci., 17(1), 83-97.
77. Tonkin, M., and J. Doherty (2009), Calibration-constrained Monte Carlo analysis of highly parameterized models using subspace techniques, Water Resour. Res., 45,W00B10, doi:10.1029/2007WR006678.
78. Tonkin, M. J., and J. Doherty (2005), A hybrid regularized inversion methodology for highly parameterized environmental models, Water Resour. Res., 41,W10412, doi:10.1029/2005WR003995. (Pubitemid 41705697)
79. van Leeuwen, P. J., and G. Evensen (1996), Data assimilation and inverse methods in terms of a probabilistic formulation, Mon. Weather Rev., 124, 2898-2913. (Pubitemid 126636673)
80. Vrugt, J. A., C. J. F. T. Braak, M. P. Clark, J. M. Hyman, and B. A. Robinson (2008), Treatment of input uncertainty in hydrologic modeling: Doing hydrology backward with Markov chain Monte Carlo simulation, Water Resour. Res., 44,W00B09, doi:10.1029/2007WR006720.
81. Welter, D. E., J. Doherty, R. Hunt, C. Muffels, M. Tonkin, and W. Schreder (2012), Approaches in Highly Parameterized Inversion: PEST11, A Parameter Estimation Code Optimized for Large Environmental Models, book 7, section C5, technical report, U.S. Geol. Surv. Tech. and Methods.
82. Woodbury, A., and T. Ulrych (2000), A full-Bayesian approach to the groundwater inverse problem for steady state flow, Water Resour. Res., 36, 2081-2093, doi:10.1029/2000WR900086. (Pubitemid 30610899)
83. Yoon, H., and S. A. McKenna (2012), Highly parameterized inverse estimation of hydraulic conductivity and porosity in a three-dimensional, heterogeneous transport experiment, Water Resour. Res., 48, W10536, doi:10.1029/2012WR012149.
84. Yoon, H., D. B. Hart, and S. A. McKenna (2013), Parameter estimation and predictive uncertainty in stochastic inverse modeling of groundwater flow: Comparing null-space Monte Carlo and multiple starting point methods, Water Resour. Res., 49, 536-553, doi:10.1002/WRCR.20064.
85. Zafari, M., and A. C. Reynolds (2007), Assessing the uncertainty in reservoir description and performance predictions with the ensemble Kalman filter, SPE J., 12(3), 382-391. (Pubitemid 47629525)
86. Zhang, Y., and N. Sahinidis (2013), Uncertainty quantification in CO2 sequestration using surrogate models from polynomial chaos expansion, Ind. Eng. Chem. Res., 52(9), 3121-3132.
87. Zhou, H., J. Gomez-Hernandez, H.-J. H. Franssen, and L. Li (2011), An approach to handling non-Gaussianity of parameters and state variables in ensemble Kalman filtering, Adv. Water Resour., 34, 844-864.
88. Zimmerman, D. A., et al. (1998), A comparison of seven geostatistically based inverse approaches to estimate transmissivities for modeling advective transport by groundwater flow, Water Resour. Res., 34, 1373-1413. (Pubitemid 28253515)