An iterative representer-based scheme for data inversion in reservoir modeling

Inverse Problems

Volumn 25, Issue 3, 2009, Pages

  Iglesias, Marco A ^a   Dawson, Clint ^a  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ABSOLUTE PERMEABILITY; DARCY FLOWS; DATA ASSIMILATION; DATA INVERSION; FINITE NUMBER; FORWARD MODELS; ITERATIVE REGULARIZATION; MATHEMATICAL FRAMEWORKS; NUMERICAL RESULTS; PARAMETER IDENTIFICATION PROBLEMS; POROUS MEDIA; PRIOR KNOWLEDGE; RESERVOIR MODELING; RESERVOIR MODELS; SECOND ORDERS; STABLE APPROXIMATION; THEORETICAL RESULT; UNCERTAIN PARAMETERS;

DIFFERENTIAL EQUATIONS; GROUNDWATER; GROUNDWATER FLOW; HYDROGEOLOGY; NONLINEAR EQUATIONS; POROUS MATERIALS; UNCERTAINTY ANALYSIS;

IDENTIFICATION (CONTROL SYSTEMS);

EID: 70350306382     PISSN: 02665611     EISSN: 13616420     Source Type: Journal    
DOI: 10.1088/0266-5611/25/3/035006     Document Type: Article

References (35)

1. Arbogast T, Wheeler M F and Yotov I 1997 Mixed finite elements for elliptic problems with tensor coefficients as cell-centered finite differences SIAM J. Numer. Anal. 34 828-52
2. Baird J and Dawson C 2005 The representer method for data assimilation in single-phase Darcy flow in porous media Comput. Geosci. 9 (4) 247-71 (doi:10.1007/s10596-005-9006-2)
3. Baird J and Dawson C 2007 The representer method for two-phase flow in porous media Comput. Geosci. 11 (3) 235-48 (doi:10.1007/s10596-007-9048-8)
4. Baird J and Dawson C 2007 A posteriori error estimation of the representer method for single phase Darcy flow Comput. Methods Appl. Mech. Eng. 196 1623-32 (Pubitemid 44942909)
5. Bear J 1972 Dynamics of Fluids in Porous Media (New York: Dover)
6. Bennett A F 2002 Inverse Modeling of the Ocean and Atmosphere (Cambridge: Cambridge University Press)
7. Deutsch C V and Journel A G 1997 GSLIB: Geostatistical Software Library 2nd edn (New York: Oxford University Press)
8. Dimet F Le and Talagrand O 1986 Variational algorithms for analysis and assimilation of meteorological observations Tellus 38A 97-110
9. Dong Y, Gu Y and Oliver D S 2006 Sequential assimilation of 4D seismic data for reservoir description using the Ensemble Kalman Filter J. Pet. Sci. Eng. 53 83-99
10. Engl H W, Hanke M and Neubauer A 1996 Regularization of Inverse Problems 1st edn (Dordrecht: Kluwer)
11. Evans L C 1998 Partial Differential Equations 1st edn (Providence, RI: American Mathematical Society)
12. Evensen G 1994 Sequential data assimilation with a non-linear quasi-geostrophic model using Monte-Carlo methods to forecast error statistics J. Geophys. Res. 99 10143-62
13. Evensen G 2007 Data Assimilation 1st edn (Heidelberg: Springer)
14. Evensen G, Hove J, Meisingset H C, Reiso E and Seim K S 2007 Using the EnKF for assisted history matching of a North Sea reservoir model SPE Reservoir Simulation Symp. (Woodlands, TX, 26-28 February 2007, SPE 106184)
15. Gao C, Rajeswaran T and Nakagawa E 2007 A literature review on smart-well technology Proc. SPE Production and Operations Symp. (Oklahoma City, OK, 31 March-3 April 2007, SPE 106011)
16. Giudici M 1991 Identifiability of distributed physical parameters in diffusive-like systems Inverse Problems 7 231-45
17. Gu Y and Oliver D S 2005 History matching of the PUNQ-S3 reservoir model using the Ensemble Kalman Filter SPE J. 10 51-65
18. Gu Y and Oliver D S 2006 The ensemble Kalman filter for continuous updating of reservoir simulation models J. Energy Resour. Technol. 128 79-87 (Pubitemid 44058071)
19. Hanke M 1997 A regularizing Levenberg-Marquardt scheme, with applications to inverse groundwater filtration problems Inverse Problems 13 79-95
20. http://www.spe.org/csp/ (Spe 10th comparative project)
21. Iglesias M A and Dawson C 2007 The representer method for state and parameter estimation in single-phase Darcy flow Comput. Methods Appl. Mech. Eng. 196 4577-96 (Pubitemid 47324020)
22. Kalman R E 1960 A new approach to linear filtering and prediction problems Trans. ASME J. Basic Eng. 82 35-45
23. Lions J L and Magenes E 1972 Non-Homogeneous Boundary Value Problems and Applications vol II (Berlin: Springer)
24. Liu N and Oliver D S 2005 Ensemble Kalman filter for automatic history matching of geologic facies J. Pet. Sci. Eng. 47 147-61 (Pubitemid 40829359)
25. Lorentzen R J, Naevdal G, Valls B and Berg A M 2005 Analysis of the ensemble Kalman filter for estimation of permeability and porosity in reservoir models SPE Annual Technical Conf. and Exhibition (Dallas, TX, 9-12 October 2005, SPE 96375)
26. Naevdal G, Johnsen L M, Aanonsen S I and Vefring E H 2005 Reservoir monitoring and continuous model updating using ensemble Kalman filter SPE J. 10 66-74
27. Naevdal G, Mannseth T and Vefring E H 2002 Near-well reservoir monitoring through ensemble Kalman filter SEP/DOE Improved Oil Recovery Symp. (Tulsa, OK, April 2002, SPE 75235)
28. Oliver D S 1998 Calculation of the inverse of the covariance Math. Geol. 30 911-33
29. Przybysz-Jarnut J K, Hanea R G, Jansen J D and Heemink A W 2007 Application of the representer method for parameter estimation in numerical reservoir models Comput. Geosci. 11 73-85
30. Rosmond T and Xu L 2006 Development of NAVDAS-AR: non-linear formulation and outer loop test Tellus A 58 45-58
31. Skjervheim J A, Evensen G, Aanonsen S I, Ruud B O and Johansen T A 2005 Incorporating 4d seismic data in reservoir simulation models using Ensemble kalman filter SPE Annual Technical Conf. and Exhibition (Dallas, TX, 9-12 October 2005, SPE 95789)
32. Tarantola A 1987 Inverse Problems Theory: Methods for Data Fitting and Model Parameter Estimation 1st edn (New York: Elsevier)
33. Valstar J R, McLaughlin D B, te Stroet C B M and van Geer F C 2004 A representer-based inverse method for groundwater flow and transport applications Water Resour. Res. 40 W05116 (doi:10.1029/2003WR002922)
34. Xu L and Daley R 2000 Towards a true 4-dimensional data assimilation algorithm: application of a cycling representer algorithm to a simple transport problem Tellus 52A 109-28
35. Xu Q 2005 Representation of inverse covariance by differential operators Adv. Atmos. Sci. 22 181-98