Multi-level parameter structure identification for two-phase porous-media flow problems using flexible representations

Advances in Water Resources

Volumn 32, Issue 12, 2009, Pages 1777-1788

  Berre, Inga ^a   Lien, Martha ^a   Mannseth, Trond ^a  

^a UNIVERSITY OF BERGEN   (Norway)

Author keywords

Parameter identification; Reparametrization; Two phase porous media flow

Indexed keywords

ABSOLUTE PERMEABILITY; CHOSEN REPRESENTATION; COMPUTATIONAL GRIDS; CONSTANT PARAMETERS; IDENTIFICATION OF THE PARAMETERS; IMPLICIT REPRESENTATION; LEVEL SETS; LIMITING CASE; LOCAL MINIMUMS; MULTI-LEVEL; NON-LINEARITY; NOVEL SOLUTIONS; NUMERICAL EXAMPLE; OBJECTIVE FUNCTIONS; ON TIME; PARAMETER FUNCTIONS; PARAMETER IDENTIFICATION; PARAMETER STRUCTURE; PERMEABILITY DISTRIBUTION; POROUS-MEDIA FLOW; PRESSURE DATA; REPARAMETRIZATION; RESOLUTION LEVEL; SHARP TRANSITION;

CAPILLARITY; SENSITIVITY ANALYSIS; TIME SERIES;

PARAMETER ESTIMATION;

ESTIMATION METHOD; NONLINEARITY; PARAMETERIZATION; PERMEABILITY; POROUS MEDIUM; SENSITIVITY ANALYSIS; TIME SERIES ANALYSIS; TWO PHASE FLOW;

EID: 71549148394     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.advwatres.2009.10.002     Document Type: Article

References (43)

1. Ben Ameur H., Chavent G., and Jaffré J. Refinement and coarsening indicators for adaptive parameterization: application to the estimation of hydraulic transmissivities. Inverse Probl 18 3 (2002) 775-794
2. Anterion F, Eymard R, Karcher B. Use of parameter gradients for reservoir history matching. In: SPE symposium on reservoir simulation, Houston, Texas, SPE 18433. Soc Petr Eng; 1989.
3. Bates D.M., and Watts D.G. Relative curvature measures of nonlinearity. J R Statist Soc Ser B 42 1 (1980) 1-25
4. Berre I., Clément F., Lien M., and Mannseth T. Data driven reparameterization structure for estimation of fluid conductivity. Calibration and reliability in groundwater modelling: credibility of modelling vol. 320 (2008), IAHS Publ. 310-315
5. Berre I., Lien M., and Mannseth T. A level-set corrector to an adaptive multiscale permeability prediction. Comput Geosci 11 1 (2007) 27-42
6. Carrera J. State of the art of the inverse problem applied to the flow and solute transport equation. In: Custiodio E, Gurgui A, Lobo Ferreira JP, editors. Proceedings of the NATO advanced workshop on advances in analytical and numerical groundwater flow and quality modelling (Lisbon, Portugal, June 2-6, 1987). Groundwater flow and quality modelling, vol. 224 of NATO ASI Series, Series C: mathematical and physical sciences. Dordrecht, Holland: D. Reidel Publishing Company; 1988. p. 549-83.
7. Carrera J., Alcolea A., Medina A., Hidalgo J., and Slooten L.J. Inverse problem in hydrogeology. Hydrogeol J 13 1 (2005) 206-222
8. Chan T.F., and Shen J. Image processing and analysis-variational, PDE, wavelet, and stochastic methods (2005), SIAM, Philadelphia
9. Dorn O., and Lesselier D. Level set methods for inverse scattering. Inverse Probl 22 4 (2006) 67-131
10. Dorn O., and Villegas R. History matching of petroleum reservoirs using a level set technique. Inverse Probl 24 3 (2008) 035015 29pp.
11. Emsellem Y., and de Marsily G. An automatic solution for the inverse problem. Water Resour Res 7 5 (1971) 1264-1283
12. Engl H.W., Hanke M., and Neubauer A. Regularization of inverse problems (1996), Kluwer Academic Publishers, Boston
13. Feng T., and Mannseth T. Improvements on a predictor-corrector strategy for parameter estimation with several data types. Inverse Probl 25 10 (2009)
14. Gaganis P., and Smith L. Evaluation of the uncertainty of groundwater model predictions associated with conceptual errors: a per-datum approach to model calibration. Adv Water Res 29 4 (2005) 503-514
15. Grimstad A.-A., and Mannseth T. Nonlinearity scale and sensitivity for parameter estimation problems. SIAM J Sci Comput 21 6 (2000) 2096-2113
16. Grimstad AA, Mannseth T. Comparison of methods for downscaling coarse scale permeability estimates. In: 9'th European conference on the mathematics of oil recovery, Cannes, France, September 2004, Paper B008; 2004.
17. Grimstad A.-A., Mannseth T., Nævdal G., and Urkedal H. Adaptive multiscale permeability estimation. Comput Geosci 7 1 (2003) 1-25
18. Haber E. A multilevel, level-set method for optimizing eigenvalues in shape design problems. J Comput Phys 198 (2004) 518-534
19. Hayek M., Ackerer P., and Sonnendrücker E. A new refinement indicator for adaptive parameterization: application to the estimation of the diffusion coefficient in an elliptic problem. J Computat Appl Math 224 1 (2009) 307-319
20. Hayek M., Lehmann F., and Ackerer P. Adaptive multi-scale parameterization for one-dimensional flow in unsaturated porous media. Adv Water Resour 31 1 (2008) 28-43
21. Jacquard P. Théorie de l'interprétation des mesures de pression. Revue IFP, XIX; March 1964.
22. Jacquard P., and Jain C. Permeability distribution from field pressure data. SPE J December (1965)
23. Lee T.-Y., Kravaris C., and Seinfeld J.H. History matching by spline approximation and regularization in single-phase areal reservoirs. SPE Reservoir Eng (1986) September
24. Lien M., Berre I., and Mannseth T. Combined adaptive multiscale and level-set parameter estimation. Multiscale Model Simulat 4 4 (2005) 1349-1372
25. Mannseth T. Permeability identification from pressure observations: some foundations for multiscale regularization. Multiscale Model Simulat 5 1 (2006) 21-44 [Electronic]
26. de Marsily G, Delhomme JP, Coudrain-Ribstein A, Lavenue AM. Four decades of inverse problems in hydrogeology. In: Zhang D, Winter CL, editors. Theory modeling and field investigation in hydrogeology: a special volume in honor of Shlomo P. Neuman's 60th Birthday, special paper 348. Geological Society of America; 2000. p. 1-17.
27. McLaughlin D., and Townley L.R. A reassessment of the groundwater inverse problem. Water Resour Res 32 5 (1996) 1031-1061
28. Moré J.J. The Levenberg-Marquardt algorithm: implementation and theory, numerical analysis lecture notes in mathematics (1977), Springer Verlag, Berlin [chapter 630]
29. Oliver D.S., Reynolds A.C., Bi Z., and Abacioglu Y. Integration of production data into reservoir models. Petroleum Geosci 7 (2001) 65-73
30. Sen A., and Srivastava M. Regression analysis: theory, methods and applications (1990), Springer-Verlag, New York
31. Sun N.-Z. Inverse problems in groundwater modeling (1994), Kluwer Academic Publishers, Dordrecht
32. Sun NZ, Sun AY. Parameter identification of environmental systems. In: Environmental Fluid Mechanics, ASCE; 2002 [chapter 9].
33. Sun N.-Z. Structure reduction and robust experimental design for distributed parameter identification. Inverse Probl 21 (2005) 739-758
34. Sun N.-Z., Yang S.-L., and Yeh W.W.-G. A proposed stepwise regression method for model structure identification. Water Resour Res 34 10 (1998) 2561-2572
35. Tai X.-C., and Chan T.F. A survey on multiple level set methods with applications for identifying piecewise constant functions. Int J Numer Anal Model 1 1 (2004) 25-47
36. Tarantola A. Inverse problem theory and methods for model parameter estimation (2005), Society for Industrial and Applied Mathematics [chapter 1]
37. Tsai F.T.-C., Sun N.-Z., and Yeh W.W.-G. A combinatorial optimization scheme for parameter structure identification in ground water modeling. Ground Water 41 2 (2003) 156-169
38. Tsai F.T.-C., and Yeh W.W.-G. Characterization and identification of aquifer heterogeneity with generalized parameterization and Bayesian estimation. Water Resour Res 40 (2004) W10102 10.1029/2003WR002893
39. Tsai F.T.-C., Sun N.-Z., and Yeh W.W.-G. Geophysical parameterization and parameter structure identification using natural neighbors in groundwater inverse problems. J Hydrol (2005)
40. Vese L.A., and Chan T.F. A multiphase level set framework for image segmentation via the Mumford and Shah model. Int J Comput Vision (2002)
41. Yeh W.W.-G. Review of parameter identification procedures in groundwater hydrology: the inverse problem. Water Resour Res 22 2 (1986) 95-108
42. Yeh W.W.-G., and Yoon Y.S. Aquifer parameter identification with optimum dimension in parameterization. Water Resour Res 17 3 (1981) 664-672
43. Yoon Y.S., and Yeh W.W.-G. Parameter identification in an inhomogeneous medium with the finite-element method. Soc Petrol Eng J (1976)