Adaptive multiscale permeability estimation

Computational Geosciences

Volumn 7, Issue 1, 2003, Pages 1-25

  Grimstad, Alv Arne ^a   Mannseth, Trond ^a   Nævdal, Geir ^a   Urkedal, Hege ^a  

^a RF Rogaland Research   (Norway)

Author keywords

Adaptive parameterization; Inverse problem; Porous medium; Regularization

Indexed keywords

MATHEMATICAL METHOD; PERMEABILITY; POROUS MEDIUM;

NUMERICAL METHOD; PARAMETERIZATION; PERMEABILITY; POROUS MEDIUM;

EID: 0037234526     PISSN: 14200597     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022417923824     Document Type: Article

References (25)

1. K. Aziz and A. Settari, Petroleum Reservoir Simulation (Applied Science, London, 1979).
2. Y. Bard, Nonlinear Parameter Estimation (Academic Press, New York, 1974).
3. D.M. Bates and D.G. Watts, Relative curvature measures of nonlinearity, J. Roy. Statist. Soc. Ser. B 42(1) (1980) 1-25.
4. H. Ben Ameur, G. Chavent and J. Jaffré, Refinement and coarsening of parameterization for the estimation of hydraulic transmissivity, in: Proc. of the 3rd Internat. Conf. on Inverse Problems in Engineering: Theory and Practice, Port Ludlow, WA, USA, June 1999.
5. R. Bissell, O. Dubrule, P. Lamy, P. Swaby and O. Lepine, Combining geostatistical modelling with gradient information for history matching: the pilot-point method, SPE 38730 (1997).
6. K. Brusdal and T. Mannseth, Effects of basis-element norm rescaling on the convergence speed for a nonlinear parameter estimation problem, SIAM J. Sci. Comput. 21(6) (2000) 2114-2125.
7. G. Chavent and R. Bissell, Indicator for the refinement of parameterization, in: Proc. of the 3rd Internat. Symposium on Inverse Problems, ISIP '98, Nagano, Japan, eds. M. Tanaka and G.S. Dulikravich (Elsevier, Amsterdam, 1998) pp. 309-314.
8. G. Chavent and K. Kunisch, New results on the non-linearity and the sensitivity of the estimation of the diffusion coefficient in a 2d elliptic equation, in: Proc. of the 3rd Internat. Conf. on Inverse Problems in Engineering: Theory and Practice, Port Ludlow, WA, USA, June 1999.
9. G. Chavent and J. Liu, Multiscale parametrization for the estimation of a diffusion coefficient in elliptic and parabolic problems, in: Fifth IFAC Symposium on Control of Distributed Parameter Systems, Perpignan, France, June 1989.
10. A.J.W. Duijndam, Bayesian estimation in seismic inversion. Part 1: Principles, Geophysical Prospecting 36 (1988) 878-898.
11. J. Glimm, S. Hou, H. Kim, Y. Lee, D.H. Sharp, K. Ye and Q. Zou, Risk management for petroleum reservoir production: A simulation-based study of prediction, Comput. Geosci. 5 (2001) 172-197.
12. A.-A. Grimstad and T. Mannseth, Nonlinearity, scale, and sensitivity for parameter estimation problems, SIAM J. Sci. Comput. 21(6) (2000) 2096-2113.
13. A.-A. Grimstad, T. Mannseth, G. Nævdal and H. Urkedal, Scale splitting approach to reservoir characterization, in: SPE Reservoir Simulation Symposium, Paper SPE66394, Houston, TX, February 2001.
14. A.-A. Grimstad, T. Mannseth, J.-E. Nordtvedt and G. Nævdal, Reservoir characterization through scale splitting, in: 7th European Conf. on the Mathematics of Oil Recovery, European Association of Geoscientists and Engineers, September 2000.
15. A.-A. Grimstad, T. Mannseth, J-E. Nordtvedt and G. Nævdal, Scale splitting can reduce cost and complexity of reservoir characterization, in: Proc. of the 62nd EAGE Conference and Exhibition, Glasgow, 2000 (extended abstract).
16. A. Kirsch, An Introduction to the Theory of Inverse Problems, Applied Mathematical Sciences, Vol. 120 (Springer, New York, 1996).
17. J. Liu, A multiresolution method for distributed parameter estimation, SIAM J. Sci. Comput. 14(2) (1993) 398-405.
18. T. Mannseth, Prediction uncertainty assessment through scale splitting, in: Proc. of the EAGE/SPE 3rd Internat. Symposium on Petroleum Geostatistics, Toulose, France, April 1999 (extended abstract).
19. T. Mannseth, K. Brusdal, A.-A. Grimstad, J.-E. Nordtvedt and G. Nævdal, Nonlinearity, scale, and sensitivity for parameter estimation problems: Some implications for estimation algorithms, in: Proc. of the 3rd Internat. Conf. on Inverse Problems in Engineering: Theory and Practice, Port Ludlow, WA, USA, June 1999.
20. T. Mannseth, J.-E. Nordtvedt and G. Nævdal, Optimal management of advanced wells through fast updates of the near-well reservoir model, in: 7th European Conf. on the Mathematics of Oil Recovery. European Association of Geoscientists and Engineers, September 2000.
21. A.J. Miller, Subset Selection in Regression, Monographs on Statistics and Applied Probability. Vol. 40 (Chapman and Hall, London, 1990).
22. J.J. Moré, The Levenberg-Marquardt algorithm: Implementation and theory, in: Numerical Analysis, ed. G.A. Watson, Lecture Notes in Mathematics, Vol. 630 (Springer, Berlin, 1977) pp. 105-116.
23. G.A.F. Seber and C.J. Wild, Nonlinear Regression (Wiley, New York, 1989).
24. A. Sen and M. Srivastava, Regression Analysis; Theory, Methods, and Applications (Springer, Berlin, 1990).
25. S. Yoon, A.H. Malallah, A. Datta-Gupta, D.W. Vasco and R.A. Behrens, A multiscale approach to production data integration using streamline models, in: 1999 SPE Annual Technical Conference and Exhibition, SPE 56653, Society of Petroleum Engineers, October 1999.