A multiscale adjoint method to compute sensitivity coefficients for flow in heterogeneous porous media

Advances in Water Resources

Volumn 33, Issue 6, 2010, Pages 698-709

  Fu, Jianlin ^a   Tchelepi, Hamdi A ^a   Caers, Jef ^a  

^a STANFORD UNIVERSITY   (United States)

Author keywords

Gradient; High resolution history matching; Model calibration; Multiscale adjoint model; Multiscale finite volume method

Indexed keywords

ADJOINT METHODS; ADJOINT MODELS; ADJOINT PROBLEMS; ADJOINTS; CALIBRATED MODEL; COARSE GRID; COMPUTATIONALLY EFFICIENT; DYNAMIC DATA; FINE GRIDS; FINITE DIFFERENCE; FINITE-VOLUME; FLOW PROBLEMS; GEOLOGIC FORMATIONS; HETEROGENEOUS POROUS MEDIA; HIGH RESOLUTION; HISTORY MATCH; HISTORY MATCHING; MODEL PARAMETERS; MODEL RESPONSE; MULTISCALE METHOD; MULTISCALES; OBJECTIVE FUNCTIONS; SCALE MODELS; SENSITIVITY COEFFICIENT; SUB-GRIDS; SUB-PROBLEMS; SUBSURFACE FLOW;

CALIBRATION; FINITE VOLUME METHOD; POROUS MATERIALS;

INVERSE PROBLEMS;

ADJOINT METHOD; FINITE VOLUME METHOD; FLOW MODELING; FLUID FLOW; INVERSE PROBLEM; NUMERICAL MODEL; POROUS MEDIUM; SENSITIVITY ANALYSIS; SUBSURFACE FLOW;

EID: 77953123579     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.advwatres.2010.04.005     Document Type: Article

References (24)

1. Aanonsen S.I. Efficient history matching using a multiscale technique. SPE Reserv Eval Eng 2008, 11(1):154-164. 10.2118/92758-PA.
2. Carrera J., Neuman S.P. Estimation of aquifer parameters under transient and steady state conditions: 2. Uniqueness, stability, and solution algorithms. Water Resour Res 1986, 21(2):211-227.
3. Chen W.H., Gavalas G.R., Seinfeld J.H., Wasserman M.L. A new algorithm for automatic history matching. SPE J 1974, 14(6):593-608. 10.2118/4545-PA.
4. Dettinger M.D., Wilson J.L. First order analysis of uncertainty in numerical models of groundwater flow: part 1. Mathematical development. Water Resour Res 1981, 17(1):149-161.
5. Director S.W., Rohrer R.A. The generalized adjoint network and network sensitivities. IEEE Trans Circuit Theory 1969, CT-16:313-323.
6. J. Fu, J. Caers, H. Tchelepi. A multiscale method for inverse modeling: single-phase transient flow. Submitted for publication.
7. Giering R., Kaminski T. Recipes for adjoint code construction. ACM Trans Math Software 1998, 24(4):437-474.
8. Gómez-Hernández J.J., Journel A.G. Joint simulation of multiGaussian random variables. Geostatistics Troia'92 1993, vol. 1:85-94. Kluwer. A. Soares (Ed.).
9. Hajibeygi H., Bonfigli G., Hesse M.A., Jenny P. Iterative multiscale finite-volume method. J Comput Phys 2009, 227:8604-8621.
10. Jenny P., Lee S.H., Tchelepi H.A. Multiscale finite-volume method for elliptic problems in subsurface flow simulation. J Comput Phys 2003, 187:47-67.
11. Jenny P., Lee S.H., Tchelepi H.A. Adaptive multiscale finite-volume method for multiphase flow and transport in porous media. Multiscale Model Simul 2004, 3(1):50-64.
12. Jenny P., Lee S.H., Tchelepi H.A. Adaptive fully implicit multiscale finite-volume method for multiphase flow and transport in heterogeneous porous media. J Comput Phys 2006, 217:627-641.
13. Krogstad S., Hauge V.L., Gulbransen A.F. Adjoint multiscale mixed finite elements. SPE 2009, 119112:1-11.
14. Lee S.H., Malallah A., Datta-Gupta A., Higdon D. Multiscale data integration using Markov random fields. SPE Reserv Eval Eng 2002, 5(1):68-78. 10.2118/76905-PA.
15. Lee S.H., Wolfsteiner C., Tchelepi H.A. Multiscale finite volume formulation for multiphase flow simulation in porous media: black oil formulation of compressible, three-phase flow with gravity. Comput Geosci 2008, 12:351-366.
16. Liu Y., Journel A.G. A package for geostatistical integration of coarse and fine scale data. Comput Geosci 2009, 35(3):527-547.
17. Lu A.H. Development of an adjoint sensitivity method for site characterization, uncertainty analysis, and code calibration/validation. Presented at Environmental Remediation Symposia, Pasco, Washington, Sept. 8-11, 1991 1991.
18. Lunati I., Jenny P. Multiscale finite-volume method for compressible multiphase flow in porous media. J Comput Phys 2006, 216:616-636.
19. Sykes J.F., Wilson J.L., Andrews R.W. Sensitivity analysis for steady sate groundwater flow using adjoint operators. Water Resour Res 1985, 21(3):359-371.
20. Tchelepi H.A., Jenny P., Lee S.H., Wolfsteiner C. Adaptive multiscale finite-volume framework for reservoir simulation. SPE J 2007, 12(2):188-195. 10.2118/93395-PA.
21. Townley L.R., Wilson J.L. Computationally efficient algorithsm for paraemter estimation and uncertainty propagation in numerical models of groundwater flow. Water Resour Res 1985, 21(12):1851-1860.
22. Tran T.T., Wen X.-H., Behrens R.A. Efficient conditioning of 3D fine-scale reservoir model to multiphase production data using streamline-based coarse-scale inversion and geostatistical downscaling. SPE J 2001, 6(4):364-374. 10.2118/74708-PA.
23. Wilson J.L., Metcalfe D.E. Illustration and verification of adjoint sensitivity theory for steady state groundwater flow. Water Resour Res 1985, 21(11):1602-1610.
24. Yoon S., Malallah A.H., Datta-Gupta A., Vasco D.W., Behrens R.A. A multiscale approach to production-data integration using streamline models. SPE J 2001, 6(2):182-192. 10.2118/71313-PA.