Upscaling of channel systems in two dimensions using flow-based grids

Transport in Porous Media

Volumn 51, Issue 3, 2003, Pages 343-366

  Wen, X H ^a   Durlofsky, L J ^a,b   Edwards, M G ^c  

^a CHEVRON ENERGY TECHNOLOGY COMPANY   (United States)

^b STANFORD UNIVERSITY   (United States)

^c SWANSEA UNIVERSITY   (United Kingdom)

Author keywords

Effective permeability; Gridding; Heterogeneity; Irregular geometry; Reservoir simulation; Streamlines; Tensor permeability; Upscaling

Indexed keywords

FINITE ELEMENT METHOD; MECHANICAL PERMEABILITY; TENSORS;

CHANNEL SYSTEMS;

CHANNEL FLOW;

CHANNEL FLOW; GEOLOGY; POROUS MEDIUM; SCALE EFFECT;

FLUID FLOW; POROUS MEDIUM; UPSCALING;

EID: 0037409207     PISSN: 01693913     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022318926559     Document Type: Article

References (34)

1. Aavatsmark, I., Barkve, T., Boe, O. and Mannseth, T.: 1996, Discretization on non-orthogonal, quadrilateral grids for inhomogeneous, anisotropic media, J. Comp. Phys. 127, 2-14.
2. Castellini, A., Edwards, M. G. and Durlofsky, L. J.: 2000, Flow based modules for grid generation in two and three dimensions, In: Proceedings of the 7th European Conference on the Mathematics of Oil Recovery, Baveno, Italy, September 5-8.
3. Christie, M. A. and Blunt, M. J.: 2001, Tenth SPE Comparative Solution Project: a comparison of upscaling techniques, paper SPE 66599 presented at the SPE Reservoir Simulation Symposium, Houston, February 11-14.
4. Damsleth, E., Tjolsen, C. B., Omre, H. and Haldorsen, H. H.: 1992, A two-stage stochastic model applied to a North Sea reservoir, J. Pet. Tech. 22, 402.
5. Deutsch, C. V. and Journel, A. G.: 1998, GSLIB: Geostatistical Software Library and User's Guide, 2nd edn., Oxford University Press, New York.
6. Durlofsky, L. J.: 1991, Numerical calculation of equivalent grid block permeability tensors for heterogeneous porous media, Water Resour. Res. 27, 699-708.
7. Durlofsky, L. J., Jones, R. C. and Milliken, W. J.: 1997, A nonuniform coarsening approach for the scale-up of displacement processes in heterogeneous porous media, Adv. Water Resour. 20, 335-347.
8. Edwards, M. G. and Rogers, C. F.: 1998, Finite volume discretization with imposed flux continuity for the general tensor pressure equation, Comp. Geosci. 2, 259-290.
9. Edwards, M. G., Agut, R. and Aziz, K.: 1998, Quasi K-orthogonal streamline grids: gridding and discretization, paper SPE 49072 presented at the SPE Annual Technical Conference and Exhibition, New Orleans, September 27-30.
10. Efendiev, Y. R.: 1999, The multiscale finite element method (MsFEM) and its applications, PhD Thesis, California Institute of Technology.
11. Garcia, M. H., Journel, A. G. and Aziz, K.: 1992, Automatic grid generation for modeling reservoir heterogeneities, SPE Res. Eng. 7, 278-284.
12. Gomez-Hernandez, J. J. and Journel, A. G.: 1994, Stochastic characterization of grid block permeabilities, SPE Form. Eval. 9, 93-99.
13. He, C., Edwards, M. G. and Durlofsky, L. J.: 2002, Numerical calculation of equivalent cell permeability tensors for general quadrilateral control volumes, Comp. Geosci. 6, 29-47.
14. Hewett, T. A. and Yamada, T.: 1997, Theory for the semi-analytical calculation of oil recovery and effective relative permeabilities using streamtubes, Adv. Water Resour. 20, 279-292.
15. Holden, L. and Lia, O.: 1992, A tensor estimator for the homogenization of absolute permeability, Transport in Porous Media 8, 37-46.
16. Hou, T. Y. and Wu, X. H.: 1997, A multiscale finite element method for elliptic problems in composite materials and porous media, J. Comp. Phys. 134, 169-189.
17. King, M. J., MacDonald, D. G., Todd, S. P. and Leung, H.: 1998, Application of novel upscaling approaches to the Magnus and Andrew reservoirs, paper SPE 50643 presented at the SPE European Petroleum Conference, The Hague, The Netherlands, October 20-22.
18. King, M. J. and Mansfield, M.: 1999, Flow simulation of geologic models, SPE Res. Eval. Eng. 2, 351-367.
19. Knupp, P.: 1995, Mesh generation using vector-fields, J. Comp. Phys. 119, 142-148.
20. Knupp, P.: 1996, Jacobian-weighted elliptic grid generation, SIAM J. Sci. Comput. 17, 1475-1490.
21. Lee, S. H., Durlofsky, L. J., Lough, M. F. and Chen, W. H.: 1998, Finite difference simulation of geologically complex reservoirs with tensor permeabilities, SPE Res. Eval. Eng. 1, 567-574.
22. Mao, S. and Journel, A. G.: 1998, Generation of a reference petrophysical/seismic data set: the Stanford V Reservoir, Stanford Center for Reservoir Forecasting Report.
23. Portella, R. C. M. and Hewett, T. A.: 2000, Upscaling, gridding, and simulation using streamtubes, SPEJ 5, 315-323.
24. Prevost, M., Edwards, M. G. and Blunt, M. J.: 2001, Streamline tracing on curvilinear structured and unstructured grids, SPEJ 7, 139-148.
25. Renard, P. and de Marsily, G.: 1997, Calculating equivalent permeability: a review, Adv. Water Resour. 20, 253-278.
26. Ruge, J. W. and Stuben, K.: 1987, Algebraic multigrid (AMG), In: S. F. Mc Cormick (ed.), Multigrid Methods. SIAM Front. Appl. Math. 3, 73-130.
27. Tran, T. T.: 1995, Stochastic simulation of permeability fields and their scale up for flow modeling, PhD Thesis, Stanford University.
28. Verma, S. and Aziz, K.: 1997, A control volume scheme for flexible grids in reservoir simulation, paper SPE 37999 presented at the SPE Reservoir Simulation Symposium, Dallas, June 8-11.
29. Wallis, J. R., Kendall, R. P. and Little, T. E.: 1985, Constrained residual acceleration of conjugate residual method, paper SPE 13536 presented at the SPE Reservoir Simulation Symposium, Dallas, February 10-13.
30. Wen, X. H. and Gomez-Hernandez, J. J.: 1996a, Selective upscaling of hydraulic conductivities, in: E. Baafi and N. Schofield (eds), Geostatistics Wollongong '96, Kluwer Academic Publishers, Dordrecht, The Netherlands, pp. 1112-1123.
31. Wen, X. H. and Gomez-Hernandez, J. J.: 1996b, Upscaling hydraulic conductivities in heterogeneous media: an overview, J. Hydrol. 183. ix-xxxii.
32. Wen, X. H. and Gomez-Hernandez, J. J.: 1998, Upscaling hydraulic conductivities in cross-bedded formations, Math. Geol. 30, 181-211.
33. Wen, X. H., Durlofsky, L. J. and Edwards, M. G.: 2002, Improved upscaling of complex geological models on Cartesian grids, in review for Math. Geol.
34. Wen, X. H., Durlofsky, L. J., Lee, S. H. and Edwards, M. G.: 2000, Full tensor upscaling of geologically complex reservoir descriptions, paper SPE 62928 presented at the SPE Annual Technical Conference and Exhibition, Dallas, October 1-4.