A two-scale numerical subgrid technique for waterflood simulations

SPE Journal

Volumn 7, Issue 4, 2002, Pages 446-457

  Arbogast, Todd ^a   Bryant, Steven L ^a  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; MECHANICAL PERMEABILITY; MONTE CARLO METHODS; MULTIPHASE FLOW; OIL WELLS; POROSITY;

COARSE GRID COMPUTATION; TWO SCALE NUMERICAL SUBGRID TECHNIQUES; WATERFLOOD SIMULATIONS;

WELL FLOODING;

EID: 0036962026     PISSN: 1086055X     EISSN: None     Source Type: Journal    
DOI: 10.2118/81909-PA     Document Type: Article

References (24)

1. Renard, P. and de Marsily, G.: "Calculating equivalent permeability: a review," Advances in Water Resources (1997) 20, 253.
2. Kasap, E., and Lake, L.W.: "Calculating the Effective Permeability Tensor of a Gridblock," SPEFE (June 1990) 192.
3. Durlofsky, L.J.: "Numerical calculation of equivalent grid block permeability tensors for heterogeneous porous media," Water Resources Research (1991) 27, 699.
4. Amaziane, B., Bourgeat, A., and Koebbe, J.: "Numerical simulation and homogenization of two-phase flow in heterogeneous porous media," Transport in Porous Media (1991) 9, 519.
5. Christie, M.A. et al.: "A renormalization-based upscaling technique for WAG floods in heterogeneous reservoirs," paper SPE 29127 presented at the 1995 SPE Symposium on Reservoir Simulation, San Antonio, Texas, 12-15 February.
6. King, M.J. et al.: "Effective properties of flow calculations," Transport in Porous Media (1995) 20, 169.
7. Hou, T.Y. and Wu, X.H.: "A multiscale finite element method for elliptic problems in composite materials and porous media," J. Comput. Phys. (1997) 134, 169.
8. Hughes, T.J.R. et al.: "The variational multiscale method-a paradigm for computational mechanics," Comp. Meth. in Appl. Mech. and Engng. (1998) 166, 3.
9. Brezzi, F. and Fortin, M.: Mixed and Hybrid Finite Element Methods, Springer-Verlag, New York City (1991).
10. Durlofsky, L.J.: "Accuracy of mixed and control volume finite element approximations to Darcy velocity and related quantities," Water Resources Research (1994) 30, 965.
11. Raviart, R.A. and Thomas, J.M.: "A mixed finite element method for 2nd order elliptic problems," Mathematical Aspects of the Finite Element Method, Lecture Notes in Math. 606, Springer-Verlag, New York City (1977) 292-315.
12. Brezzi, F., Douglas, J. Jr., and Marini, L.D.: "Two families of mixed elements for second order elliptic problems," Numer. Math. (1985) 88, 217.
13. Brezzi, F. et al.: "Mixed finite elements for second order elliptic problems in three variables," Numer. Math. (1987) 51, 237.
14. Russell, T.F. and Wheeler, M.F.: "Finite element and finite difference methods for continuous flows in porous media," The Mathematics of Reservoir Simulation, Frontiers in Applied Mathematics 1, Ewing, R.E. (ed.), Society for Industrial and Applied Mathematics, Philadelphia (1983) Ch. II, 35-106.
15. Weiser, A. and Wheeler, M.F.: "On convergence of block-centered finite-differences for elliptic problems," SIAM J. Numer. Anal. (1988) 25, 351.
16. Arbogast, T., Wheeler, M.F., and Yotov, I.: "Mixed finite elements for elliptic problems with tensor coefficients as cell centered finite differences," SIAM J. Numer. Anal. (1997) 34, 828.
17. Arbogast, T.: "Implementation of a locally conservative numerical subgrid upscaling scheme for two-phase Darcy flow," Computational Geosciences, to appear
18. Chavent, G. and Jaffre, J.: "Mathematical Models and Finite Elements for Reservoir Simulation, Elsevier Science Publishers, New York City (1986)
19. Arbogast T., Wheeler, M.F., and Zhang, N.-Y.: "A nonlinear mixed finite element method for a degenerate parabolic equation arising in flow in porous media,"
20. Arbogast T.: "Numerical subgrid upscaling of two-phase flow in porous media," Numerical Treatment of Multiphase Flows in Porous Media, Lecture notes in Physics 552, Z. Chen, R.E. Ewing, and Z.-C. Shi (eds.), Springer, Berlin, (2000) 35-49
21. Arbogast, T. and Bryant, S.: "Efficient forward modeling for DNAPL site evaluation and remdiation," in Computational Methods in Water Resources XIII, L.R. Bentley, et. al. (eds.), Balkema, Rotterdam (2000) 161-166
22. Peaceman, D.W.: "Interpretation of Well-Block pressures in numerical reservoir simulation with nonsquare Gridblocks and anisotropic permeability," SPEJ (June 1983) 531
23. Christie, M.A. and Blunt, M.J.: "Tenth SPE comparative solution project: A comparison of upscaling techniques," SPEREE (August 2001) 308
24. White, C.D. and Horne, R.N.: " Computing absolute transmissibility in the presence of fine-scale heterogeneity," paper SPE 16011 presented at the 1987 SPE symposium on reservoir simulation, San Antonio, Texas, 1-4 February