A finite-volume method with hexahedral multiblock grids for modeling flow in porous media

Computational Geosciences

Volumn 6, Issue 3-4, 2002, Pages 353-379

  Lee, S H ^a   Jenny, P ^a   Tchelepi, H A ^a  

^a CHEVRON ENERGY TECHNOLOGY COMPANY   (United States)

Author keywords

Finite volume; Multiblock grid; Porous media

Indexed keywords

FAULT BOUNDARY; FINITE VOLUME TECHNIQUE; FLUID FLOW; HYDROCARBON RESERVOIR; MATHEMATICAL MODELING; POROUS MEDIUM;

FAULT; FINITE VOLUME METHOD; FLUID FLOW; HYDROCARBON RESERVOIR; NUMERICAL MODEL; PETROLEUM HYDROCARBON; POROUS MEDIUM;

EID: 0036924076     PISSN: 14200597     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1021287013566     Document Type: Article

References (32)

1. I. Aavatsmark, T. Barkve, O. Bøe and T. Mannseth, Discretization on non-orthogonal, quadrilateral grids for inhomogeneous, anisotropic media, J. Comput. Phys. 127 (1996) 2-14.
2. I. Aavatsmark, T. Barkve and T. Mannseth, Control volume discretization methods for 3D quadrilateral grids in inhomogeneous, anisotropic reservoirs, SPE J. 3 (1998) 146-154.
3. I. Aavatsmark, O. Bøe and E. Reiso, Hybrid MPFA-methods with application to field simulation, in: Proc. of 6th European Conf. on the Mathematics of Oil Recovery, Peebles, Scotland, 1998.
4. T. Arbogast, L. Cowsar, M.F. Wheeler and I. Yotov, Mixed finite element methods on nonmatching multiblock grids, SIAM J. Numer. Anal. 37 (2000) 1295-1315.
5. T. Arbogast, P.T. Keenan, M.F. Wheeler and I. Yotov, Logically rectangular mixed methods for Darcy flow on general geometry, in: Proc. of 13th SPE Symposium on Reservoir Simulation, San Antonio, TX, 1995, pp. 51-59.
6. J.H. Bramble, R.E. Ewing, J.E. Pasciak and A.H. Schatz, A preconditioning technique for the efficient solution of problems with local grid refinement, Comput. Methods Appl. Mech. Engrg. 67 (1988) 149-159.
7. S. Chakravarthy, A unified-grid finite volume formulation for computational fluid dynamics, Internat. J. Numer. Methods Fluids 31 (1999) 309-323.
8. M.C.H. Chien and E.J. Northrup, Vectorization and parallel processing of local grid refinement and adaptive implicit schemes in a general purpose reservoir simulator, in: Proc. of 12th SPE Symposium on Reservoir Simulation, New Orleans, LA, 1993, pp. 279-290.
9. M.C.H. Chien, H.A. Tchelepi, H.E. Yardumian and W.H. Chen, A scaleable parallel multi-purpose reservoir simulator, in: Proc. of 14th SPE Symposium on Reservoir Simulation, Dallas, TX, 1997, pp. 17-30.
10. J.H. Cushman, An introduction to hierarchical porous media, in: Dynamics of Fluids in Hierarchical Porous Media, ed. J.H. Cushman, (Academic Press, London, 1990) pp. 1-6.
11. C.V. Deutsch and A.G. Journel, GSLIB: Geostatistical Software Library and User's Guide (Oxford Univ. Press, New York, 1998).
12. L.J. Durlofsky, Numerical calculation of equivalent grid block permeability tensors for heterogeneous porous media, Water Resourc. Res. 27 (1991) 699-708.
13. M.G. Edwards, Superconvergent renormalization and tensor approximation, in: Proc. of 5th European Conf. on the Mathematics of Oil Recovery, ed. Z.E. Heinemann, Leoben, Austria, 1996, pp. 9-19.
14. M.G. Edwards, Cross-flow, tensor and finite volume approximation with deferred correction, Comput. Methods Appl. Mech. Engrg, 151 (1998) 143-161.
15. M.G. Edwards, Simulation with a full tensor coefficient velocity field recovered from a diagonal tensor solution, SPE 49073, in: Proc. of the SPE Annual Technical Exhibitions and Conferences, New Orleans, LA, 1998.
16. M.G. Edwards, M-matrix flux splitting for general full tensor discretization operators on structured and unstructured grids, J. Comput. Phys. 160 (2000) 1-28.
17. M.G. Edwards and C.F. Rogers, Finite volume discretization with imposed flux continuity for the general tensor pressure equation, Comput. Geosci. 2 (1998) 259-290.
18. P.R. Eiseman, Applications of algebraic grid generation, in: Proc. of AGARD Fluid Dynamics Panel Specialists' Meeting, Loen, Norway, 1989, pp. 40-51.
19. C.W. Gable, H. Trease and T. Cherry, Geological applications of automatic grid generation tools for finite elements applied to porous flow modeling, in: Numerical Grid Generation in Computational Fluid Dynamics and Related Fields, eds. B.K. Soni, J.F. Thompson, H. Hausser and P.R. Eiseman (Mississippi State Univ. Press, 1996).
20. Z.E. Heinemann, G.F. Heinemann and B.M. Tranta, Modeling heavily faulted reservoirs, in: Proc. of 15th SPE Symposium on Reservoir Simulation, Houston, TX, 1999, pp. 9-19.
21. R. Huber and R. Helmig, Node-centered finite volume discretization for the numerical simulation of multiphase flow in heterogeneous porous media. Comput, Geosci. 4 (2000) 141-164.
22. P. Jenny, C. Wolfsteiner, S.H. Lee and L.J. Durlofsky, Modeling flow in geometrically complex reservoirs using hexahedral multi-block grids, SPE Paper 66357, in: Proc. of 16th SPE Symposium on Reservoir Simulation, Houston, TX, 2001.
23. S.H. Lee, L.J. Durlofsky, M.F. Lough and W.H. Chen, Finite difference simulation of geologically complex reservoirs with tensor permeabilities, SPE Res. Evaluation Engrg. 1 (1998) 567-574.
24. S.H. Lee, H. Tchelepi and L.J. DeChant, Implementation of a flux-continuous finite difference method for stratigraphic, hexahedron grids, in: Proc. of 15th SPE Symposium on Reservoir Simulation, Houston, TX, 1999, pp. 231-241.
25. M.F. Lough, S.H. Lee and J. Kamath, A new method to calculate effective permeability of gridblocks used in the simulation of naturally fractured reservoirs, SPE Res. Engrg. 12 (1997) 219-224.
26. M.F. Lough, S.H. Lee and J. Kamath, An efficient boundary integral formulation for flow through fractured porous media, J. Comput. Phys. 143 (1998) 462-483.
27. PDC, GridPro interactive multi-block gridding tool (1999) www.gridpro.com.
28. D.W. Peaceman, Fundamentals of Numerical Reservoir Simulation (Elsevier Science, New York, 1977).
29. B.K. Soni, Grid generation: Past, present, and future, Appl. Numer. Math. 32 (2000) 361-369.
30. J.F. Thompson and N.P. Weatherill, Fundamental concepts and approaches, in: Handbook of Grid Generation, eds. J.F. Thompson, B.K. Soni and N.P. Weatherill (CRC Press, New York, 1999) pp. 11-130.
31. S. Verma and K. Aziz, A control volume scheme for flexible grids in reservoir simulation, SPE Paper 37999, in: Proc. of 14th SPE Symposium on Reservoir Simulation, Dallas, TX, 1997.
32. M.F. Wheeler, T. Arbogast, S. Bryant, J. Eaton, Q. Lin and M. Peszynska, A parallel multi-block/multidomain approach for reservoir reservoir simulation, in: Proc. of 15th SPE Symposium on Reservoir Simulation, Houston, TX, 1999, pp. 51-61.