Local-global two-phase upscaling of flow and transport in heterogeneous formations

Multiscale Modeling and Simulation

Volumn 8, Issue 1, 2009, Pages 125-153

  Chen, Yuguang ^a   Li, Yan ^b  

^a CHEVRON ENERGY TECHNOLOGY COMPANY   (United States)

^b TEXAS A AND M UNIVERSITY   (United States)

Author keywords

Heterogeneity; Multiscale; Pseudorelative permeability; Reservoir simulation; Subgrid; Subsurface flow; Transport; Two phase flow; Upscaling

Indexed keywords

HETEROGENEITY; MULTISCALE; PSEUDORELATIVE PERMEABILITY; RESERVOIR SIMULATION; SUB-GRIDS; SUBSURFACE FLOW; TRANSPORT; UPSCALING;

BOUNDARY CONDITIONS; NUMERICAL METHODS; PETROLEUM RESERVOIR ENGINEERING; POTENTIAL FLOW; ROADS AND STREETS; TWO PHASE FLOW;

FLOW SIMULATION;

EID: 78650696187     PISSN: 15403459     EISSN: 15403467     Source Type: Journal    
DOI: 10.1137/090750949     Document Type: Article

References (32)

1. J. AARNES AND Y. EFENDIEV, An adaptive multiscale method for simulation of fluid flow in heterogeneous porous media, Multiscale Model. Simul., 5 (2006), pp. 918-939.
2. J. W. BARKER AND P. DUPOUY, An analysis of dynamic pseudo-relative permeability methods for oil-water flows, Petroleum Geosci., 5 (1999), pp. 385-394.
3. Y. CHEN, L. J. DURLOFSKY, M. GERRISTEN, AND X. H. WEN, A coupled local-global upscaling approach for simulating flow in highly heterogeneous formations, Adv. Water Res., 26 (2003), pp. 1041-1060.
4. Y. CHEN AND L. J. DURLOFSKY, Adaptive local-global upscaling for general flow scenarios in heterogeneous formations, Transp. Porous Media, 62 (2006), pp. 157-185.
5. Y. CHEN AND L. J. DURLOFSKY, Efficient incorporation of global effects in upscaled models of two-phase flow and transport in heterogeneous formations, Multiscale Model. Simul., 5 (2006), pp. 445-475.
6. Y. CHEN AND L. J. DURLOFSKY, Ensemble-level upscaling for efficient estimation of fine-scale production statistics, SPE J., 13 (2008), pp. 400-411.
7. Y. CHEN, Upscaling and Sub grid Modeling of Flow and Transport in Heterogeneous Reservoirs, Ph.D. thesis, Stanford University, Stanford, CA, 2005.
8. M. A. CHRISTIE, T. C. WALLSTROM, L. J. DURLOFSKY, S. HOU, D. H. SHARP, AND Q. ZOU, Effective medium boundary conditions in upscaling, in Proceedings of the 7th European Conference on the Mathematics of Oil Recovery, Baveno, Italy, European Association of Geoscientists & Engineers (EAGE), 2000.
9. M. A. CHRISTIE, Flow in porous media-scale up of multiphase flow, Curr. Opinion in Colloid Interface Sci., 6 (2001), pp. 236-241.
10. A. DATTA-DUPTA AND M. J. KING, Streamline Simulation: Theory and Practice, Society of Petroleum Engineers, Richardson, TX, 2007.
11. C. V. DEUTSCH AND A. G. JOURNEL, GSLIB: Geostatistical Software Library and User's Guide, 2nd ed., Oxford University Press, New York, 1998.
12. L. J. DURLOFSKY, Numerical calculation of equivalent grid block permeability tensors for heterogeneous porous media, Water Resour. Res., 27 (1991), pp. 699-708.
13. Y. EFENDIEV AND L. J. DURLOFSKY, A generalized convection-diffusion model for subgrid transport in porous media, Multiscale Model. Simul., 1 (2003), pp. 504-526.
14. C. L. FARMER, Upscaling: A review, Internat. J. Numer. Methods Fluids, 40 (2002), pp. 63-78.
15. M. G. GERRITSEN AND L. J. DURLOFSKY, Modeling fluid flow in oil reservoirs, Annu. Rev. Fluid Mech., 37 (2005), pp. 211-238.
16. M. GERRITSEN AND J. LAMBERS, Integration of local-global upscaling and grid adaptivity for simulation of subsurface flow in heterogeneous formations, Comput. Geosci., 12 (2008), pp. 193-208.
17. T. A. HEWETT, K. SUZUKI, AND M. A. CHRISTIE, Analytical calculation of coarse-grid corrections for use in pseudofunctions, SPE J., 3 (1998), pp. 293-305.
18. T. A. HEWETT, K. SUZUKI, AND M. A. CHRISTIE, Discretization effects in coarse-grid pseudofunctions, in Proceedings of the 6th European Conference on the Mathematics of Oil Recovery, Peebles, Scotland, European Association of Geoscientists & Engineers (EAGE), 1998.
19. T. A. HEWETT AND T. YAMADA, Theory for the semi-analytical calculation of oil recovery and effective relative permeabilities using streamtubes, Adv. Water Res., 20 (1997), pp. 279-292.
20. L. HOLDEN AND B. F. NIELSEN, Global upscaling of permeability in heterogeneous reservoirs: The output least squares (OLS) method, Transp. Porous Media, 40 (2000), pp. 115-143.
21. T. Y. HOU AND X. H. WU, A multiscale finite element method for elliptic problems in composite materials and porous media, J. Comput. Phys., 134 (1997), pp. 169-189.
22. P. JENNY, S. H. LEE, AND H. A. TCHELEPI, Multi-scale finite-volume method for elliptic problems in subsurface flow simulation, J. Comput. Phys., 187 (2003), pp. 47-67.
23. S. H. LEE, H. ZHOU, AND H. A. TCHELEPI, Indirector-based, dynamic upscaling of multiphase flow in porous media, in Proceedings of the 11th European Conference on the Mathematics of Oil Recovery, Bergen, Norway, European Association of Geoscientists & Engineers (EAGE), 2008.
24. T. NAKASHIMA AND L. J. DURLOFSKY, Accurate representation of near-well effects in coarsescale models of primary oil production, Trans. Porous Media, to appear.
25. D. W. POLLOCK, Semianalytical computation of pathlines for finite-difference models, Groundwater, 26 (1988), pp. 743-750.
26. PH. RENARD AND G. DE MARSILY, Calculating effective permeability: A review, Adv. Water Res., 20 (1997), pp. 253-278.
27. K. SUZUKI AND T. A. HEWETT, Sequential upscaling method, Transp. Porous Media, 46 (2002), pp. 179-212.
28. T. C. WALLSTROM, M. A. CHRISTIE, L. J. DURLOFSKY, AND D. H. SHARP, Effective flux boundary conditions for upscaling porous media equations, Transp. Porous Media, 46 (2002), pp. 139-153.
29. T. C. WALLSTROM, S. HOU, M. A. CHRISTIE, L. J. DURLOFSKY, D. H. SHARP, AND Q. ZOU, Application of effective flux boundary conditions to two-phase upscaling in porous media, Transp. Porous Media, 46 (2002), pp. 155-178.
30. X. H. WU, Y. R. EFENDIEV, AND T. Y. HOU, Analysis of upscaling absolute permeability, Discrete Contin. Dyn. Syst. Ser. B, 2 (2002), pp. 185-204.
31. X.-H. WU, R. R. PARASHKEVOV, M. T. STONE, AND S. L. LYONS, Global scale-up on reservoir models with piecewise constant permeability field, J. Algorithms Comput. Technol., 2 (2008), pp. 223-247.
32. P. ZHANG, G. E. PICKUP, AND M. A. CHRISTIE, A new practical method for upscaling in highly heterogeneous reservoir models, SPE J., 13 (2008), pp. 68-76.