Efficient incorporation of global effects in upscaled models of two-phase flow and transport in heterogeneous formations

Multiscale Modeling and Simulation

Volumn 5, Issue 2, 2006, Pages 445-475

  Chen, Yuguang ^a,b   Durlofsky, Louis J ^a  

^a STANFORD UNIVERSITY   (United States)

^b CHEVRON ENERGY TECHNOLOGY COMPANY   (United States)

Author keywords

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

Indexed keywords

BOUNDARY CONDITIONS; COMPUTER SIMULATION; DIFFUSION; MATHEMATICAL MODELS; MECHANICAL PERMEABILITY;

EFFECTIVE FLUX BOUNDARY CONDITIONS (EFBCS); FLOW DEPENDENCY; HETEROGENEITY; PSEUDORELATIVE PERMEABILITY; SUBSURFACE FLOW; UPSCALED MODELS;

TWO PHASE FLOW;

EID: 33846203113     PISSN: 15403459     EISSN: 15403467     Source Type: Journal    
DOI: 10.1137/060650404     Document Type: Article

References (40)

1. J. E. AARNES, On the use of a mixed multiscale finite element method for greater flexibility and increased speed or improved accuracy in reservoir simulation, Multiscale Model. Simul., 2 (2004), pp. 421-439.
2. J. E. AARNES AND M. S. ESPEDAL, A new approach to upscaling for two-phase flow in heterogeneous porous media, in Fluid Flow and Transport in Porous Media: Mathematical and Numerical Treatment, Contemp. Math. 295, Z. Chen and R. E. Ewing, eds., AMS, Providence, RI, 2002, pp. 1-11.
3. I. AAVATSMARK, An introduction to multipoint flux approximations for quadrilateral grids, Comput. Geosci., 6 (2002), pp. 405-432.
4. J. W. BARKER AND P. DUPOUY, An analysis of dynamic pseudo-relative permeability methods for oil-water flows, Petroleum Geoscience, 5 (1999), pp. 385-394.
5. J. W. BARKER AND S. THIBEAU, A critical review of the use of pseudorelative permeabilities for upscaling, SPE Reservoir Engineering, 12 (1997), pp. 138-143.
6. W. H. CHEN, L. J. DURLOFSKY, B. ENGQUIST, AND S. OSHER, Minimization of grid orientation effects through use of higher order finite difference methods, SPE Advanced Technology Series, 1 (1993), pp. 43-52.
7. Y. CHEN, Upscaling and Subgrid Modeling of Flow and Transport in Heterogeneous Reservoirs, Ph.D. thesis, Stanford University, Stanford, CA, 2005.
8. 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.
9. Y. CHEN, L. J. DURLOFSKY, M. GERRITSEN, AND X. H. WEN, A coupled local-global upscaling approach for simulating flow in highly heterogeneous formations, Adv. in Water Res., 26 (2003), pp. 1041-1060.
10. Z. CHEN AND T. Y. HOU, A mixed finite element method for elliptic problems with rapidly oscillating coefficients, Math. Comp., 72 (2003), pp. 541-576.
11. M. A. CHRISTIE, Flow in porous media - scale up of multiphase flow, Current Opinion in Colloid & Interface Science, 6 (2001), pp. 236-241.
12. M. A. CHRISTIE AND M. J. BLUNT, Tenth SPE comparative solution project: A comparison of upscaling techniques, SPE Reservoir Evaluation & Engineering, 4 (2001), pp. 308-317.
13. 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, 2000.
14. N. H. DARMAN, G. E. PICKUP, AND K. S. SORBIE, A comparison of two-phase dynamic upscaling methods based on fluid potentials, Comput. Geosci., 6 (2002), pp. 5-27.
15. C. V. DEUTSCH AND A. G. JOURNEL, GSLIB: Geostatistical Software Library and User's Guide, 2nd ed., Oxford University Press, New York, 1998.
16. L. J. DURLOFSKY, Coarse scale models of two phase flow in heterogeneous reservoirs: Volume averaged equations and their relationship to existing upscaling techniques, Comput. Geosci., 2 (1998), pp. 73-92.
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), pp. 259-290.
18. 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.
19. Y. R. EFENDIEV AND L. J. DURLOFSKY, Accurate subgrid models for two-phase flow in heterogeneous reservoirs, SPE Journal, 9 (2004), pp. 219-226.
20. C. L. FARMER, Upscaling: A review, Internat. J. Numer. Methods Fluids, 40 (2002), pp. 63-78.
21. S. E. GASDA AND M. A. CELIA, Upscaling relative permeabilities in a structured porous medium, Adv. in Water Res., 28 (2005), pp. 493-506.
22. M. G. GERRITSEN AND L. J. DURLOFSKY, Modeling fluid flow in oil reservoirs, in Annual Review of Fluid Mechanics, Vol. 37, Annual Reviews, Palo Alto, CA, 2005, pp. 211-238.
23. C. HE AND L. J. DURLOFSKY, Structured flow-based gridding and upscaling for modeling sub-surface flow, Adv. in Water Res., to appear.
24. 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.
25. 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.
26. M. HUI, Upscaling of Multiphase Flow Parameters for Modeling Near- Well and Miscible Displacements, Ph.D. thesis, Stanford University, Stanford, CA, 2005.
27. P. JENNY, S. H. LEE, AND H. A. TCHELEPI, Adaptive multiscale finite-volume method for multiphase flow and transport in porous media Multiscale Model. Simul., 3 (2004), pp. 50-64.
28. J. R. KYTE AND D. W. BERRY, New pseudo functions to control numerical dispersion, SPE Journal, 15 (1975), pp. 269-275.
29. S. MAO AND A. G. JOURNEL, Generation of a Reference Petrophysical/Seismic Data Set: The Stanford V Reservoir, Stanford Center for Reservoir Forecasting Report, Stanford University, Stanford, CA, 1999.
30. C. T. MILLER, G. CHRISTAKOS, P. T. IMHOFF, J. F. MCBRIDE, J. A. PEDIT, AND J. A. TRANGENSTEIN, Multiphase flow and transport modeling in heterogeneous porous media: Challenges and approaches, Adv. in Water Res., 21 (1998), pp. 77-120.
31. PH. RENARD AND G. DE MARSILY, Calculating effective permeability: A review, Adv. in Water Res., 20 (1997), pp. 253-278.
32. R. K. ROMEU AND B. NOETINGER, Calculation of internodal transmissivities in finite difference models of flow in heterogeneous porous media, Water Resources Research, 31 (1995), pp. 943-959.
33. SCHLUMBERGER, PSEUDO Reference Manual 2004A, Schlumberger, 2004.
34. K. SUZUKI AND T. A. HEWETT, Sequential upscaling method, Transp. Porous Media, 46 (2002), pp. 179-212.
35. S. THIBEAU, J. W. BARKER, AND PH. SOUILLARD, Dynamical upscaling techniques applied to compositional flows, in Proceedings of the SPE Symposium on Reservoir Simulation, San Antonio, TX, 1995, paper SPE 29128.
36. 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.
37. 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.
38. X. H. WEN AND J. J. GÓMEZ-HERNÁNDEZ, Upscaling hydraulic conductivities in heterogeneous media: An overview, J. Hydrology, 183 (1996), pp. ix-xxxii.
39. P. ZHANG, G. E. PICKUP, AND M. A. CHRISTIE, A new upscaling approach for highly heterogeneous reservoirs, in Proceedings of the SPE Symposium on Reservoir Simulation, Houston, TX, 2005, paper SPE 93339.
40. W. ZIJL AND A. TRYKOZKO, Numerical homogenization of two-phase flow in porous media, Comput. Geosci., 6 (2002), pp. 49-71.