Uncertainty quantification for subsurface flow problems using coarse-scale models

Lecture Notes in Computational Science and Engineering

Volumn 83, Issue , 2012, Pages 163-202

  Durlofsky, Louis J ^a   Chen, Yuguang ^b  

^a STANFORD UNIVERSITY   (United States)

^b CHEVRON ENERGY TECHNOLOGY COMPANY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DISTRIBUTION FUNCTIONS; GEOLOGY; NUMERICAL ANALYSIS; UNCERTAINTY ANALYSIS;

COARSE-SCALE PERMEABILITY; COMPUTATIONAL COSTS; CUMULATIVE DISTRIBUTION FUNCTION; GEOLOGICAL FORMATION; NUMERICAL HOMOGENIZATION; RELATIVE PERMEABILITY CURVES; STATISTICAL PREDICTION; UNCERTAINTY QUANTIFICATIONS;

NUMERICAL METHODS;

EID: 84969695818     PISSN: 14397358     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-642-22061-6_6     Document Type: Conference Paper

References (75)

1. Aarnes JE (2004) On the use of a mixed multiscale finite element method for greater flexibility and increased speed or improved accuracy in reservoir simulation. Multiscale Modeling and Simulation 2:421-439
2. Aarnes JE, Efendiev Y (2007) Mixed multiscale finite element methods for stochastic porous media flows. SIAM Journal on Scientific Computing 30(5):2319-2339
3. Aarnes JE, Krogstad S, Lie KA (2006) A hierarchical multiscale method for two-phase flow based upon mixed finite elements and nonuniform coarse grids. Multiscale Modeling and Simulation 5(2):337-363
4. Aavatsmark I (2002) An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences 6:405-432
5. Arbogast T (2002) Implementation of a locally conservative numerical subgrid upscaling scheme for two-phase Darcy flow. Computational Geosciences 6:453-481
6. Aziz K, Settari A (1986) Petroleum Reservoir Simulation. Elsevier, New York
7. Barker JW, Thibeau S (1997) A critical review of the use of pseudorelative permeabilities for upscaling. SPE Reservoir Engineering 12:138-143
8. Bourgeat A (1984) Homogenized behavior of two-phase flows in naturally fractured reservoirs with uniform fractures distribution. ComputerMethods in AppliedMechanics and Engineering 47:205-216
9. Chen T, Gerritsen MG, Durlofsky LJ, Lambers JV (2009) Adaptive local-global VCMP methods for coarse-scale reservoir modeling. Paper SPE 118994 presented at the SPE Reservoir Simulation Symposium, The Woodlands, Texas, February 2-4
10. Chen T, Gerritsen MG, Lambers JV, Durlofsky LJ (2010) Global variable compact multipoint methods for accurate upscaling with full-tensor effects. Computational Geosciences 14:65-81
11. Chen Y, Durlofsky LJ (2006) Adaptive local-global upscaling for general flow scenarios in heterogeneous formations. Transport in Porous Media 62:157-185
12. Chen Y, Durlofsky LJ (2006) Efficient incorporation of global effects in upscaled models of two-phase flow and transport in heterogeneous formations. Multiscale Modeling and Simulation 5:445-475
13. Chen Y, Durlofsky LJ (2008) Ensemble-level upscaling for efficient estimation of fine-scale production statistics. SPE Journal 13:400-411
14. Chen Y, Li Y (2009) Local-global two-phase upscaling of flow and transport in heterogeneous formations. Multiscale Modeling and Simulation 8:125-153
15. Chen Y, Li Y (2010) Incorporation of global effects in two-phase upscaling for modeling flow and transport with full-tensor anisotropy. In: Proceedings of the 12th European Conference on the Mathematics of Oil Recovery, Oxford, UK
16. Chen Y, Wu XH (2008) Upscaled modeling of well singularity for simulating flow in heterogeneous formations. Computational Geosciences 12:29-45
17. Chen Y, Durlofsky LJ, Gerritsen M, Wen XH (2003) A coupled local-global upscaling approach for simulating flow in highly heterogeneous formations. Advances in Water Resources 26:1041-1060
18. Chen Y, Durlofsky LJ, Wen XH (2004) Robust coarse scale modeling of flow and transport in heterogeneous reservoirs. In: Proceedings of the 9th European Conference on the Mathematics of Oil Recovery, Cannes, France
19. Chen Y, Mallison BT, Durlofsky LJ (2008) Nonlinear two-point flux approximation for modeling full-tensor effects in subsurface flow simulations. Computational Geosciences 12:317-335
20. Chen Y, Park K, Durlofsky LJ (2011) Statistical assignment of upscaled flow functions for an ensemble of geological models. Computational Geosciences 15:35-51
21. Chen Z, Hou TY (2003) A mixed finite element method for elliptic problems with rapidly oscillating coefficients. Mathematics of Computation 72:541-576
22. Chen Z, Yue X (2003) Numerical homogenization of well singularities in the flow transport through heterogeneous porous media. Multiscale Modeling and Simulation 1:260-303
23. Christie MA (2001) Flow in porous media-scale up of multiphase flow. Current Opinion in Colloid & Interface Science 6:236-241
24. Christie MA, Blunt MJ (2001) Tenth SPE comparative solution project: a comparison of upscaling techniques. SPE Reservoir Evaluation & Engineering 4:308-317
25. Darman NH, Pickup GE, Sorbie KS (2002) A comparison of two-phase dynamic upscaling methods based on fluid potentials. Computational Geosciences 6:5-27
26. Deutsch CV, Journel AG (1998) GSLIB: Geostatistical Software Library and User’s Guide, 2nd edition. Oxford University Press, New York
27. Ding Y (1995) Scaling-up in the vicinity of wells in heterogeneous field. Paper SPE 29137 presented at the SPE Symposium on Reservoir Simulation, San Antonio, Texas, February 12-15
28. Durlofsky LJ (1991) Numerical calculation of equivalent grid block permeability tensors for heterogeneous porous media. Water Resources Research 27:699-708
29. Durlofsky LJ, Milliken WJ, Bernath A (2000) Scaleup in the near-well region. SPE Journal 5:110-117
30. Durlofsky LJ, Efendiev YR, Ginting V (2007) An adaptive local-global multiscale finite volume element method for two-phase flow simulations. Advances in Water Resources 30: 576-588
31. Efendiev Y, Hou TY (2009) Multiscale Finite Element Methods: Theory and Applications. Springer, New York
32. Efendiev Y, Ginting V, Hou T, Ewing R (2006) Accurate multiscale finite element methods for two-phase flow simulations. Journal of Computational Physics 220(1):155-174
33. Efendiev YR, Durlofsky LJ (2003) A generalized convection-diffusion model for subgrid transport in porous media. Multiscale Modeling and Simulation 1:504-526
34. Efendiev YR, Durlofsky LJ, Lee SH (2000) Modeling of subgrid effects in coarse scale simulations of transport in heterogeneous porous media. Water Resources Research 36: 2031-2041
35. Farmer CL (2002) Upscaling: a review. International Journal for Numerical Methods in Fluids 40:63-78
36. Gerritsen M, Lambers J (2008) Integration of local-global upscaling and grid adaptivity for simulation of subsurface flow in heterogeneous formations. Computational Geosciences 12:193-218
37. Gerritsen MG, Durlofsky LJ (2005) Modeling fluid flow in oil reservoirs. Annual Review of Fluid Mechanics 37:211-238
38. Hajibeygi H, Jenny P (2009) Multiscale finite-volume method for parabolic problems arising from compressible multiphase flow in porous media. Journal of Computational Physics 228(14):5129-5147
39. Hesse MA, Mallison BT, Tchelepi HA (2008) Compact multiscale finite volume method for heterogeneous anisotropic elliptic equations. Multiscale Modeling and Simulation 7(2): 934-962
40. Hewett TA, Yamada T (1997) Theory for the semi-analytical calculation of oil recovery and effective relative permeabilities using streamtubes. Advances in Water Resources 20:279-292
41. Holden L, Nielsen BF (2000) Global upscaling of permeability in heterogeneous reservoirs: the output least squares (OLS) method. Transport in Porous Media 40:115-143
42. Hou TY, Wu XH (1997) A multiscale finite element method for elliptic problems in composite materials and porous media. Journal of Computational Physics 134:169-189
43. Hou TY, Westhead A, Yang D (2006) A framework for modeling subgrid effects for two-phase flows in porous media. Multiscale Modeling and Simulation 5(4):1087-1127
44. Hui M, Durlofsky LJ (2005) Accurate coarse modeling of well-driven, high-mobility-ratio displacements in heterogeneous reservoirs. Journal of Petroleum Science and Engineering 49:37-56
45. Jenny P, Lunati I (2009) Modeling complex wells with the multi-scale finite-volume method. Journal of Computational Physics 228(3):687-702
46. Jenny P, Lee SH, Tchelepi HA (2003) Multi-scale finite-volume method for elliptic problems in subsurface flow simulation. Journal of Computational Physics 187:47-67
47. Jiang L, Efendiev Y, Mishev I (2010) Mixed multiscale finite element methods using approximate global information based on partial upscaling. Computational Geosciences 14(2):319-341
48. Juanes R, Dub FX (2008) A locally conservative variational multiscale method for the simulation of porous media flow with multiscale source terms. Computational Geosciences 12(3):273-295
49. Kolyukhin D, Espedal M (2010) Modified adaptive local-global upscaling method for discontinuous permeability distribution. Computational Geosciences 14(4):675-689
50. Krogstad S, Durlofsky LJ (2009) Multiscale mixed-finite-element modeling of coupled wellbore/near-well flow. SPE Journal 14(1):78-87
51. Kyte JR, Berry DW(1975) New pseudo functions to control numerical dispersion. SPE Journal 15:269-275
52. Lambers J, Gerritsen M, Mallison B (2008) Accurate local upscaling with compact multipoint transmissibility calculations. Computational Geosciences 12:399-416
53. Lee SH, Zhou H, Tchelepi HA (2009) Adaptive multiscale finite-volume method for nonlinear multiphase transport in heterogeneous formations. Journal of Computational Physics 228(24):9036-9058
54. Muggeridge AH, Cuypers M, Bacquet C, Barker JW (2002) Scale-up of well performance for reservoir flow simulation. Petroleum Geoscience 8:133-139
55. Nakashima T, Durlofsky LJ (2010) Accurate representation of near-well effects in coarse-scale models of primary oil production. Transport in Porous Media 83:741-770
56. Nielsen BF, Tveito A (1998) An upscaling method for one-phase flow in heterogeneous reservoirs. A weighted output least squares (WOLS) approach. Computational Geosciences 2:93-123
57. Niessner J, Helmig R (2007) Multi-scale modeling of three-phase-three-component processes in heterogeneous porous media. Advances in Water Resources 30(11):2309-2325
58. Oren P, Bakke S (2003) Reconstruction of Berea sandstone and pore-scale modelling of wettability effects. Journal of Petroleum Science and Engineering 39(3-4):177-199
59. Peaceman DW (1983) Interpretation of well-block pressures in numerical reservoir simulation with nonsquare grid blocks and anisotropic permeability. SPE Journal 23:531-543
60. Pickup GE, Ringrose PS, Jensen JL, Sorbie KS (1994) Permeability tensors for sedimentary structures. Mathematical Geology 26:227-250
61. Potsepaev R, Farmer CL, Fitzpatrick AJ (2009) Multipoint flux approximations via upscaling. Paper SPE 118994 presented at the SPE Reservoir Simulation Symposium, The Woodlands, Texas, February 2-4
62. Renard P, de Marsily G (1997) Calculating effective permeability: a review. Advances inWater Resources 20:253-278
63. Romeu R, Noetinger B (1995) Calculation of internodal transmissivities in finite difference models of flow in heterogeneous porous media. Water Resources Research 31:943-959
64. Stone HL (1991) Rigorous black oil pseudo functions. Paper SPE 21207 presented at the SPE Symposium on Reservoir Simulation, Anaheim, California, February 17-20
65. Suzuki K, Hewett TA (2002) Sequential upscaling method. Transport in Porous Media 46: 179-212
66. Wallstrom TC, Hou S, Christie MA, Durlofsky LJ, Sharp DH, Zou Q (2002) Application of effective flux boundary conditions to two-phase upscaling in porous media. Transport in Porous Media 46:155-178
67. Wen XH, Gómez-Hernández JJ (1996) Upscaling hydraulic conductivities in heterogeneous media: an overview. Journal of Hydrology 183:ix-xxxii
68. Wen XH, Durlofsky LJ, Edwards MG (2003) Use of border regions for improved permeability upscaling. Mathematical Geology 35:521-547
69. White CD, Horne RN (1987) Computing absolute transmissibility in the presence of fine-scale heterogeneity. Paper SPE 16011 presented at the SPE Symposium on Reservoir Simulation, San Antonio, Texas, February 1-4
70. Wolfsteiner C, Lee SH, Tchelepi HA (2006) Well modeling in the multiscale finite volume method for subsurface flow simulation. Multiscale Modeling and Simulation 5:900-917
71. Wu XH, Efendiev YR, Hou TY (2002) Analysis of upscaling absolute permeability. Discrete and Continuous Dynamical Systems, Series B 2:185-204
72. Wu XH, Parashkevov R, Stone M, Lyons S (2008) Global scale-up on reservoir models with piecewise constant permeability field. Journal of Algorithms & Computational Technology 2:223-247
73. Yue X, E W (2007) The local microscale problem in the multiscale modeling of strongly heterogeneous media: effects of boundary conditions and cell size. Journal of Computational Physics 222(2):556-572
74. Zhang P, Pickup GE, Christie MA (2008) A new practical method for upscaling in highly heterogeneous reservoir models. SPE Journal 13:68-76
75. Zijl W, Trykozko A (2001) Numerical homogenization of the absolute permeability using the conformal-nodal and mixed-hybrid finite element method. Transport in Porous Media 44: 33-62