The future of stochastic and upscaling methods in hydrogeology

Hydrogeology Journal

Volumn 13, Issue 1, 2005, Pages 184-201

  Nœtinger, Benoît ^a   Artus, Vincent ^a   Zargar, Ghassem ^b  

^a IFP ENERGIES NOUVELLES   (France)

^b NATIONAL IRANIAN SOUTH OIL COMPANY   (Iran)

Author keywords

[No Author keywords available]

Indexed keywords

GROUNDWATER RESOURCE; HYDROGEOLOGY; STOCHASTICITY; UPSCALING;

EID: 17044429852     PISSN: 14312174     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10040-004-0427-0     Document Type: Review

References (106)

1. Ababou R (1994) Solutions of stochastic groundwater flow by infinite series, and convergence of the one-dimensional expansion. Stoch Hydrol Hydr 8:139-155
2. Adler PM (1992) Porous media: Geometry and transports. Butterworth/ Heinemann
3. Ahmadi A, Labastie A, Quintard M (1993) Large scale properties for flow through a stratified medium various approaches. SPERE pp 214-220
4. Ahmadi A, Quintard M (1996) Large scale properties for two phase flow in random porous media. J Hydrol 183:69-99
5. Alabert FG (1989) Constraining description of randomly heterogeneous reservoirs to pressure test data: A Monte-Carlo study, SPE 19600 SPE 64th Ann. Tech. Conf. and Exh. San Antonio, 207-221
6. Arbogast T, Bryant SL (2001) Numerical subgrid upscaling for waterflood simulations, SPE No. 66375, SPE Reservoir Simulation Symposium, Houston, 11-14 Febr 2001
7. Artus V, Nœtinger B, Ricard L (2004) Dynamics of the water oil front for two-phase, immiscible flow in heterogeneous porous media. 1 Stratified Media. Trans Por Med 56:283-303
8. Avellaneda M (1996) Homogenization and renormalization, the mathematics of multiple scale random media and turbulent diffusion. Lect Appl Math 31:251-268
9. Badea A, Bourgeat A (1995) Homogenization of two phase flow through randomly heterogeneous porous media. Proceedings of the Conference on "Mathematical Modelling of Flow through Porous Media", St Etienne, Bourgeat, A
10. Badea A, Bourgeat A (1996). Homogenization of two-phase flows in randomly heterogeneous porous media. Zeitschrift für Angewandte Mathematik und Mechanik. ZAMM 76:(4)81-84
11. Barker JW, Thibeau SA (1996) A critical review of the use of pseudo-relative permeabilities for upscaling SPE paper 35491, EUROPEC, Stavanger Norway
12. Blanc G, Guérillot D, Rahon D, Roggero F (1996) Building geostatistical models constrained by dynamic data-a posteriori constraint. spe 35478, European 3D Reservoir Modeling Conference, Stavanger, Norway, pp 19-33
13. Bourgeat A, Quintard M, Whitaker S (1988) Eléments de Comparaison entre la méthode d'homogéneisation et la Prise de Moyenne avec Fermeture. CR Acad Sci Paris 306(2):463-466
14. A Bourgeat 1996 Homogenization of two-phase flow through porous media. Chapter 5 U Hornung (eds) Homogenization and Porous Media. Interdisciplinary Applied Mathemathics Series, Springer Berlin Heidelberg New York
15. Cherblanc F (1999) Etude du Transport Miscible en Milieu Poreux Hétérogènes: Prise en Compte du Non Equilibre. [Study of miscible transport in heterogeneous porous media accounting of non equilibrium] Thèse de l'Université Bordeaux 1
16. Christakos G, Miller CT, Oliver DS (1993) Stochastic perturbation analysis of groundwater flow. spatially variable soils, semi infinite domains and large fluctuations. Stoch Hydrol Hydrauli 7(3):213-239
17. Christakos G, Hristopulos, Miller CT (1995) Stochastic diagrammatic analysis of groundwater flow in heterogeneous porous media. Water Resour Res 31(7):1687-1703
18. Coats KH, Smith BD (1964) Dead-end pore volume and dispersion in porous media. SPE J 4:73-84
19. L Cosentino 2001 Integrated Reservoir Studies, Editions Technip Paris
20. Cushman JH (1984) On unifying the concepts of scale, Instrumentation, and stochastics in the development of multiphase theory. Water Resour Res 20(11)1668-1676
21. Cushman JH, Ginn TR (1993) Non local dispersion in porous media with continuously evolving scale of heterogeneity. Trans Porous Med 13(1):123-138
22. Cushman JH, Bennethum LS, Hu BH (2002) A primer on upscaling tools for porous media. Adv Water Resour 25:1043-1067
23. Cvetkovic V, Dagan G (1996) Reactive transport and immiscible flow in geological media. II-Applications. Proc Royal Soc Lon 452:303-328
24. Dagan G, Cvetkovic V (1996) Reactive transport and immiscible flow in geological media. I-General Theory. Proc Royal Society of London 452:285-301
25. G Dagan 1989 Flow and transport in porous formations Springer Berlin Heidelberg New York
26. Daviau F (1986) Interprétation des essais de puits [Well test interpretation] Editions Technip, Paris
27. de Marsily G (1981) Hydrogeologie quantitative [Quantitative Hydrology] Masson
28. Desbarats AJ (1992) Spatial averaging of hydraulic conductivity in 3-dimensional heterogenous porous-media'. Math Geol 24:249-267
29. Deutsch CV, Journel AG (1992) Geostatistical software library and user's guide. Oxford University Press
30. de Witt A (1995) Correlation structure dependence of the effective permeability of heterogeneous porous media. Physics of Fluids 7(11):2553-2562
31. Duquerroix JP, Lemouzy P, Nœtinger B, Kruel Romeu R (1993) Influence of the permeability anisotropy ratio on the large scale properties of heterogeneous reservoirs. SPE 26648 68 th Annual Tech. Conf. and Exhb. of the SPE Houston 29-40
32. Durlovsky LJ (1991) Numerical calculation of equivalent grid block permeability tensors for heterogeneous porous media. Water Resour Res 27:699-708
33. Eschard R, Doligez BD, Rahon D, Ravenne C, Leloch G (1991) A new approach for reservoirs description and simulation using geostatistical methods, Advances in Reservoir Technology, Characterization Modeling and Management
34. Feitosa GS, Lifu Chu, Thompson LG, Reynolds AC (1993) Determination of permeability distribution from well test pressure data. SPE 26:407
35. Galli A, Guérillot D, Ravenne C, Heresim-Group (1990) Combining geology, geostatistics and multiphase fluid flow for 3D reservoir studies. In: Guérillot D, Guillon O (eds) ECMOR II - 2nd European Conference on the Mathematics of Oil Recovery, Arles, Sep. 11-14, Proceedings, pp 11-19
36. Gautier Y, Nœtinger B (1997) Preferential flow-paths detection for heterogeneous reservoirs using a new renormalization technique. Trans Por Med 26:1-23
37. Gautier Y, Nœtinger B (1998) Determination of geostatistical parameters using well-test data, SPE 73rd ATCE, 27-30, New-Orleans, USA
38. Gautier Y, Blunt MJ, Christie MA (1999) Nested gridding and streamline-based simulation for fast reservoir performance prediction. Comput Geosci 3:295-320
39. Gavalas GR, Shah PC (1976) Reservoir history matching by bayesian estimation. Soc Pet Eng J 16(6):337-350
40. Gelhar LW (1993) Stochastic subsurface hydrology. Prentice Hall
41. Germano M (1992) Turbulence: The Filtering Approach. J Fluid Mech 238:325-336
42. Glimm J, Lindquist B, Pereira F, Peirls R (1992) The multifractal hypothesis and anomalous diffusion. Math App Comput 11(2):189-207
43. Goldenfeld N (1992) Lectures on Phase Transitions and the Renormalization Group, Frontiers in physics, Addison Wesley
44. Gomez-Hernandez J (2005) A Stochastic Approach to the Simulation of Block Conductivity Fields Conditioned upon Data Measured at a Smaller Scale, PhD at Stanford University
45. Gorell S, Basset R (2001) Trends in reservoir simulation: Big models, scalable models? Will you please make up your mind? SPE 71 596, SPE ATCE New Orleans
46. Granjeon D, Joseph P, Doligez B (1998) Using a 3D stratigraphic model to optimise reservoir description. Hart's Petro Eng Int, Nov, pp 51-58
47. Guérillot DR, Rudkiewicz JL, Ravenne C, Renard G, Galli A (1989) An integrated model for computer aided reservoir, description: From outcrop study to fluid flow simulations. Improved oil recovery. 5th European symposium, Budapest, April 25-27, Proceedings, pp 651-660
48. Guérillot DR, Lemouzy P, Ravenne C (1991) How reservoir characterization can help to improve production forecasts. Improved oil recovery. 6th european symposium, Stavanger, May 21-23 1991, Proceedings, pp 3-12
49. Guérillot DR, Verdière S (1995) Different pressure grids for reservoir simulation in heterogeneous reservoirs. SPE 29148, 1995 SPE Symposium on Reservoir Simulation San Antonio
50. Haas A, Nœtinger B (1996) Stochastic reservoir modelling constrained by well test permeabilities, Fifth International Geostatistics Congress 22-27 Sept., Wollongong, Australia
51. Haas A, Nœtinger B (1995) 3D permeability averaging for stochastic reservoir modelling constrained by well tests, Reservoir description forum - The Heriot-Watt and Stanford University - 10-14 Sept. 1995, Puebles Hydro, UK
52. Heiba AA, Sahimi M, Scriven LH (1992) Percolation theory of two phase relative permeability SPE. Reservoir Evaluation 123:132
53. Hou TY, Wu XH (1997) A multiscale finite element method for elliptic problems in composite materials and porous media. J Comput Phys 134:169-189
54. Hou TY, Wu XH, Cai X (1999) Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients. Math Comput 227:913-943
55. Hu LY, le Ravalec M, Roggero F, Blanc G, Nœtinger B, Haas A (1999a) An overview of the gradual deformation approach for constraining Gaussian-related stochastic models to dynamic data. EAGE/SPE International Symposium on Petroleum Geostatistics, 20-23 April 1999, Toulouse
56. Hu LY, le Ravalec M, Blanc G, Corre B, Haas A, Nœtinger B, Roggero F (1999b) Reducing uncertainties in production forecasts by constraining geological modeling using dynamic data, 74th Annual Technical Conference and Exhibition, 3-6 Oct. 1999, Houston, USA, SPE 56703
57. Hunt AG (1998) Upscaling in subsurface transport using cluster statistics of percolation. Trans Porous Med 30:177-198
58. Hunt AG (2001) Application of percolation theory to porous media with distributed local conductances. Adv Water Res 24:279-307 10.1016/ S0309-1708(00)00058-0
59. Indelman P, Abramovich B (1994) A higher order approximation to effective conductivity in media of anisotropic random structure. Water Resour Res 30(6):1857-1864
60. Indelman P, Abramovich B (1995) Effective permittivity of log normal isotropic random media. J Phys A: Math Gen 28:693-700
61. Indelman P, (1996) Averaging of unsteady flows in heterogeneous media of stationary conductivity. J Fluid Mech 310:39-61
62. Jaekel U, Vereecken H (1997) Renormalization group analysis of macrodispersion in a directed random flow. Water Resour Res 33(10):2287-2299
63. VV Jikov SM Kozlov OA Oleinik 1994 Homogenization of Differential Operators Springer Berlin Heidelberg New York
64. King P (1987) The use of field theoretic methods for the study of flow in heterogeneous porous medium. J Phys A.: Math Gen 20:3935-3947
65. King P (1989) The use of renormalisation for calculating effective permeability. Trans Por Med 4:37-58
66. Koslov SM (1993) Central limit theorem for multiscaled permeability. Porous Media Meeting, Birkhauser, pp 19-33
67. Kretz VM, le Ravalec M, Roggero F (2002) An integrated reservoir characterization study matching production data and 4D seismic. SPE - Annual Technical Conference and Exhibition of the Society of Petroleum Engineers, San Antonio, 29 Sep.-2 Oct.
68. LD Landau EM Lifschitz 1960 Electrodynamics of continuous media Pergamon Oxford
69. Langlo P, Espedal (1994) Macrodispersion for two-phase, immiscible flow in porous media. Adv Water Resour 17:217-316
70. Lenormand R, Thiele M (1996) Determining flow equations from stochastic properties of a permeability field: The MHD model. SPE J pp 179-190
71. le Ravalec M, Hu LY, Nœtinger B (2001) Stochastic reservoir modeling constrained to dynamic data: Local calibration and inference of structural parameters, SPE 68883, SPE J
72. le Ravalec M, Hu LY, Nœtinger B (1999) Stochastic reservoir model constrained to dynamic data: Local calibration and inference of the structural parameters, 74th Annual Technical Conference and Exhibition, 3-6 Oct. 1999, Houston, USA, SPE 56556
73. le Ravalec M, Hu LY, Nœtinger B (2000) The FFT moving average (FFT-MA) method: An efficient tool for generating and conditioning Gaussian simulations. Math Geol 32(6)
74. Lesieur M, Métais O (1996) New Trends in Large Eddy Simulations of Turbulence. Ann Rev Fluid Mech 28:45-82
75. Loggia D, Rakotomalala N, Salin D, Yortsos Y (1996) Phase Diagram of Stable Miscible Displacements in Layered Porous Media. Europhys Lett 36(2):105-110
76. Mallet JL (1997) Discrete Modeling for Natural Objects. J Math Geol 29(2):199-219
77. Marle CM (1981) Multiphase flow in porous media, TECHNIP
78. Marle CM, Simandoux P, Pacsirszky J, Gaulier C (1967) Etude du déplacement de fluides miscibles en milieu poreux stratifí, '[Study of the displacement of miscible fluids in stratified porous media]. Revue de L'Institut Fran ̧ais du Pétrole 22:272-294
79. Matheron G (1967a) Eléments pour une théorie des milieux poreux [Elements of a theory of porous media] Masson, Paris
80. Matheron G (1967b) Composition des Perméabilités en Milieu Poreux Hétérogène: Méthode de Schwydler et Règles de Pondération, [Composing permeabilities in heterogeneous porous media. Swindler method and averaging rules]. Revue de l'Institut Fraņais du Pétrole 22(3):443-466
81. Neuman SP, Orr S (1993) Prediction of steady state flow in nonuniform geologic media by conditional moments: Exact non local formalism, effective conductivities and weak approximation. Water Resour Res 29(2):341-364
82. Nœtinger B, Artus V, Ricard L (2004) Dynamics of the water oil front for two-phase, immiscible flow in heterogeneous porous media. 2 Isotropic Media. Trans Por Med 56:305-328
83. Nœtinger B (2000) Computing the effective permeability of log-normal permeability fields using renormalization methods. C.R. Acad Des Sciences, Sciences de la Terre et des Planètes 331:353-357
84. Nœtinger B, Gautier Y (1998) Use of the Fourier-Laplace transformation and of diagrammatical methods to interpret pumping tests in heterogeneous reservoirs. Adv Water Resour 21:581-590 10.1016/ S0309-1708(97)00014-6
85. Nœtinger B (1994) The effective permeability of a heterogeneous porous medium. Transport in Porous Media 15:99-127
86. Nœtinger B, Haas A (1996) Permeability averaging for well-tests in 3D stochastic reservoir models, SPE Annual Technical Conference and Exhibition, 6-9 Oct. 1996, Denver, USA, SPE 36653
87. Nœtinger B, Jacquin C (1991) Experimental tests of a simple permeability composition formula, 66th Annual Technical Conference and Exhibition of the Society of Petroleum Engineers, 6-9 Oct. 1991, Dallas, USA, SPE 22841
88. Oliver DS (1989) The averaging process in permeability estimation from well test data, SPE 19845 SPE 64th Ann. Tech. Conf. and Exh.
89. Oliver DS, He N, Reynolds AC (1996) Conditioning permeability to well test data. 5th ECMOR conf. proc. Leoben, pp 259-268
90. Pianelo L, Guérillot D, Gallouët T (2000a) Inversion simultanée des données sismiques et des données de production. [Simulataneous inversion of seismic data and production data] Oil and Gas Science and Technology - Revue de l'IFP 55(3):235-248
91. Pianelo L, Guérillot D, Gallouöt T (2000b) Coupled inversion of permeability and acoustical impedance an outstanding data integration. ECMOR VII - 7th European Conference on the Mathematics of Oil Recovery, Baveno, Sept. 5-8 2000, Proceedings, Paper M-16, 8p
92. Quintard M, Whitaker S (1994) Transport in ordered an disordered porous media ii: Generalized volume averaging. Trans Porous Med 14:179-206
93. Ramé M, Killough JE (1991) A new approach to the simulation of flows in highly heterogeneous porous media SPE 21247. SPE Symposium on Reservoir Simulation, Anaheim
94. Renard Ph, de Marsily G (1997) Calculating equivalent permeability: A review. Adv Water Resour 20(5-6):253-378
95. Romeu RK, Nœtinger B (1995) Calculation of internodal transmissibilities in finite-difference models of flow in heteregeneous media. Water Resour Res 31(4):943-959
96. Romeu RK, Lara AQ, Nœtinger B, Renard G (1996) Well testing in heterogeneous media: A general method to calculate the permeability weighting function. Four Latin American and Caribbean Petroleum Engineering Conference, 23-26 April 1996, Port-of-Spain, Trinidad and Tobago
97. Saffman PG, Taylor G (1958) The penetration of a fluid into a porous medium or hele shaw cell Containing a more viscous fluid. Proc Royal Soc Lond A245:312-329
98. Schaaf TM, Mezghani M, Chavent G (2002) Direct conditioning of fine-scale facies models to dynamic data by combining the gradual deformation and numerical upscaling techniques. Proc. 8th European Conference on the Mathematics of Oil Recovery, Freiberg, Germany
99. D Stauffer 1985 Introduction to percolation theory Taylor and Francis London, Philadelphia
100. Strebelle S, Journel A (2000) Sequential simulation drawing dtructures from training images. In: Kleingeld, Krige (eds) Geostatistics 2000 Cape Town, vol. 1
101. Stepanayants YA, Teodorovitch EV (2003) Effective hydraulic conductivity of a randomly heterogeneous porous medium. Water Resour Res 39(3):1065
102. Tarantola A (1987) Inverse problem theory. Elsevier
103. Wood BD, Cherblanc F, Quintard M, Whitaker S (2003) Volume averaging for determining the effective dispersion tensor: Closure using periodic unit cells and comparison with ensemble averaging. Water Resour Res 39(8)
104. Yortsos YC (1992) Analytical studies for processes at vertical equilibrium. SPE paper 26022
105. Zhang D, Li L, Tchelepi HA (1999) A stochastic formulation for uncertainty assessment of two phase flow in heterogeneous reservoirs, SPE paper 51930, SPE Reservoir Simulation Symposion, Houston, TX
106. Zhang Q (1992) A multiple scale theory of the anomalous mixing length growth for tracer flow in heterogeneous porous media. J Stat Phys 505:485-501