Upscaling hydraulic conductivities in heterogeneous media: An overview

Journal of Hydrology

Volumn 183, Issue 1-2, 1996, Pages

  Wen, Xian Huan ^a   Gómez Hernández, J Jaime ^a  

^a UNIVERSITAT POLITÈCNICA DE VALÈNCIA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

FLUID FLOW; GROUNDWATER; HETEROGENEOUS MEDIUM; HYDRAULIC CONDUCTIVITY; UPSCALING;

AQUIFERS; COMPUTER SIMULATION; FLOW OF FLUIDS; GEOMETRY; INVERSE PROBLEMS; MASS TRANSFER; MONTE CARLO METHODS; TENSORS;

ELASTIC GRIDDING; UPSCALING;

HYDRAULIC CONDUCTIVITY;

EID: 0030455072     PISSN: 00221694     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0022-1694(96)80030-8     Document Type: Review

References (86)

1. Ababou, R. and Wood, E.F., 1990. Comment on 'Effective groundwater model parameter values: Influence of spatial variability of hydraulic conductivity, leakage, and recharge' by J.J. Gómez-Hernández and S.M. Gorelick, Water Resour. Res., 26(8): 1843-1846.
2. Aris, R., 1956. On the dispersion of a solute in a fluid flowing through a tube. Proc. R. Soc. London. Ser. A, 235: 67-77.
3. Bachu, S. and Cuthiell, D., 1990. Effects of core-scale heterogeneity on steady state and transient fluid flow in porous media: Numerical analysis. Water Resour. Res., 26(5): 683-874.
4. Begg, S.H. and King, P.R., 1985. Modelling the effects of shales on reservoir performance: Calculation of effective vertical permeability. Paper SPE 13529.
5. Begg, S.H., Chang, D.M. and Haldorsen, H.H., 1985. A simple statistical method for calculating the effective vertical permeability of a reservoir containing discontinuous shales. Paper SPE 14271.
6. Begg, S.H. and Carter, R.R., 1987. Assigning effective values to simulator grid-block parameter for heterogeneous reservoir. Paper SPE 16754.
7. Begg, S.H., Carter, R.R. and Dranfield, P., 1989. Assigning effective values to simulator gridblock parameters for heterogeneous reservoirs. SPE Reservoir Engineering, November: 455-463.
8. Bøe, Ø., 1994. Analysis of an upscaling method based on conservation of dissipation. Transport in Porous Media, 17(1): 77-86.
9. Bouwer, H., 1969. Planing and interpreting soil permeability measurements. J. of the Irrigation and Drainage Division of the A.S.C.E., IE(3): 391-402.
10. Brenner, H., 1980. Dispersion resulting from flow through spatially periodic porous media. Philos. Trans. R. Soc. London, Ser. A, 297 (1498): 81-133.
11. Cardwell, W.T. and Parsons, R.L., 1945. Averaging permeability of heterogeneous oil sands. Trans. Am. Inst. Min. Metall. Pet. Eng., 160: 34-42.
12. Clifton, M.P. and Neuman, S.P., 1982. Effect of kriging and inverse modelling on conditional simulation of the Avra Valley aquifer in Southern Arizona. Water Resour. Res., 18(4): 1215-1234.
13. Dagan, G., 1979. Models of groundwater flow in statistically homogeneous porous formations. Water Resour. Res., 15(1): 47-63.
14. Dagan, G., 1982a. Stochastic modeling of groundwater flow by unconditional and conditional probabilities, 1: Conditional simulation and the direct problem. Water Resour. Res., 18(4): 813-833.
15. Dagan, G., 1982b. Analysis of flow through heterogeneous random aquifers, 2: Unsteady flow in confined formations. Water Resour. Res., 18: 1571-1585.
16. Dagan, G., 1985. Stochastic modeling of groundwater flow by unconditional and conditional probabilities, 2: The inverse problem. Water Resour. Res., 21(1): 65-72.
17. Dagan, G., 1989. Flow and Transport in Porous Formations. Springer-Verlag, New York.
18. Desbarats, A.J., 1987. Numerical estimation of effective permeability in sand-shale formation. Water Resour. Res., 23(2): 273-286.
19. Desbarats, A.J., 1989. Support effect and the spatial averaging of transport properties. Math. Geology, 21(3): 383-389.
20. Desbarats, A.J., 1992a. Spatial averaging of transmissivity in heterogeneous fields with flow toward a well. Water Resour. Res., 28(3): 757-767.
21. Desbarats, A.J., 1992b. Spatial averaging of hydraulic conductivity in three-dimensional heterogeneous porous media. Math. Geology, 24(3): 249-267.
22. Desbarats, A.J., 1993. Geostatistical analysis of interwell transmissivity in heterogeneous aquifers. Water Resour. Res., 29(4): 1239-1246.
23. Desbarats, A.J. and Dimitrakopoulos, R., 1990. Geostatistical modeling of transmissivity for two-dimensional reservoir studies. SPE Formation Evaluation, Dic.: 437-443.
24. Deutsch, C., 1989. Calculating effective absolute permeability in sandstone/shale sequences. SPE Formation Evaluation, September: 343-348.
25. Deutsch, C. and Journel, A.G., 1992. GSLIB: Geostatistical Software Library and User's Guide. Oxford University Press, New York, 340pp.
26. Durlofsky, L.J. and Chung, E.Y., 1990. Effective permeability of heterogeneous reservoir regions. 2nd European Conference on the Mathematics of Oil Recovery, Paris, 1990, pp. 57-64.
27. Durlofsky, L.J., 1991. Numerical calculation of equivalent grid block permeability tensors for heterogeneous porous media. Water Resour. Res., 27(5): 699-708.
28. Durlofsky, L.J., 1992. Representation of grid block permeability in coarse scale models of randomly heterogeneous porous media. Water Resour. Res., 28(7): 1791-1800.
29. Durlofsky, L.J., Jones, R.C. and Milliken, W.J., 1994a. A new method for the scale up of displacement processes in heterogeneous reservoirs. 4th European Conference on the Mathematics of Oil Recovery, Roros, Norway, June, 1994.
30. Durlofsky, L.J., Milliken, W.J., Dehghani, K. and Jones, R.C., 1994b. Application of a new scale up methodology to the simulation of displacement process in heterogeneous reservoirs. SPE International Petroleum Conference & Exhibition of Mexico, Veracruz, October 1994.
31. Dykaar, B.B. and Kitanidis, P.K., 1992a. Determination of the effective hydraulic conductivity for heterogeneous porous media using a numerical spectral approach, 1: Method. Water Resour. Res., 28(4): 1155-1166.
32. Dykaar, B.B. and Kitanidis, P.K., 1992b. Determination of the effective hydraulic conductivity for heterogeneous porous media using a numerical spectral approach, 2: Method. Water Resour. Res., 28(4): 1167-1178.
33. Farmer, C.L., Heath, D.E. and Moody, R.O., 1991. A global optimization approach to grid generation. 11th SPE Symposium on Reservoir Simulation, Anaheim, CA, February 1991, pp. 341-350.
34. Payers, F.J. and Hewett, T.A., 1992. A review of current trends in petroleum reservoir description and assessment of the impacts on oil recovery. Adv. in Water Resources, 15(4): 341-365.
35. Garcia, M.H., Journel, A.G. and Aziz, K., 1990. An automatic grid generation and adjustment method for modeling reservoir heterogeneities. Report 3, Stanford Center for Reservoir Forecasting, Stanford, CA.
36. Garcia, M.H., Journel, A.G. and Aziz, K., 1992. Automatic grid generation for modeling reservoir heterogeneities. SPE Reservoir Engineering: 278-284.
37. Gelhar, L.W. and Axness, C.L., 1983. Three-dimensional stochastic analysis of macrodispersion in aquifers. Water Resour. Res., 19(1): 161-180.
38. Gómez-Hernández, J.J. and Gorelick, S.M., 1989. Effective groundwater model parameter values: Inference of spatial variability of hydraulic conductivity, leakance, and recharge. Water Resour. Res., 25(3): 405-419.
39. Gómez-Hernández, J.J., 1990. Simulation of block permeability conditioned upon data measured at a different scale. In: ModelCARE 90: Calibration and Reliability in Groundwater Modelling, IAHS Publ. no. 195, pp. 407-416.
40. Gómez-Hernández, J.J., 1991. A stochastic approach to the simulation of block conductivity fields conditioned upon data measured at a smaller scale. Ph.D. thesis, Stanford University, CA.
41. Gómez-Hernández, J.J. and Wen, X.H., 1994. Probabilistic assessment of travel times in groundwater modeling. J. Stochastic Hydrology and Hydraulics, 8(1): 19-55.
42. Grindheim, A.O., 1990. An evaluation of homogenization techniques for estimating effective absolute block permeability by use of a stochastic reservoir description simulator. Master thesis, Norwegian Institute of Technology (NTH).
43. Gutjahr, A.L., Gelhar, L.W., Bakr, A.A. and MacMillan, J.R., 1978. Stochastic analysis of spatial variability in subsurface flows, 2: Evaluation and application. Water Resour. Res., 14(5): 953-959.
44. Haldorsen, H.H. and Lake, L.W., 1984. A new approach of shales management in field scale simulation models. Soc. of Petrol. Eng. Jour., 24 (August): 447-457.
45. Haldorsen, H.H., 1986. Simulation parameters assignment and the problem of scale in reservoir engineering. In: Lake, L.W. and Carroll, H.B. (eds.), Reservoir Characterization. Academic Press, pp. 445-485.
46. Haldorsen, H.H. and Chang, D.M., 1986. Notes on stochastic shales; from outcrop to simulation model. In: Lake, L.W. and Carroll, H.B. (eds.), Reservoir Characterization. Academic Press, pp. 445-485.
47. Hoeksema, R.J. and Kitanidis, P.K., 1984. An application of the geostatistical approach to the inverse problem in two-dimensional groundwater modeling. Water Resour. Res., 20(7): 1003-1020.
48. Hoeksema, R.J. and Kitanidis, P.K., 1985. Comparison of Gaussian conditional mean and kriging estimation in the geostatistical solution of the inverse problem. Water Resour. Res., 21(6): 825-836.
49. Holden, L., Hoiberg, J. and Lia, O., 1989. Homogenization of absolute permeability. Norwegian Computer Centre (NCC) Report.
50. Holden, L. and Lia, O., 1992. A tensor estimator for the homogenization of absolute permeability. Transport in Porous Media, 8: 37-46.
51. Indelman, P. and Dagan, G., 1993a. Upscaling of permeability of anisotropic heterogeneous formations, 1: The general framework. Water Resour. Res., 29(4): 917-923.
52. Indelman, P. and Dagan, G., 1993b. Upscaling of permeability of anisotropic heterogeneous formations, 2: General structure and small perturbation analysis. Water Resour. Res., 29(4): 925-933.
53. Journel, A.G., Deutsch, C. and Desbarats, A.J., 1986. Power averaging for block effective permeability. SPE 15128.
54. Journel, A.G. and Huijbregts, C.J., 1978. Mining Geostatistics. Academic Press, London.
55. Kasap, E. and Lake, L.W., 1989. An analytical method to calculate the effective permeability tensor of a grid block and its application in an outcrop study. SPE 18434.
56. King, P.R., 1989. The use of renormalization for calculating effective permeability. Transport in Porous Media, 4(1): 37-58.
57. Kirkpatrick, S., 1973. Percolation and conduction. Rev. Mod. Phys., 45(4): 574-588.
58. Kitanidis, P.K., 1990. Effective hydraulic conductivity for gradually varying flow. Water Resour. Res., 26(6): 1197-1208.
59. Lake, L.W., 1988. The origins of anisotropy. J. of Petroleum Tech.: 395-396.
60. Malick, K.M., 1995. Boundary effects in the successive upscaling of absolute permeability. Master thesis, Stanford University, CA.
61. Mantoglou, A. and Gelhar, L.W., 1987. Effective hydraulic conductivity of transient unsaturated flow in stratified soils. Water Resour. Res., 23(1): 57-67.
62. Matheron, G., 1967. Éléments pour une théorie des milieux. Mason et Cie.
63. Mohanty, S. and Sharma, M.M., 1990. A recursive method for estimating single and multiphase permeabilities. SPE paper 20477 presented at the 65th Annual Technical Conference and Exhibition in New Orleans, LA, September 23-26, 1990.
64. Muggeridge, A.H., 1991. Generation of effective relative permeabilities from detailed simulation of flow in heterogeneous porous media. In: Lake, L.W., Carroll, H.B. and Wesson, T.C. (eds.), Reservoir Characterization II. Academic Press, San Diego, pp. 197-225.
65. Naff, R.L., 1991. Radial flow in heterogeneous porous media: An analysis of specific discharge. Water Resour. Res., 27(3): 307-316.
66. Neuman, S.P. and Orr, S., 1993. Prediction of steady state flow in nonuniform geologic media by conditional moments: Exact nonlocal formalism, effective conductivities, and weak approximation. Water Resour. Res., 29(2): 341-364.
67. Pickup, G.E., Jensen, J.L., Ringrose, P.S. and Sorbie, K.S., 1992. A method for calculating permeability tensors using perturbed boundary conditions. In: 3rd European Conf. on the Mathematics of Oil Recovery, Delft, The Netherlands, June 1992.
68. Pickup, G.E., Ringrose, P.S., Jensen, J.L. and Sorbie, K.S., 1994. Permeability tensors for sedimentary structures. Math. Geology, 26(2): 227-250.
69. Poley, A.D., 1988. Effective permeability and dispersion in locally heterogeneous aquifers. Water Resour. Res., 24(11): 1921-1926.
70. Robey, T.H., 1995. An adaptive grid technique for minimizing heterogeneity of cells or elements. Math. Geology, 27(6): 706-729.
71. Rubin, Y. and Gómez-Hernández, J.J., 1990. A stochastic approach to the problem of upscaling of conductivity in disordered media: Theory and unconditional numerical simulations. Water Resour. Res., 26(4): 691-701.
72. Russo, D., 1992. Upscaling of hydraulic conductivity in partially saturated heterogeneous porous formation. Water Resour. Res., 28(2): 397-409.
73. Sáez, A., Otero, C.J. and Rusinek, I., 1989. The effective homogeneous behavior of heterogeneous porous media. Transport in Porous Media, 4: 213-238.
74. Sánchez-Vila, X., 1995. On the geostatistical formulations of the groundwater flow and solute transport equations. Ph.D. thesis, Universitat Politética de Catalunya, Barcelona, Spain.
75. Sánchez-Vila, X., Girardi, J.P. and Carrera, J., 1995. A synthesis of approaches to upscaling of hydraulic conductivity. Water Resour. Res., 31(4): 867-882.
76. Shah, N. and Ottino, J.M., 1986. Effective transport properties of disordered, multiphase composites: Application of real-space renormalization group theory. Chem. Eng. Sci., 41(2): 283-296.
77. Tran, T.T., 1995. Stochastic simulation of permeability field and their scale-up for flow modeling. Ph.D. thesis, Stanford University, CA.
78. Tran, T.T. and Journel, A.G., 1995. Automatic generation of corner-point-geometry flow simulation grids from detailed geostatistical descriptions. Adv. of Water Resour., in press.
79. Warren, I.E. and Price, H.H., 1961. Flow in heterogeneous porous media. Society of Petroleum Engineering Journal, 1: 153-169.
80. Wen, X.H., 1996. Stochastic simulation of groundwater flow and mass transport in heterogeneous formations: Conditioning and problem of scales. Ph.D. thesis, Universidad Politécnica de Valencia, Spain, in preparation.
81. White, C.D., 1987. Representation of heterogeneity for numerical reservoir simulation. Ph.D. thesis, Stanford University, CA.
82. White, C.D. and Horne, R.N., 1987. Computing absolute transmissivity in the presence of fine-scale heterogeneity. Paper SPE 16011, pp. 209-221.
83. Williams, J.K., 1989. Simple renormalization schemes for calculating effective properties of heterogeneous reservoirs. In: 1st European Conf. on the Mathematics of Oil Recovery, Cambridge, UK, July 1989, pp. 281-298.
84. Wilson, K.G., 1979. Problems in physics with many scales length. Sci. Am. 241 (August): 158-179.
85. Yamada, T., 1995. A dissipation-based coarse grid system and its application to the scale-up of two phase problems. Ph.D. thesis, Stanford University, CA.
86. Yeh, T.C., Gelhar, L.W. and Gutjahr, A.L., 1985. Stochastic analysis of unsaturated flow in heterogeneous soils, 1: Statistically isotropic media. Water Resour. Res., 21(4): 447-456.