Effective conductivity of periodic media with cuboid inclusions

Advances in Water Resources

Volumn 27, Issue 10, 2004, Pages 1017-1032

  Harter, Thomas ^a   Knudby, Christen ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANISOTROPY; COMPUTER SIMULATION; ELECTRIC CONDUCTIVITY; ENTROPY; NUMERICAL METHODS; PARAMETER ESTIMATION; PROBLEM SOLVING; WATER RESOURCES;

GEOMETRIC PARAMETERS; ISOTROPIC INCLUSION; NUMERICAL SOLUTIONS; OCTAHEDRAL LATTICE;

FLOW OF FLUIDS;

HETEROGENEOUS MEDIUM; HYDRAULIC CONDUCTIVITY; NUMERICAL METHOD;

EID: 6444230273     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.advwatres.2004.07.004     Document Type: Article

References (63)

1. D. Baltean T. Levy S. Balint Diffusion-convection in porous medium with impervious inclusions at low flow rates Transport Porous Media 51 2003 19-39
2. Bear J. Dynamics of fluids in porous media. New York; 1972
3. Beran MJ. Statistical continuum physics. New York; 1968, 424pp
4. C. Bishop Neural networks for pattern recognition 1995 University Press Oxford
5. D.A.G. Bruggeman Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen Ann. Phys. (Leipzig) 24 1935 636-679
6. J. Byström Influence of the inclusions distribution on the effective properties of heterogeneous media Composites Part B 34 2003 587-592
7. S.F. Carle G.E. Fogg Transition probability-based indicator geostatistics Math. Geol. 28 4 1996 453-477
8. S.F. Carle G.E. Fogg Modeling spatial variability with one- and multi-dimensional continuous Markov chains Math. Geol. 29 7 1997 891-917
9. J.R. Carr Statistical self-affinity, fractal dimension, and geologic interpretation Eng. Geol. 48 1997 269-282
10. Cushman JH. An introduction to hierarchical porous media. In: Cushman JH, editor. Dynamics of fluids in hierarchical porous media. London; 1990. p. 1-6
11. G. Dagan Models of groundwater flow in statistically homogeneous porous formations Water Resour. Res. 15 1979 47-63
12. G. Dagan Analysis of flow through heterogneous random aquifers by the method of embedding matrix, 1. Steady flow Water Resour. Res. 17 1981 107-122
13. G. Dagan Statistical theory of groundwater flow and transport: pore to laboratory, laboratory to formation, and formation to regional scale Water Resour. Res. 22 9 1986 120S-134S
14. Dagan G. Flow and transport in porous formations. Berlin-New York; 1989. 465p
15. G. Dagan S.P. Neuman Subsurface flow and transport: a stochastic approach 1997 UNESCO, Cambridge University Press 241p
16. G. Dagan S.C. Lessoff Solute transport in heterogeneous formations of bimodal conductivity distribution, 1. Theory Water Resour. Res. 37 3 2001 465-472
17. A.J. Desbarats Numerical estimation of effective permeability in sand-shale formations Water Resour. Res. 23 2 1987 273-286
18. A.J. Desbarats Dispersion in sand-shale sequences Water Resour. Res. 26 1 1990 153-163
19. L.J. Durlofsky Numerical calculation of equivalent grid block permeability tensors for heterogeneous porous media Water Resour. Res. 27 5 1991 699-708
20. A.M. Dykhne Conductivity of two-dimensional two-phase system Sov. Phys. JETP 32 1971 63-65
21. L.G. Fel I.V. Kaganov Relation between effective conductivity and susceptibility of two-component rhombic checkerboard J. Phys. A: Math. Gen. 36 2003 5349-5358
22. K.D. Fisher D. Stroud Conductivity and magnetoresistance of a periodic composite by network discretization Phys. Rev. B 56 22 1997 14366-14373
23. R.S. Govindaraju editor. Stochastic methods in subsurface contaminant hydrology 2002 American Society of Civil Engineers
24. Harbaugh AW, Banta ER, Hill MC, McDonald MG. MODFLOW- 2000, The US Geological Survey Modular Ground-Water Model - User Guide to Modularization Concepts and The Ground-Water Flow Process. Open-File Report 00-92, United States Geological Survey, Boulder, CO; 2000. 121p
25. Z. Hashin S. Shtrikman A variational approach to the theory of the effective magnetic oermeability of multiohase materials J. Appl. Phys. 33 1962 3125-3131
26. L. Hui B. Ke-da Effective conductivity in a checkerboard geometry at high conductance ratio and high concentration Phys. Rev. B 46 14 1992 9209-9212
27. C.-T. Hsu P. Cheng K.W. Wong A lumped-parameter model for stagnant thermal conductivity of spatially periodic porous media J. Heat Transfer 117 1995 264-269
28. C.T. Hsu Heat conduction in porous media. In: K. Vafai editor. Handbook of porous media 2000 Dekker New York 171-201
29. A. Journel Ch.J. Huijbregts Mining geostatistics 1978 Academic Press 600p
30. B. Ke-da J. Axell G. Grimvall Electrical conduction in checkerboard geometries Phys. Rev. B 41 7 1990 4330-4333
31. Knudby C, Carrera J. On the relationship between geostatistical, flow, and transport connectivitiy measures. Adv Water Resour, in press
32. S.-Y. Lu Effective conductivities of rectangular arrays of aligned spheroids J. Appl. Phys. 85 1 1999 264-269
33. K.Z. Markov Elementary micromechanics of heterogeneous media. In: K.Z. Markov L. Preziosi editors. Heterogeneous media: micromechanics modeling methods and simulations 2000 Basel Switzerland 1-162
34. K.Z. Markov L. Preziosi editors. Heterogeneous media: micromechanics modeling methods and simulations 2000 Basel Switzerland 477p
35. D.H. McLain Drawing contours from arbitrary data points Comput. J. 17 1974 318-324
36. J.C. Maxwell Treatise on electricity and magnetism, vol. I 2nd ed. 1881 Clarendon Press Oxford [reprinted by Dover, New York, 1954]
37. T. Miloh Y. Benveniste A generalized self-consistent method for the effective conductivity of composites with ellipsoidal inclusions and cracked bodies J. Appl. Phys. 63 3 1988 689-696
38. G.W. Milton Bounds on the complex permittivity of a two-component composite material J. Appl. Phys. 52 8 1981 5286-5293
39. G.W. Milton The theory of composites 2002 Cambridge United Kingdom 719pp
40. F.J. Molz G.K. Boman A fractal-based stochastic interpolation scheme in subsurface hydrology Water Resour. Res. 29 1993 3769-3774
41. F.J. Molz G.K. Boman Further evidence of fractal structure in hydraulic conductivity distributions Geophys. Res. Lett. 22 18 1995 2545-2548
42. S. Nozad R.G. Carbonell S. Whitaker Heast conduction inmultiphase systems. I: Theory and experiments for two-phase systems Chem. Eng. Sci. 40 1985 843-855
43. Y.V. Obsonov Periodic heterogeneous structures: new explicit solutions and effective characteristics of refraction of an imposed field SIAM J. Appl. Math. 59 4 1999 1267-1287
44. J.A. Ochoa-Tapia P. Stroeve S. Whitaker Diffusive transport in two-phase media: Spatially periodic models and Maxwell's theory for isotropic and anisotropic systems Chem. Eng. Sci. 49 1994 709-726
45. A.D. Poley Effective permeability and dispersion in locally heterogeneous aquifers Water Resour. Res. 24 11 1988 1921-1926
46. Ph. Renard G. de Marsily Calculating equivalent permeability: a review Adv. Water Res. 20 5-6 1997 253-278
47. P. Renault The effect of spatially correlated blocking-up of some bonds or nodes of a network on the percolation threshold Transport Porous Media 6 1991 451-468
48. J.A. Roberson C.T. Crowe Engineering fluid mechanics 1997 John Wiley and Sons 698p
49. D.E. Rumelhart J. McClelland editors. Parallel distributed processing vol. 1 1986 MIT Press Cambridge, MA
50. Sahimi M. Applications of percolation theory. London, Great Britain; 1994. 258p
51. M. Sahimi Fractal-wavelet neural-network approach to characterization and upscaling of fractured reservoirs Comput. Geosci. 26 2000 877-905
52. Statsoft, Inc. STATISTICA 6.0, Tulsa, OK; 2002
53. Torquato S. Random heterogeneous media: microstructure and macroscopic properties. Berlin; 2001. 712pp
54. H.-J. Vogel K. Roth Moving through scales of flow and transport in soil J. Hydrol. 272 2003 95-106
55. A.S. Weigend D.E. Rumelhart B.A. Huberman Generalization by weight-elimination with application to forecasting. In: R.P. Lippmann J.E. Moody D.S. Touretzky editors. Advances in neural information processing systems vol. 3 1991 Morgan Kaufmann San Mateo, CA 875-882
56. G.S. Weissmann S.F. Carle G.E. Fogg Three-dimensional hydrofacies modeling based on soil surveys and transition probability geostatistics Water Resour. Res. 35 6 1999 1761-1770
57. Wiener O. Abhandlungen der Mathematischen-Physischen Klasse der Königlichen Sächsischen Gesellschaft der Wissenschaften 1912 32 509
58. S.W. Wheatcraft S.W. Tyler An explanation of scale-dependent dispersivity in heterogeneous aquifers using concepts of fractal geometry Water Resour. Res. 24 4 1988 566-578
59. S. Whitaker The method of volume averaging 1999 Dordrecht The Netherlands 217p
60. J. Wu B.X. Hu D. Zhang C. Shirly A three-dimensional numerical method of moments for groundwater flow and solute transport in a nonstationary conductivity field Adv. Water Resour. 26 2003 1149-1169
61. K. Yao M.T. Habibian C.R. O'Melia Water and wastewater filtration: concepts and application Environ. Sci. Technol. 5 11 1971 1105-1112
62. I.-W. Yeo R.W. Zimmerman Accuracy of the renormalization method for computing effective conductivities of heterogenous media Transport Porous Media 45 2001 129-138
63. P. Zehner E.U. Schlunder Thermal conductivity of granular materials at moderate temperatures Chem. Ing. Technol. 42 1970 933-941