Permeability fluctuations in heterogeneous networks with different dimesionality and topology

Journal of Geophysical Research: Solid Earth

Volumn 108, Issue 7, 2003, Pages

  Bernabé, Yves ^a   Bruderer Weng, Céline ^b   Maineult, Alexis ^a  

^a UNIVERSITÉ DE STRASBOURG   (France)

^b UNIV MONTPELLIER   (France)

Author keywords

Effective rock properties; Heterogeneous media; Porosity and permeability fluctuations

Indexed keywords

HETEROGENEOUS MEDIUM; PERMEABILITY; PIPE FLOW; POROSITY; POROUS MEDIUM; TOPOLOGY;

EID: 0142197667     PISSN: 21699313     EISSN: 21699356     Source Type: Journal    
DOI: None     Document Type: Article

References (49)

1. Ababou, R., D. McLaughlin, L. W. Gelhar, and A. F. B. Tompson, Numerical simulation of three-dimensional saturated flow in randomly heterogeneous porous media. Transp. Porous Media, 4, 549-565, 1989.
2. Ambegaokar, V. N., B. I. Halperin, and J. S. Langer, Hopping conductivity in disordered systems, Phys. Rev. B, 4, 2612-2620, 1971.
3. Bernabé, Y., The frequency dependence of harmonic fluid flow through networks of cracks and pores, Pure Appl. Geophys., 149, 489-506, 1997.
4. Bernabé, Y., and C. Bruderer, Effect of the variance of pore size distribution on the transport properties of heterogeneous networks, J. Geophys. Res., 103, 513-525, 1998.
5. Brace, W. F., Permeability of crystalline and argillaceous rocks, Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 17, 241-251, 1980.
6. Brown, G. O., H. T. Hsieh, and D. A. Lucero, Evaluation of laboratory dolomite core sample size using representative elementary volume concepts, Water Resour. Res., 36, 1199-1207, 2000.
7. Bruderer, C., and Y. Bernabé, Network modeling of dispersion: Transition from Taylor dispersion in homogeneous networks to mechanical dispersion in very heterogeneous ones, Water Resour. Res., 37, 897-908, 2001.
8. Cushman, J. H., On measurement, scale, and scaling, Water Resour. Res., 22, 129-134, 1986.
9. Dagan, G., Statistical theory of groundwater flow and transport: Pore to laboratory, laboratory to formation, and formation to regional scale, Water Resour. Res., 22, 120S-134S, 1986.
10. de Dreuzy, J.-R., P. Davy, and O. Bour, Hydraulic properties of two-dimensional random fracture networks following a power law length distribution: 1. Effective connectivity, Water Resour. Res., 37, 2065-2078, 2001a.
11. de Dreuzy, J.-R., P. Davy, and O. Bour, Hydraulic properties of two-dimensional random fracture networks following a power law length distribulion: 2. Permeability of networks based on lognormal distribution of apertures, Water Resour. Res., 37, 2079-2095, 2001b.
12. Di Federico, V., and S. P. Neuman, Scaling of random fields by means of truncated power variograms and associated spectra, Water Resour. Res., 33, 1075-1085, 1997.
13. Durlofsky, L. J., Numerical calculation of equivalent grid block permeability tensors for heterogeneous porous media, Water Resour. Res., 27, 699-708, 1991.
14. Durlofsky, L. J., Representation of grid block permeability in coarse scale models of randomly heterogeneous porous media, Water Resour. Res., 28, 1791-1800, 1992.
15. Evans, I. S., Salt crystallization and rock weathering: A review, Rev. Geomorph. Dyn., 4, 153-177, 1969.
16. Fredrich, J. T., and W. B. Lindquist, Statistical characterization of the three-dimensional microgeometry of porous media and correlation with macroscopic transport properties, Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 34, paper 085, 1997.
17. Fredrich, J. T., B. Menendez, and T.-F. Wong, Imaging the pore structure of geomaterials, Science, 268, 276-279, 1995.
18. Friedman, S. P., and N. A. Seaton, Critical path analysis of the relationship between permeability and electrical conductivity of three-dimensional pore networks, Water Resour. Res., 34, 1703-1710, 1998.
19. Garbesi, K., R. G. Sextro, A. L. Robinson, J. D. Wooley, J. A. Owens, and W. W. Nazaroff, Scale dependence of soil permeability to air: Measurement method and field investigation, Water Resour. Res., 32, 547-560, 1996.
20. Gelhar, L. W., Stochastic Subsurface Hydrology, 390 pp., Prentice-Hall, Old Tappan, N. J., 1993.
21. Gelhar, L. W., and C. L. Axness, Three-dimensional stochastic analysis of macrodispersion in aquifers, Water Resour. Res., 19, 161-180, 1983.
22. Goggin, D. J., M. A. Chandler, G. Kocurek, and L. W. Lake, Permeability transects of eolian sands and their use in generating random permeability fields, SPE Form. Eval., 7, 7-16, 1992.
23. Henriette, A., C. G. Jacquin, and P. M. Adler, The effective permeability of heterogeneous porous media, PCH PhysicoChem. Hydrodyn., 11, 63-80, 1989.
24. Hunt, A. G., Upscaling in subsurface transport using cluster statistics of percolation, Transp. Porous Media, 30, 177-198, 1998.
25. Hunt, A. G., Applications of percolation theory to porous media with distributed local conductances, Adv. Water Resour., 24, 279-307, 2001.
26. Hunt, A. G., Some comments on the scale dependence of the hydraulic conductivity in the presence of nested heterogeneity, Adv. Water Resour., 26, 71-77, 2003.
27. Jeannette, D., Originalité des mécanismes d'altération sur les vestiges archéologiques de Delos (Cyclades Grèce), C.R. Acad. Sci., Ser. II, 330, 683-688, 2000.
28. Lindquist, W. B., S.-M. Lee, D. A. Coker, K. W. Jones, and P. Spanne, Medial axis analysis of void structure in three-dimensional tomographic images of porous media, J. Geophys. Res., 101, 8297-8310, 1996.
29. Lindquist, W. B., A. Venkatarangan, J. Dunsmuir, and T.-F. Wong, Pore and throat size distributions measured from synchrotron X-ray tomographic images of Fontainebleau sandstones, J. Geophys. Res., 105, 21,509-21,527, 2000.
30. Mattax, C. C., and R. L. Dalton, Reservoir Simulation, SPE Monogr., vol. 13, 173 pp., Sec. Of Pet. Eng., Richardson, Tex., 1990.
31. Netto, A. S. T., Pore-size distribution in sandstones, AAPG Bull., 77, 1101-1104, 1993.
32. Newman, S. P., Generalized scaling of permeabilities: Validation and effect of support scale, Geophys. Res. Lett., 21, 349-352, 1994.
33. Painter, S., Evidence for non-Gaussian scaling behavior in heterogeneous sedimentary formations, Water Resour. Res., 32, 1183-1195, 1996.
34. Pollak, M. A., Percolation treatment of dc hopping conduction, J. Non Cryst. Solids, 11, 1-24, 1972.
35. Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd. ed., 994 pp., Cambridge Univ. Press, New York, 1992.
36. Purvance, D. T., and R. Andricevic, On the electrical-hydraulic conductivity correlation in aquifers, Water Resour. Res., 36, 2905-2913, 2000a.
37. Purvance, D. T., and R. Andricevic, Geoelectric characterization of the hydraulic conductivity field and its spatial structure at variable scales, Water Resour. Res., 36, 2915-2924, 2000b.
38. Renard, P., and G. de Marsily, Calculating equivalent permeability: A review, Adv. Water Resour., 20, 253-278, 1997.
39. Sahimi, M., Flow and Transport in Porous Media and Fractured Rock, 482 pp., John Wiley, Hoboken, N. J., 1995.
40. Schulze-Makuch, D., D. A. Carlson, D. S. Cherkauer, and P. Malik, Scale dependency of hydraulic conductivity in heterogeneous media, Ground Water, 37, 904-919, 1999.
41. Spanne, P., J. Thovert, C. Jacquin, W. B. Lindquist, K. Jones, and P. Adler, Synchrotron computed microtomography of porous media: Topology and transports, Phys. Rev. Lett., 73, 2001-2004, 1994.
42. Stauffer, D., and A. Aharony, Introduction to Percolation Theory, 2nd. ed., 180 pp., Taylor and Francis, Washington, D. C., 1992.
43. Tidwell, V. C., and J. L. Wilson, Laboratory method for investigating permeability upscaling, Water Resour. Res., 33, 1607-1616, 1997.
44. Tidwell, V. C., and J. L. Wilson, Permeability upscaling measured on a block of Berea sandstone: Results and interpretation, Math Geol., 31, 749-769, 1999a.
45. Tidwell, V. C., and J. L. Wilson, Upscaling experiments conducted on a block of volcanic tuff: Results for a bimodal permeability distribution, Water Resour. Res., 35, 3375-3387, 1999b.
46. Tidwell, V. C., and J. L. Wilson, Heterogeneity, permeability patterns, and permeability upscaling: Physical characterization of a block of Massilon sandstone exhibiting nested scales of heterogeneity, SPE Reservoir Eng. Eval. Eng., 3, 283-291, 2000.
47. Wong, T.-F., J. Fredrich, and G. D. Gwanmesia, Crack aperture statistics and pore space fractal geometry of Westerly granite and Rutland quartzite: Implications for elastic contact models of rock compressibility, J. Geophys. Res., 94, 10,267-10,278, 1989.
48. Zhang, D., R. Zhang, S. Chen, and W. E. Soll, Pore scale study of flow in porous media: Scale dependency, REV, and statistical REV, Geophys. Res. Lett., 27, 1195-1198, 2000.
49. Zhu, W., and T.-F. Wong, Network modeling of the evolution permeability and dilatancy in compact rock, J. Geophys. Res., 104, 2963-2971, 1999.