Using two-point correlation functions to characterize microgeometry and estimate permeabilities of sandstones and porous glass

Journal of Geophysical Research: Solid Earth

Volumn 101, Issue 9, 1996, Pages 20359-20375

  Blair, Stephen C ^a   Berge, Patricia A ^a   Berryman, James G ^a  

^a LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

IMAGE ANALYSIS; IMAGE PROCESSING; MICROSTRUCTURE; PERMEABILITY; PORE GEOMETRY; POROSITY; SANDSTONE; SCANNING ELECTRON MICROSCOPY;

EID: 0030439703     PISSN: 21699313     EISSN: 21699356     Source Type: Journal    
DOI: 10.1029/96jb00879     Document Type: Article

References (50)

1. Adler, P. M., Porous Media: Geometry and Transports, 544 pp., Butterworth-Heinemann, Newton, Mass., 1992.
2. Agrawal, D. L., N. G. W. Cook, and L. R. Myer, The effect of percolating structures on petrophysical properties of Berea sandstone, in Rock Mechanics as a Multidisciplinary Science, Proceedings of the 32nd U.S. Symposium on Rock Mechanics, edited by J.-C. Roegiers, pp. 345-354, A. A. Balkema, Rotterdam, 1991.
3. Archie, G. E., The electrical resistivity log as an aid in determining some reservoir characteristics, Trans. Am. Inst. Min. Metall. Pet. Eng., 146, 54-62, 1942.
4. Beran, M. J., Statistical Continuum Theories, John Wiley, New York, 1968.
5. Berge, P. A., B. P. Bonner, and J. G. Berryman, Ultrasonic velocity-porosity relationships for sandstone analogs made from fused glass beads, Geophysics, 60, 108-119, 1995.
6. Bernabé, Y., The transport properties of networks of cracks and pores, J. Geophys. Res., 100, 4231-4241, 1995.
7. Berryman, J. G., Measurement of spatial correlation functions using image processing techniques, J. Appl. Phys., 57, 2374-2384, 1985.
8. Berryman, J. G., Relationship between specific surface area and spatial correlation functions for anisotropic porous media, J. Math. Phys., 28, 244-245, 1987.
9. Berryman, J. G., and S. C. Blair, Use of digital image analysis to estimate fluid permeability of porous materials: Application of two-point correlation functions, J. Appl. Phys., 60, 1930-1938, 1986.
10. Berryman, J. G., and S. C. Blair, Kozeny-Carman relations and image processing methods for estimating Darcy's constant, J. Appl. Phys., 62, 2221-2228, 1987.
11. Berryman, J. G., and G. W. Milton, Normalization constraint for variational bounds on fluid permeability, J. Chem. Phys., 83, 754-760, 1985.
12. Blair, S. C., and J. G. Berryman, Estimates of permeability and relative permeability for sandstone using image analysis of cross-sections, in Rock Mechanics as a Multidisciplinary Science, Proceedings of the 32nd U.S. Symposium on Rock Mechanics, edited by J.-C. Roegiers, pp. 365-374, A. A. Balkema, Rotterdam, 1991.
13. Blair, S. C., W. J. Deutsch, and P. J. Mitchell, Permeability, geochemical, and water quality tests in support of an aquifer thermal energy storage site in Minnesota, Rep. PNL-5438, 78 pp., Pac. Northwest Lab., Richland, Wash., 1985.
14. Blair, S. C., P. A. Berge, and J. G. Berryman, Estimates of permeability of porous materials using image analysis of cross sections, in Proceedings of Engineering Foundation Conference on Digital Image Processing: Techniques and Applications in Civil Engineering, Kona, Hawaii, edited by J. D. Frost and J. R. Wright, pp. 109-116, Am. Soc. of Civ. Eng., New York, 1993a.
15. Blair, S. C., P. A. Berge, and J. G. Berryman, Two-point correlation functions to characterize microgeometry and estimate permeability of synthetic and natural sandstones. Rep. UCRL-LR-114182, Lawrence Livermore Natl. Lab., Livermore, Calif., 1993b.
16. Bourbié, T., O. Coussy, and B. Zinszner, Acoustics of Porous Media, 323 pp., Gulf Publ. Co., Houston, Tex., 1987.
17. Brace, W. F., Permeability from resistivity and pore shape, J. Geophys. Res., 82, 3343-3349, 1977.
18. Burns, D. R., C. H. Cheng, and R. H. Wilkens, Sandstone pore aspect ratio spectra from direct observations and velocity inversion, Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 27, 315-323, 1990.
19. Carman, P. C., Flow of Gases Through Porous Media, 182 pp., Academic, San Diego, Calif., 1956.
20. Caruso, L., G. Simmons, and R. Wilkens, The physical properties of a set of sandstones, I, The samples, Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 22, 381-392, 1985.
21. Corson, P., Correlation functions for predicting properties of heterogeneous materials, I, Experimental measurement of spatial correlation functions in multiphase solids, J. Appl. Phys., 45, 3159-3164, 1974a.
22. Corson, P., Correlation functions for predicting properties of heterogeneous materials, II, Empirical construction of spatial correlation functions for two-phase solids, J. Appl. Phys., 45, 3165-3170, 1974b.
23. Coyner, K. B., Effects of stress, pore pressure, and pore fluids on bulk strain, velocity, and permeability in rocks, Ph.D. thesis, Mass. Inst. of Technol., Cambridge, 1984.
24. Daily, W. D., and W. Lin, Laboratory-determined transport properties of Berea sandstone, Geophysics, 50, 775-784, 1985.
25. Darcy, H., Les Fontaines Publiques de la Ville de Dijon, 590 pp., Victor Dalmint, Paris, 1856.
26. Debye, P., H. R. Anderson Jr., and H. Brumberger, Scattering by an inhomogeneous solid, II, The correlation function and its application, J. Appl. Phys., 28, 679-683, 1957.
27. Doyen, P. M., Permeability, conductivity, and pore geometry of sandstone, J. Geophys. Res., 93, 7729-7740, 1988.
28. Dullien, F. A. L., Porous Media - Fluid Transport and Pore Structure, 396 pp., Academic, San Diego, Calif., 1979.
29. Ehrlich, R., S. K. Kennedy, S. J. Crabtree, and R. L. Cannon, Petrographic image analysis, I, Analysis of reservoir pore complexes, J. Sediment. Petrol., 54, 1365-1378, 1984.
30. Fredrich, J. T., B. Menendez, and T. F. Wong, Imaging the pore structure of geomaterials, Science, 268, 276-279, 1995.
31. Johnson, D. L., T. J. Plona, C. Scala, F. Pasierb, and H. Kojima, Tortuosity and acoustic slow waves, Phys. Rev. Lett., 49, 1840-1844, 1982.
32. Johnson, D. L., J. Koplik, and L. M. Schwartz, New pore-size parameter characterizing transport in porous media, Phys. Rev. Lett., 20, 2564-2567, 1986.
33. Katz, A. J., and A. H. Thompson, Quantitative prediction of permeability in porous rock, Phys. Rev. B, 34, 8179-8181, 1986.
34. Koplik, J., C. Lin, and M. Vermette, Conductivity and permeability from microgeometry, J. Appl. Phys., 56, 3127-3131, 1984.
35. Kostek, S., L. M. Schwartz, and D. L. Johnson, Fluid permeability in porous media: Comparison of electrical estimates with hydrodynamical calculations, Phys. Rev. B, 45, 186-195, 1992.
36. Kuo, C. Y., and J. D. Frost, Quantifying the fabric of granular materials - An image analysis approach, NSF Rep. GIT CEE/GEO-95-1, Natl. Sci. Found., Arlington, Va., 1995.
37. Lindquist, W. B., S. M. Lee, D. Coker, K. 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.
38. Paterson, M. S., The equivalent channel model for permeability and resistivity in fluid-saturated rock - A reappraisal, Mech. Mater., 2, 345-352, 1983.
39. Peña, C., S. C. Blair, and P. A. Berge, Image analysis of tuff from the Yucca Mountain Project, Eos Trans. AGU, 76(46), Fall Meet. Suppl., 197, 1995.
40. Prager, S., Viscous flow through porous media, Phys. Fluids., 4, 1477-1482, 1961.
41. Rubinstein, J., and S. Torquato, Flow in random porous media: Mathematical formulation, variational principles, and rigorous bounds, J. Fluid Meek., 208, 25-46, 1988.
42. Sahimi, M., Flow phenomena in rocks: From continuum models to fractals, percolation, cellular automata, and simulated annealing, Rev. Mod. Phys., 65, 1393-1534, 1993.
43. Schlueter, E. M., N. G. W. Cook, R. W. Zimmerman, and P. A. Witherspoon, Predicting permeability and electrical conductivity of sedimentary rocks from microgeometry, in Rock Mechanics as a Multidisciplinary Science, Proceedings of the 32nd U.S. Symposium on Rock Mechanics, edited by J.-C. Roegiers, pp. 355-364, A. A. Balkema, Rotterdam, 1991.
44. Schwartz, L. M., N. Martys, D. P. Bentz, E. J. Garboczi, and S. Torquato, Cross-property relations and permeability estimation in model porous media, Phys. Rev. E., 48, 4584-4591, 1993.
45. Sen, P. N., C. Scala, and M. H. Cohen, A self-similar model for sedimentary rocks with application to the dielectric constant of fused glass beads, Geophysics, 46, 781-795, 1981.
46. Thompson, A. H., A. J. Katz, and C. E. Krohn, The microgeometry and transport properties of sedimentary rocks, Adv. Phys., 36, 625-694, 1987.
47. Walsh, J. B., and W. F. Brace, The effect of pressure on porosity and the transport properties of rock, J. Geophys. Res., 89, 9425-9431, 1984.
48. Walton, M. S., The aquifer thermal energy storage program at the University of Minnesota, in Proceedings of the International Conference on Seasonal Thermal Energy Storage and Compressed Air Energy Storage, CONF-811066, pp. 132-140, Natl. Tech. Inf. Serv., Springfield, Va., 1981.
49. Wissler, T. M., Sandstone pore structure: A quantitative analysis of digital SEM images, Ph.D. thesis, Mass. Inst. of Technol., Cambridge, 1987.
50. Wong, P.-Z., J. Koplik, and J. P. Tomanic, Conductivity and permeability of rocks, Phys. Rev. B, 30, 6606-6614, 1984.