Abstract
The pore space fractal dimension was measured using a model of a porous body based on the Menger sponge and mercury porosimetry data for selected samples of the reservoir sandstones of the Weglowka oil field (SE Poland) in a pore-throat diameter range between 91 and 0.0090 \(\upmu \)m. Based on the digital analyses of the two-dimensional images of thin sections impregnated with blue-dyed epoxy and taken under an optical microscope as well as the images of thin sections taken under a cold field emission gun scanning electron microscope (FEGSM) in the backscattered electron image mode, the current paper tries to quantify the pore space of sandstones by using the box counting method. The results derived from analysis of the pore-throat diameter distribution by mercury porosimetry revealed the multifractal structure of the pore space of sandstone in two separated ranges of the pore-throat size considerably lesser than the pore-throat diameters (10–50 \(\upmu \)m) corresponding to threshold pressures. This means that only the pore throats connecting wider parts of the pore network (pores) exhibit the fractal structure. The assumption that the fractal dimension monitoring the distribution of the pore-space volume within the smallest pore-throat diameters characterizes the overall pore-throat network in the rock sample provides a device to set apart the distribution of the pore-throat volume from the distribution of the pore volume. On the other hand, the fractal dimensions derived from the image analysis of thin sections describe the pore space as a whole.
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R.F. Angulo, V. Alvarado, H. Gonzalez, Fractal dimensions from mercury intrusion capillary tests. SPE 23695, 255–263 (1992)
F.S. Anselmetti, S. Luthi, G.P. Eberli, Quantitative characterization of carbonate pore systems by digital image analysis. AAPG Bull. 82(10), 1815–1836 (1998)
F. Bartoli, N.R.A. Bird, V. Gomendy, H. Vivier, S. Niquet, The relation between silty soil structures and their mercury porosimetry curve counterparts: fractals and percolation. Eur. J. Soil. Sci. 50, 9–22 (1999)
R. Ehrlich, S.J. Crabtree, S.K. Kennedy, R.L. Cannon, Petrographic image analysis I, analysis of reservoir pore complexes. J. Sediment. Petrology 54(4), 1365–1378 (1984)
R. Ehrlich, S.J. Crabtree, K.O. Horkowitz, J.P. Horkowitz, Petrography and reservoir physics I: objective classification of reservoir porosity. AAPG Bull. 75(10), 1547–1562 (1991)
J.P. Hansen, A.T. Skjeltorp, Fractal pore space and rock permeability implications. Phys. Rev. B 38(4), 2635–2638 (1988)
J.P. Hyslip, L.E. Vallejo, Fractal analysis of the roughness and size distribution of granular materials. Eng. Geol. 48, 231–244 (1997)
A.J. Katz, A.H. Thompson, Fractal sandstone pores: implications for conductivity and pore formation. Phys. Rev. Lett. 54(12), 1325–1328 (1985)
A.J. Katz, A.H. Thompson, Quantitative prediction of permeability in porous rock. Phys. Rev. B 34(11), 8179–8181 (1986)
A.J. Katz, A.H. Thompson, Prediction of rock electrical conductivity from mercury injection measurements. J. Geophys. Res. 92, 599–607 (1987)
B.H. Kaye, Image analysis techniques for characterizing fractal structures, in The Fractal Approach to Heterogeneous Chemistry, ed. by D. Avnir (Wiley, Chichester, 1989), pp. 55–66
C.E. Krohn, Sandstone fractal and Euclidean pore volume distributions. J. Geophys. Res. 93(B4), 3286–3296 (1988)
C.E. Krohn, Fractal measurements of sandstones, shales, and carbonates. J. Geophys. Res. 93(B4), 3297–3305 (1988)
C.E. Krohn, A.H. Thompson, Fractal sandstone pores: automated measurements using scanning-electron-microscope images. Phys. Rev. B 33(9), 6366–6374 (1986)
B.B. Mandelbrot, The Fractal Geometry of Nature (Freeman, New York, 1983)
C.A. McCreesh, R. Ehrlich, S.J. Crabtree, Petrography and reservoir physics II: relating thin section porosity to capillary pressure, the association between pore types and throat size. AAPG Bull. 75(10), 1563–1578 (1991)
J.D. Orford, W.B. Whalley, The use of the fractal dimension to quantify the morphology of irregular-shaped particles. Sedimentology 30, 655–668 (1983)
H.O. Peitgen, H. Jürgens, D. Saupe, Chaos and Fractals: New Frontiers of Science (Springer, New York, 1992)
J.L. Pérez Bernal, M.A. Bello López, The fractal dimension of stone pore surface as weathering descriptor. Appl. Surface Sci. 161, 47–53 (2000)
P. Pfeifer, D. Avnir, Chemistry in noninteger dimensions between two and three. I. Fractal theory of heterogeneous surfaces. Jour. Chem. Phys. 79(7), 3558–3565 (1983)
P. Pfeifer, M. Obert, Fractals: basic concepts and terminology, in The Fractal Approach to Heterogeneous Chemistry, ed. by D. Avnir (Wiley, Chichester, 1989), pp. 11–43
E.D. Pittman, Relationship of porosity and permeability to various parameters derived from mercury injection-capillary pressure curves for sandstone. AAPG Bull. 76(2), 191–198 (1992)
P. Such, G. Lesniak, Study of pore space parameters of rocks. Prace Instytutu Gornictwa Naftowego i Gazownictwa 119, 3–63 (2003) (summary in English)
A.H. Thompson, A.J. Katz, C.E. Krohn, The microgeometry and transport properties of sedimentary rock. Adv. Phys. 36(5), 625–694 (1987)
D.L. Turcotte, Fractals and Chaos in Geology and Geophysics (Cambridge University Press, Cambridge, 1992)
D.L. Turcotte, J. Huang, Fractal distribution in geology, scale invariance, and deterministic chaos, in Fractals in the Earth Sciences, ed. by C.C. Barton, P.R. La Pointe (Plenum Press, New York, 1995), pp. 1–40
C.L. Vavra, J.G. Kaldi, R.M. Sneider, Geological applications of capillary pressure: a review. AAPG Bull. 76(6), 840–850 (1992)
Acknowledgments
The FEGSM examinations were conducted at the Laboratory of Field Emission Scanning Electron Microscopy and Microanalysis of the Institute of Geological Sciences of the Jagiellonian University. This work was financed by the AGH-UST (statutory grant No. 11.11.140.320).
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Stanczak, G. (2014). Fractal Analysis of the Pore Space in Sandstones as Derived from Mercury Porosimetry and Image Analysis. In: Polychroniadis, E., Oral, A., Ozer, M. (eds) International Multidisciplinary Microscopy Congress. Springer Proceedings in Physics, vol 154. Springer, Cham. https://doi.org/10.1007/978-3-319-04639-6_8
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