Abstract
The complex pore space considerably affects the unique properties of diatomite and its significant potential for many industrial applications. The pore network in the diatomite from the Lower Miocene strata of the Skole nappe (the Jawornik deposit, SE Poland) has been investigated using a fractal approach. The fractal dimension of the pore-space volume was calculated using the Menger sponge as a model of a porous body and the mercury porosimetry data in a pore-throat diameter range between 10,000 and 10 nm. Based on the digital analyses of the two-dimensional images from thin sections taken under a scanning electron microscope at the backscattered electron mode at different magnifications, the authors tried to quantify the pore spaces of the diatomites using the box counting method. The results derived from the analyses of the pore-throat diameter distribution using mercury porosimetry have revealed that the pore space of the diatomite has the bifractal structure in two separated ranges of the pore-throat diameters considerably smaller than the pore-throat sizes corresponding to threshold pressures. Assuming that the fractal dimensions identified for the ranges of the smaller pore-throat diameters characterize the overall pore-throat network in the Jawornik diatomite, we can set apart the distribution of the pore-throat volume (necks) and the pore volume from the distribution of the pore-space volume (pores and necks together).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
A.H. Thompson, A.J. Katz, C.E. Krohn, The microgeometry and transport properties of sedimentary rock. Adv. Phys. 36(5), 625–694 (1987)
C.M. Ross, A.R. Kovscek, Pore microstructure and fluid distribution in a diatomaceous reservoir. SPE 75190, 1–9 (2002)
L. Jia, C.M. Ross, A.R. Kovscek, A pore-network-modeling approach to predict petrophysical properties of diatomaceous reservoir rock. SPE 93806, 597–608 (2007)
A.J. Katz, A.H. Thompson, Fractal sandstone pores: implications for conductivity and pore formation. Phys. Rev. Lett. 54(12), 1325–1328 (1985)
C.E. Krohn, A.H. Thompson, Fractal sandstone pores: automated measurements using scanning-electron-microscope images. Phys. Rev. B 33(9), 6366–6374 (1986)
J.P. Hansen, A.T. Skjeltorp, Fractal pore space and rock permeability implications. Phys. Rev. B 38(4), 2635–2638 (1988)
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)
B.B. Mandelbrot, The Fractal Geometry of Nature (Freeman, New York, 1983)
P. Pfeifer, D. Avnir, Chemistry in noninteger dimensions between two and three. I. Fractal theory of heterogeneous surfaces. J. Chem. Phys. 79(7), 3558–3565 (1983)
J. Kotlarczyk, Leszczawka Diatomite Horizon in diatomite quarry near Jaworowice (former Jawornik Ruski), in Geotraverse Kraków-Baranów-Rzeszów-Przemyśl-Ustrzyki Dolne-Komańcza-Dukla, Guide to Excursion 4, Carpatho-Balkan Geological Association, XIII Congress, Cracow, Poland, ed. by J. Kotlarczyk (Geological Institute, Warszawa, 1985), pp. 145–147
S. Boggs Jr., Petrology of Sedimentary Rocks (Cambridge University Press, Cambridge, 2009)
W. Yang, P.J. Lopez, G. Rosengarten, Diatoms: self assembled silica nanostructures, and templates for bio/chemical sensors and biomimetic membranes. Analyst 136, 42–53 (2011)
W. Rasband, ImageJ, 1.42 g ed. National Institutes of Health, USA Java 1.6.0_20 (64-bit). http://rsbweb.nih.gov/ij
A. Karperien, FracLac for ImageJ http://rsb.info.nih.gov/ij/plugins/fraclac/FLHelp/ (1999–2013)
C.L. Vavra, J.G. Kaldi, R.M. Sneider, Geological applications of capillary pressure: a review. AAPG Bull. 76(6), 840–850 (1992)
IUPAC, Manual of symbols and terminology for physicochemical quantities and units—appendix II. Definitions, terminology and symbols in colloid and surface chemistry. Part II: heterogeneous catalysis. Pure Appl. Chem. 46(1), 71–90 (1976)
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
D.L. Turcotte, Fractals and Chaos in Geology and Geophysics (Cambridge University Press, Cambridge, 1992)
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.F. Angulo, V. Alvarado, H. Gonzalez, Fractal dimensions from mercury intrusion capillary tests. SPE 23695, 255–263 (1992)
J.D. Bonny, H. Leuenberger, Determination of fractal dimensions of matrix-type solid dosage forms and their relation with drug dissolution kinetics. Eur. J. Pharm. Biopharm. 39(1), 31–37 (1993)
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)
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
P. Such, G. Lesniak, Study of pore space parameters of rocks. Prace Instytutu Gornictwa Naftowego i Gazownictwa 119, 3–63 (2003) (summary in English)
G. Stanczak, Fractal analysis of the pore space in sandstones as derived from mercury porosimetry and image analysis, in International Multidisciplinary Microscopy Congress, ed. by E.K. Polychroniadis, A.Y. Oral, M. Ozer (Springer Proceedings in Physics 154, 2014) pp. 51–60
Acknowledgments
This work was financially supported by the AGH-UST statutory grant No. 11.11.140.320.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Stańczak, G., Rembiś, M., Figarska-Warchoł, B., Toboła, T. (2015). Fractal Characteristics of the Pore Network in Diatomites Using Mercury Porosimetry and Image Analysis. In: Polychroniadis, E., Oral, A., Ozer, M. (eds) 2nd International Multidisciplinary Microscopy and Microanalysis Congress. Springer Proceedings in Physics, vol 164. Springer, Cham. https://doi.org/10.1007/978-3-319-16919-4_11
Download citation
DOI: https://doi.org/10.1007/978-3-319-16919-4_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-16918-7
Online ISBN: 978-3-319-16919-4
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)