Advertisement

Arabian Journal of Geosciences

, 10:388 | Cite as

Fractal dimension of pore space in carbonate samples from Tushka area (Egypt)

  • Yi DingEmail author
  • Andreas Weller
  • Zeyu Zhang
  • Mohamed Kassab
Original Paper

Abstract

To investigate inhomogeneous and porous structures in nature, the concept of fractal dimension was established. This paper briefly introduces the definition and measurement methods of fractal dimension. Three different methods including mercury injection capillary pressure (MICP), nuclear magnetic resonance (NMR), and nitrogen adsorption (BET) were applied to determine the fractal dimensions of the pore space of eight carbonate rock samples taken from West Tushka area, Egypt. In the case of fractal behavior, the capillary pressure P c and cumulative fraction V c resulting from MICP are linearly related with a slope of D-3 in a double logarithmic plot with D being the value of fractal dimension. For NMR, the cumulative intensity fraction V c and relaxation time T 2 show a linear relation with a slope of 3-D in a double logarithmic plot. Fractal dimension can also be determined by the specific surface area S por derived from nitrogen adsorption measurements and the effective hydraulic radius. The fractal dimension D shows a linear relation with the logarithm of S por . The fractal dimension is also used in models of permeability prediction. To consider a more comprehensive data set, another 34 carbonate samples taken from the same study area were integrated in the discussion on BET method and permeability prediction. Most of the 42 rock samples show a good agreement between measured permeability and predicted permeability if the mean surface fractal dimension for each facies is used.

Keywords

Capillary pressure method Fractal dimension Pore-space geometry 

Notes

Acknowledgements

The authors thank Mostafa Behery, Wolfgang Debschütz, and Carsten Prinz for their help during sample preparation and petrophysical investigations. We are grateful to Matthias Halisch. His constructive comments and remarks helped to improve the manuscript.

References

  1. Billi A, Storti F (2004) Fractal distribution of particle size in carbonate cataclastic rocks from the core of a regional strike-slip fault zone. Tectonophysics 384:115–128.  https://doi.org/10.1016/j.tecto.2004.03.015 CrossRefGoogle Scholar
  2. Brunauer S, Emmett P, Teller E (1938) Adsorption of gases on multimolecular layers. J Am Chem Soc 60:309–319CrossRefGoogle Scholar
  3. Carman P (1937) Fluid flow through a granular bed. Trans Inst Chem Eng 15:150–167Google Scholar
  4. Clark B, Kleinberg A (2002) Physics in oil exploration. Phys Today 55:48–53CrossRefGoogle Scholar
  5. El Shazly EM, Abd El Hady MA (1977) Geology and groundwater conditions of Tushka basin area, Egypt: 11th International Symposium on Remote Sensing of Environment, Groundwater in Arid Areas in Egypt, pp 25–29Google Scholar
  6. El-Sayed AMA, Kassab MA, El Safori YA, Abass AE (2005) Carbonate facies and its reservoir properties, West Tushka, South Western Desert, Egypt. First International Conference on the Geology of the Tethys, Cairo University, pp 267–278Google Scholar
  7. Halisch M, Weller, A, Kassab MA (2014) Impedance spectroscopy on carbonates. Proceeding of the annual symposium of the Society of Core Analysis, paper A036Google Scholar
  8. Kassab MA, Weller A (2013) Porosity estimation from compressional wave velocity: a study based on Egyptian carbonate samples. J Earth Sci Eng 3:314–321Google Scholar
  9. Keating K, Falzone A (2012) Relating nuclear magnetic resonance relaxation time distributions to void-size distributions for unconsolidated sand packs. Geophysics 78(6):461–472.  https://doi.org/10.1190/GEO2012-0461.1 CrossRefGoogle Scholar
  10. Keating K, Knight A (2007) A laboratory study to determine the effect of iron oxides on proton NMR measurements. Geophysics 72(1):27–32.  https://doi.org/10.1190/1.2399445 CrossRefGoogle Scholar
  11. Kenyon WE (1997) Petrophysical principles of applications of NMR logging. Log Anal 38:21–43Google Scholar
  12. Kozeny J (1927) Über kapillare Leitung des Wassers im Boden. Sitzungsberichte der Akademie der Wissenschaften in Wien 136:271–306Google Scholar
  13. Krohn CE (1988) Fractal measurements of sandstones, shales and carbonates. J Geophys Res 93(B4):3297–3305CrossRefGoogle Scholar
  14. Mianowski A, Owczarek M (2000) Fractal analysis of carbonized porous material on the basis of mercuric porosimetry. Pol J Appl Chem 44(2-3):95–103Google Scholar
  15. Pape H, Clauser C, Iffland J (1999) Permeability prediction based on fractal pore-space geometry. Geophysics 64:1447–1460CrossRefGoogle Scholar
  16. Pape H, Arnold J, Pechnig R, Clauser C, Talnishnikh E, Anferova S, Blümlich B (2009) Permeability prediction for low porosity rocks by mobile NMR. Pure Appl Geophys 166:1125–1163CrossRefGoogle Scholar
  17. Pfeifer P, Avnir D (1983) Chemistry in noninteger dimensions between two and three. I Fractal theory of heterogeneous surfaces. J Chem Phys 79(7):3558–3565CrossRefGoogle Scholar
  18. Said R (1962) The geology of Egypt. Elsevier Publishing Company, AmsterdamGoogle Scholar
  19. Vega S, Jouini MS (2015) 2D multifractal analysis and porosity scaling estimation in Lower Cretaceous carbonates. Geophysics 80(6):D575–D586.  https://doi.org/10.1190/GEO2014-0596.1 CrossRefGoogle Scholar
  20. Verrecchia EP (1995) On the relationship between the pore-throat morphology index (“a”) and fractal dimension (Df) of pore networks in carbonate rocks discussion. J Sediment Res 65(4a):701–702CrossRefGoogle Scholar
  21. Weller A, Slater L, Binley A, Nordsiek S, Xu S (2015) Permeability prediction based on induced polarization: Insights from measurements on sandstone and unconsolidated samples spanning a wide permeability range. Geophysics 80(2):D161–D173CrossRefGoogle Scholar
  22. Westphal H, Surholt I, Kiesl C, Thern HF, Kruspe T (2005) NMR measurements in carbonate rocks: problems and an approach to a solution. Pure Appl Geophys 16(3):549–570CrossRefGoogle Scholar
  23. Xie S, Cheng Q, Ling Q, Li B, Bao Z, Fan P (2010) Fractal and multifractal analysis of carbonate pore-scale digital images of petroleum reservoirs. Mar Pet Geol 27:476–485.  https://doi.org/10.1016/j.marpetgeo.2009.10.010 CrossRefGoogle Scholar
  24. Zhang Z, Weller A (2014) Fractal dimension of pore-space geometry of an Eocene sandstone formation. Geophysics 79(6):D377–D387.  https://doi.org/10.1190/geo2014-0143.1 CrossRefGoogle Scholar

Copyright information

© Saudi Society for Geosciences 2017

Authors and Affiliations

  • Yi Ding
    • 1
    Email author
  • Andreas Weller
    • 2
  • Zeyu Zhang
    • 3
  • Mohamed Kassab
    • 4
  1. 1.Georg-August-Universität Göttingen, Geowissenschaftliches ZentrumGöttingenGermany
  2. 2.Technische Universität Clausthal, Institut für GeophysikClausthal-ZellerfeldGermany
  3. 3.School of Earth Science and TechnologySouthwest Petroleum UniversityChengduChina
  4. 4.Egyptian Petroleum Research Institute (EPRI)CairoEgypt

Personalised recommendations