Advertisement

Transport in Porous Media

, Volume 86, Issue 1, pp 135–154 | Cite as

Statistical Synthesis of Imaging and Porosimetry Data for the Characterization of Microstructure and Transport Properties of Sandstones

  • E. S. Amirtharaj
  • M. A. IoannidisEmail author
  • B. Parker
  • C. D. Tsakiroglou
Article

Abstract

The microstructure of a suite of sandstone samples is quantitatively analyzed using a method which combines information from thin section micrographs of the pore space with mercury injection porosimetry in a statistical framework. This method enables the determination of a continuous distribution of pore sizes ranging from few nanometre to several hundred micrometre. The data obtained unify fractal and Euclidean aspects of the void space geometry, yield estimates of the pore-to-throat aspect ratio and challenge the ability of commonly used network models to describe fluid percolation in multiscale porous media. Application of critical path analysis to the prediction of flow permeability and electrical conductivity of sandstone core samples using the new information produces results comparable to those obtained by the classical approach—a fact attributed to the presence of macroscopic heterogeneity at the scale of several millimetres.

Keywords

Fractal Percolation Porous media Imaging Permeability Conductivity Correlation Scattering Magnetic resonance 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Adler P.M., Jacquin C.G., Quiblier J.A.: Flow in simulated porous media. Int. J. Multiph. Flow 16, 691 (1990)CrossRefGoogle Scholar
  2. Bakke S., Oren P.: 3D pore-scale modeling of sandstones and flow simulations in pore networks. SPE J. 2(2), 136–149 (1997)Google Scholar
  3. Bekri S., Howard J., Muller J., Adler P.M.: Electrical resistivity index in multiphase flow through porous media. Transp. Porous Med. 51, 41–65 (2003)CrossRefGoogle Scholar
  4. Blacher S., Heinrichs B., Sahouli B., Pirard R., Pirard J.-P.: Fractal characterization of wide pore range catalysts: Application to Pd–Ag/SiO2 xerogels. J. Colloid Interface Sci. 226, 123–130 (2000)CrossRefGoogle Scholar
  5. Blair S.C., Berge P.A., Berryman J.G.: Using two-point correlation functions to characterize microgeometry and estimate permeabilities of sandstones and porous glass. J. Geophys. Res. 101(B9), 20359–20375 (1996)CrossRefGoogle Scholar
  6. Broseta D., Barre L., Vizika O., Shahidzadeh N., Guilbaud J.P., Lyonnard S.: Capillary condensation in a fractal porous medium. Phys. Rev. Lett. 86, 5313–5316 (2001)CrossRefGoogle Scholar
  7. Chang D., Ioannidis M.A.: Magnetization evolution in network models of porous rock under conditions of drainage and imbibition. J. Colloid Interface Sci. 253, 159–170 (2002)CrossRefGoogle Scholar
  8. Chatzis I., Dullien F.A.L.: Modeling pore structure by 2D and 3D networks with application to sandstones. J. Can. Petrol. Technol. 16, 97–108 (1977)Google Scholar
  9. Chatzis I., Morrow N.R., Lim H.T.: Magnitude and detailed structure of residual oil saturation. SPE J. 23, 311–326 (1983)Google Scholar
  10. Chen Q., Gingras M.K., Balcom B.J.: A magnetic resonance study of pore filling processes during spontaneous imbibition in Berea sandstone. J. Chem. Phys. 119, 9609–9616 (2003)CrossRefGoogle Scholar
  11. Dong H., Blunt M.J.: Pore-network extraction from micro-computerized-tomography images. Phys. Rev. E 80, 036307 (2009)CrossRefGoogle Scholar
  12. Dullien F.A.L.: Porous Media: Fluid Transport and Pore Structure. Academic Press, San Diego (1992)Google Scholar
  13. Dunn K.J., Bergman D.J., LaTorraca G.A.: Nuclear magnetic resonance: petrophysical and logging applications. In: Helbig, K., Treitel, S. (eds) Handbook of Geophysical Exploration, vol. 32, Pergamon Press, Oxford (2002)Google Scholar
  14. Ehrburger-Dolle F., Lavanchy A., Stoeckli F.: Determination of the surface fractal dimension of active carbons by mercury porosimetry. J. Colloid Interface Sci. 166, 451–461 (1994)CrossRefGoogle Scholar
  15. Glatter O., Kratky O.: Small-Angle X-ray Scattering. Academic Press, London (1982)Google Scholar
  16. Han M., Youssef S., Rosenberg E., Fleury M., Levitz P.: Deviation from Archie’s law in partially saturated porous media: Wetting film versus disconnectedness of the conducting phase. Phys. Rev. E 79, 031127 (2009)CrossRefGoogle Scholar
  17. Hinde A.L.: PRINSAS—a Windows-based computer program for the processing and interpretation of small-angle scattering data tailored to the analysis of sedimentary rocks. J. Appl. Crystallogr. 37, 1020–1024 (2004)CrossRefGoogle Scholar
  18. Ioannidis M.A., Chatzis I.: Network modeling of pore structure and transport properties of porous media. Chem. Eng. Sci. 48, 951–972 (1993)CrossRefGoogle Scholar
  19. Ioannidis M.A., Chatzis I., Dullien F.A.L.: Macroscopic percolation model of immiscible displacement: effects of buoyancy and spatial structure. Water Resour. Res. 32, 3297–3310 (1996)CrossRefGoogle Scholar
  20. Ioannidis M.A., Chatzis I., Sudicky E.A.: The effect of spatial correlation on the accessibility characteristics of 3-dimensional cubic pore network as related to drainage displacements in porous media. Water Resour. Res. 29, 1777–1785 (1993)CrossRefGoogle Scholar
  21. Ioannidis M.A., Kwiecien M.J., Chatzis I.: Statistical analysis of the porous microstructure as a method for estimating reservoir permeability. J. Petrol. Sci. Eng. 16, 251–261 (1996)CrossRefGoogle Scholar
  22. Ioannidis, M.A., Kwiecien, M.J., Chatzis, I., Macdonald, I.F., Dullien, F.A.L.: Comprehensive pore structure characterization using 3D computer reconstruction and stochastic modeling. SPE Preprint 38713, presented at the 1997 SPE annual technical conference and exhibition. San Antonio, Texas (1997)Google Scholar
  23. Katz A.J., Thompson A.H.: Fractal sandstone pores: implications for conductivity and pore formation. Phys. Rev. Lett. 54, 1325–1328 (1985)CrossRefGoogle Scholar
  24. Katz A.J., Thompson A.H.: Quantitative prediction of permeability in porous rock. Phys. Rev. B 34, 8179–8181 (1986)CrossRefGoogle Scholar
  25. Katz A.J., Thompson A.H.: Prediction of rock electrical conductivity from mercury injection measurements. J. Geophys. Res.–Solid Earth and Planets 92(B1), 599–607 (1987)CrossRefGoogle Scholar
  26. Larson R.G., Morrow N.R.: Effects of sample size on capillary pressures in porous media. Powder Technol. 30, 123–138 (1981)CrossRefGoogle Scholar
  27. Liang Z., Ioannidis M.A., Chatzis I.: Permeability and electrical conductivity of porous media from 3D stochastic replicas of the microstructure. Chem. Eng. Sci. 55, 5247–5262 (2000)CrossRefGoogle Scholar
  28. Lindquist W.B., Venkatarangan A., Dunsmuir J., Wong T.F.: Pore and throat size distributions measured from synchrotron X-ray tomographic images of Fontainebleau sandstones. J. Geophys. Res.–Solid Earth 105(B9), 21509–21527 (2000)CrossRefGoogle Scholar
  29. Lock P.A., Jing X.-D., Zimmerman R.W., Schlueter E.M.: Predicting the permeability of sandstone from image analysis of pore structure. J. Appl. Phys. 92, 6311–6319 (2002)CrossRefGoogle Scholar
  30. Meng B.: Resolution-dependent characterization of interconnected pore systems: development and suitability of a new method. Mater. Struct. 27, 63–70 (1994)CrossRefGoogle Scholar
  31. Padhy G.S., Lemaire C., Amirtharaj E.S., Ioannidis M.A.: Pore size distribution in mulitscale porous media as revealed by DDIF-NMR, mercury porosimetry and statistical image analysis. Colloids Surf. A–Physicochemical and Engineering Aspects 300, 222–234 (2007)CrossRefGoogle Scholar
  32. Pfeifer P., Avnir D.: Chemistry in non-integer dimensions between two and three. 1. Fractal theory of heterogeneous surfaces. J. Chem. Phys. 79, 3558–3565 (1983)CrossRefGoogle Scholar
  33. Pomerantz A.E., Tilke P., Song Y.-Q.: Inverting MRI measurements to heterogeneity spectra. J. Magn. Reson. 193, 243–250 (2008)CrossRefGoogle Scholar
  34. Radlinski A.P., Radlinska E.Z., Agamalian M., Wignall G.D., Lindner P., Randl O.G.: Fractal geometry of rocks. Phys. Rev. Lett. 82, 3078–3081 (1999)CrossRefGoogle Scholar
  35. Radlinski A.P., Boreham C.J., Lindner P., Randl O., Wignall G.D., Hinde A.L., Hope J.M.: Small-angle neutron scattering signature of oil generation in artificially and naturally matured hydrocarbon source rocks. Org. Geochem. 31, 1–14 (2000)CrossRefGoogle Scholar
  36. Radlinski A.P., Ioannidis M.A., Hinde A.L., Hainbuchner M., Baron M., Rauch H., Kline S.R.: Angstrom to millimeter characterization of sedimentary rock microstructure. J. Colloid Interface Sci. 274, 607–612 (2004)CrossRefGoogle Scholar
  37. Seth S., Morrow N.R.: Efficiency of the conversion of work of drainage to surface energy for sandstone and carbonate. SPE Reserv. Eval. Eng. 10(4), 338–347 (2007)Google Scholar
  38. Sisavath S., Jing X.-D., Pain C.C., Zimmerman R.W.: Creeping flow through an axisymmetric sudden contraction or expansion. J. Fluids Eng.–Trans. AMSE 124, 273–278 (2002)CrossRefGoogle Scholar
  39. Song Y.Q.: Pore sizes and pore connectivity in rocks using the effect of internal field. Magn. Reson. Imaging 19, 417–421 (2001)CrossRefGoogle Scholar
  40. Song Y.Q., Ryu S.G., Sen P.N.: Determining multiple length scales in rocks. Nature 406, 178–181 (2000)CrossRefGoogle Scholar
  41. Spanne P., Thovert J.-F., Jacquin C.G., Lindquist W.B., Jones K., Adler P.M.: Synchrotron computed microtomography of porous media: Topology and transports. Phys. Rev. Lett. 73, 2001–2004 (1994)CrossRefGoogle Scholar
  42. Stauffer D., Aharony A.: Introduction to Percolation Theory. Taylor & Francis, London (1992)Google Scholar
  43. Talukdar M.S., Torsaeter O., Ioannidis M.A., Howard J.J.: Stochastic reconstruction of chalk from 2D images. Transp. Porous Med. 48, 101–123 (2002)CrossRefGoogle Scholar
  44. Thompson A.H., Katz A.J., Krohn C.E.: The microgeometry and transport properties of sedimentary rock. Adv. Phys. 36, 625–694 (1987)CrossRefGoogle Scholar
  45. Thovert J.-F., Yousefian F., Spanne P., Jacquin C.G., Adler P.M.: Grain reconstruction of porous media: application to a low-porosity Fontainebleau sandstone. Phys. Rev. E 63, 061307 (2001)CrossRefGoogle Scholar
  46. Torquato S.: Random Heterogeneous Materials: Microstructure and Macroscopic Properties. Springer-Verlag, New York (2002)Google Scholar
  47. Tsakiroglou C.D., Ioannidis M.A.: Dual-porosity modelling of the pore structure and transport properties of a contaminated soil. Eur. J. Soil Sci. 59, 744–761 (2008)CrossRefGoogle Scholar
  48. Tsakiroglou C.D., Ioannidis M.A., Amirtharaj E., Vizika O.: A new approach for the characterization of the pore structure of dual porosity rocks. Chem. Eng. Sci. 64, 847–859 (2009)CrossRefGoogle Scholar
  49. Tsakiroglou C.D., Payatakes A.C.: Pore wall roughness as a fractal surface and theoretical simulation of mercury intrusion-retraction in porous media. J. Colloid Interface Sci. 159, 287–301 (1993)CrossRefGoogle Scholar
  50. Tsakiroglou C.D., Payatakes A.C.: Characterization of the pore structure of reservoir rocks with the aid of serial sectioning analysis, mercury porosimetry and network simulation. Adv. Water Res. 23, 773–789 (2000)CrossRefGoogle Scholar
  51. Wardlaw N.C., Cassan J.P.: Oil recovery efficiency and the rock-pore properties of some sandstone reservoirs. Bull. Can. Petrol. Geol. 27, 117 (1979)Google Scholar
  52. Wong P.-Z., Howard J.: Surface roughening and the fractal nature of rocks. Phys. Rev. Lett. 57, 637–640 (1986)CrossRefGoogle Scholar
  53. Xu K., Daian J.-F., Quenard D.: Multiscale structures to describe porous media. 1. Theoretical background and invasion by fluids. Transp. Porous Med. 26, 51–73 (1997)CrossRefGoogle Scholar
  54. Zielinski L.J., Song Y.-Q., Ryu S., Sen P.N.: Characterization of coupled pore systems from the diffusion eigenspectrum. J. Chem. Phys. 117, 5361–5365 (2002)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • E. S. Amirtharaj
    • 1
  • M. A. Ioannidis
    • 1
    Email author
  • B. Parker
    • 2
    • 3
  • C. D. Tsakiroglou
    • 4
  1. 1.Department of Chemical EngineeringUniversity of WaterlooWaterlooCanada
  2. 2.Department of Earth SciencesUniversity of WaterlooWaterlooCanada
  3. 3.School of EngineeringUniversity of GuelphGuelphCanada
  4. 4.Foundation for Research and Technology HellasInstitute of Chemical Engineering and High Temperature Chemical ProcessesPatrasGreece

Personalised recommendations