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Pore space microstructure transitions in porous media under compaction

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Abstract

Pore space microstructure transitions in porous media are investigated by means of simulations of pore networks subject to a random compaction mechanism. With critical path analysis we track the characteristic pore length of the media. This pore length becomes singular at transition porosities, exhibiting kinks and even discontinuities if compaction is strong. The transitions arise from the appearance of new modes in the pore size distribution. Different modes control the transport properties in different porosity intervals where the characteristic pore length is continuous. These continuous pieces of pore length correspond to structurally different media. A transition occurs when the pore fraction controlling flow equals the critical percolation probability of the underlying lattice representing the pore space. To prove the validity of the transitions discovered by simulation we develop an analytical description of the pore-size distribution of media under compaction by using a detailed balance of pore populations. Analytical transition porosities agree precisely with simulations. At the first pore space microstructure transition the change in characteristic length l P exhibits a critical scaling Δl P α (λc − λ)υ, with υ = 1 and λ a compaction factor. Within this approach many aspects of the pore space microstructure transitions observed in the simulations are explained.

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References

  • Ambegaokar V., Halperin B.I., Langer J.S.: Hopping conductivity in disordered systems. Phys. Rev. B 4, 2612–2620 (1971)

    Article  Google Scholar 

  • Arns C.H., Knackstedt M.A., Martys N.S.: Cross-property correlations and permeability estimation in sandstone. Phys. Rev. E 72, 046304 (2005)

    Article  Google Scholar 

  • Bauget, F., Turner, M., Arns, C., Saadatfar, M., Sheppard, A., Sok, R., Knackstedt, M.: Society of Petroleum Engineers, 2005 Annual technical conference and exhibition, Dallas, SPE 95950, (2005)

  • Bernabé Y.: The transport properties of networks of cracks and pores. J. Geophys. Res. 100, 4231–4241 (1995)

    Article  Google Scholar 

  • Boggs S.: Petrology of sedimentary rocks. Macmillan Publishing Company, New York (1992)

    Google Scholar 

  • Bustos C.I., Toledo P.G.: Pore-level modeling of gas and condensate flow in two- and three-dimensional pore network: Pore size distribution effects on the relative permeability of gas and condensate. Trans. Porous Med. 53, 281–315 (2003)

    Article  Google Scholar 

  • Coniglio A.: Cluster structure near the percolation threshold. J. Phys. A: Math. Gen. 15, 3829–3844 (1982)

    Article  Google Scholar 

  • Erdös P., Haley S.B.: Random-network models of the conductance of disordered condensed matter. Phys. Rev. B 13, 1720–1727 (1976)

    Article  Google Scholar 

  • Essam J.W.: Percolation theory. Rep. Prog. Phys. 43, 833–912 (1980)

    Article  Google Scholar 

  • Grimmett G.: Percolation. 2nd edn. Springer-Verlag, Berlin (1999)

    Google Scholar 

  • Idowu N.A., Blunt M.J.: Pore-scale modeling of rate effects in water flooding. Trans. Porous Med. 83, 151–169 (2010)

    Article  Google Scholar 

  • Katz A.J., Thompson A.H.: Quantitative prediction of permeability in porous rock. Phys. Rev. B 34, 8179–8181 (1986)

    Article  Google Scholar 

  • Kirkpatrick S.: Percolation and Conduction. Rev. Mod. Phys. 45, 574–588 (1973)

    Article  Google Scholar 

  • Martys N., Garboczi E.J.: Length scales relating the fluid permeability and electrical conductivity in random two-dimensional model porous media. Phys. Rev. B 46, 6080–6090 (1992)

    Article  Google Scholar 

  • Sahimi M.: Flow phenomena in rocks: from continuum models to fractals, percolation, cellular automata, and simulated annealing. Rev. Mod. Phys. 65, 1393–1534 (1993)

    Article  Google Scholar 

  • Sahimi M.: Flow and transport in porous media and fractured rock: from classical methods to modern approaches. Wiley-VCH, New York (1995)

    Google Scholar 

  • Stauffer D., Aharony A.: Introduction to percolation theory. 2nd edn. Taylor & Francis, London (1992)

    Google Scholar 

  • Toledo P.G., Scriven L.E., Davis H.T.: SPE formation. Evaluation 9, 46–54 (1994)

    Google Scholar 

  • Wong P.Z., Koplik J., Tomanic J.P.: Conductivity and permeability of rocks. Phys. Rev. B 30, 6606–6614 (1984)

    Article  Google Scholar 

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Authors and Affiliations

  1. Institut für Theoretische Physik der Weichen Materie, Heinrich Heine-Universität Düsseldorf, Universitätsstraße 1, 40225, Düsseldorf, Germany

    R. E. Rozas

  2. Department of Chemical Engineering and Surface Analysis Laboratory (ASIF), University of Concepción, Concepción 160-C, Correo 3, Chile

    P. G. Toledo

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  1. R. E. Rozas
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  2. P. G. Toledo
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Correspondence to R. E. Rozas.

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Rozas, R.E., Toledo, P.G. Pore space microstructure transitions in porous media under compaction. Transp Porous Med 91, 741–752 (2012). https://doi.org/10.1007/s11242-011-9855-1

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  • DOI: https://doi.org/10.1007/s11242-011-9855-1

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