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Gradient stabilized and destabilized invasion percolation

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  • Meakin, Paul
  • Birovljev, Aleksandar
  • Frette, Vidar
  • Feder, Jens
  • Jøssang, Torstein

Abstract

The effects of gravity stabilization and destabilization on the slow displacement of a wetting fluid by a non-wetting fluid in two-dimensional and three-dimensional porous media have been investigated experimentally. The characteristic features of the resulting displacement patterns can be reproduced quite well by invasion percolation models with a spatial gradient added to the usual random threshold distribution. In the case of destabilized displacement the patterns can be described in terms of a string of blobs of size ξ that form a directed walk. The internal structure of the blobs is like that of an invasion percolation cluster (with trapping in the two-dimensional case). In the stabilized case the structure is like that of a fractal invasion percolation cluster on short length scales (lengths ⪡ξ) and is uniform on longer lengths. The correlation length (ξ) also describes the maximum hole diameter. The invasion front is a self-similar fractal on length scales shorter than ξ and flat on longer length scales. In both the experiments and the simulations the correlation length ξ is related to the Bond number (B0, the ratio between buoyancy and capillary forces) by ξ ∼ |B0|−ʋ(ʋ+1) where ʋ is the ordinary percolation correlation length exponent) in accord with the theoretical arguments of Wilkinson (Phys. Rev. A 30 (1984) 520; 34 (1986) 1380).

Suggested Citation

  • Meakin, Paul & Birovljev, Aleksandar & Frette, Vidar & Feder, Jens & Jøssang, Torstein, 1992. "Gradient stabilized and destabilized invasion percolation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 191(1), pages 227-239.
  • Handle: RePEc:eee:phsmap:v:191:y:1992:i:1:p:227-239
    DOI: 10.1016/0378-4371(92)90532-U
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    1. Aharony, Joseph & Saunders, Anthony & Swary, Itzhak, 1988. "The effects of DIDMCA on bank stockholders' returns and risk," Journal of Banking & Finance, Elsevier, vol. 12(3), pages 317-331, September.
    2. Thulin, Andrew J. & Schwab, Gerald D. & Hilker, James H., 1987. "The Shape of the Swine Production Industry Today and Tomorrow," Staff Paper Series 200928, Michigan State University, Department of Agricultural, Food, and Resource Economics.
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    Cited by:

    1. Onody, Roberto N. & Zara, Reginaldo A., 1996. "Multiple invasion percolation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 231(4), pages 375-392.
    2. Wagner, G. & Meakin, P. & Feder, J. & Jøssang, T., 1997. "Buoyancy-driven invasion percolation with migration and fragmentation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(3), pages 217-230.
    3. Meakin, Paul & Wagner, Geri & Feder, Jens & Jøssang, Torstein, 1993. "Simulations of migration, fragmentation and coalescence of non-wetting fluids in porous media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 200(1), pages 241-249.

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