Abstract
We consider capillary displacement of immiscible fluids in porous media in the limit of vanishing flow rate. The motion is represented as a stepwise Monte Carlo process on a finite lattice, where at each step the fluid interface moves through the lattice element of least resistance. The displacement process exhibits considerable fingering and trapping of displaced phase at all length scales, with non-trivial associated fractal dimensions, and with some interesting qualitative differences between two and three dimensions. We interpret our results in terms of percolation theory concepts, and argue that capillary displacement corresponds to a modified percolation process with its own universality class.
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© 1983 Springer-Verlag
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Koplik, J., Wilkinson, D., Willemsen, J.F. (1983). Percolation and capillary fluid displacement. In: Hughes, B.D., Ninham, B.W. (eds) The Mathematics and Physics of Disordered Media: Percolation, Random Walk, Modeling, and Simulation. Lecture Notes in Mathematics, vol 1035. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0073259
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DOI: https://doi.org/10.1007/BFb0073259
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