Department of Physics, University of Oslo, Box 1048, Blindern, Oslo 0316, Norway
Center for Advanced Study at The Norwegian Academy of Science and Letters, Box 7585, Skillebekk, Oslo 0205, Norway
Abstract:
A model based on invasion percolation was used to simulate the migration on a non-wetting fluid through a porous medium filled with an immiscible wetting fluid under the influence of a gradient such as that provided by gravity. The migrating fluid clusters undergo both fragmentation and coalescence. The fragment size distribution obtained from two-dimensional simulations in which the gradient g is slowly increased from 0 can be represented by the scaling form Ns(g)s-2ƒ(s|g|-z where z=1+(D−1)ν(ν+1). Here D is the fractal dimensionality of invasion percolation, with trapping, and ν is the ordinary percolation correlation length exponent.