Anomalous diffusion on clusters in steady-state two-phase flow in porous media in two dimensionsG. Tørå1, T. Ramstad2 and A. Hansen1
1 Department of Physics, Norwegian University of Science and Technology - N-7491 Trondheim, Norway
2 Numerical Rocks AS - Stiklestadveien 1, N-7041 Trondheim, Norway
received 13 November 2008; accepted in final form 19 August 2009; published September 2009
published online 18 September 2009
We study diffusion processes on clusters of non-wetting fluid dispersed in a wetting one flowing in a two-dimensional porous medium under steady-state conditions using a numerical model. At the critical saturation and capillary number of 10-5, where the cluster size distribution follows a power law, we find anomalous diffusion characterized by two critical exponents, = 2.35 0.05 in the average flow direction and = 3.51 0.05 in the perpendicular direction. We determine the conductivity exponents to be = 1.6 0.2 and = 1.25 0.1, respectively. The high-frequency scaling exponents of the AC conductivity we find to be =0. 37 0.1 and = 0.36 0.1, respectively.
47.56.+r - Flows through porous media.
64.60.ah - Percolation.
07.05.Tp - Computer modeling and simulation.
© EPLA 2009