Effective and relative permeabilities of anisotropie porous media

A model composed of a three-dimensional orthogonal network of capillary tubes was used to simulate the flow behavior in an unsaturated anisotropic soil. The anisotropy in the network's permeability was introduced by randomly selecting the radii in the three mutually orthogonal directions of the network tubes from three different lognormal probability distributions, one for each direction. These three directions were assumed to be the principal directions of anisotropy. The sample was gradually drained, with only tubes smaller than a certain diameter remaining full at each degree of saturation. Computer experiments were conducted to determine the network's effective permeability as a function of saturation. The main conclusion was that the relationship between saturation and effective permeability depends on direction. Consequently the concept of relative permeability used in unsaturated flow should be limited to isotropic media and not extended to anisotropic ones.