Influence of buoyancy on drainage of a fractal porous medium

Abstract

The influence of stabilizing hydrostatic pressure gradients on the drainage of a fractal porous medium is studied. The invasion process is treated with invasion percolation (IP) in a gradient. Fractality is mimicked by randomly closing bonds of a network. Two length scales govern the problem: the characteristic length of the pore structure [formula presented] and a length scale [formula presented] above which buoyancy determines the structure of the cluster. When [formula presented] the local structure of the invading cluster is governed by the interplay of capillarity and the fractal properties of the pore space. Only parts of the backbone of the pore structure can be invaded. Therefore, the obtained fractal dimension for small systems [formula presented] is much lower (1.40) than the one for ordinary IP (1.82). On larger length scales, [formula presented] the fractality of the pore space is no longer important and the cluster grows as in ordinary IP. When [formula presented] gravity becomes important and [formula presented] scales with the bond number B as [formula presented] as in ordinary IP, while the fractal dimension becomes equal to the Euclidean one. When [formula presented] gravity is already important on length scales where the fractality of the medium has to be considered too. On small scales [formula presented] where only capillarity and fractality play a role the cluster structure is again characterized by the fractal dimension of 1.40. On larger length scales, [formula presented] gravity promotes a more efficient invasion of the pore space and a different fractal dimension of 1.52 is found. The length scale [formula presented] no longer follows ordinary IP scaling: [formula presented] When [formula presented] the fractal dimension of the invading cluster equals the Euclidean one and [formula presented]. © 2002 The American Physical Society.