Influence of buoyancy on drainage of a fractal porous medium.
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 xi(s) and a length scale xi(g) above which buoyancy determines the structure of the cluster. When xi(s)<xi(g) 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 L<xi(s) is much lower (1.40) than the one for ordinary IP (1.82). On larger length scales, xi(s)<L<xi(g), the fractality of the pore space is no longer important and the cluster grows as in ordinary IP. When L>xi(g), gravity becomes important and xi(g) scales with the bond number B as xi(g) proportional, variant B-0.57, as in ordinary IP, while the fractal dimension becomes equal to the Euclidean one. When xi(g)<xi(s) gravity is already important on length scales where the fractality of the medium has to be considered too. On small scales L<xi(g), 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, xi(g)<L<xi(s), gravity promotes a more efficient invasion of the pore space and a different fractal dimension of 1.52 is found. The length scale xi(g) no longer follows ordinary IP scaling: xi(g) proportional, variant B-0.69. When L>xi(s) the fractal dimension of the invading cluster equals the Euclidean one and xi(g) proportional, variant B-0.69.
Huinink
H P
HP
Department of Applied Physics, Technische Universiteit Eindhoven, P.O. Box 513, 5600 MB Eindhoven, The Netherlands. h.p.huinink@tue.nl
Michels
M A J
MA