Invasion percolation is a mathematical model of realistic
fluid distributions for slow immiscible fluid invasion in porous media, in
percolation theory
In statistical physics and mathematics, percolation theory describes the behavior of a network when nodes or links are added. This is a geometric type of phase transition, since at a critical fraction of addition the network of small, disconnected ...
.
It "explicitly takes into account the transport process taking place". A wetting fluid such as water takes over from a non-wetting fluid such as oil, and capillary forces are taken into account. It was introduced by Wilkinson and Willemsen (1983).
Invasion percolation proceeds in
avalanche
An avalanche is a rapid flow of snow down a Grade (slope), slope, such as a hill or mountain. Avalanches can be triggered spontaneously, by factors such as increased precipitation or snowpack weakening, or by external means such as humans, othe ...
s or bursts, and thus exhibits a form of
intermittency
In dynamical systems, intermittency is the irregular alternation of phases of apparently periodic and chaotic dynamics ( Pomeau–Manneville dynamics), or different forms of chaotic dynamics (crisis-induced intermittency).
Experimentally ...
. This avalanche behavior has been likened to
self-organized criticality
Self-organized criticality (SOC) is a property of dynamical systems that have a critical point as an attractor. Their macroscopic behavior thus displays the spatial or temporal scale-invariance characteristic of the critical point of a phas ...
.
[D. Sornette, A. Johansen, I. Dornic, J. Phys. I (France) 5, 325 (1995)]
References
Percolation theory
Fluid dynamics
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