Transport in Porous Media

, Volume 102, Issue 2, pp 301–312

A Fast Algorithm for Invasion Percolation


DOI: 10.1007/s11242-014-0277-8

Cite this article as:
Masson, Y. & Pride, S.R. Transp Porous Med (2014) 102: 301. doi:10.1007/s11242-014-0277-8


We present a computationally fast Invasion Percolation (IP) algorithm. IP is a numerical approach for generating realistic fluid distributions for quasi-static (i.e., slow) immiscible fluid invasion in porous media. The algorithm proposed here uses a binary-tree data structure to identify the site (pore) connected to the invasion cluster that is the next to be invaded. Gravity is included. Trapping is not explicitly treated in the numerical examples but can be added, for example, using a Hoshen–Kopelman algorithm. Computation time to percolation for a 3D system having \(N\) total sites and \(M\) invaded sites at percolation goes as \(O(M \log M)\) for the proposed binary-tree algorithm and as \(O(M N)\) for a standard implementation of IP that searches through all of the uninvaded sites at each step. The relation between \(M\) and \(N\) is \(M = N^{D/E}\), where \(D\) is the fractal dimension of an infinite cluster and \(E\) is Euclidean space dimension. In numerical practice, on finite-sized cubic lattices with invasion structures influenced by the injection boundary and boundary conditions lateral to the flow direction, we observe the scaling \(M = N^{0.852}\) in 3D (valid through the second decimal place) instead of \(M= N^{0.843}\) based on the infinite cluster fractal dimension \(D=2.53\).


Two-phase flowInvasion percolationNumerical simulation

Copyright information

© Springer Science+Business Media Dordrecht (outside the USA) 2014

Authors and Affiliations

  1. 1.Institut de Physique du Globe de ParisParisFrance
  2. 2.Lawrence Berkeley National LaboratoryBerkeleyUSA