On three-dimensional lattices, Renault observed that t he percolation threshold decreased as the correlation length increased, reaching an asymptotic value with little change beyond correlations of approximately five bond lengths. This may be interpreted to mean that statistically reproducible results occur within each correlated sub region for sizes beyond those implied by a correlation length of five. This concept of structure, leading to two distinct length scales, leads naturally to a concept of larger-scale percolation. The local entry pressure serves to define the displacement rule. Once invaded, a site attains a local saturation based on the local Pc-S curve.
Trapping is included in the algorithm.
This corresponds to a local Pc-S curves that is a step function. The lack of intermediate saturations makes the algorithm computationally equivalent to standard network models, such that two-dimensional bicontinua fail to exist. Yortsos and Satik also calculated effective permeabilities on the large-scale lattice. This statement reflects continuing uncertainties about imbibition mechanisms and the role of wetting films.