Pore-level modelling of wetting on correlated porous media

The displacement of a non-wetting fluid by a wetting one in a porous medium is influenced, among other things, by two competing mechanisms: the flow of the wetting phase along crevices, giving the possibility of snapping off in throats; and its advance through the centres of the pore space under various pore- and throat-filling conditions, leading to a cooperative filling. The percolation process associated with these two mechanisms on porous networks in two and three dimensions is well understood; it is a classic bond percolation problem competing with an invasion percolation one. We present a three-dimensional pore-level model that describes these effects on a site and bond network representing pores and throats, respectively. The network elements may have various degrees of correlation among their sizes. Site and bond-size distributions may be any kind of function representing a real pore space. In this work, we are able to predict various kinds of patterns that arise when the two aforementioned mechanisms compete and to study the effect of the correlation's strength on the onset of each pattern, revealing the strong influence of the topology of the network in determining which process will dominate. Buoyancy forces are not taken into account in the present work.