simultaneous capillary dominated displacement of the wetting and non-wetting phases are processes of interest in many disciplines including modeling of the penetration of polluting liquids in hydrology or the secondary migration in petroleum reservoir engineering. percolation models and in particular invasion percolation is well suited to characterize the slow immiscible displacement of two flu...

The interplay between two-dimensional percolation growth models and one-dimensional particle processes has been a fruitful source of interesting mathematical phenomena. In this paper we develop a connection between the construction of Busemann functions in the Hammersley last-passage percolation model with i.i.d. random weights, and the existence, ergodicity and uniqueness of equilibrium (or ti...

This work presents a methodology for determining the interface between wetting and nonwetting phases inside a three-dimensional porous space, at a given equilibrium state. The work is limited to the study of mechanical equilibrium. The method is based on a three dimensional extension of the opening method from image analysis presented in [1] and applied on threedimensional stochastically recons...

We extend some relations between percolation and the dependence of Gibbs states on boundary conditions known for Ising ferromagnets to other systems and investigate their general validity: percolation is defined in terms of the agreement of a configuration with one of the ground states of the system. This extension is studied via examples and counterexamples, including the antiferromagnetic Isi...

A multi-scale scheme for the invasion percolation of rock fracture networks with heterogeneous fracture aperture fields is proposed. Inside fractures, fluid transport is calculated on the finest scale and found to be localized in channels as a consequence of the aperture field. The channel network is characterized and reduced to a vectorized artificial channel network (ACN). Different realizati...

During drainage, as a voxel of porous material is being actively invaded prior to percolation, the invading nonwetting fluid cannot be transmitted neighboring downstream until critical saturation (Snc) reached. This occurs when forms percolating path across voxel. We present novel laboratory observations gravitationally stable, air/water drainage in thin bead packs, with 2D fields monitored at ...

We investigate clogging in depth filtration, in which a dirty fluid is ‘‘cleaned’’ by the trapping of dirt particles within the pore space during flow through a porous medium. This leads to a self-generated gradient percolation process that exhibits a power-law distribution for the density of trapped particles at downstream distance x from the input. To achieve a nonpathological clogging ~perco...

We study the time constant for first-passage percolation, and the Vickery-Clarke-Groves (VCG) payment for the shortest path, on a width-2 strip with random edge costs. These statistics attempt to describe two seemingly unrelated phenomena, arising in physics and economics respectively: the first-passage percolation time predicts how long it takes for a fluid to spread through a random medium, w...

A phase diagram of argon based upon percolation transition loci determined from literature experimental p-V isotherms, and simulation values using a Lennard-Jones model shows three fluid phases. The liquid phase spans all temperatures, from a metastable amorphous ground state at 0 K, to ultra-high T. There is a supercritical mesophase bounded by percolation transition loci, and a gas phase. Int...

Recent developments in hydraulic fracturing (fracking) have enabled the recovery of large quantities of natural gas and oil from old, low-permeability shales. These developments include a change from low-volume, high-viscosity fluid injection to high-volume, low-viscosity injection. The injected fluid introduces distributed damage that provides fracture permeability for the extraction of the ga...