Related papers: Loopless non-trapping invasion percolation model f…
Hydraulic fracturing (fracking) using high pressures and a low viscosity fluid allow the extraction of large quantiles of oil and gas from very low permeability shale formations. The initial production of oil and gas at depth leads to high…
Injections of large volumes of water into tight shale reservoirs allows the extraction of oil and gas not previously accessible. This large volume "super" fracking induces damage that allows the oil and/or gas to flow to an extraction well.…
We investigate the process of invasion percolation between two sites (injection and extraction sites) separated by a distance r in two-dimensional lattices of size L. Our results for the non-trapping invasion percolation model indicate that…
While the hydraulic fracturing technology, aka fracking (or fraccing, frac), has become highly developed and astonishingly successful, a consistent formulation of the associated fracture mechanics that would not conflict with some…
Experimental two-phase invasion percolation flow patterns were observed in hydrophobic micro-porous networks designed to model fuel cell specific porous media. In order to mimic the operational conditions encountered in the porous…
Loss of circulation while drilling is a challenging problem that may interrupt operations, reduce efficiency, and may contaminate the subsurface. When a drilled borehole intercepts conductive faults or fractures, lost circulation manifests…
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…
The main purpose of this work is to simulate two-phase flow in the form of immiscible displacement through anisotropic, three-dimensional (3D) discrete fracture networks (DFN). The considered DFNs are artificially generated, based on a…
Modeling important engineering problems related to flow-induced damage (in the context of hydraulic fracturing among others) depends critically on characterizing the interaction of porous media and interstitial fluid flow. This work…
A new kind of invasion percolation is introduced in order to take into account the inertia of the invader fluid. The inertia strength is controlled by the number N of pores (or steps) invaded after the perimeter rupture. The new model…
The fractal dimension of minimal spanning trees on percolation clusters is estimated for dimensions $d$ up to $d=5$. A robust analysis technique is developed for correlated data, as seen in such trees. This should be a robust method…
We present a loop-opening model that accounts for the molecular details of the intrinsic fracture energy for fracturing polymer networks. This model includes not only the energy released from the scission of bridging chains but also the…
We have simulated a one dimensional capillary fiber bundle model with fracking events while acted between a pressure gradient across the system. The hydraulic fractures are incorporated through a decreasing nature of capillary thresholds…
Invasion bond percolation (IBP) is mapped exactly into Prim's algorithm for finding the shortest spanning tree of a weighted random graph. Exploring this mapping, which is valid for arbitrary dimensions and lattices, we introduce a new IBP…
Percolation phenomena are pervasive in nature, ranging from capillary flow, crack propagation, ionic transport, fluid permeation, etc. Modeling percolation in highly-branched media requires the use of numerical solutions, as problems can…
In this work, we consider compressible single-phase flow problems in a porous media containing a fracture. In the latter, a non-linear pressure-velocity relation is prescribed. Using a non-overlapping domain decomposition procedure, we…
Extending the Schramm--Loewner Evolution (SLE) to model branching structures while preserving conformal invariance and other stochastic properties remains a formidable research challenge. Unlike simple paths, branching structures, or trees,…
The random-cluster model, a correlated bond percolation model, unifies a range of important models of statistical mechanics in one description, including independent bond percolation, the Potts model and uniform spanning trees. By…
In this paper, we extend the reinterpreted discrete fracture model for flow simulation of fractured porous media containing flow blocking barriers on non-conforming meshes. The methodology of the approach is to modify the traditional…
Through this research, embedded synthetic fracture networks in rock masses are studied. To analysis the fluid flow complexity in fracture networks with respect to the variation of connectivity patterns, two different approaches are…