Related papers: How to share underground reservoirs
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…
We study how much water can be retained without leaking through boundaries when each unit square of a two-dimensional lattice is randomly assigned a block of unit bottom area but with different heights from zero to $n-1$. As more blocks are…
We study sequences of partitions of the unit interval into subintervals, starting from the trivial partition, in which each partition is obtained from the one before by splitting its subintervals in two, according to a given rule, and then…
The present work is aimed to find suitable exchange conditions for saturated fluid flow in a porous medium, when a fractal microstructure is embedded in the porous matrix. Two different deterministic models are introduced and rigorously…
Composite materials are often stronger than their constituents. We demonstrate this through a spring network model on a square lattice. Two different types of sites (A and B) are distributed randomly on the lattice, representing two…
Cohesive particles form agglomerates that are usually very porous. Their geometry, particularly their fractal dimension, depends on the agglomeration process (diffusion-limited or ballistic growth by adding single particles or…
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…
Blockage of pores by particles is found in many processes, including filtration and oil extraction. We present filtration experiments through a linear array of ten channels with one dimension which is sub-micron, through which a dilute…
This paper proposes a simple, generic and robust method to extract the grains from experimental tridimensionnal images of granular materials obtained by X-ray tomography. This extraction has two steps: segmentation and splitting. For the…
Porous materials made up of impermeable polyhedral grains constrain fluid flow to voids around the impenetrable constituent barrier particles. A percolation transition marks the boundary between assemblies of grains which contain system…
Fractional, anomalous diffusion in space-periodic potentials is investigated. The analytical solution for the effective, fractional diffusion coefficient in an arbitrary periodic potential is obtained in closed form in terms of two…
Motivated by recent experiments, we investigate the scattering properties of percolation clusters generated by numerical simulations on a three dimensional cubic lattice. Individual clusters of given size are shown to present a fractal…
For a spatial characteristic, there exist commonly fat-tail frequency distributions of fragment-size and -mass of glass, areas enclosed by city roads, and pore size/volume in random packings. In order to give a new analytical approach for…
Simulations of fluid flow in naturally fractured rocks have implications for several subsurface applications, including energy storage and extraction, and waste storage. We are interested in flow in discrete fracture networks, which…
We show that when a non-wetting fluid drains a stratified porous medium at sufficiently small capillary numbers Ca, it flows only through the coarsest stratum of the medium; by contrast, above a threshold Ca, the non-wetting fluid is also…
Many porous media are mixtures of inert and reactive materials, manifesting spatio-chemical heterogeneity. We study the evolution of scalar transport in a chemically heterogeneous material that mimics a green roof soil substrate,…
Information ratchets extract work from heat baths using low entropy information reservoirs. We find that the structure of the reservoirs affects both their performance and phase diagram. By deriving exact probabilities of recurrence in…
The change of the effective dimension of spacetime with the probed scale is a universal phenomenon shared by independent models of quantum gravity. Using tools of probability theory and multifractal geometry, we show how dimensional flow is…
The permeability of complex porous materials can be obtained via direct flow simulation, which provides the most accurate results, but is very computationally expensive. In particular, the simulation convergence time scales poorly as…
Predicting the permeability of porous media in saturated and partially saturated conditions is of crucial importance in many geo-engineering areas, from water resources to vadose zone hydrology or contaminant transport predictions. Many…