Hydrofracture in various contexts:
In a saturated porous medium, large fluid sources can create pressure gradients overcoming the cohesive forces between the solid elements and hydrofracture the matrix, i.e. modify its structure irreversibly. Depending on the nature of the intersticial fluid, nature of the cohesive forces and geometry and intensity of the source, different patterns are so created.
Pattern formation during air injection in a granular material confined in a Hele-Shaw cell.
A granular material confined in thin layers is naturally stable due to the friction forces that can be mobilized along the confining structure. Central injection of fluid can create paths of high permeability.
|Stable displacement pattern obtained after 1s in a 20 cm size region around the injection point (P=0.05 Atm)|
The pattern formation due to fluid/grain interactions during air injection at low Reynolds number in a granular layer is investigated. Spherical glass beads of diameters ranging from 70 to 100 microns are stacked under gravity in a vertical Hele-Shaw cell, consisting of two circular plates of metric diameter and fixed 1 mm width. Air is next injected in the center of the horizontaly placed cell, with open side boundaries and a central pressure maintained constant to a few percents of the atmospheric one.
The resulting patterns develop in a few seconds, and exhibit typically after the growth of a central region empty of grains, wide radial branching fingers. As these grow, grains are rearranged in a more compacted configuration around them, over some growing depth as the fingers advance. When the mobilized friction against the confining plates in this compacted region balances the drag from the fluid, these radial fingers stop growing, and quasi circular wide fingers can form, starting from the tip of the first ones - see figure. These large circular fingers can be prolongated by very localized displacement structures (fine fracture-like fingers). At higher injection pressures, the outer compacted region can be progressively rearranged and evacuated, and a single finger eventually breaks through from the central structure. Various patterns are observed as function of the central pressure, granulometry of the material, and the friction coupling with the confining plates.
|1 cm large cell, 2D particles around 100 microns diam. Pcenter=0.1 Atm. Color code on the particles proportional to local coarse grained permeability (blue: dense packed, green, loose packed, white: background value)|
These patterns are also investigated with numerical simulations based on a quasi 2D coupled fluid/grain flow model. This model is based on a Darcy law for the dynamics of the fluid component, whose inertia is neglected compared to the one of the solid phase. The permeability is obtained from the local porosity, coarse grained over a few grains, through a Carman-Cozeny relation. The particles follow a molecular dynamics scheme, driven by central elastic interactions, pressure gradient from the fluid, and a friction term exerted by the confining plates, the out-of-plane stresses being determined by a Janssen hypothesis, i.e. are assumed proportional to the in-plane stresses. Two stages of such a simulation are displayed in the above figure.
that link for an animation.
Fragmentation of a solid under the effect of an extended fluid source
We have started preliminary experiments and simulations of hydrofracture in a different context (different fluid and interaction potentials between the solid elements of the porous material): Using nonmagnetic microspheres in a ferrofluid layer, submitted to an external oscillating conic magnetic field, crystals of spheres can be grown, with a tunable equilibrium distance between particles - click here about the basic theory on the effective interaction potentials in these systems. When this equilibrium distance is suddenly tuned to smaller values, the intersticial fluid needs to escape, and the induced overpressure leadss to fragmentation of the solid. - see figure. This situation is analogous to a system where the interaction potentials between the solid elements would be fixed, as a fluid is homogeneously produced in the entire system.
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