Size invariance of the granular Rayleigh-Taylor instability

Vinningland, Jan Ludvig; Johnsen, Øistein; Flekkøy, Eirik Grude; Toussaint, Renaud; Måløy, Knut Jørgen

doi:10.1103/physreve.81.041308

Cited by 23 publications

(24 citation statements)

References 14 publications

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“…Granular fingering instabilities have also been studied in closed vertical cells, where gravity drives the flow as heavier beads fall down from a granular layer at the top of a lighter fluid layer [48][49][50][51][52][53]. When the beads detach at the front, they form fingers of falling granular material surrounding fingerlike bubbles of rising fluid.…”

Section: Introductionmentioning

confidence: 99%

Pneumatic fractures in confined granular media

et al. 2017

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We perform experiments where air is injected at a constant overpressure P in , ranging from 5 to 250 kPa, into a dry granular medium confined within a horizontal linear Hele-Shaw cell. The setup allows us to explore compacted configurations by preventing decompaction at the outer boundary, i.e., the cell outlet has a semipermeable filter such that beads are stopped while air can pass. We study the emerging patterns and dynamic growth of channels in the granular media due to fluid flow, by analyzing images captured with a high speed camera (1000 images/s). We identify four qualitatively different flow regimes, depending on the imposed overpressure, ranging from no channel formation for P in below 10 kPa, to large thick channels formed by erosion and fingers merging for high P in around 200 kPa. The flow regimes where channels form are characterized by typical finger thickness, final depth into the medium, and growth dynamics. The shape of the finger tips during growth is studied by looking at the finger width w as function of distance d from the tip. The tip profile is found to follow w(d) ∝ d β , where β = 0.68 is a typical value for all experiments, also over time. This indicates a singularity in the curvaturee., more rounded tips rather than pointy cusps, as they would be for the case β > 1. For increasing P in , the channels generally grow faster and deeper into the medium. We show that the channel length along the flow direction has a linear growth with time initially, followed by a power-law decay of growth velocity with time as the channel approaches its final length. A closer look reveals that the initial growth velocity v 0 is found to scale with injection pressure as v 0 ∝ P 3 2 in , while at a critical time t c there is a cross-over to the behavior v(t) ∝ t −α , where α is close to 2.5 for all experiments. Finally, we explore the fractal dimension of the fully developed patterns. For example, for patterns resulting from intermediate P in around 100-150 kPa, we find that the box-counting dimensions lie within the range D B ∈ [1.53,1.62], similar to viscous fingering fractals in porous media.

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Section: Introductionmentioning

confidence: 99%

Pneumatic fractures in confined granular media

et al. 2017

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“…Johnsen et al worked on the coupled behavior by air injection into the porous material both in fluid saturated and non-saturated cases to study multiphase flow numerically and experimentally [23,25,26]. Aero-granular coupling in a free falling porous medium in a vertical Hele-Shaw cell was studied numerically and experimentally by Vinningland et al [27][28][29]. Varas et al conducted experiments of air injection into the saturated porous media in a Hele-Shaw cell [30,31] and in a cylinder box [32].…”

Section: Introductionmentioning

confidence: 99%

Bridging aero-fracture evolution with the characteristics of the acoustic emissions in a porous medium

et al. 2015

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The characterization and understanding of rock deformation processes due to fluid flow is a challenging problem with numerous applications. The signature of this problem can be found in Earth Science and Physics, notably with applications in natural hazard understanding, mitigation or forecast (e.g., earthquakes, landslides with hydrological control, volcanic eruptions), or in industrial applications such as hydraulic-fracturing, steam-assisted gravity drainage, CO 2 sequestration operations or soil remediation. Here, we investigate the link between the visual deformation and the mechanical wave signals generated due to fluid injection into porous medium. In a rectangular Hele-Shaw Cell, side air injection causes burst movement and compaction of grains along with channeling (creation of high permeability channels empty of grains). During the initial compaction and emergence of the main channel, the hydraulic fracturing in the medium generates a large non-impulsive low frequency signal in the frequency range 100 Hz-10 kHz. When the channel network is established, the relaxation of the surrounding medium causes impulsive aftershock-like events, with high frequency (above 10 kHz) acoustic emissions, the rate of which follows an Omori Law. These signals and observations are comparable to seismicity induced by fluid injection. Compared to the data obtained during hydraulic fracturing operations, low frequency seismicity with evolving spectral characteristics have also been observed. An Omori-like decay of microearthquake rates is also often observed after injection shut-in, with a similar exponent p ≈ 0.5 as observed here, where the decay rate of aftershock follows a scaling law dN/dt ∝ (t − t 0 ) −p . The physical basis for this modified Omori law is explained by pore pressure diffusion affecting the stress relaxation.

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“…In this way the hydrodynamics evolve 5 intrinsically with irreversible micro deformation in a solid matrix through the use of the Kozeny- 6 Carman porosity-permeability relation. The solution procedure adopted for this coupled problem is based on the same basic 9 principles that were successfully used in simulations to model instabilities in fluid filled granular grains falling in a gas [J. L. Vinningland et al, , 2007bVinningland et al, , 2009aVinningland et al, , 2009bVinningland et al, , 2010, or a fluid 13 [Niebling et al, 2010a[Niebling et al, , 2010bVinningland et al, 2012], and in situations of aerofracturing, i.e. 14 injection of gas in granular media [Niebling et al, 2012a[Niebling et al, , 2012b.…”

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Dynamic Development of Hydrofracture

Ghani

Koehn

Toussaint

et al. 2013

Pure Appl. Geophys.

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23Many natural examples of complex joint and vein networks in layered sedimentary rocks are 1 hydro-fractures that form by a combination of pore fluid overpressure and tectonic stresses. In 2 this paper, a two-dimensional hybrid hydro-mechanical formulation is proposed to model the Darcy based pore-pressure diffusion as continuum description for the fluid. This combination 6 yields a porosity controlled coupling between an evolving fracture network and the associated 7 hydraulic field. The model is tested on some basic cases of hydro-driven fracturing commonly 8 found in nature i.e., fracturing due to local fluid overpressure in rocks subjected to hydrostatic 9 and nonhydrostatic tectonic loadings. In our models we find that seepage forces created by 10 hydraulic pressure gradients together with poroelastic feedback upon discrete fracturing play a 11 significant role in subsurface rock deformation. These forces manipulate the growth and [Fyfe et al., 1978]. A number of fluid expansion mechanisms e.g., The mechanism of hydrofracturing has great implications in the interpretation of field 21 observations and for the prediction of natural or industrial problems in a broad range of research 22 disciplines. After pioneering work of [Hubbert and Willis, 1957;Hubbert and Rubey, 1959] 23 which explored pore fluid pressure as an important factor for small scale hydrofracturing in 1 tectonic processes, significant efforts have been made in the development of theoretical 2 fundamentals [Biot et al., 1986; J M Cleary and Illinois State Geological Survey., 1958; 3 Daneshy, 1973;Secor, 1965;Valkó and Economides, 1995]. Apart from theoretical aspects, a 4 significant amount of analytical and numerical solutions have also been put forward by many 5 investigators to address this coupled process in a qualitative and quantitative manner [M P 6 Cleary and Wong, 1985;Flekkøy et al., 2002;Gordeyev and Zazovsky, 1992;Meyer, 1986; 7 Tzschichholz et al., 1994;Yu.N, 1993]. 15Some porosity controlled models [Boone and Ingraffea, 1990;Flekkøy et al., 2002; Mourgues 16 and Cobbold, 2003;Olson et al., 2009;Wangen, 2002] revealed that the potential response of 17 inherent poroelastic mechanics is an important parameter in hydro-driven rock failure, where the 18 seepage forces caused by pore pressure gradients [Engelder and Lacazette, 1990;Rozhko, 2010; 19 Rozhko et al., 2007] in porous rocks affect the driving stress for fracture initiation and growth. 20Regardless of the underlying driving agent hydrofracturing is a complex process which 21 incorporates the dynamic coupling of at least three sub-processes [Adachi et al., 2007]; 1) 22Restructuring of rock skeleton upon elastic/in-elastic strain. 2) Corresponding alteration of both 23

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Size invariance of the granular Rayleigh-Taylor instability

Cited by 23 publications

References 14 publications

Pneumatic fractures in confined granular media

Pneumatic fractures in confined granular media

Bridging aero-fracture evolution with the characteristics of the acoustic emissions in a porous medium

Dynamic Development of Hydrofracture

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