Interface evolution during radial miscible viscous fingering

Chui, J.; Anna, Pietro de; Juanes, Rubén

doi:10.1103/physreve.92.041003

Cited by 30 publications

(18 citation statements)

References 72 publications

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“…Note that the propagation of multiple water fingers can also be observed in a smooth‐walled fracture (Hele‐Shaw cell) under the conditions of the limit of zero interfacial tension [ Bischofberger et al ., ; Chui et al ., ], i.e., the absence of capillary force. In this case, the number of fingers increases with the injection rate Q regardless of the viscosity ratio [ Chui et al ., ], which is consistent with our experimental observations (see Figures a, e, and i). Finally, the mean water‐filled aperture is smaller than that in the capillary fingering regime, which is clearly illustrated in Figures and .…”

Section: Resultsmentioning

confidence: 99%

Visualizing and quantifying the crossover from capillary fingering to viscous fingering in a rough fracture

Chen

Fang

et al. 2017

Water Resources Research

122

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Immiscible fluid‐fluid displacement in permeable media is important in many subsurface processes, including enhanced oil recovery and geological CO2 sequestration. Controlled by capillary and viscous forces, displacement patterns of one fluid displacing another more viscous one exhibit capillary and viscous fingering, and crossover between the two. Although extensive studies investigated viscous and capillary fingering in porous media, a few studies focused on the crossover in rough fractures, and how viscous and capillary forces affect the crossover remains unclear. Using a transparent fracture‐visualization system, we studied how the two forces impact the crossover in a horizontal rough fracture. Drainage experiments of water displacing oil were conducted at seven flow rates (capillary number log10Ca ranging from −7.07 to −3.07) and four viscosity ratios (M=1/1000,1/500,1/100 and 1/50). We consistently observed lower invading fluid saturations in the crossover zone. We also proposed a phase diagram for the displacement patterns in a rough fracture that is consistent with similar studies in porous media. Based on real‐time imaging and statistical analysis of the invasion morphology, we showed that the competition between capillary and viscous forces is responsible for the saturation reduction in the crossover zone. In this zone, finger propagation toward the outlet (characteristic of viscous fingering) as well as void‐filling in the transverse/backward directions (characteristic of capillary fingering), are both suppressed. Therefore, the invading fluid tends to occupy larger apertures with higher characteristic front velocity, promoting void‐filling toward the outlet with thinner finger growth and resulting in a larger volume of defending fluid left behind.

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Section: Resultsmentioning

confidence: 99%

Visualizing and quantifying the crossover from capillary fingering to viscous fingering in a rough fracture

Chen

Fang

et al. 2017

Water Resources Research

122

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“…For their experiments on miscible rectilinear flow through a relatively wide gap, Snyder and Tait (1998) argued that λ/b was insensitive to mobility ratio and that 1 λ/b 3. Chui et al (2015) suggest that there are two regimes for the evolution of the fluid-fluid interface. At early times, interface length increases linearly with time, which is typical of the Saffman-Taylor instability.…”

Section: Saffman-taylor Instabilitymentioning

confidence: 99%

Radial viscous fingering of hot asthenosphere within the Icelandic plume beneath the North Atlantic Ocean

Schoonman

White

Pritchard³

2017

Earth and Planetary Science Letters

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The Icelandic mantle plume has had a significant influence on the geologic and oceanographic evolution of the North Atlantic Ocean during Cenozoic times. Full-waveform tomographic imaging of this region shows that the planform of this plume has a complex irregular shape with significant shear wave velocity anomalies lying beneath the lithospheric plates at a depth of 100–200 km. The distribution of these anomalies suggests that about five horizontal fingers extend radially beneath the fringing continental margins. The best-imaged fingers lie beneath the British Isles and beneath western Norway where significant departures from crustal isostatic equilibrium have been measured. Here, we propose that these radial fingers are generated by a phenomenon known as the Saffman-Taylor instability. Experimental and theoretical analyses show that fingering occurs when a less viscous fluid is injected into a more viscous fluid. In radial, miscible fingering, the wavelength and number of fingers are controlled by the mobility ratio (i.e. the ratio of viscosities), by the Péclet number (i.e. the ratio of advective and diffusive transport rates), and by the thickness of the horizontal layer into which fluid is injected. We combine shear wave velocity estimates with residual depth measurements around the Atlantic margins to estimate the planform distribution of temperature and viscosity within a horizontal asthenospheric layer beneath the lithospheric plate. Our estimates suggest thathe mobility ratio is at least 20–50, that the Péclet number is Ο(104), and that the asthenospheric channel is 100 ± 20 km thick. The existence and planform of fingering is consistent with experimental observations and with theoretical arguments. A useful rule of thumb is that the wavelength of fingering is 5 ± 1 times the thickness of the horizontal layer. Our proposal has been further tested by examining plumes of different vigor and planform (e.g. Hawaii, Cape Verde, Yellowstone). Our results support the notion that dynamic to pography of the Earth’s surface can be influenced by fast, irregular horizontal flow within thin, but rapidly evolving, asthenospheric fingers

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“…Zimmerman & Homsy (1992) similarly suggested that the asymptotic behaviour may include multiple steadily propagating fingers under the assumption that tip splitting may balance the upwards cascade in the scale of the fingers, but were unable to extend their numerical simulations to a final state. In experiments in a radial geometry, Chui et al (2015) showed a transition in finger growth from a scaling with t to one with t 1 2 corresponding to the shutdown of the instability. However, the ultimate fate and final form of the fingers remains unclear.…”

Section: Introductionmentioning

confidence: 99%

The dynamics of miscible viscous fingering from onset to shutdown

2018

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We examine the full ‘life cycle’ of miscible viscous fingering from onset to shutdown with the aid of high-resolution numerical simulations. We study the injection of one fluid into a planar two-dimensional porous medium containing another, more viscous fluid. We find that the dynamics are distinguished by three regimes: an early-time linearly unstable regime, an intermediate-time nonlinear regime and a late-time single-finger exchange-flow regime. In the first regime, the flow can be linearly unstable to perturbations that grow exponentially. We identify, using linear stability theory and numerical simulations, a critical Péclet number below which the flow remains stable for all times. In the second regime, the flow is dominated by the nonlinear coalescence of fingers which form a mixing zone in which we observe that the convective mixing rate, characterized by a convective Nusselt number, exhibits power-law growth. In this second regime we derive a model for the transversely averaged concentration which shows good agreement with our numerical experiments and extends previous empirical models. Finally, we identify a new final exchange-flow regime in which a pair of counter-propagating diffusive fingers slow exponentially. We derive an analytic solution for this single-finger state which agrees well with numerical simulations. We demonstrate that the flow always evolves to this regime, irrespective of the viscosity ratio and Péclet number, in contrast to previous suggestions.

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Interface evolution during radial miscible viscous fingering

Cited by 30 publications

References 72 publications

Visualizing and quantifying the crossover from capillary fingering to viscous fingering in a rough fracture

Visualizing and quantifying the crossover from capillary fingering to viscous fingering in a rough fracture

Radial viscous fingering of hot asthenosphere within the Icelandic plume beneath the North Atlantic Ocean

The dynamics of miscible viscous fingering from onset to shutdown

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