Two-phase displacement in Hele-Shaw cells: experiments on viscously driven instabilities

Park, C.-W.; Gorell, Sheldon; Homsy, G. M.

doi:10.1017/s0022112084000847

Cited by 63 publications

(29 citation statements)

References 5 publications

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“…For small values of Ca, perform asymptotic expansions in order to determine the dominant wavelength. Their results, which were confirmed by the experiments of Park, Gorell & Homsy (1984), yield much larger wavelengths than found here. Subsequently, Maxworthy (1989) compiled experimental results by several authors for the dominant wavelength over a range of Ca (10 −3 < Ca < 30).…”

Section: Comparison With Results Obtained From Darcy's Lawsupporting

confidence: 90%

Miscible displacements in Hele-Shaw cells: two-dimensional base states and their linear stability

Goyal

Meiburg

2006

J. Fluid Mech.

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Miscible fingering in a Hele-Shaw cell is studied by means of Stokes simulations and linear stability analysis. The two-dimensional simulations of miscible displacements in a gap indicate the existence of a quasi-steady state near the tip of the displacement front for sufficiently large Péclet numbers and viscosity ratios, in agreement with earlier work by other authors. The front thickness of this quasi-steady state is seen to scale with Pe −1/2 , while it depends only weakly on the viscosity ratio. The nature of the viscosity-concentration relationship is found to have a significant influence on the quasi-steady state. For the exponential relationship employed throughout most of the investigation, we find that the tip velocity increases with Pe for small viscosity ratios, while it decreases with Pe for large ratios. In contrast, for a linear viscosityconcentration relationship the tip velocity is seen to increase with Pe for all viscosity ratios. The simulation results suggest that in the limit of high Pe and large viscosity contrast, the width and tip velocity of the displacement front asymptote to the same values as their immiscible counterparts in the limit of large capillary numbers.In a subsequent step, the stability of the quasi-steady front to spanwise perturbations is examined, based on the three-dimensional Stokes equations. For all values of Pe, the maximum growth rate is found to increase monotonically with the viscosity ratio. The influence of Pe on the growth of the instability is non-uniform. For mild viscosity contrasts, a larger Pe is found to be destabilizing, while for large viscosity contrasts an increase in Pe has a slightly stabilizing influence. A close inspection of the instability eigenfunction reveals the presence of two sets of counter-rotating roll-like structures, with axes aligned in the cross-gap and streamwise directions, respectively. The former lead to the periodic acceleration and deceleration of the front, while the latter result in the widening and narrowing of the front. These roll-like structures are aligned in such a way that the front widens where it speeds up, and narrows where it slows down. The findings from the present stability analysis are discussed and compared with their Darcy counterparts, as well as with experimental data by other authors for miscible and immiscible flows.

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Section: Comparison With Results Obtained From Darcy's Lawsupporting

confidence: 90%

Miscible displacements in Hele-Shaw cells: two-dimensional base states and their linear stability

Goyal

Meiburg

2006

J. Fluid Mech.

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“…This indicates that the capillary pressure is controlled by the interface curvature in the plane of the fracture. This result was already noticed in numerous studies of immiscible fluids displacement in a Hele Shaw cell (Bensimon et al 1986;Park et al 1984;Zhang et al 1998). We have seen, in the aperture field measurement section, that the correlation length of the aperture is of the same order of magnitude as the mean aperture.…”

Section: Finger Widthsupporting

confidence: 81%

“…This allows defining the conditions required to get fingering and to investigate the length scale of the fingers. A slight modification of the calculation of the capillary pressure was performed (Park et al 1984), giving a better agreement with the width of the fingers. Recent studies have shown that a quantitative analysis of fingering in a heterogeneous fracture is confronted to an indetermination of the capillary pressure.…”

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confidence: 99%

Experimental Study of Upward Oil Migration in a Fracture

Loggia

Luo

et al. 2009

Transp Porous Med

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International audienceThe upward oil migration in a transparent and rough fracture containing a liquid of higher density is studied experimentally using a light transmission technique. The aperture heterogeneity is also measured by light transmission. The injection of oil in a fracture containing a heavier fluid produces a gravitational fingering instability. Depending on the injection velocity (capillary number, Ca) and the density difference between the two fluids (Bond number, Bo), different patterns are observed during the oil displacements. The width of the finger and its velocity are measured as a function of Bo and Ca. A stability analysis of the interface, based on a generalised Darcy equation in a two-dimensional fracture, allows an accurate description of the experimental results. The order of magnitude of the finger width and its velocity are in good agreement with the calculations, with small disparities due to various unknown fluid flow parameters: capillary pressure, finger thickness in the gap of the fracture, finger tortuosity and oil velocity field into the finger. The theoretical approach allows constructing a (Ca, Bo) phase diagram of stability of the interface

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“…Since Hill (1952) reported his pioneering observation on viscous fingering phenomenon, this issue has been intensively studied by many researchers both experimentally and theoretically. As for experimental researches, the Hele-Shaw cell, which is composed of two closely spaced parallel plates, is often employed to investigate the similar fluid state in porous media due to the mathematical analogy of motions in both situations (Park et al 1984;Moore et al 2002;Toussaint et al 2005). Although Homsy pointed out that the analogy fails completely in the case of immiscible displacement because the forces associated with the propagation of the menisci through the pore space are not considered in Hele-Shaw geometry, the Hele-Shaw cell is of fundamental interest and still helpful for developing useful concepts (Zimmerman and Homsy 1991).…”

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confidence: 99%

LBM Simulation of Viscous Fingering Phenomenon in Immiscible Displacement of Two Fluids in Porous Media

Dong

Yan

2011

Transp Porous Med

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This article presents the lattice Boltzmann simulation of viscous fingering phenomenon in immiscible displacement of two fluids in porous media. Such phenomenon generally takes place when a less viscous fluid is used to displace a more viscous fluid, and it can be found in many industrial fields. Dimensionless quantities, such as capillary number, Bond number and viscosity ratio between displaced fluid and displacing fluid are introduced to illustrate the effects of capillary force, viscous force, and gravity on the fluid behaviour. The surface wettability, which has an impact on the finger pattern, is also considered in the simulation. The numerical procedure is validated against the experiment about viscous fingering in a Hele-Shaw cell. The displacement efficiency is investigated using the parameter, areal sweep efficiency. The present simulation shows an additional evidence to demonstrate that the lattice Boltzmann method is a useful method for simulating some multiphase flow problems in porous media.

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Two-phase displacement in Hele-Shaw cells: experiments on viscously driven instabilities

Cited by 63 publications

References 5 publications

Miscible displacements in Hele-Shaw cells: two-dimensional base states and their linear stability

Miscible displacements in Hele-Shaw cells: two-dimensional base states and their linear stability

Experimental Study of Upward Oil Migration in a Fracture

LBM Simulation of Viscous Fingering Phenomenon in Immiscible Displacement of Two Fluids in Porous Media

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