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Viscous fingering

About: Viscous fingering is a research topic. Over the lifetime, 1353 publications have been published within this topic receiving 37191 citations.


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Journal ArticleDOI
TL;DR: In this paper, it was shown that a flow is possible in which equally spaced fingers advance steadily at very slow speeds, such that behind the tips of the advancing fingers the widths of the two columns of fluid are equal.
Abstract: When a viscous fluid filling the voids in a porous medium is driven forwards by the pressure of another driving fluid, the interface between them is liable to be unstable if the driving fluid is the less viscous of the two. This condition occurs in oil fields. To describe the normal modes of small disturbances from a plane interface and their rate of growth, it is necessary to know, or to assume one knows, the conditions which must be satisfied at the interface. The simplest assumption, that the fluids remain completely separated along a definite interface, leads to formulae which are analogous to known expressions developed by scientists working in the oil industry, and also analogous to expressions representing the instability of accelerated interfaces between fluids of different densities. In the latter case the instability develops into round-ended fingers of less dense fluid penetrating into the more dense one. Experiments in which a viscous fluid confined between closely spaced parallel sheets of glass, a Hele-Shaw cell, is driven out by a less viscous one reveal a similar state. The motion in a Hele-Shaw cell is mathematically analogous to two-dimensional flow in a porous medium. Analysis which assumes continuity of pressure through the interface shows that a flow is possible in which equally spaced fingers advance steadily. The ratio λ = (width of finger)/(spacing of fingers) appears as the parameter in a singly infinite set of such motions, all of which appear equally possible. Experiments in which various fluids were forced into a narrow Hele-Shaw cell showed that single fingers can be produced, and that unless the flow is very slow λ = (width of finger)/(width of channel) is close to , so that behind the tips of the advancing fingers the widths of the two columns of fluid are equal. When λ = 1/2 the calculated form of the fingers is very close to that which is registered photographically in the Hele-Shaw cell, but at very slow speeds where the measured value of λ increased from 1/2 to the limit 1.0 as the speed decreased to zero, there were considerable differences. Assuming that these might be due to surface tension, experiments were made in which a fluid of small viscosity, air or water, displaced a much more viscous oil. It is to be expected in that case that λ would be a function of μU/T only, where μ is the viscosity, U the speed of advance and T the interfacial tension. This was verified using air as the less viscous fluid penetrating two oils of viscosities 0.30 and 4.5 poises.

2,634 citations

Journal ArticleDOI
TL;DR: Mecanisme de digitation visqueuse. as discussed by the authors : Deplacements non miscibles en cellules de Hele Shaw. Butteau et al. describe a set of ecoulements in a cellule.
Abstract: Mecanisme de digitation visqueuse. Ecoulements de Hele Shaw. Deplacements non miscibles en cellules de Hele Shaw

1,430 citations

Journal ArticleDOI
TL;DR: In this paper, the authors present the results of network simulators (100 × 100 and 25 × 25 pores) based on the physical rules of the displacement at the pore scale, and they show the existence of the three basic domains (capillary fingering, viscous fingering and stable displacement) within which the patterns remain unchanged.
Abstract: Immiscible displacements in porous media with both capillary and viscous effects can be characterized by two dimensionless numbers, the capillary number C, which is the ratio of viscous forces to capillary forces, and the ratio M of the two viscosities. For certain values of these numbers, either viscous or capillary forces dominate and displacement takes one of the basic forms: (a) viscous fingering, (b) capillary fingering or (c) stable displacement. We present a study in the simple case of injection of a non-wetting fluid into a two-dimensional porous medium made of interconnected capillaries. The first part of this paper presents the results of network simulators (100 × 100 and 25 × 25 pores) based on the physical rules of the displacement at the pore scale. The second part describes a series of experiments performed in transparent etched networks. Both the computer simulations and the experiments cover a range of several decades in C and M. They clearly show the existence of the three basic domains (capillary fingering, viscous fingering and stable displacement) within which the patterns remain unchanged. The domains of validity of the three different basic mechanisms are mapped onto the plane with axes C and M, and this mapping represents the ‘phase-diagram’ for drainage. In the final section we present three statistical models (percolation, diffusion-limited aggregation (DLA) and anti-DLA) which can be used for describing the three ‘basic’ domains of the phase-diagram.

1,378 citations

Book
22 Feb 1995
TL;DR: In this paper, the authors present a review of the history of percolation processes in porous media and fracture models of porous media, including a brief overview of the current state of the art.
Abstract: Part 1 Continuum versus discrete models: a hierarchy of heterogeneities and length scales long-range correlations, fractals and percolation continuum versus discrete models. Part 2 The equations of change: the equation of continuity the momentum equation the diffusion and convective-diffusion equations. Part 3 Fractal concepts and percolation theory: box-counting method and self-similar fractals self-affine fractals multifractal systems fractional Brownian motion and long-range correlations percolation processes a glance at history. Part 3 Diagenetic processes and formation of rock: diagenetic and metasomatic processes continuum models of diagenetic processes geometrical models of diagenetic processes in granular rock a geometrical model of carbonate rock diagenetic processes of fractured rock. Part 5 Morphology of porous media and fractured rock: porosity, specific surface area and tortuosity fluid saturation, capillary pressure and contact angle pore size distribution topological properties of porous media fractal properties of porous media porosity and pore size distribution of fractal porous media morphology of fractured rocks. Part 6 Models of porous media: models of macroscopic porous media models of pore surface roughness models of megascopic porous media interpolation schemes and conditional simulation. Part 7 Models of fractured rock: continuum approach - the multi-porosity models network models simulated annealing model synthetic fractal models mechanical fracture models. Part 8 Flow and transport in porous media: the volume-averaging method and derivation of Darcy's law the Brinkman and Forchheimer equations predicting the permeability, conductivity and diffusivity fractal transport and non-local formulation of diffusion derivation of Archie's law relation between permeability and electrical conductivity relation between permeability and nuclear magnetic resonance dynamic permeability. Part 9 Dispersion in porous media: the phenomenon of dispersion mechanisms of dispersion processes the convective-diffusion equation measurement of dispersion coefficients dispersion in simple systems dependence of dispersion coefficients on the Peclet number models of dispersion in macroscopic porous media long-time tails - dead-end pores versus disorder dispersion in short porous media dispersion in porous media with percolation disorder dispersion in megascopic porous media dispersion in stratified porous media. Part 10 Flow and dispersion in fractured rock: flow in a single fracture - continuum and discrete models flow in fractured rock dispersion in a single fracture dispersion in fractured rock. Part 11 Miscible displacements: factors affecting miscible displacement processes viscous fingering continuum models of miscible displacements in Hele-Shaw cells continuum models of miscible displacements in porous media. (Part contents).

788 citations

Journal ArticleDOI
08 Feb 1990-Nature
TL;DR: In this paper, the interplay between the macroscopic driving force associated with the phase transition and the microscopic interfacial dynamics was studied, leading to complex patterns which are generically similar to those found in viscous fingering, aggregation and electrochemical deposition.
Abstract: Crystal growth under non-equilibrium conditions can give rise to complex patterns which are generically similar to those found in processes such as viscous fingering, aggregation and electrochemical deposition. Recent theoretical understanding focuses on the interplay between the macroscopic driving force associated with the phase transition and the microscopic interfacial dynamics.

652 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202380
2022124
202162
202074
201969
201870