An overview of instability and fingering during immiscible fluid flow in porous and fractured media

Chen, G.; Neuman, Shlomo P.; Taniguchi, Masateru

doi:10.2172/93758

Cited by 14 publications

(11 citation statements)

References 80 publications

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“…Unstable interfaces between immiscible fluids in porous media have been reported in many field tests and laboratory experiments ͑e.g., Chen et al 1 ͒. The onset of instability can be understood in general terms within the context of theories developed for the immiscible displacement of one fluid by another in a Hele-Shaw cell ͑Saffman and Taylor 2 ͒ and in a macroscopically uniform porous medium ͑Chuoke et al 3 ͒; see Neuman and Chen 4 for a recent extension.…”

Section: Introductionmentioning

confidence: 99%

“…The onset of instability can be understood in general terms within the context of theories developed for the immiscible displacement of one fluid by another in a Hele-Shaw cell ͑Saffman and Taylor 2 ͒ and in a macroscopically uniform porous medium ͑Chuoke et al 3 ͒; see Neuman and Chen 4 for a recent extension. Extensive background material can be found in the relatively recent works of Chen et al, 1 Pelce, 5 and de Rooij. 6 In natural soils and rocks, the phenomenon of interface instability is strongly colored by systematic and random spatial variations in macroscopic medium properties.…”

Section: Introductionmentioning

confidence: 99%

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Immiscible front evolution in randomly heterogeneous porous media

2003

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The evolution of a sharp interface between two immiscible fluids in a randomly heterogeneous porous medium is investigated analytically using a stochastic moment approach. The displacing fluid is taken to be at constant saturation and to have a much larger viscosity than does the displaced fluid, which is therefore effectively static. Capillary pressure at the interface is related to porosity and permeability via the Leverett J-function. Whereas porosity is spatially uniform, permeability forms a spatially correlated random field. Displacement is governed by stochastic integro-differential equations defined over a three-dimensional domain bounded by a random interface. The equations are expanded and averaged in probability space to yield leading order recursive equations governing the ensemble mean and variance of interface position, rate of propagation and pressure gradient within the displacing fluid. Solutions are obtained for one-dimensional head-and flux-driven displacements in statistically homogeneous media and found to compare well with numerical Monte Carlo simulations. The manner in which medium heterogeneity affects the mean pressure gradient is indicative of how it impacts the stability of the mean interface. Capillary pressure at the interface is found to have a potentially important effect on its mean dynamics and stability.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Immiscible front evolution in randomly heterogeneous porous media

2003

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“…Chen et al, 1995]. The onset of instability can be understood in general terms within the context of linear theories developed for the im miscible displacement of one fluid by another in a Hele-Shaw cell [Saffman and Taylor, 1958] and in a macroscopically uniform porous medium [Chuoke et al, 1959]; see for a recent extension.…”

Section: Introductionmentioning

confidence: 99%

Wetting front evolution in randomly heterogeneous soils

Tartakovsky

Neuman

Tartakovsky

2002

Environmental Mechanics: Water, Mass and Energy Transfer in the Biosphere

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Philip [1975] was the first to investigate the stability of a wetting front in a stratified soil using rigorous hydrodynamic arguments. He based his analysis on the Green and Ampt [1911] model and treated permeability as a known function of depth. We adopt the same model to develop integro-differential equations for leading statistical moments of wetting front propagation in a three-dimensional, randomly heterogeneous soil. We solve these equations analytically for mean front position and mean pressure head gradient in one spatial dimension, to second order in the standard deviation of log conductiv ity. We do the same for second moments of front positions and pressure head gradient, which serve as measures of predictive uncertainty. To verify the ac curacy of our solution, we compare it with the results of numerical Monte Carlo simulations.

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“…When surface water infiltrates into this partially saturated vadose zone, it may spread laterally and/or propagate downward as a wetting front. Under some circumstances (discussed in a recent overview by Chen et al, 1995), the wetting front may become unstable and give rise to fingers that travel faster than would be anticipated on the basis of flat wetting front. This may cause water and dissolved contaminants from shallow depths to reach the water table faster than would otherwise be the case, therefore accelerating the degradation of subsurface water quality.…”

Section: Introductionmentioning

confidence: 99%

Wetting front instability and fingering in random permeability fields

Chen¹,

Neuman²,

Hills³

2000

Theory, Modeling, and Field Investigation in Hydrogeology: A Special Volume in Honor of Shlomo P. Neumans 60th Birthday

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Numerical simulations are used to investigate wetting front instability and finger evolution in the vertical plane during surface-water infiltration into a randomly heterogeneous soil. As is common in the literature, the natural log permeability of the soils is taken to be a random, multivariate Gaussian function of space. The mean (expectation) of this function is constant and its fluctuations about the mean are statistically homogeneous and isotropic with constant variance and autocorrelation scale. The wetting front is allowed to diffuse in accord with Richards' equation of flow in a partially saturated soil. The infiltrating water is labeled with a passive tracer, the 50% concentration contour of which is taken to indicate the position of the wetting front. The variogram of the contour is introduced to characterize the length and width of the fingers. Results show that whereas mean finger length grows at a nonlinear rate that diminishes monotonically with time, mean finger width remains constant in time. Both mean finger growth rate and mean finger width increase with the variances and correlation scale of permeability.

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An overview of instability and fingering during immiscible fluid flow in porous and fractured media

Cited by 14 publications

References 80 publications

Immiscible front evolution in randomly heterogeneous porous media

Immiscible front evolution in randomly heterogeneous porous media

Wetting front evolution in randomly heterogeneous soils

Wetting front instability and fingering in random permeability fields

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