Viscous fingering with permeability heterogeneity

Tan, Changhui; Homsy, G. M.

doi:10.1063/1.858227

Cited by 112 publications

(71 citation statements)

References 8 publications

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“…6 and 4 shows that the preferred wavelength when ϭ0.01 is that imposed by the viscous instability, and that there is a favorable interaction between the layering and the tip spitting, leading to an increased growth rate, similar to that hypothesized by Tan and Homsy. 3 If the permeability field is now layered, but with a larger value of ϭ0.1 and n y ϭ8, we recover the channeling regime, as shown in Fig. 7.…”

Section: Viscously Unstable Large Systemsmentioning

confidence: 85%

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Viscous fingering in periodically heterogeneous porous media. II. Numerical simulations

Wit

Homsy

1997

The Journal of Chemical Physics

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We study nonlinear viscous fingering in heterogeneous media through direct numerical simulation. A pseudospectral method is developed and applied to our spatially periodic model introduced in Paper I ͓J. Chem. Phys. 107, 9609 ͑1997͔͒. The problem involves several parameters, including the Peclet number, Pe, the magnitude and wave numbers of the heterogeneity, , n x , n y , respectively, and the log of the viscosity ratio R. Progress is made by fixing R at 3.0 and then working first with layered systems n x ϭ0 and finally with ''checkerboard'' systems in which both wave numbers are nonzero. Strongly nonlinear finger dynamics are compared and contrasted with those occurring in the homogeneous case. For layered systems, it is found that very low levels of heterogeneity leads to an enhancement of the growth rate of the fingered zones, and that both harmonic and subharmonic resonances between the intrinsic scale of nonlinear fingering and those of the heterogeneity occur. We also find that the fingering regime of layered systems can be completely disrupted by modest levels of heterogeneity, leading to a ''channeling'' regime and dispersive behavior which is identified as a Taylor dispersion mechanism. The effective axial dispersion coefficient in this regime is found to be strongly dependent on the viscosity ratio. The situation becomes more complex for the checkerboard case. The channeling regime can in turn be disrupted by the axial dependence of the heterogeneity, which stimulates tip splitting and a return to complex nonlinear finger dynamics in regions of parameter space, including very large , that would otherwise be strongly dispersive. The effectiveness of the axial variation in stimulating tip splitting is studied by a short parametric study in n x , and is found to be maximized for certain axial frequencies in a manner similar to that found in Paper I. All our results are found to be in general qualitative agreement with available ͑but limited͒ experimental visualizations.

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Section: Viscously Unstable Large Systemsmentioning

confidence: 85%

“…2 as adapted to heterogeneous media in Ref. 3. It consists of a Fourier spectral method using periodic boundary conditions in both longitudinal and transverse directions.…”

Section: Methodsmentioning

confidence: 99%

Viscous fingering in periodically heterogeneous porous media. II. Numerical simulations

Wit

Homsy

1997

The Journal of Chemical Physics

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“…Because of the influence of such fingers on the physical and chemical processes, numerous studies have analyzed to what extent the fingering instability can be affected, for instance, by heterogeneities of the medium [7], the non-Newtonian character of flows [8], particle accretion [9], the presence of a magnetic field [10], etc.…”

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confidence: 99%

Fingering of Chemical Fronts in Porous Media

Wit

2001

Phys. Rev. Lett.

143

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The influence of chemical reactions on the hydrodynamical fingering instability is analyzed for miscible systems in porous media. Using a realistic reaction scheme, it is shown that the stability of chemical fronts towards density fingering crucially depends on the width and the speed of the front which are functions of chemical parameters. The major difference between the pure and chemically driven fingering is that, in the presence of chemical reactions, the dispersion curves do not vary in time which has important practical experimental consequences. Good agreement with recent experimental data is found.

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“…Effect of DP and spatial correlation of log permeability on water saturation profiles after injection of one pore volume into a randomly heterogeneous medium filled with oil at a viscosity ratio of 100 (after Khataniar and Peters, 1992). context of miscible displacement (e.g., Moissis 1988;Kelkar and Gupta, 1991;Tan and Homsy, 1991;Waggoner et al, 1992;Araktingi and Orr, 1993;Moissis et al, 1993;Tchelepi and Orr, 1993). As the present report focuses on immiscible displacement, these studies fall outside its scope and are not discussed.…”

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confidence: 99%