Nonlinear viscous fingering in miscible displacement with anisotropic dispersion

Zimmerman, William B.; Homsy, G. M.

doi:10.1063/1.857916

Cited by 192 publications

(145 citation statements)

References 22 publications

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“…After an initial growth in ͱt due to dispersive mixing of the two fluids, a linear growth follows as soon as fingering with several fingers sets in. 45 In narrow systems, if only one or two fingers remain present, the motion of tip and rear can depart from such a linear growth because of transverse diffusion 35,51 as seen in Fig. 6.…”

Section: B Position Of the Tip And Rear Of The Fingered Zonementioning

confidence: 99%

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Miscible density fingering of chemical fronts in porous media: Nonlinear simulations

Wit

2004

Physics of Fluids

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Nonlinear interactions between chemical reactions and Rayleigh-Taylor type density fingering are studied in porous media or thin Hele-Shaw cells by direct numerical simulations of Darcy's law coupled to the evolution equation for the concentration of a chemically reacting solute controlling the density of miscible solutions. In absence of flow, the reaction-diffusion system features stable planar fronts traveling with a given constant speed v and width w. When the reactant and product solutions have different densities, such fronts are buoyantly unstable if the heavier solution lies on top of the lighter one in the gravity field. Density fingering is then observed. We study the nonlinear dynamics of such fingering for a given model chemical system, the iodate-arsenious acid reaction. Chemical reactions profoundly affect the density fingering leading to changes in the characteristic wavelength of the pattern at early time and more rapid coarsening in the nonlinear regime. The nonlinear dynamics of the system is studied as a function of the three relevant parameters of the model, i.e., the dimensionless width of the system expressed as a Rayleigh number Ra, the Damköhler number Da, and a chemical parameter d which is a function of kinetic constants and chemical concentration, these two last parameters controlling the speed v and width w of the stable planar front. For small Ra, the asymptotic nonlinear dynamics of the fingering in the presence of chemical reactions is one single finger of stationary shape traveling with constant nonlinear speed VϾv and mixing zone WϾw. This is drastically different from pure density fingering for which fingers elongate monotonically in time. The asymptotic finger has axial and transverse averaged profiles that are self-similar in unit lengths scaled by Ra. Moreover, we find that W/Ra scales as Da Ϫ0.5 . For larger Ra, tip splittings are observed.

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Section: B Position Of the Tip And Rear Of The Fingered Zonementioning

confidence: 99%

“…Such characterization of the nonlinear dynamics of miscible fingering has been performed in numerous articles devoted to pure viscous and density fingering. [33][34][35][36][37][38][39] It is of interest to have a quantitative idea on how chemical reactions can change such nonlinear properties of the fingers.…”

Section: Introductionmentioning

confidence: 99%

Miscible density fingering of chemical fronts in porous media: Nonlinear simulations

Wit

2004

Physics of Fluids

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“…In order to obtain high accuracy with the spectral method, in the streamwise direction, a periodic extension of the displacement front at Pe/4 is added. [9,32] Under the unfavourable mobility ratio, VF only presents at the left interface, while the right interface is always stable and does not affect the propagation of VF before the two interfaces interact. This method was proved to be very effective in dealing with such boundary conditions.…”

Section: Numerical Techniquesmentioning

confidence: 99%

Investigation of concentration‐dependent diffusion on frontal instabilities and mass transfer in homogeneous porous media

et al. 2017

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Mass transfer plays an important role in influencing the efficiency of miscible displacements in solvent-based processes in enhanced oil recovery. The mass transfer rate because of the pure molecular diffusion is very slow. However, this process can be greatly enhanced by the appearance of frontal instabilities called viscous fingering mechanisms, which are beneficial for improving the mixing and mass transfer between the injected solvent and oil. Instead of a piston-like displacement, the interface between solvent and oil is very convoluted with intricate finger-like patterns of the less viscous solvent intruding into the highly viscous oil. This intrusion significantly increases the surface area of contact of the two fluids and leads to more efficient mass transfer and mixing. Experimental measurements on the diffusion coefficients of two miscible fluids indicate that, instead of a constant diffusion coefficient (CDC), a concentration-dependent diffusion coefficient (CDDC) is more realistic. In the present study, a CDDC relation in which the diffusion coefficient is exponentially proportional to concentration is adopted. Its effect on the development of frontal instabilities is examined through highly accurate nonlinear numerical simulations. The differences between the CDDC case and the widely assumed CDC case are discussed. Furthermore, the enhancement of frontal instabilities on mass transfer when the CDDC is considered is investigated at various mobility ratios and Peclet numbers. The special characteristics for the CDDC case indicate its important role in miscible displacements. Eventually, the relation of breakthrough time to parameters is correlated to accurately predict the breakthrough time in any CDDC scenario.

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“…Its wide applicabilities, e.g., enhanced oil recovery [1], CO 2 sequestration [2], chromatographic separation [3,4], contaminant transport in aquifers [5], mixing in low-Reynolds number flow [6], intrinsic characteristics of nonlinear dynamics and pattern formation have fascinated active theoretical, numerical [6][7][8][9][10][11][12][13], and experimental [14] researchers for more than half a decade. Both rectilinear and radial displacements have been investigated rigorously and have their own significance that can be investigated independently as well as comparatively.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a Highly Viscous Circular Blob in Homogeneous Porous Media

Sharma

Pramanik

Mishra

2017

Fluids

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Viscous fingering is ubiquitous in miscible displacements in porous media, in particular, oil recovery, contaminant transport in aquifers, chromatography separation, and geological CO 2 sequestration. The viscosity contrasts between heavy oil and water is several orders of magnitude larger than typical viscosity contrasts considered in the majority of the literature. We use the finite element method (FEM)-based COMSOL Multiphysics simulator to simulate miscible displacements in homogeneous porous media with very large viscosity contrasts. Our numerical model is suitable for a wide range of viscosity contrasts covering chromatographic separation as well as heavy oil recovery. We have successfully captured some interesting and previously unexplored dynamics of miscible blobs with very large viscosity contrasts in homogeneous porous media. We study the effect of viscosity contrast on the spreading and the degree of mixing of the blob. Spreading (variance of transversely averaged concentration) follows the power law t 3.34 for the blobs with viscosity ∼ O(10 2 ) and higher, while degree of mixing is found to vary non-monotonically with log-mobility ratio. Moreover, in the limit of very large viscosity contrast, the circular blob behaves like an erodible solid body and the degree of mixing approaches the viscosity-matched case.

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Nonlinear viscous fingering in miscible displacement with anisotropic dispersion

Cited by 192 publications

References 22 publications

Miscible density fingering of chemical fronts in porous media: Nonlinear simulations

Miscible density fingering of chemical fronts in porous media: Nonlinear simulations

Investigation of concentration‐dependent diffusion on frontal instabilities and mass transfer in homogeneous porous media

Dynamics of a Highly Viscous Circular Blob in Homogeneous Porous Media

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