Dispersion driven instability in miscible displacement in porous media

Yortsos, Y.C.; Zeybek, Murat

doi:10.1063/1.866918

Cited by 104 publications

(64 citation statements)

References 12 publications

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“…9 The stability analysis focused on the flow with a velocity-dependent dispersion coefficient. Following convection-dispersion formalism, the base state at conditions of unfavorable mobility contrast was analyzed.…”

Section: Introductionmentioning

confidence: 99%

The effect of anisotropic dispersion on the convective mixing in long‐term CO₂ storage in saline aquifers

2011

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in Wiley Online Library (wileyonlinelibrary.com).Carbon dioxide storage in deep saline aquifers is considered a possible option to bring greenhouse gas emissions under control. The understanding of the underlying mechanisms, such as convective mixing and associated mechanisms, affecting this mixing may have an impact on the long-term sequestration process in deep saline aquifers. One of the significant aspects of the flow of miscible species in porous media is velocity dependent dispersion. The effect of dispersion on dissolution of carbon dioxide (CO 2 ) into brine is investigated by full nonlinear numerical simulations. This study reveals that dispersion may dramatically change the trend of CO 2 dissolution into brine. It was found that the dissolution of CO 2 increases as dispersion strength increases. The mixing pattern also shows three different mechanisms: diffusion, convection, and a highly nonlinear interaction mechanism. However, the medium dispersivity ratios were found to slightly affect the mixing, while having an impact on the fingering pattern.

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Section: Introductionmentioning

confidence: 99%

The effect of anisotropic dispersion on the convective mixing in long‐term CO₂ storage in saline aquifers

2011

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“…The values for CO 2 -water system are estimated from Gmelin 1 and Bando et al 33 as R = 0.13, S = 0.02, which means that R is below the value for which velocity effects on the diffusion coefficient have to be taken into account. 22 Notice that ρ =ρ c=1 −ρ c=0 = ρ 0 S, which implies…”

Section: Dimensionless Form Of the Equationsmentioning

confidence: 99%

“…19 In the long-wave limit, this correction In Ref. 22, the influence of the velocity U on the diffusion coefficient was studied. An analytic expression for the dispersion relation was found in terms of a parameter η which depends (among others) on R (see Eq.…”

Section: Hele-shaw Problemmentioning

confidence: 99%

The effect of interface movement and viscosity variation on the stability of a diffusive interface between aqueous and gaseous CO2

2013

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Carbon dioxide injected in an aquifer rises quickly to the top of the reservoir and forms a gas cap from where it diffuses into the underlying water layer. Transfer of the CO 2 to the aqueous phase below is enhanced due to the high density of the carbon dioxide containing aqueous phase. This paper investigates the behavior of the diffusive interface in an enclosed space in which initially the upper part is filled with pure carbon dioxide and the lower part with liquid. Our analysis differs from a conventional analysis as we take the movement of the diffusive interface due to mass transfer and the composition dependent viscosity in the aqueous phase into account. The same formalism can also be used to describe the situation when an oil layer is underlying the gas cap. Therefore we prefer to call the lower phase the liquid phase. In this paper we include these two effects into the stability analysis of a diffusive interface between CO 2 and a liquid in the gravity field. We identify the relevant bifurcation parameter as q = Ra, where is the width of the interface. This implies the (well known) scaling of the critical time ∼Ra −2 and wavelength ∼Ra −1 (The critical time t c and critical wavelength k c are defined as follows: σ (k) ≤ 0 ∀t ≤ t c ; equality only holds for t = t c and k = k c ). Inclusion of the interface upward movement leads to earlier destabilization of the system. Increasing viscosity for increasing CO 2 concentration stabilizes the system. The theoretical results are compared to bulk flow visual experiments using the Schlieren technique to follow finger development in aquifer sequestration of CO 2 . In the appendix, we include a detailed derivation of the dispersion relation σ (k) in the Hele-Shaw case [C. T. Tan and G. M. Homsy, Phys. Fluids 29, 3549-3556 (1986)] which is nowhere explicitly given. C 2013 AIP Publishing LLC. [http://dx

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“…For more exhaustive references on various numerical, experimental, and theoretical works, the review articles of Saffman (see [20]) and Kessler et al (see [13]) are worth mentioning. Towards this end, works of Hickernell and Yortsos (see [8]), Yortsos and Zeybek (see [30]), Loggia et al (see [15]), and Shariati and Yortsos (see [24]) on two-layer miscible flows should also be cited.…”

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confidence: 99%

On diffusive slowdown in three-layer Hele-Shaw flows

Daripa

Paşa

2010

Quart. Appl. Math.

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Abstract. In a recently published article of Daripa and Pasa [Transp. Porous Media (2007) 70:11-23], the stabilizing effect of diffusion in three-layer Hele-Shaw flows was proved using an exact analysis of normal modes. In particular, this was established from an upper bound on the growth rate of instabilities which was derived from analyzing stability equations. However, the method used there is not constructive in the sense that the upper bound derived from actual numerical discretization of the problem could be significantly different from the exact one reported depending on the scheme used. In this paper, a numerical approach to solve the stability equations using a finite difference scheme is presented and analyzed. An upper bound on the growth rate is derived from numerical analysis of the discrete system which also shows the diffusive slowdown of instabilities. Upper bounds obtained by this numerical approach and by the analytical approach are compared. The present approach is constructive and directly leads to the implementation of the numerical approach to obtain approximate solutions in the presence of diffusion. The contributions of the paper are the novelty of the approach and a bound on the growth rates that does not depend on the solution itself.

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Dispersion driven instability in miscible displacement in porous media

Cited by 104 publications

References 12 publications

The effect of anisotropic dispersion on the convective mixing in long‐term CO₂ storage in saline aquifers

The effect of anisotropic dispersion on the convective mixing in long‐term CO₂ storage in saline aquifers

The effect of interface movement and viscosity variation on the stability of a diffusive interface between aqueous and gaseous CO2

On diffusive slowdown in three-layer Hele-Shaw flows

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Dispersion driven instability in miscible displacement in porous media

Cited by 104 publications

References 12 publications

The effect of anisotropic dispersion on the convective mixing in long‐term CO2 storage in saline aquifers

The effect of anisotropic dispersion on the convective mixing in long‐term CO2 storage in saline aquifers

The effect of interface movement and viscosity variation on the stability of a diffusive interface between aqueous and gaseous CO2

On diffusive slowdown in three-layer Hele-Shaw flows

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The effect of anisotropic dispersion on the convective mixing in long‐term CO₂ storage in saline aquifers

The effect of anisotropic dispersion on the convective mixing in long‐term CO₂ storage in saline aquifers