Synergetic Fluid Mixing from Viscous Fingering and Alternating Injection

Jha, Birendra; Cueto‐Felgueroso, Luis; Juanes, Rubén

doi:10.1103/physrevlett.111.144501

Cited by 58 publications

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“…VF occurs typically in a porous medium when a fluid of given viscosity displaces a more viscous and hence less mobile one (Homsy 1987;Mishra et al 2010;Jha et al 2011a). It deforms the interface into 'fingers', which enhances mixing (Jha et al 2011a;Jha, Cueto-Felgueroso & Juanes 2011b;Dentz et al 2011;Jha, Cueto-Felgueroso & Juanes 2013) between the two fluids and is usually detrimental to displacement efficiency. † Email address for correspondence: satyajit.math16@gmail.com c Cambridge University Press 2015 Several articles have been devoted to analysing miscible VF of either a single interface between two semi-infinite regions (Homsy 1987;Tan & Homsy 1988;Pramanik & Mishra 2013 or a finite-size rectangular plug in a rectilinear displacement De Wit et al 2005;Mishra, Martin & De Wit 2008).…”

Section: Introductionmentioning

confidence: 99%

Viscous fingering and deformation of a miscible circular blob in a rectilinear displacement in porous media

2015

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The deformation of an initially circular miscible blob in a rectilinear displacement is investigated numerically for porous media when the blob is more viscous than the displacing fluid. We find in the parameter space spanned by the Péclet number and log-mobility ratio the existence of a new lump-shaped instability zone between two distinct regimes of comet and viscous fingering (VF) deformations. The more viscous circular blob is destabilized by VF only over a finite window of log-mobility ratio, contrary to the displacement of a more viscous finite slice with planar interfaces. This difference is attributed to the initial curvature of the miscible blob.

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Section: Introductionmentioning

confidence: 99%

Viscous fingering and deformation of a miscible circular blob in a rectilinear displacement in porous media

2015

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“…On the other, the well-known viscous fingering hydrodynamic instability [16][17][18][19] induces phase branching, splitting, and pinch off [20][21][22]. While many aspects of viscous fingering have been studied-including its role on fluid mixing [23][24][25] and ensuing chemical reactions [26][27][28]-its impact on phase separation of a fluid mixture remains unexplored.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamic coarsening arrested by viscous fingering in partially miscible binary mixtures

Cueto‐Felgueroso

Juanes

2016

Phys. Rev. E

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We study the evolution of binary mixtures far from equilibrium, and show that the interplay between phase separation and hydrodynamic instability can arrest the Ostwald ripening process characteristic of nonflowing mixtures. We describe a model binary system in a Hele-Shaw cell using a phase-field approach with explicit dependence of both phase fraction and mass concentration. When the viscosity contrast between phases is large (as is the case for gas and liquid phases), an imposed background flow leads to viscous fingering, phase branching, and pinch off. This dynamic flow disorder limits phase growth and arrests thermodynamic coarsening. As a result, the system reaches a regime of statistical steady state in which the binary mixture is permanently driven away from equilibrium.

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“…Beyond their intrinsic interest for the understanding of a fundamental hydrodynamic instability [14,15,51,56,57], our results suggest that the shutdown of the viscous fingering instability in a radial configuration could be important for predicting the effectiveness of enhanced oil recovery by miscible flooding [7,72], where well-to-well flows are dominated by radial displacements during the early stages of the flood [52,53,73].…”

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“…While diffusion is disregarded in their analysis, here we identify molecular diffusion as the mechanism responsible for the shutdown of the instability at late times. In our experiments, the long-enough times (or small-enough strain rates) imply that diffusion plays a major role in the evolution of the interface, and that Korteweg stresses and nonequilibrium surface tension effects do not [56,[58][59][60][61][62][63][64][65][66]. As the unstable front grows in fingerlike structures [ Figs.…”

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confidence: 99%

“…Other studies have also focused on the effects of anisotropic dispersion [31,33,36], medium heterogeneity [32,[37][38][39][40], gravity [41][42][43][44][45][46], chemical reactions [3,[47][48][49], absorption [50], and flow configuration [51][52][53][54][55] on the viscous fingering instability. Despite the extensive work done, the effect of viscous fingering on mixing has only recently been investigated numerically for a rectilinear geometry [14,56]. While the dynamics of the interface between two miscible fluids is crucial to explain and predict the rate of mixing [1,16], a solid understanding of the temporal evolution of the viscously unstable fluid-fluid interface is still missing.…”

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Interface evolution during radial miscible viscous fingering

2015

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We study experimentally the miscible radial displacement of a more viscous fluid by a less viscous one in a horizontal Hele-Shaw cell. For the range of tested injection rates and viscosity ratios we observe two regimes for the evolution of the fluid-fluid interface. At early times the interface length increases linearly with time, which is typical of the Saffman-Taylor instability for this radial configuration. However, as time increases, the interface growth slows down and scales as ∼t 1 2 , as one expects in a stable displacement, indicating that the overall flow instability has shut down. Surprisingly, the crossover time between these two regimes decreases with increasing injection rate. We propose a theoretical model that is consistent with our experimental results, explains the origin of this second regime, and predicts the scaling of the crossover time with injection rate and the mobility ratio. The key determinant of the observed scalings is the competition between advection and diffusion time scales at the displacement front, suggesting that our analysis can be applied to other interfacial-evolution problems such as the Rayleigh-Bénard-Darcy instability. A large number of natural and industrial flow processes depend on both the degree and the rate of mixing between fluids, such as chemical reactions [1][2][3][4], combustion [5], microbial activity [6], and enhanced oil recovery [7]. In such mixing-driven systems, the flow responsible for fluid displacement reflects the heterogeneity of the host medium structure [8][9][10][11] or the physical properties of the fluids, such as density [3,12,13] or viscosity [14,15]. Mixing takes place at the fluid-fluid interface and is determined by the combined action of molecular diffusion, which acts to reduce the local concentration gradients, and advection, which controls the interface dynamics [16][17][18][19][20][21]. Understanding the interface dynamics between two miscible fluids is therefore crucial to explaining and predicting the rate of mixing.When a less viscous fluid displaces a more viscous one, their interface is deformed and stretched by a hydrodynamical instability known as viscous fingering [15,22,23], and this results in complex interface dynamics [16,17,24]. Much work has focused on characterizing miscible viscous fingering, including laboratory experiments [25][26][27], numerical simulations [28][29][30][31][32], and linear stability analyses to model the onset and growth of instabilities for rectilinear [33] and radial [34,35] geometries. Other studies have also focused on the effects of anisotropic dispersion [31,33,36] [50], and flow configuration [51-55] on the viscous fingering instability. Despite the extensive work done, the effect of viscous fingering on mixing has only recently been investigated numerically for a rectilinear geometry [14,56]. While the dynamics of the interface between two miscible fluids is crucial to explain and predict the rate of mixing [1,16], a solid understanding of the temporal evolution of the viscously unstable fl...

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Synergetic Fluid Mixing from Viscous Fingering and Alternating Injection

Cited by 58 publications

References 39 publications

Viscous fingering and deformation of a miscible circular blob in a rectilinear displacement in porous media

Viscous fingering and deformation of a miscible circular blob in a rectilinear displacement in porous media

Thermodynamic coarsening arrested by viscous fingering in partially miscible binary mixtures

Interface evolution during radial miscible viscous fingering

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