Resonance-like dynamics in radial cyclic injection flows of immiscible fluids in homogeneous porous media

Lins, Tiago; Azaiez, Jalel

doi:10.1017/jfm.2017.186

Cited by 22 publications

(22 citation statements)

References 31 publications

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“…One advantage of the level set method is that it can be used describe the evolution of complex interfacial patterns using a uniform grid, eliminating the need to generate meshes that adapt as the interface evolves. The level set method has previously been used to study interfacial instabilities in a variety of moving boundary problems, including Hele-Shaw flow (Hou et al 1997;Lins & Azaiez 2017) and Stefan problems (Chen et al 1997). We summarise the details of our scheme in Appendix A.…”

Section: Numerical Schemementioning

confidence: 99%

“…As such, there is a significant body of research devoted to devising strategies for controlling the pattern formation and/or suppressing the viscous fingering (Rabbani et al 2018). The majority of these studies consider injecting the inviscid fluid at a time-dependent flow rate (linearly increasing in time (Dias et al 2012), piecewise constant ) and sinusoidal (Lins & Azaiez 2017)), while in recent times researchers have proposed to alter the geometry of the Hele-Shaw cell to affect the fingering pattern. Examples of such alterations include separating the plates in a timedependent fashion (Zheng et al 2015;Vaquero-Stainer et al 2019), tapering the Hele-Shaw plates so that they are no longer parallel (Al-Housseiny et al 2012;Anjos et al 2018;Bongrand & Tsai 2018;Dias & Miranda 2013;Jackson et al 2017;Lu et al 2018;Stone 2017), and replacing one of the plates with an elastic membrane Lister et al 2013;Pihler-Puzović et al 2013, 2014, 2018.…”

Section: Introductionmentioning

confidence: 99%

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Numerical investigation of controlling interfacial instabilities in non-standard Hele-Shaw configurations

2019

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Viscous fingering experiments in Hele-Shaw cells lead to striking pattern formations which have been the subject of intense focus among the physics and applied mathematics community for many years. In recent times, much attention has been devoted to devising strategies for controlling such patterns and reducing the growth of the interfacial fingers. We continue this research by reporting on numerical simulations, based on the level set method, of a generalised Hele-Shaw model for which the geometry of the Hele-Shaw cell is altered. First, we investigate how imposing constant and time-dependent injection rates in a Hele-Shaw cell that is either standard, tapered or rotating can be used to reduce the development of viscous fingering when an inviscid fluid is injected into a viscous fluid over a finite time period. We perform a series of numerical experiments comparing the effectiveness of each strategy to determine how these non-standard Hele-Shaw configurations influence the morphological features of the inviscid-viscous fluid interface. Surprisingly, a converging or diverging taper of the plates leads to reduced metrics of viscous fingering at the final time when compared to the standard parallel configuration, especially with carefully chosen injection rates; for the rotating plate case, the effect is even more dramatic, with sufficiently large rotation rates completely stabilising the interface. Next, we illustrate how the number of non-splitting fingers can be controlled by injecting the inviscid fluid at a time-dependent rate while increasing the gap between the plates. Our simulations compare well with previous experimental results for various injection rates and geometric configurations. We demonstrate how the number of non-splitting fingers agrees with that predicted from linear stability theory up to some finger number; for larger values of our control parameter, the fully nonlinear dynamics of the problem lead to slightly fewer fingers than this linear prediction. † Email address for correspondence: scott.mccue@qut.edu.au arXiv:1901.00288v4 [physics.flu-dyn] 7 Jul 2019 , (5.3)

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Section: Numerical Schemementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Numerical investigation of controlling interfacial instabilities in non-standard Hele-Shaw configurations

2019

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“…So far, there is a limited number of studies on the mechanisms of how the time‐dependent displacement rate affects VF in subsurface porous media, and most of which were done in 2010s. For the immiscible displacements, the optimal injection rates were reported which are able to suppress the VF and stabilize the flows in two‐dimensional (2‐D) and three‐dimensional geometries . For the miscible displacements without considering dispersion or inertia, we found the time‐dependent rates have either stabilizing or destabilizing effects .…”

Section: Introductionmentioning

confidence: 85%

Control of viscous fingering and mixing in miscible displacements with time‐dependent rates

et al. 2018

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In miscible displacements encountered in enhanced oil recovery processes, the unfavorable viscosity contrast between injected solvent and oil usually leads to viscous fingering (VF), a hydrodynamic instability which may result in a lower sweep efficiency and oil recovery. This phenomenon can be observed in a wide range of flows in subsurface porous media. This study examined a simple cyclic time‐dependent displacement rate and its effects on the onset and longer development of VF. It is found that such varying displacement rate can either stabilize or destabilize VF, depending on the cycle period, amplitude, and displacement scenarios. The most important mechanism is that such time‐dependent rate can effectively change the competition between convection (destabilizing effect) and dispersion (stabilizing effect). This is different from the widely used constant injection rate where the flow instability is actually determined by the Peclet number and mobility contrast for a given scenario. This study therefore provided a new aspect to control VF, either enhance or reduce, with low additional costs. It is therefore both scientifically and practically important for a wide range of flows in subsurface porous media. © 2017 American Institute of Chemical Engineers AIChE J, 65: 360–371, 2019

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“…The mathematical model describing the immiscible displacement consists of the continuity equation (mass conservation) and Darcy's law (momentum conservation) [10]:…”

Section: Governing Equationsmentioning

confidence: 99%

“…In terms of studies dealing with immiscible displacements, one must mention the pioneering work [7] who have analyzed the early development of the instabilities in radial Hele-Shaw cells. Subsequent studies analyzed the effects of the injection flow rate, surface tension and fluids viscosity [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Interfacial Instabilities of Shear-Thinning Fluids in Homogeneous Porous Media

Lee¹,

Azaiez²,

Gates³

2018

Proceedings of the 3rd World Congress on Momentum, Heat and Mass Transfer

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In this study, radial immiscible flow displacements in homogeneous porous media are modelled numerically in the case where the displacing fluid is Newtonian while the displaced one may be Newtonian or shear-thinning governed by Carreau's rheological model. The governing equations and interfacial jump conditions are solved numerically using the Immersed Interface Method and the Level Set Method to track the two fluids interfaces. The effects of four parameters, namely the mobility ratio and Capillary number for Newtonian flows and the Deborah number De and power-law index n, for shear thinning fluids are examined. Time contours of the interface revealing the finger structures that develop as a result of the viscosity mismatch between the two fluids are obtained to analyse and discuss the effects of the different parameters on the interfacial instability. Even though both characteristics of the shear-thinning fluid; De and n were found to affect the interfacial instability, it is revealed that the latter has a stronger effect, at least for the range of parameters that have been considered in this study.

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Resonance-like dynamics in radial cyclic injection flows of immiscible fluids in homogeneous porous media

Cited by 22 publications

References 31 publications

Numerical investigation of controlling interfacial instabilities in non-standard Hele-Shaw configurations

Numerical investigation of controlling interfacial instabilities in non-standard Hele-Shaw configurations

Control of viscous fingering and mixing in miscible displacements with time‐dependent rates

Interfacial Instabilities of Shear-Thinning Fluids in Homogeneous Porous Media

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