Numerical simulations of a viscous-fingering instability in a fluid with a temperature-dependent viscosity

Holloway, Kristi E.; Bruyn, John R. de

doi:10.1139/p06-052

Cited by 8 publications

(8 citation statements)

References 17 publications

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“…Numerical studies of various miscible displacements regimes agree qualitatively with the stability analyses above [2,18,19,20,21]. In general, at the late stages of interfacial growth, they find that at sufficiently low values of thermal lag, or if the thermal regime is highly diffusive, the evolution depends entirely on the solutal viscosity ratio.…”

Section: Introductionsupporting

confidence: 68%

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Immiscible thermo-viscous fingering in Hele-Shaw cells

2017

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We investigate immiscible radial displacement in a Hele-Shaw cell with a temperature dependent viscosity using two coupled high resolution numerical methods. Thermal gradients created in the domain through the injection of a low viscosity fluid at a different temperature to the resident high viscosity fluid can lead to the formation of unstable thermo-viscous fingers, which we explore in the context of immiscible flows. The transient, multi-zone heat transfer is evaluated using a newly developed auxiliary radial basis function-finite collocation (RBF-FC) method, which locally captures variation in flux and field variable over the moving interface, without the need for ghost node extrapolation. The viscosity couples the transient heat transfer to the Darcy pressure/velocity field, which is solved using a boundary element -RBF-FC method, providing an accurate and robust interface tracking scheme for the full thermo-viscous problem.We explore the thermo-viscous problem space using systematic numerical experiments, revealing that the early stage finger growth is controlled by the pressure gradient induced by the varying temperature and mobility field. In hot injection regimes, negative temperature gradients normal to the interface act to accelerate the interface, promoting finger bifurcation and enhancing the viscous fingering instability. Correspondingly, cold injection regimes stabilise the flow compared to isothermal cases, hindering finger formation. The interfacial mobility distribution controls the late stage bifurcation mode, with non-uniformities induced by the thermal diffusivity creating alternate bifurcation modes. Further numerical experiments reveal the neutral stability of the thermal effects on the fingering evolution, with classical viscous fingering dynamics eventually dominating the evolution. We conclude the paper with a mechanistic summary of the immiscible thermo-viscous fingering regime, providing the first detailed analysis of the thermal problem in immiscible flows.

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Section: Introductionsupporting

confidence: 68%

“…Here, we summarise the solution procedure to evaluate the transient temperature field and quasi-static pressure in order to reconstruct the interface velocity with equation (21).…”

Section: Methodsmentioning

confidence: 99%

Immiscible thermo-viscous fingering in Hele-Shaw cells

2017

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“…Sheorey and Muralidhar [5] performed a numerical simulation of the displacement of oil by hot water in porous media and found that the displacement patterns change according to the non-isothermal fields which results in higher oil recovery compared to isothermal cases. Holloway and de Bruyn [6,7] experimentally and numerically studied the viscous fingering that occurs when hot glycerin displaces cooler, more-viscous glycerin in a radial HeleShaw cell. They showed that fingering occurred for sufficiently large temperature difference between the injected and the displaced liquid and for sufficiently high flow rate.…”

Section: Introductionmentioning

confidence: 99%

An experimental study of non-isothermal miscible displacements in a Hele-Shaw cell

Nagatsu

Fujita

Kato

et al. 2009

Experimental Thermal and Fluid Science

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“…As a result, interest in the control of the properties of this instability by mechanical, [1][2][3][4][5][6][7] thermal, [8][9][10][11][12][13] or chemical [14][15][16][17][18][19][20][21][22][23][24] ways for instance are of constant interest in the literature. Numerous experimental and theoretical works have already shown that the properties of the fingers (such as their mixing length or their area) can be strongly affected by in situ changes in the viscosity field distribution induced by gradients of temperature or composition in the solutions.…”

Section: Introductionmentioning

confidence: 99%

“…15,20 Riolfo et al have furthermore evidenced that a reaction can even trigger fingering when a viscous polymer solution displaces a less viscous reactive solution. 22 Qualitative understanding of the thermally-or chemically-driven control of fingering properties typically rely on numerical computation of the spatio-temporal evolution of the temperature 9,12 or concentrations 18,21,22 fields. The viscosity field is then deduced on the basis of a state equation relating the viscosity to temperature or chemical concentrations.…”

Section: Introductionmentioning

confidence: 99%

Reconstruction by fluorescence imaging of the spatio-temporal evolution of the viscosity field in Hele-Shaw flows

et al. 2014

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We study the spatio-temporal evolution of the viscosity field during stable and unstable radial flows of glycerol-water solutions in a horizontal Hele-Shaw cell where a localized temperature gradient is imposed. The viscosity field is reconstructed from the measurement of the fluorescence emitted by a viscosity-sensitive molecular probe (Auramine O). For an immiscible flow, the viscosity and temperature fields are obtained accurately. For miscible displacements, we show how the interplay between the viscosity changes of both fluids and the variation of the fluid thickness in the gap prevents obtaining strict quantitative reconstruction of the viscosity field. We explain how the reconstructed viscosity field can nevertheless be interpreted to obtain information about the fluid thickness and the local viscosity and temperature.

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Numerical simulations of a viscous-fingering instability in a fluid with a temperature-dependent viscosity

Cited by 8 publications

References 17 publications

Immiscible thermo-viscous fingering in Hele-Shaw cells

Immiscible thermo-viscous fingering in Hele-Shaw cells

An experimental study of non-isothermal miscible displacements in a Hele-Shaw cell

Reconstruction by fluorescence imaging of the spatio-temporal evolution of the viscosity field in Hele-Shaw flows

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