Reconstructing temperature fields for thermally-driven flows under quasi-steady state

Supercritical ${\rm CO}_2$ injection and dissolution into deep brine aquifers allow its sequestration within geological formations. After injection, ${\rm CO}_{2}$ gas phase is buoyancy-driven over the denser aqueous brine, reaching an apparent gravitational stable distribution. However, ${\rm CO}_2$ dissolution in brine propels convection since the mixture is even denser than the underlying brine. This process still needs to be characterised comprehensively. Here, we investigate the irreversible mixing of dissolved ${\rm CO}_2$ in brine through laboratory-scale numerical experiments utilising the Hele-Shaw model (Letelier et al., J. Fluid Mech., vol. 864, 2019, pp. 746–767) and a fully miscible two-fluid system. In this scenario, mixing the less dense fluid – mimicking ${\rm CO}_{2}$ gas phase – with the heavier fluid – representing aqueous brine – catalyses cabbeling-powered convection. Our numerical simulations recover the laboratory results in porous media by Neufeld et al. (Geophys. Res. Lett., vol. 37, issue 22, 2010, L22404) and may explain the scaling law obtained by Backhaus et al. (Phys. Rev. Lett., vol. 106, issue 10, 2011, 104501) in Hele-Shaw cells. More remarkably, we show that the mass flux between the two analogue fluids, characterised by the Sherwood number $ {{Sh}}$ , obeys the universal scaling law $ {{Sh}}\sim {{Ra}}\, \vartheta _{scalar}$ , with $ {{Ra}}$ the Rayleigh number and $\vartheta _{scalar}$ the mean scalar dissipation rate. This paper sheds light on the fluid dynamics and solubility trapping in geological carbon sequestration.

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Scaling CO₂–brine mixing in permeable media via analogue models

Letelier

Ulloa

Leyrer

et al. 2023

J. Fluid Mech.

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Stratified horizontal convection

Noto,

Ulloa,

Yanagisawa

et al. 2023

J. Fluid Mech.

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Surface differential heating on a stably stratified fluid body drives an overturning circulation confined to the upper fluid region – here coined stratified horizontal convection (SHC). In this manuscript, we investigate the dynamics of SHC via laboratory experiments, exploring local and global flow properties. By considering the available potential energy of the system, we derive a unique length scale of SHC and introduce the Péclet number $Pe$ that captures both the stabilising effect of stratification and the destabilising effect of the baroclinic adjustment. We found that $Pe$ characterises local and global flow properties, including the fluid transport of the overturning circulation, the available mechanical energy and the flow dimensionality. Our study provides insights into the fluid dynamics of stratified environments that experience horizontal convection, such as lakes, oceans and atmospheres.

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Quasi-steady transitions in confined convection

Yanagisawa,

Takano,

Noto

et al. 2024

J. Fluid Mech.

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We study the effect of geometrical confinement on thermal convection by laboratory experiments and direct numerical simulations using Hele-Shaw geometries (typically the gap-to-height aspect ratio $0.12$ ) for the Prandtl number $Pr \geq 40$ and the Rayleigh number $Ra \leq 6 \times 10^7$ . Under such strong unidirectional confinement, the convective flows are forced to squeeze within the narrow gap and exhibit unique spatiotemporal signatures, which contrast those in unconfined systems. With the increase of $Ra$ , we identify that the system experiences five convective regimes that can be classified from two aspects, time dependency and flow dimensionality: (I) quasi-two-dimensional (quasi-2-D) steady flow; (II) quasi-2-D flow with oscillatory corner rolls; (III) three-dimensional (3-D) flow with oscillatory corner rolls; (IV) 3-D steady flow; and (V) 3-D time-dependent motion of plumes around sidewalls. Notably, unsteadiness does not emerge globally, but is localised near the sidewalls as oscillatory corner rolls, resulting in the regime transitions happening in a quasi-steady manner. We confirm that these regime transitions show less dependence on both $Pr$ and the other (wider) horizontal scale of the geometry. Moreover, we find that a recently proposed criterion ‘degree of confinement’ (Noto et al., Proc. Natl Acad. Sci. USA, vol. 121, issue 28, 2024, e2403699121) successfully explains the emergence of 3-D structures, expanding its applicable range to smaller $Ra$ . This study deepens the comprehension of the thermal convection emerging in tight geometries, impacting across disciplines, such as Earth and planetary science, and thermal engineering.

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Reconstructing temperature fields for thermally-driven flows under quasi-steady state

Cited by 6 publications

References 10 publications

Scaling CO₂–brine mixing in permeable media via analogue models

Scaling CO₂–brine mixing in permeable media via analogue models

Stratified horizontal convection

Quasi-steady transitions in confined convection

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Reconstructing temperature fields for thermally-driven flows under quasi-steady state

Cited by 6 publications

References 10 publications

Scaling CO2–brine mixing in permeable media via analogue models

Scaling CO2–brine mixing in permeable media via analogue models

Stratified horizontal convection

Quasi-steady transitions in confined convection

Contact Info

Product

Resources

About

Scaling CO₂–brine mixing in permeable media via analogue models

Scaling CO₂–brine mixing in permeable media via analogue models