Dissolution-driven convection in a Hele–Shaw cell

Abstract

Motivated by convection in the context of geological carbon-dioxide (CO2) storage, we present an experimental study of dissolution-driven convection in a Hele–Shaw cell for Rayleigh numbers \documentclass[12pt]{minimal}\begin{document}$\mathcal {R}$\end{document}R in the range \documentclass[12pt]{minimal}\begin{document}$100 < \mathcal {R}< 1700$\end{document}100<R<1700. We use potassium permanganate (KMnO4) in water as an analog for CO2 in brine and infer concentration profiles at high spatial and temporal resolution and accuracy from transmitted light intensity. We describe behavior from first contact up to 65% average saturation and measure several global quantities including dissolution flux, average concentration, amplitude of perturbations away from pure one-dimensional diffusion, and horizontally averaged concentration profiles. We show that the flow evolves successively through distinct regimes starting with a simple one-dimensional diffusional profile. This is followed by linear growth in which fingers are initiated and grow quasi-exponentially, independently of one-another. Once the fingers are well-established, a flux-growth regime begins as fresh fluid is brought to the interface and contaminated fluid removed, with the flux growing to a local maximum. During this regime, fingers still propagate independently. However, beyond the flux maximum, fingers begin to interact and zip together from the root down in a merging regime. Several generations of merging occur before only persistent primary fingers remain. Beyond this, the reinitiation regime begins with new fingers created between primary existing ones before merging into them. Through appropriate scaling, we show that the regimes are universal and independent of layer thickness (equivalently \documentclass[12pt]{minimal}\begin{document}$\mathcal {R}$\end{document}R) until the fingers hit the bottom. At this time, progression through these regimes is interrupted and the flow transitions to a saturating regime. In this final regime, the flux gradually decays in a manner well described by a Howard-style phenomenological model.

Convective shutdown in a porous medium at high Rayleigh number

“…Since Ra 0 O(1), we expect the convective time to dominate: thus t 1 can be assumed to be independent of Ra 0 , and t 2 ≈ 2t 1 . We find numerically that t 1 ≈ 7.5 and t 2 ≈ 15, in broad agreement with the experimental results of Slim et al (2013). For t > t 2 , the horizontally averaged concentration C(z, t) is approximately independent of z away from the boundary layer, and C increases steadily over time (figure 4c,d).…”

“…The qualitative behaviour of the flux in this 'shutdown' regime has been observed in numerical simulations by Hassanzadeh et al (2007) for Ra < 1000, although they provided no theoretical analysis of the system. Slim et al (2013) presented experimental results in this regime for 100 < Ra < 1700, and derived a phenomenological model that describes the evolution of the flux based on an ad hoc parametrization of the typical boundary-layer depth. We are not aware of any studies that explore the shutdown regime, in which the convective flux steadily decreases, for Ra > 1700.…”

“…There have been a number of numerical studies for Ra O(10 3 ) that examine the evolution of the dynamics and the merging of descending plumes before they interact with the lower boundary (Hassanzadeh et al 2007;Pau et al 2010). Slim et al (2013) performed experiments in a Hele-Shaw cell for 100 < Ra < 1700, and categorized the evolution of the system from the onset of convection in detail. Further experimental studies by Neufeld et al (2010) for 5×10 4 < Ra < 6×10 5 in a quasi-twodimensional porous medium, and by Backhaus et al (2011) for 6 × 10 3 < Ra < 9 × 10 4 in a Hele-Shaw cell, provided measurements of the convective flux after the onset of convection.…”

“…Many previous studies of one-sided convective systems have focused on the conditions required for the onset of convection, which presents significant theoretical challenges because the diffusive base state is both time-dependent and nonlinear. Various theoretical studies (Hassanzadeh, Pooladi-Darvish & Keith 2006;Riaz et al 2006;Xu, Chen & Zhang 2006;Slim & Ramakrishnan 2010) have been complemented by direct numerical investigations (Riaz et al 2006;Hassanzadeh, Pooladi-Darvish & Keith 2007) and laboratory experiments (Fernandez et al 2002;Backhaus, Turitsyn & Ecke 2011;Slim et al 2013) that explore the onset of convection.…”

Plume dynamics in Hele-Shaw porous media convection

“…Laboratory experiments, however, have not been able to capture the main features of instability and mass transfer in realistic highpressure supercritical CO 2 brine systems. Thus, researchers have explored analogue experiments that capture the main features of buoyancy-driven porous media convection [11][12][13][14][15]. Here, we describe details of our analogue approach [13] and concentrate on properties of our system rather than upon justifying the analogy or reviewing other work in this area (see, for example, [16] for an analysis of the limitations of this analogy).…”