Vigorous convection in porous media

Abstract

The problem of convection in a fluid-saturated porous medium is reviewed with a focus on ‘vigorous’ convective flow, when the driving buoyancy forces are large relative to any dissipative forces in the system. This limit of strong convection is applicable in numerous settings in geophysics and beyond, including geothermal circulation, thermohaline mixing in the subsurface and heat transport through the lithosphere. Its manifestations range from ‘black smoker’ chimneys at mid-ocean ridges to salt-desert patterns to astrological plumes, and it has received a great deal of recent attention because of its important role in the long-term stability of geologically sequestered CO 2 . In this review, the basic mathematical framework for convection in porous media governed by Darcy’s Law is outlined, and its validity and limitations discussed. The main focus of the review is split between ‘two-sided’ and ‘one-sided’ systems: the former mimics the classical Rayleigh–Bénard set-up of a cell heated from below and cooled from above, allowing for detailed examination of convective dynamics and fluxes; the latter involves convection from one boundary only, which evolves in time through a series of regimes. Both set-ups are reviewed, accounting for theoretical, numerical and experimental studies in each case, and studies that incorporate additional physical effects are discussed. Future research in this area and various associated modelling challenges are also discussed.

Stability and dynamics of convection in dry salt lakes

“…Hewitt, Neufeld & Lister 2014; Loodts, Rongy & De Wit 2014). For example, Hewitt (2020) gives a recent review of their applications to vigorous convection in porous media.…”

“…2014; Slim 2014; Hewitt 2020). Similarly, in many cases a slab geometry of fixed height is modelled, where a scaling based on the layer thickness can be made (Ruith & Meiburg 2000; Riaz & Meiburg 2003; Hewitt 2020). We will instead follow a scheme where and where the group in (2.6) reduces to the Rayleigh number, .…”

“…The similarity of models is such that an exchange of methods, insights and results is possible, in both directions. In this context, our study relates to a variation on one-sided convection (Hewitt 2020). For example, analogously to the study by Slim (2014), we numerically investigate the time-dependence of the dynamics of solutal convection in a porous medium, driven from one side, and we find similar regimes of behaviour, ranging from initiation to coarsening and eventually a dynamic steady state.…”

“…The dynamics of thermally driven convection in porous media has also been extensively investigated in the past, for a variety of boundary conditions, and the equations are equivalent to the solutal-driven convection discussed here (see e.g. a recent review by Hewitt 2020). Of special interest has been the critical value of the Rayleigh number, , above which a system is unstable to convective motion, for a variety of situations.…”

Lagrangian dynamics and heat transfer in porous-media convection

“…The flow pattern and flux in buoyancy-driven porous-media flow have received much attention, for its relevance to various processes in nature and industry, such as geothermal energy recovery and geological sequestration of carbon dioxide (Huppert & Neufeld 2014;Hewitt 2020). Recently, it has been found that hydrodynamic dispersion has a significant effect on the flow properties of porous-media convection (Hidalgo & Carrera 2009;Emami-Meybodi, Hassanzadeh & Ennis-King 2015;Wen, Chang & Hesse 2018;De Paoli, Alipour & Soldati 2020).…”