Convective shutdown in a porous medium at high Rayleigh number

Abstract

Convection in a closed domain driven by a dense buoyancy source along the upper boundary soon starts to wane owing to the increase of the average interior density. In this paper, theoretical and numerical models are developed of the subsequent long period of shutdown of convection in a two-dimensional porous medium at high Rayleigh number Ra. The aims of this paper are twofold. Firstly, the relationship between this slowly evolving 'one-sided' shutdown system and the statistically steady 'two-sided' Rayleigh-Bénard (RB) cell is investigated. Numerical measurements of the Nusselt number Nu from an RB cell (Hewitt et al., Phys. Rev. Lett., vol. 108, 2012, 224503) are very well described by the simple parametrization Nu = 2.75 + 0.0069Ra. This parametrization is used in theoretical box models of the one-sided shutdown system and found to give excellent agreement with high-resolution numerical simulations of this system. The dynamical structure of shutdown can also be accurately predicted by measurements from an RB cell. Results are presented for a general power-law equation of state. Secondly, these ideas are extended to model more complex physical systems, which comprise two fluid layers with an equation of state such that the solution that forms at the (moving) interface is more dense than either layer. The two fluids are either immiscible or miscible. Theoretical box models compare well with numerical simulations in the case of a flat interface between the fluids. Experimental results from a Hele-Shaw cell and numerical simulations both show that interfacial deformation can dramatically enhance the convective flux. The applicability of these results to the convective dissolution of geologically sequestered CO 2 in a saline aquifer is discussed.

Constraints on the Magnitude and Rate of CO2 Dissolution at Bravo Dome Natural Gas Field

“…In this case, the connectivity of the individual sandbodies is likely crucial in determining the rate of convective overturn. Given that only 25% of the brine immediately available beneath the gas-water contact has been saturated with CO 2 , it is unlikely that the low average dissolution rates can be explained by convective shutdown (22,56) or limitations due to the lateral migration of dissolved CO 2 as a dense gravity current (14,57).…”

Plume dynamics in Hele-Shaw porous media convection

“…Relative to the standard conditions of Rayleigh-Bénard convection where there is a fixed horizontal boundary, the boundary conditions for either a miscible or immiscible interface allow the interface to distort. This distortion results in enhanced mass transport relative to a flat interface [9,16] the nucleation of new plumes in the boundary-layer regime between major plumes [9,10,13,15]. From numerical simulations [10], one gets a constant dimensionless mass transport of Sh = 0.017 (note that the Nusselt number, the ratio of the mass flux to the steady state, i.e.…”

“…The hydrodynamic instability of two-phase porous media convection is similar to the thickening and instability of thermal layers in thermal convection [2], although in that case the flow rapidly becomes fully nonlinear whereas the porous media allow for a simpler formulation. Analytic calculations and numerical simulations have been performed [3][4][5][6][7][8][9][10] to evaluate the time to instability and the resulting mass transport efficiency. 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.…”

Pattern formation and coarsening dynamics in three-dimensional convective mixing in porous media

“…It is natural to ask whether the coarsening regimes of the length scale near the boundary layer are reflected in the time evolution of dissolution flux. Indeed, the dissolution flux exhibits three dynamic regimes as well: diffusive, convection-dominated and saturation [21,24,25,32]. Here we compare these two quantitiescharacteristic length scale and dissolution flux-for both a three-dimensional simulation with Ra = 6400 and a two-dimensional simulation with Ra = 25 000 (figure 7).…”