Convection in porous media with dispersion

Abstract

We investigate the effect of dispersion on convection in porous media by performing direct numerical simulations (DNS) in a two-dimensional Rayleigh-Darcy domain. Scaling analysis of the governing equations shows that the dynamics of this system are not only controlled by the classical Rayleigh-Darcy number based on molecular diffusion, $R{a}_m$, and the domain aspect ratio, but also controlled by two other dimensionless parameters: the dispersive Rayleigh number $R{a}_d=H/{\alpha }_t$ and the dispersivity ratio $r={\alpha }_l/{\alpha }_t$, where $H$ is the domain height, ${\alpha }_t$ and ${\alpha }_l$ are the transverse and longitudinal dispersivities, respectively. For $\Delta =R{a}_d/R{a}_m>O(1)$, the influence from the mechanical dispersion is minor; for $\Delta \ll 1$, however, the flow pattern is controlled by $R{a}_d$ while the convective flux is $F\sim R{a}_m$ for large $R{a}_m$, but with a prefactor that has a non-monotonic dependence on $R{a}_d$. Our DNS results also show that the increase of mechanical dispersion, i.e. decreasing $R{a}_d$, will coarsen the convective pattern by increasing the plume spacing. Moreover, the inherent anisotropy of mechanical dispersion breaks the columnar structure of the mega-plumes at large $R{a}_m$, if $R{a}_d<5000$. This results in a fan-flow geometry that reduces the convective flux.

References in corpus (4)

• Convective instability and mass transport of diffusion layers in a Hele-Shaw geometry
• Mechanisms of Dispersion in a Porous Medium
• Wall to Wall Optimal Transport
• Dynamics of convective carbon dioxide dissolution in a closed porous media system

Cited by in corpus (9)

• Convective mixing in porous media: A review of Darcy, pore-scale and Hele-Shaw studies
• Effects of Pore-scale on the Macroscopic Properties of Natural Convection in Porous Media
• Transport scaling in porous media convection
• Convective dissolution of CO${}_2$ in 2D and 3D porous media: the impact of hydrodynamic dispersion
• Convective carbon dioxide dissolution in a closed porous medium at high-pressure real-gas conditions
• Lagrangian dynamics and heat transfer in porous media convection
• Reduced modeling of porous media convection in a minimal flow unit at large Rayleigh number
• Solute mixing in porous media with dispersion and buoyancy
• CO${}_2$ convective dissolution in a 3-D granular porous medium: an experimental study