Convection in porous media with dispersion: experiments, pore-scale and Darcy simulations*

Convection in porous media is ubiquitous in natural and industrial processes. For mass transport in geophysical systems, solute dispersion is an important effect to be understood, and this dispersion cannot be described by molecular diffusion alone. The presence of solid obstacles in the porous matrix induces an additional solute spreading, due to the convoluted fluid movements through the medium. Modelling the dispersion effect remains a challenging task due to the vast parameter space encompassing medium properties such as porosity and permeability, fluid characteristics including buoyancy forces and diffusivity, and domain attributes like the height of the medium. As a result, multiple methods are required to understand the flow dynamics at the different scales involved, ranging from the level of the pores, with a sub-millimetre characteristic length, to the Darcy scale, involving hundreds of pores and relevant to practical applications. In this work, we investigate convection in porous media with dispersion using a combination of Hele-Shaw-like experiments in bead packs, pore-scale simulations and Darcy simulations. Building upon our previous work (De Paoli et al., J. Fluid Mech., 987, A1, 2024), we present additional experimental results along with three-dimensional pore-scale simulations and Darcy simulations incorporating dispersion effects. The mechanism of dispersion is accounted for by employing a Fickian anisotropic dispersion model (Wen et al., Phys. Rev. Fluids, 3, 12, 2018). The system considered is the Rayleigh-Taylor instability, consisting of two miscible fluids of different density in an unstable configuration, filling a saturated, homogeneous and isotropic porous medium. Results are compared in terms of global response parameters associated with the flow structure and mixing state of the system (namely, wavenumber, mixing length and mean scalar dissipation). In this idealised configuration, which is well-defined and controllable, we compare our findings to derive simple physical models and to identify suitable parameters to model the effect of dispersion at the Darcy scale.