Spatial Moment Analysis of Convective Mixing in Three-Dimensional Porous Media Using X-ray CT Images

Dissolution trapping is one of the primary mechanisms of carbon dioxide (CO2) storage in deep saline aquifers. The determination of the realized rates of CO2 dissolution requires an understanding of the mixing process that takes place following the emplacement of CO2 into the formation. Owing to the difficulty of reproducing the time-dependent convective process in porous media, experiments so far have largely focused on 2D systems (e.g., Hele-Shaw cells) and used analogue fluid pairs with properties that differ from the subsurface CO2/brine system. Here, we present a novel experimental approach to investigate the evolution of the convective mixing process in 3D porous media (homogeneous packings of glass beads) using X-ray computed tomography (CT). We explore a range of Rayleigh numbers (Ra = 3000-55000) and observe directly the mixing structures that arise upon dissolution. We compute from the images the temporal evolution of the spatial moments of the concentration distribution, including the cumulative dissolved mass, the location of the center of mass, and the standard deviation of the concentration field. The scalings of the spatial moments suggest an impact of hydrodynamic dispersion on the longitudinal mixing. We propose a simplified representation of the mixing process by analogy with the 1D advection-dispersion model. This enables the estimation of the bulk advective velocity and the effective longitudinal dispersion coefficient for each bead packing. These estimates suggest that the presence of the finger pattern and the counter-current flow structure enhance the longitudinal spreading of the solute by roughly 1 order of magnitude compared to unidirectional dispersion of a single-solute plume.