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

Abstract

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.

Convective mixing in porous media: a review of Darcy, pore-scale and Hele-Shaw studies

“…This discrepancy may be due to the relatively short range and small values of explored, which is well below the value in correspondence of which the system is observed to attain an asymptotic linear scaling [ 54 , 59 ]. Employing the same measurement technique but different fluids, Eckel et al [ 114 ] achieved larger Rayleigh–Darcy numbers ( 55,000). Through qualitative and quantitative observations of flow evolution, they also observed an enhanced longitudinal spreading of the solute, but in this case a sublinear scaling for holds.…”

Numerical Investigation of the Influence of Hydrodynamic Dispersion on Solutal Natural Convection

“…The reason for this exclusion is that Hele‐Shaw cells consist of no porous medium and mechanical dispersion cannot develop in these setups. Three of the experiments were obtained in 3D systems (Eckel et al., 2023; Liyanage et al., 2019; Wang et al., 2016), while the rest used 2D systems. Six of the eight numerical studies, including the results presented here, suggest that in the absence of dispersion, $$Sh\propto Ra$$ (Elenius & Johannsen, 2012; Hewitt et al., 2014; Hidalgo et al., 2012; Pau et al., 2010; Slim, 2014; Wen et al., 2018).…”

Towards the understanding of convective dissolution in confined porous media: thin bead pack experiments, two-dimensional direct numerical simulations and physical models

“…On the one hand, mechanical dispersion produces additional spreading of solute and can be several orders of magnitude more effective than molecular diffusion (Delgado 2007). It has been also observed (Eckel et al 2022) that the presence of the finger pattern and the counter-current flow structure enhance the longitudinal spreading of the solute compared with unidirectional dispersion of a single-solute plume. This additional spreading is responsible for the reduction of the local density gradients, diminishing the strength of convective motions and coupling convection and diffusion as mechanisms controlling the mixing process.…”