Convective dissolution of carbon dioxide in two- and three-dimensional porous media: The impact of hydrodynamic dispersion

Abstract

Convective dissolution is the process by which CO2 injected in geological formations dissolves into the aqueous phase and thus remains stored perennially by gravity. It can be modeled by buoyancy-coupled Darcy flow and solute transport. The transport equation should include a diffusive term accounting for hydrodynamic dispersion, wherein the effective diffusion coefficient is proportional to the local interstitial velocity. We investigate the impact of the hydrodynamic dispersion tensor on convective dissolution in two-dimensional (2D) and three-dimensional (3D) homogeneous porous media. Using a novel numerical model, we systematically analyze, among other observables, the time evolution of the fingers' structure, dissolution flux in the quasi-constant flux regime, and mean concentration of the dissolved CO2; we also determine the onset time of convection, [Formula: see text]. For a given Rayleigh number Ra, the efficiency of convective dissolution over long times is controlled by [Formula: see text]. For porous media with a dispersion anisotropy commonly found in the subsurface, [Formula: see text] increases as a function of the longitudinal dispersion's strength ( S), in agreement with previous experimental findings and in contrast to previous numerical findings, a discrepancy that we explain. More generally, for a given strength of transverse dispersion, longitudinal dispersion always slows down convective dissolution, while for a given strength of longitudinal dispersion, transverse dispersion always accelerates it. Furthermore, a systematic comparison between 2D and 3D results shows that they are consistent on all accounts, except for a slight difference in [Formula: see text] and a significant impact of Ra on the dependence of the finger number density on S in 3D.

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

“…Most studies on convective dissolution did not consider this effect. Much of the focus in systems, which do incorporate dispersion, was given to the effect of dispersion on the onset of convection (Dhar et al., 2022; Ghesmat et al., 2011; Hassanzadeh et al., 2009; Hidalgo & Carrera, 2009). While Ghesmat et al.…”

“…Much of the focus in systems, which do incorporate dispersion, was given to the effect of dispersion on the onset of convection (Dhar et al, 2022;Ghesmat et al, 2011;Hassanzadeh et al, 2009;Hidalgo & Carrera, 2009). While Ghesmat et al (2011), Hidalgo and Carrera (2009), and Dhar et al (2022), considered only the effect of hydrodynamic dispersion, Hassanzadeh et al (2009) also considered the effect of natural groundwater flow. Although the findings of these studies did not appear to coincide, Wen et al (2018) reported that the source of this discrepancy was due to different choices of scaling and that dispersion generally delays the onset time and decreases the dissolution flux.…”

Two-dimensional micromodels for studying the convective dissolution of carbon dioxide in 2D water-saturated porous media

“…Convective dissolution has also been extensively studied by means of 2D simulations where the physical processes at stake are integrated over a ‘mesoscopic’ Darcy scale; 17–21 a few 3D numerical studies have also been performed, 22 including, recently, simulations where hydrodynamic dispersion is accounted for. 23…”

“…Convective dissolution has also been extensively studied by means of 2D simulations where the physical processes at stake are integrated over a 'mesoscopic' Darcy scale; [17][18][19][20][21] a few 3D numerical studies have also been performed, 22 including, recently, simulations where hydrodynamic dispersion is accounted for. 23 In this context, the use of patterned Hele-Shaw cells (i.e., quasi-2D porous media) is a method allowing both for heterogeneous pore flow and the pore scale measurement of the concentration field of the dissolved CO 2 , and hence, of the dissolution flux. In this article, we depict the design and the manufacturing process of such bi-dimensional porous micromodels (MM) which can allow for a direct and rigorous study of the role of pore scale flow and solute mixing in the solubility trapping of CO 2 .…”

“…Three-dimensional (3D) experiments based on xray tomography 13,14 or magnetic resonance imaging 15 allow characterizing the convection structure and convective fingers' velocity but do not provide robust measurements of dissolution fluxes, while recent 3D experiments with optical measurements have uncovered a hitherto unknown role of pore scale velocity heterogeneities 16 but do not yet provide precise measurements of the concentration fields. Convective dissolution has also been extensively studied by means of 2D simulations where the physical processes at stake are integrated over a 'mesoscopic' Darcy scale [17][18][19][20][21] ; a few 3D numerical studies have also been performed 22 , including, recently, simulations where hydrodynamic dispersion is accounted for 23 .…”