Spreading and mixing during solutal convection in uniform porous media with application to geologic CO2 storage

Abstract

Convective dissolution in saline aquifers is expected to positively impact subsurface storage of carbon dioxide (CO 2 ) by accelerating its dissolution rate into reservoir brines. By largely focusing on the dissolution flux, previous studies lack a systematic evaluation of the mixing process following CO 2 emplacement, including a quantitative analysis at conditions representative of subsurface traps (Rayleigh number, Ra ≤ 1 000). Here, we investigate solutal convection numerically in a two-dimensional uniform porous medium in the regime Ra = 100 − 10 000. The macroscopic evolution of the convective process is characterized by means of fundamental macroscopic measures of mixing that use the local spatial structure of the solute concentration field. It is shown that the intensity of segregation closely mimics the evolution of the in-situ convective pattern arising from the stretching and merging of downwelling plumes. The spreading length and the dilution index both confirm that the mixing process accelerates over time (t) with a power law scaling (∝ t α ) that transitions from diffusive (α = 0.5) to super-diffusive mixing (α ≥ 1) irrespective of Ra. This transition time scales τ on ∝ Ra −2 and is used as a measure of the onset time of convection. The dilution index indicates that the time needed to reach close-to-complete mixing reduces linearly with Ra.On the contrary, the non-dimensional mass flux, expressed in terms of the Sherwood number, Sh, reveals a natural logarithmic scaling for Ra ≤ 2 500.

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

“…The numerical solution of the corresponding 1D purely diffusive scenario is included for comparison (see also Eckel and Pini). 66 While the latter follows the expected behavior (i.e., M norm ∝ t 0.5 ), the experiments show a ballistic behavior (M norm ∝ t 1 ), as indicated by the trend lines fitted to the data in the advanced convective regime (additional details in the caption of Figure 6). The NMSE values and the 95% confidence bounds of the three scalings are reported in Table S2.…”

“…The NMSE values and the 95% confidence bounds of the three scalings are reported in Table S2. A ballistic increase of the zeroth moment in the advanced convective regime is evidence for a quasi-steady flux (see Figure ) and gives an indication for a constant vertical fluid velocity of the downwelling plumes. , …”

“…There is a clear horizontal shift between experiments carried out with different bead sizes, reflecting the impact of permeability (and hence Ra ) on the rate of mixing. The numerical solution of the corresponding 1D purely diffusive scenario is included for comparison (see also Eckel and Pini) . While the latter follows the expected behavior (i.e., M norm ∝ t 0.5 ), the experiments show a ballistic behavior ( M norm ∝ t 1 ), as indicated by the trend lines fitted to the data in the advanced convective regime (additional details in the caption of Figure ).…”

“…This is in contrast to the linear growth behavior (σ/H ∝ t) reported in previous numerical studies that do not include hydrodynamic dispersion in their applied models. 66,67 The reduction in the exponent values in both the standard deviation and the center of mass suggests that the effect of hydrodynamic dispersion on the longitudinal mixing needs to be further evaluated. governed by diffusive mass transport, fingers begin to form.…”

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

“…Three-dimensional (3D) experiments based on X-ray 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 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.…”