Effect of permeability heterogeneity on reactive convective dissolution

TL;DR

The paper investigates how permeability heterogeneity shapes reactive buoyancy-driven convective dissolution for the bimolecular reaction $A+B\rightarrow C$ in porous media. Using a variable-density solver with three permeability structures (homogeneous, horizontally stratified, vertically stratified, and log-normal) and multiple anisotropy and variance scenarios, it quantifies front dynamics, mixing, and dissolution fluxes across reactive regimes. Key findings show vertical stratification and log-normal fields generally enhance mixing, front progression, reaction rate, and product mass, while horizontal stratification acts as a barrier to vertical fingering and reduces mixing efficacy; the impact of heterogeneity is strongly modulated by the anisotropy ratio $\lambda_x/\lambda_z$ and the reaction regime (R1, R2, R3). The results have practical relevance to CO$_2$ sequestration, informing aquifer selection and management strategies to maximize mixing and minimize leakage, and point to future work involving real porous media data and other reaction chemistries.

Abstract

The impact of permeability heterogeneity on reactive buoyancy-driven convective dissolution is analyzed numerically in the case of a bimolecular A+B$\to$C reaction across varying Rayleigh numbers. The convective dynamics is compared in homogeneous, horizontally stratified, vertically stratified, and log-normally distributed permeability fields. Key variables, such as the total amount of product, mixing length, front position and width, reaction and scalar dissipation rates, and dissolution fluxes, are strongly influenced by the type of permeability heterogeneity. Vertically stratified and log-normally distributed permeability fields lead to larger values for all parameters compared to homogeneous fields. Horizontally stratified fields act as an obstacle to convective flow, resulting in slower front progression, thicker fingers, wider reaction fronts, and the lowest dissolution fluxes among all cases. When the reaction stabilizes convection, flow stagnation occurs near the extremum of the non-monotonic density profile, even in vertically stratified systems, highlighting the complex interaction between reactions and dissolution-driven convection. In log-normally distributed fields, the flow behavior depends on the permeability structure: smaller horizontal correlation lengths cause fingers to spread more horizontally, while larger horizontal correlation lengths promote more vertical movement with shorter wavelengths. Overall, a shorter horizontal correlation length relative to the vertical one leads to an increase in the value of all aforementioned parameters and thus to a more efficient mixing. These findings reveal how heterogeneity affects convective dynamics by influencing the reaction front, dissolution rates, mixing behavior, and mass transport efficiency, emphasizing the intricate role of permeability structure in reactive convective processes.

Figures (19)

• Figure 1: Different realizations of the log-permeability fields for the horizontally stratified, vertically stratified, and multi-Gaussian permeability structures with variable correlation lengths $\lambda_{x}$ and $\lambda_{z}$. All realizations have $\sigma_{\log k}^{2} =1$.
• Figure 2: Density patterns for the homogeneous case at time t=8000 and the vertically stratified permeability with different variances at $t=4000$ for R1, R2 and R3 cases. Fingers in the homogeneous case are smoother with rounded tips whereas vertically stratified ones are thinner, elongated and with sharp tips. In R1, the non-monotonic density profile with a minimum stabilizes convection and the front looks like stuck. In contrast, in the more unstable R2 and R3 cases, the fingers reach the bottom of the domain faster. Increasing $\sigma^2_{\log k}$ makes the fingers reach the bottom of the domain even earlier
• Figure 3: Density patterns for the horizontally stratified permeability with different variances at $t=8000$ for R1, R2 and R3 cases. Fingers are thick and spread laterally. Merging is more pronounced in R2 and R3 cases when $\sigma^2_{\log k}$ is increased. Fingers advance more slowly in R1 as $\sigma^2_{\log k}$ is increased
• Figure 4: Density profiles of the reactive homogeneous and stratified cases at $t=6000$. R1 shows a non-monotonic density profile whereas R2 and R3 feature a monotonic decreasing density.
• Figure 5: Log-Normally distributed permeability cases density at $t=4000$ for different correlation lengths and for $\sigma_{\log k}^{2}=1$. Cases with $\lambda_{x}<\lambda_{z}$ ((b) and (d)) present fingers similar in shape with the horizontally stratified ones whereas cases with $\lambda_{x}>\lambda_{z}$ ((c) and (e)) present fingers similar in shape with the vertically stratified ones. The isotropic case (a) exhibits fingers that resemble roots or small channels. As previously observed for the stratified cases, increasing $\sigma_{\log k}^{2}$ accelerates convection.