Effect of permeability heterogeneity on reactive convective dissolution

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.

💡 Research Summary

This paper investigates how spatial heterogeneity in permeability influences buoyancy‑driven reactive convective dissolution, focusing on a bimolecular reaction A + B → C. Using the open‑source CFD framework SECUReFoam (based on OpenFOAM), the authors solve the Darcy flow coupled with advection‑diffusion‑reaction equations for three species in a two‑dimensional porous domain. The governing equations are nondimensionalized, with Rayleigh numbers (R_A, R_B, R_C) quantifying each species’ contribution to fluid density. Three reaction scenarios are examined: R1 (non‑monotonic density profile with a minimum, stabilizing convection), R2 (monotonically increasing density, strongly destabilizing), and R3 (initially stable but becomes unstable as product C builds up).

Permeability fields are generated as log‑normally distributed random fields with variances σ²_log k = 1, 2, 3. Three structural classes are considered: (i) horizontally stratified (infinite horizontal correlation, finite vertical correlation λ_z = 50), (ii) vertically stratified (finite horizontal correlation λ_x = 100, infinite vertical correlation), and (iii) multi‑Gaussian fields with prescribed horizontal (λ_x) and vertical (λ_z) correlation lengths, allowing systematic variation of anisotropy (λ_x/λ_z). Each heterogeneous case is simulated ten times with different white‑noise realizations to obtain statistically robust averages.

Key findings:

1. Finger morphology – In homogeneous media, convective fingers are relatively uniform with rounded tips. Vertically stratified media guide fingers along high‑permeability channels, producing thin, elongated structures. Horizontally stratified media act as barriers; fingers become thicker, spread laterally, and vertical progression is suppressed. In multi‑Gaussian fields, the anisotropy ratio controls the dominant direction: λ_x/λ_z > 1 yields lateral spreading and faster finger merging, whereas λ_x/λ_z < 1 promotes vertical penetration with thinner fingers.

2. Density profile and reaction effects – R1 creates a non‑monotonic density profile with a minimum; the reaction therefore stabilizes convection and confines flow to an upper layer. R2, where all species increase density (R_C = 2), yields a monotonic, strongly destabilizing profile, leading to the fastest finger growth and the highest mixing length and dissolution flux. R3 starts stable (R_A < 0) but becomes unstable as C accumulates, showing intermediate dynamics.

3. Mixing length and dissolution flux – Mixing length is defined as the vertical distance where the density deviation exceeds 10⁻³. Prior to instability, it follows a √t diffusion scaling; after onset, a linear (t) growth characteristic of the nonlinear regime appears. In vertically stratified cases, increasing σ²_log k enlarges the mixing length, whereas in horizontally stratified cases it reduces it. The dissolution flux mirrors these trends: the largest fluxes occur for R2 in vertically stratified or anisotropic (λ_x/λ_z < 1) multi‑Gaussian fields; the smallest fluxes are observed for horizontally stratified media.

4. Impact of anisotropy and variance – Shorter horizontal correlation lengths relative to vertical ones (λ_x < λ_z) enhance vertical channeling, increasing mixing efficiency and flux. Conversely, longer horizontal correlation lengths create low‑permeability barriers that impede vertical motion, reducing overall transport. Higher variance (σ²_log k) amplifies these effects: it accelerates mixing in vertically dominated structures but slows it in horizontally dominated ones.

The study concludes that permeability heterogeneity profoundly modulates reactive convective dissolution by altering finger geometry, front propagation, and mass‑transfer rates. Vertically stratified and anisotropic fields with λ_x/λ_z < 1 are most favorable for efficient mixing and CO₂ dissolution, while horizontal stratification hinders transport. These insights are directly relevant to geological carbon sequestration, contaminant remediation, and any subsurface process where chemical reactions couple with buoyancy‑driven convection. Understanding and quantifying the interplay between reaction kinetics, density stratification, and permeability structure is essential for accurate prediction and optimal design of such systems.