Pore-scale study of dissolution-driven density instability with reaction $A+B\to C$ in porous media

Dissolution-driven density instability (DI) occurs when a species $A$ dissolves into a host fluid and introduces a buoyantly unstable stratification. Such an instability has positive effects in related applications and may be affected if species $A$ reacts with solute $B$ in the host fluid. In this paper, the lattice Boltzmann (LB) method is employed to simulate the dynamics of such an instability coupled with reaction $A+B\to C$ in porous media at the pore scale. Numerical simulations in homogeneous media have demonstrated that six types of dissolution-driven DI can be classified based on the Rayleigh numbers of three chemical species ${\text{Ra}}_r$ (ratio of buoyancy to viscous forces), and reaction can accelerate, delay or even trigger the development of DI. Then, a parametric study has indicated that, increasing $\mathrm{\Delta }{\text{Ra}}_{CB}$ (${\text{Ra}}_C-{\text{Ra}}_B$) can intensify density instability and reaction, promote the diffusion of species $A$, and also introduce either stabilizing or destabilizing effects of reaction. Besides, the increase of initial reactant concentration or/and Damköhler number $\text{Da}$ (ratio of flow time to chemical time) can enhance the influence of chemistry. Finally, simulations are carried out in three types of heterogeneous media HE1–HE3, and six groups of fingering scenarios can also be observed in each medium. However, compared with the homogeneous case, heterogeneous media HE1 with randomly distributed solid grains can introduce deeper advancing position and rougher density fingering, and media HE2 and HE3 with vertical variations of pore spaces can affect the developing speed of fingering obviously. In terms of the storage of species $A$ in the host fluid, medium HE2 with large pore size in the top layer is favorable. The present study is of significant importance for applications such as carbon capture and storage.

Figure 1

The computational configuration.

Figure 2

Density fields for Tests NR and R1–R3 in homogeneous medium HO.

Figure 3

Horizontally averaged density profiles for Tests NR and R1–R3 in homogeneous medium HO.

Figure 4

Time evolutions of the mixing length for Test I in homogeneous medium HO.

Figure 5

Schematic diagram of homogeneous media HO1–HO3 with different aspect ratios.

Figure 6

Time evolutions of the mixing length for Test IV in homogeneous media HO1–HO3.

Figure 7

Time evolution of the mixing length for Tests II and III in homogeneous medium HO.

Figure 8

Time evolution of the volume-averaged reaction rate for Test I in homogeneous medium HO.

Figure 9

Time evolution of the storage of species $A$ for Test I in homogeneous medium HO.

Figure 10

Schematic diagrams of heterogeneous media HE1–HE3.

Figure 11

(a) Measuring positions $P_n$ and volumes $V_m$ based on the structure of medium HO; (b), (c) Vertical evolution of horizontally averaged pore size and porosity in both homogeneous medium HO and heterogeneous media HE1–HE3.

Figure 12

Density fields for Test R2 in heterogeneous media HE1A–HE3.

Figure 13

Outlines of density fingering in both homogeneous medium HO and heterogeneous media HE1A–HE3 at $t^{*}=160$.

Figure 14

Time evolution of the mixing length for Test R2 in both homogeneous medium HO and heterogeneous media HE1–HE3.

Figure 15

Time evolution of the storage of species $A$ for Test R2 in both homogeneous medium HO and heterogeneous media HE1–HE3.

Figure 16

Schematic diagram of homogeneous media HOA-HOB with different pore sizes.

Figure 17

Time evolution of the mixing length and the storage of species $A$ for Test R2 in both homogeneous media HOA and HOB and heterogeneous media HE1A–HE1C.