Enhanced steady-state dissolution flux in reactive convective dissolution

Chemically Enhanced Convective Dissolution of CO_{2}

Convective dissolution, one of the main mechanisms for geological storage of CO_{2}, occurs when supercritical or gas CO_{2} dissolves partially into an aqueous solution, thus triggering downward convection of the denser CO_{2}-enriched liquid. Chemical reaction in the liquid can greatly enhance the process. Here, experimental measurements of convective flow inside a cylinder filled with a sodium hydroxide (NaOH) solution show that the plume's velocity can be increased tenfold as compared to a situation with no NaOH. This tremendous effect is predicted by a model with no adjusting parameters.

Effect of variable solubility on reactive dissolution in partially miscible systems

When two partially miscible systems are put in contact, one phase, A, can dissolve into the other one with a given solubility. Chemical reactions in the host phase can impact this dissolution by consuming A and by generating products that impact the solubility of A. Here, we study theoretically the optimal conditions for transfer of a reactant A in a host phase containing a species B when a bimolecular A + B → C reaction generates a product C that linearly decreases the solubility of A. We have quantified numerically the influence of this variable solubility on the reaction-diffusion (RD) concentration profiles of all species in the host phase, on the temporal evolution of the position of the reaction front, and on the flux of A through the interface. We have also computed the analytical asymptotic concentration profiles, solutions at long times of the RD governing equations. For a fixed negative effect of C on the solubility of A, an increase in the initial concentration of reactant B or an increase in the diffusion rate of species B and C results in a larger flux of A and hence a larger amount of A dissolved in the host solution at a given time. However, when the influence of C on the solubility increases, the mass transfer decreases. Our results help understand to what extent a chemical reaction can optimize the reactive transfer of a solute to a host phase with application to, among other things, the geological sequestration of carbon dioxide in an aquifer.

Nonlinear development of convective patterns driven by a neutralization reaction in immiscible two-layer systems

This article provides the results of a theoretical and experimental study of buoyancy-driven instabilities triggered by a neutralization reaction in an immiscible two-layer system placed in a vertical Hele-Shaw cell. Flow patterns are predicted by a reaction-induced buoyancy number [Formula: see text], which we define as the ratio of densities of the reaction zone and the lower layer. In experiments, we observed the development of cellular convection ([Formula: see text]), the fingering process with an aligned line of fingertips at a slightly denser reaction zone ([Formula: see text]) and the typical Rayleigh-Taylor convection for [Formula: see text]. A mathematical model includes a set of reaction-diffusion-convection equations written in the Hele-Shaw approximation. The model's novelty is that it accounts for the water produced during the reaction, a commonly neglected effect. The persisting regularity of the fingering during the collapse of the reaction zone is explained by the dynamic release of water, which compensates for the heavy fluid falling and stabilizes the pattern. Finally, we present a stability map on the plane of the initial concentrations of solutions. Good agreement between the experimental data and theoretical results is observed. This article is part of the theme issue 'New trends in pattern formation and nonlinear dynamics of extended systems'.

Chemically-driven convective dissolution

When a solute A dissolves in a host phase with a given solubility, the resulting density stratification is stable towards convection if the density profile increases monotonically along the gravity field. We theoretically and numerically study the convective destabilization by reaction of this dissolution when A reacts with a solute B present in the host phase to produce C via an A + B→C type of reaction. In this reactive case, composition changes can give rise to non-monotonic density profiles with a local maximum. A convective instability can then be triggered locally in the zone where the denser product overlies the less dense bulk solution. First, we perform a linear stability analysis to identify the critical conditions for this reaction-driven convective instability. Second, we perform nonlinear simulations and compare the critical values of the control parameters for the onset of convection in these simulations with those predicted by linear stability analysis. We further show that the asymptotic dissolution flux of A can be increased in the convective regime by increasing the difference ΔR_CB = R_C-R_B between the Rayleigh numbers of the product C and reactant B above a critical value and by increasing the ratio β = B₀/A₀ between the initial concentration B₀ of reactant B and the solubility A₀ of A. Our results indicate that chemical reactions can not only initiate convective mixing but can also give rise to large dissolution fluxes, which is advantageous for various geological applications.

Enhanced convective dissolution due to an A + B → C reaction: control of the non-linear dynamics via solutal density contributions

Chemical reactions can have a significant impact on convective dissolution in partially miscible stratifications in porous media and are able to enhance the asymptotic flux with respect to the non-reactive case. We numerically study such reactive convective dissolution when the dissolving species A increases the density of the host phase upon dissolution and reacts with a reactant B present in the host phase to produce C by an A + B → C reaction. Upon varying the difference ΔR_CB = R_C-R_B between the Rayleigh numbers of the product C and the reactant B, we identify four regimes with distinct dynamics when the diffusion coefficients are the same. When ΔR_CB < 0, the density profiles are non-monotonic and the non-linear dynamics are seen to depend on the relative values of the density at the interface and the initial density of the host phase. For ΔR_CB > 0, the monotonic density profiles are destabilizing with respect to the non-reactive case above a certain critical value ΔR_cr. We analyze quantitatively the influence of varying ΔR_CB and the ratio β = B₀/A₀ of the initial concentration of B and the solubility of A on the asymptotic steady flux, the wavelength of the fingers and the position of the reaction front. In the context of CO₂ geological sequestration, understanding how such reactions can enhance the dissolution flux is crucial for improving the efficiency and safety of the process.

Differential Diffusivity Effects in Reactive Convective Dissolution

When a solute A dissolves into a host fluid containing a reactant B, an A + B → C reaction can influence the convection developing because of unstable density gradients in the gravity field. When A increases density and all three chemical species A, B and C diffuse at the same rate, the reactive case can lead to two different types of density profiles, i.e., a monotonically decreasing one from the interface to the bulk and a non-monotonic profile with a minimum. We study numerically here the nonlinear reactive convective dissolution dynamics in the more general case where the three solutes can diffuse at different rates. We show that differential diffusion can add new dynamic effects like the simultaneous presence of two different convection zones in the host phase when a non-monotonic profile with both a minimum and a maximum develops. Double diffusive instabilities can moreover affect the morphology of the convective fingers. Analysis of the mixing zone, the reaction rate, the total amount of stored A and the dissolution flux further shows that varying the diffusion coefficients of the various species has a quantitative effect on convection.

Reactive convective-dissolution in a porous medium: stability and nonlinear dynamics

We investigate the effects of a dissolution reaction, A(aq) + B(s) → C(aq), on the gravitational instability and nonlinear dynamic behaviour of a diffusive boundary layer in a porous medium. Our linear stability and numerical results reveal that, unexpectedly, even when the density contribution of the soluble product C is smaller than that of the dissolved solute A, the chemical reaction can destabilize the layer and accelerate the onset of convection. However, for a very light product, the reaction stabilizes the layer. We show that these widely disparate characteristics of the reactive-diffusive layer are outcomes of the nonlinear competition between two reaction effects, the destabilizing sharpening of the solute concentration gradient and associated increase in the solute diffusive flux, and the stabilizing replacement of the solute by a less dense product near the interface.