The impact of geochemistry on convective mixing in a gravitationally unstable diffusive boundary layer in porous media: CO₂ storage in saline aquifers

Abstract

The storage of carbon dioxide and acid gases in deep geological formations is considered a promising option for mitigation of greenhouse gas emissions. An understanding of the primary mechanisms such as convective mixing and geochemistry that affect the long-term geostorage process in deep saline aquifers is of prime importance. First, a linear stability analysis of an unstable diffusive boundary layer in porous media is presented, where the instability occurs due to a density difference between the carbon dioxide saturated brine and the resident brine. The impact of geochemical reactions on the stability of the boundary layer is examined. The equations are linearised, and the obtained system of eigenvalue problems is solved numerically. The linear stability results have revealed that geochemistry stabilises the boundary layer as reaction consumes the dissolved carbon dioxide and makes the density profile, as the source of instability, more uniform. A detailed physical discussion is also presented with an examination of vorticity and concentration eigenfunctions and streamlines' contours to reveal how the geochemical reaction may affect the hydrodynamics of the process. We also investigate the effects of the Rayleigh number and the diffusion time on the stability of a boundary layer coupled with geochemical reactions. Nonlinear direct numerical simulations are also presented, in which the evolution of density-driven instabilities for different reaction rates is discussed. The development of instability is precisely studied for various scenarios. The results indicate that the boundary layer will be more stable for systems with a higher rate of reaction. However, our quantitative analyses show that more carbon dioxide may be removed from the supercritical free phase as the measured flux at the boundary is always higher for flow systems coupled with stronger geochemical reactions.

Gaussian process modelling for uncertainty quantification in convectively-enhanced dissolution processes in porous media

“…Once there, it reacts with minerals in the geologic formation, leading to the precipitation of a secondary carbonate mineral [26]. When the CO 2 is dissolved into the brine, the density of the resulting solution is higher than that of brine, and this density di↵erence can engender flow instabilities that lead to the formation of CO 2 downward growing plumes with finger structures.…”

“…With the permeability parameter K modelled as a log Gaussian random field K = K(x) on R ⇥ ⌦, or the discrete form K given by equation (26), equations (9) become a new system of PDEs with random inputs K(x). This system is solved for the streamfunction (x) and the concentration C(x), which are also, therefore, random fields.…”

“…An approximation of K can be obtained by restricting the expansion in (26) to the first, say, D KL coe cients, i.e., to the subspace spanned by 1 , . .…”

“…Most of the literature on enhanced dissolution in CO 2 sequestration is concerned with the time evolution of the process and not with the analysis of the non-uniqueness of solutions, the corresponding bifurcation map and the stability of solutions. Moreover, in most of these works only molecular di↵usion is considered (e.g., [44]), chemical reaction is neglected (e.g., [28]) and the porous medium is taken as homogeneous (e.g., [26,56]). In this paper we target the problem of uncertainty quantification in the C-ED mechanism due to the medium heterogeneity, and taking into account dispersivity and chemical reaction, by considering possible stable (physically feasible) solutions on a bifurcation map, i.e., the long term evolution.…”

Evaluation of electro-osmotic pumping effect on microporous media flow

“…Fluid flow in micro porous media also has significant scientific and practical importance in many areas. In petroleum mining industrial, carbon dioxide is captured and made us of repelling the raw oil under earth (Ghesmat et al, 2011;Javaheri et al, 2010). In hydrogen storage, the particle diameters in the porous hydrogen storage alloys are 1-20 μm.…”