Onset of transient convection in a porous medium with an embedded low-permeability layer

TL;DR

This study theoretically investigates how layered permeability variations in porous media influence the timing of convective instability onset, emphasizing the importance of detailed geological characterization for CO2 sequestration.

Contribution

It introduces a linear stability analysis framework to understand the impact of non-monotonic permeability profiles on convection onset in layered porous formations.

Findings

Low-permeability layers can either accelerate or delay convection onset.

The effect depends on the permeability transition smoothness, Rayleigh number, and layer position.

Layer effects are negligible when near the lower boundary at high Rayleigh numbers.

Abstract

Deep saline aquifers used for CO$_2$ sequestration are commonly made of sedimentary formations consisting of several layers of distinguishable permeability. In this work, the effect of a non-monotonic, vertically varying permeability profile on the onset of convective instability is studied theoretically using linear stability analyses. The onset time depends on the interaction between the permeability profile and the location of the concentration perturbation peak beyond which the concentration of CO$_2$ decays. A thin low-permeability layer can either accelerate or delay the onset time of the convective instability depending on the nature of the permeability variation - whether the permeability transition is smooth or layered, the Rayleigh number (Ra), and the location of the permeability change ($\hat{a}$) relative to the perturbation peak ($\hat{a}_{c^{*}}$), which scales as $\hat{a}_{c^{*}}\approx 14Ra^{-1}$ for homogeneous systems. However, the low permeable layer has no effect on the onset time when it is near the lower boundary of a medium with sufficiently large Ra ($\hat{a}_{c^{*}} \ll \hat{a}$). This nontrivial dependence highlights the implication of ignoring geological features of a small spatial extent, indicating the importance of a detailed characterization of CO$_2$ storage sites.