TY - UNPB
T1 - Onset of transient convection in a porous medium with an embedded low-permeability layer
AU - Luther, Emmanuel E.
AU - Shariatipour, Seyed M.
AU - Holtzman, Ran
AU - Dallaston, Michael C.
N1 - 27 pages, 9 figures
PY - 2021/9/25
Y1 - 2021/9/25
N2 - 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.
AB - 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.
KW - Convective Instabilities
KW - Layered Porous Media
KW - Quasi-Steady-State Approximation
KW - Buoyancy-driven flow
KW - Linear stability analysis
M3 - Preprint
BT - Onset of transient convection in a porous medium with an embedded low-permeability layer
PB - arXiv
ER -