Stability of a fluid in a horizontal saturated porous layer: effect of non-linear concentration profile, initial, and boundary conditions

Abstract

Carbon dioxide injected into saline aquifers dissolves in the resident brines increasing their density, which might lead to convective mixing. Understanding the factors that drive convection in aquifers is important for assessing geological CO 2 storage sites. A hydrodynamic stability analysis is performed for non-linear, transient concentration fields in a saturated, homogenous, porous medium under various boundary conditions. The onset of convection is predicted using linear stability analysis based on the amplification of the initial perturbations. The difficulty with such stability analysis is the choice of the initial conditions used to define the imposed perturbations. We use different noises to find the fastest growing noise as initial conditions for the stability analysis. The stability equations are solved using a Galerkin technique. The resulting coupled ordinary differential equations are integrated numerically using a fourth-order Runge-Kutta method. The upper and lower bounds of convection instabilities are obtained. We find that at high Rayleigh numbers, based on the fastest growing noise for all boundary conditions, both the instability time and the initial wavelength of the convective instabilities are independent of the porous layer thickness. The current analysis provides approximations that help in screening suitable candidates for homogenous geological CO 2 sequestration sites.

Impact of pressure, salt concentration, and temperature on the convective dissolution of carbon dioxide in aqueous solutions

“…These onset time and wavenumber are in good agreement with those found in several previous theoretical studies [25][26][27][28][29][30][31] . Additionally, these onset characteristics are close to those evaluated experimentally in systems analogous to the CO 2 /water system 9,11 .…”

Chemical control of dissolution-driven convection in partially miscible systems: theoretical classification

“…In particular, the early-stage development of this instability has been characterized both theoretically and experimentally for porous media or Hele-Shaw cells with a focus on the critical time and wavenumber for the onset of convection 5,[10][11][12]16,[18][19][20][21][22][23][24][25][26][27][28][29] . Studies have reported the impact on these properties of boundary conditions 21,22,28 , anisotropy of the permeability 16,[23][24][25]28 , geometry of the system 26 , compressibility and interface movement 27 , a geothermal gradient 28,29 , and control parameters in laboratory experiments 5,[10][11][12]19 .…”

“…Studies have reported the impact on these properties of boundary conditions 21,22,28 , anisotropy of the permeability 16,[23][24][25]28 , geometry of the system 26 , compressibility and interface movement 27 , a geothermal gradient 28,29 , and control parameters in laboratory experiments 5,[10][11][12]19 . However, an important aspect that has been less investigated is the impact of chemical reactions on such instabilities.…”

Convective shutdown in a porous medium at high Rayleigh number

“…Many previous studies of one-sided convective systems have focused on the conditions required for the onset of convection, which presents significant theoretical challenges because the diffusive base state is both time-dependent and nonlinear. Various theoretical studies (Hassanzadeh, Pooladi-Darvish & Keith 2006;Riaz et al 2006;Xu, Chen & Zhang 2006;Slim & Ramakrishnan 2010) have been complemented by direct numerical investigations (Riaz et al 2006;Hassanzadeh, Pooladi-Darvish & Keith 2007) and laboratory experiments (Fernandez et al 2002;Backhaus, Turitsyn & Ecke 2011;Slim et al 2013) that explore the onset of convection.…”