Onset of convection with fluid compressibility and interface movement

Abstract

The density increase from carbon dioxide (CO 2) dissolution in water or hydrocarbons creates buoyancy-driven instabilities that may lead to the onset of convection. The convection is important for both CO 2 sequestration in deep saline aquifers and CO 2 improved oil recovery from hydrocarbon reservoirs. We perform linear stability analyses to study the effect of fluid compressibility and interface movement on the onset of buoyancy-driven convection in porous media. Compressibility relates to a non-zero divergence of the velocity field. The interface between the CO 2 phase and the aqueous or hydrocarbon phase moves with time as a result of the volume change that occurs upon CO 2 dissolution. Previous stability analyses have neglected these two aspects by assuming that the aqueous or hydrocarbon phase is incompressible and that the interface remains fixed in position. The stability analyses are used to compute two key quantities: (1) the critical time and (2) the critical wavenumber. Our results indicate that compressibility has a negligible effect on the critical time and the critical wavenumber in CO 2-water mixtures. We use thermodynamics to derive an expression which shows that the two opposing physical processes which contribute to the divergence are comparable in magnitude and largely cancel each other. This result explains why compressibility does not significantly affect the onset, and it also demonstrates the link between compressibility and the volume change that causes movement of the interface. Compared to when the interface is fixed in position, a moving interface in CO 2-water mixtures may reduce the critical time by up to around 10%, which can be significant in low permeability formations. The decrease in the critical time due to interface movement may be much more pronounced in hydrocarbons than in water. This could have important implications for CO 2 improved oil recovery.

Double diffusive natural convection of CO2 in a brine saturated geothermal reservoir: Study of non-modal growth of perturbations and heterogeneity effects

“…In such case there will be phase transition between CO 2 and brine. The flat top interface will also shift with time because of pressure and volume change occurring upon CO 2 dissolution (Myint and Firoozabadi, 2013;Farajzadeh et al, 2007a,b;.…”

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

“…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.…”

“…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 .…”

The Effect of Boundary Conditions on the Onset of Buoyancy-Driven Convection in a Brine-Saturated Porous Medium

“…Even though the effect of the various factors such as the anisotropy and heterogeneity of the porous media (Ennis-King et al 2005;Xu et al 2006;Farjazadeh et al 2011), the geochemical reaction (Andress and Cardoso 2012;Ghesmat et al 2012) and the interface movement due to swelling (Meulenbroek et al 2013;Myint and Firoozabadi 2013) on the stability criteria have been widely considered, a little attention has been paid on the interface condition between the supercritical CO 2 and the brine. However, in the CO 2 sequestration system, due to a capillary effect, a partially permeable boundary condition is more realistic than an impermeable one, which has been adopted in the previous stability analyses.…”