The effect of interface movement and viscosity variation on the stability of a diffusive interface between aqueous and gaseous CO2

Abstract

Carbon dioxide injected in an aquifer rises quickly to the top of the reservoir and forms a gas cap from where it diffuses into the underlying water layer. Transfer of the CO 2 to the aqueous phase below is enhanced due to the high density of the carbon dioxide containing aqueous phase. This paper investigates the behavior of the diffusive interface in an enclosed space in which initially the upper part is filled with pure carbon dioxide and the lower part with liquid. Our analysis differs from a conventional analysis as we take the movement of the diffusive interface due to mass transfer and the composition dependent viscosity in the aqueous phase into account. The same formalism can also be used to describe the situation when an oil layer is underlying the gas cap. Therefore we prefer to call the lower phase the liquid phase. In this paper we include these two effects into the stability analysis of a diffusive interface between CO 2 and a liquid in the gravity field. We identify the relevant bifurcation parameter as q = Ra, where is the width of the interface. This implies the (well known) scaling of the critical time ∼Ra −2 and wavelength ∼Ra −1 (The critical time t c and critical wavelength k c are defined as follows: σ (k) ≤ 0 ∀t ≤ t c ; equality only holds for t = t c and k = k c ). Inclusion of the interface upward movement leads to earlier destabilization of the system. Increasing viscosity for increasing CO 2 concentration stabilizes the system. The theoretical results are compared to bulk flow visual experiments using the Schlieren technique to follow finger development in aquifer sequestration of CO 2 . In the appendix, we include a detailed derivation of the dispersion relation σ (k) in the Hele-Shaw case [C. T. Tan and G. M. Homsy, Phys. Fluids 29, 3549-3556 (1986)] which is nowhere explicitly given. C 2013 AIP Publishing LLC. [http://dx

Effect of Salinity and Pressure on the Rate of Mass Transfer in Aquifer Storage of CO2

“…An accurate experimental measurement of the flux for the actual CO 2 -brine system is difficult. For porous media, a large number of numerical studies (Ennis-King et al, 2005;Riaz et al, 2006) show that the onset time of convection is inversely proportional to the Rayleigh number, which can be expressed as, (Bando et al, 2004)  (Duan and Sun, 2003) D (Sell et al, 2012 The experimental onset times are presented in Table 2 and are compared to the theoretical relations, derived by Riaz et al (2006), Ennis-King et al (2005), Hassanzadeh et al (2007) , Xu et al (2006), Pau et al (2010) and Meulenbroek et al (2013). In order to quantify the time evolution of the flux, we describe the late time behavior when the plumes have not yet reached the bottom boundary.…”

“…A denser phase above a less dense phase initiates convective currents that enhance the dissolution rate, thus accelerating dissolution of CO 2 in the aqueous phase. The initial stage of natural convection in a saturated porous layer with a denser fluid on top of a lighter fluid has been extensively studied by means of a linear stability analysis, numerical simulations and the energy method ( (Bachu et al, 1994;Class et al, 2009;Dentz and Tartakovsky, 2009;Elder, 1968;Ennis-King et al, 2005;Foster, 1965;Gasda, 2010;Khosrokhavar et al, 2014c;Meulenbroek et al, 2013;Moortgat et al, 2009;Myint and Firoozabadi, 2013;Nordbotten and Celia, 2011;Nordbotten et al, 2005;Pruess et al, 2003;Ranganathan et al, 2012;Riaz et al, 2006;Van Duijn et al, 2004;Walker and Homsy, 1978)). …”

Effect of swelling on the onset of buoyancy-driven convection during the CO2 dissolution process in a porous medium

“…Meulenbroek et al [17] pre-assumed Eq. (14) and determined the constant g from the experimental data.…”

“…However, all the above mentioned work has been done for the non-swelling mixtures. Very recently, Meulenbroek et al [17] and Myint and Firoozabadi [18] studied the effect of swelling on the onset of a buoyancy-driven convection in a liquid saturated porous medium. Since the swelling ratio of a CO 2 /oil mixture is much larger than a CO 2 /water system, the effect of the swelling on the gravitational instability is important in the CO 2 -IOR system.…”

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.…”