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

Meulenbroek, B.J.; Farajzadeh, R.; Bruining, J.

doi:doi:10.1063/1.4813072

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

Title

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

Author

Meulenbroek, B.J.
Farajzadeh, R.
Bruining, J.

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Date

2013-07-17

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 CO2 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 CO2 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 tc and critical wavelength kc are defined as follows: ?(k) ? 0??t ? tc; equality only holds for t = tc and k = kc). Inclusion of the interface upward movement leads to earlier destabilization of the system. Increasing viscosity for increasing CO2 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 CO2. In the appendix, we include a detailed derivation of the dispersion relation ?(k) in the Hele-Shaw case [C. T. Tan and G. M. Homsy, Phys. Fluids 29, 3549–3556 (1986)]10.1063/1.865832 which is nowhere explicitly given.

Subject

bifurcation
carbon compounds
critical phenomena
diffusion
dispersion relations
flow instability
groundwater
inclusions
mass transfer
oils
reservoirs
two-phase flow
viscosity