Effects of a capillary transition zone on the stability of a diffusive boundary layer

In geological storage of carbon dioxide (CO2), the buoyant CO2 plume eventually accumulates under the caprock. Due to interfacial tension between the CO2 phase and the water phase, a capillary transition zone develops in the plume. This zone contains supercritical CO2 as well as water with dissolved CO2. Under the plume, a diffusive boundary layer forms. We study how cross-flow between the capillary transition zone and the diffusive boundary layer affects gravitational stability of the diffusive boundary layer. Linear stability analysis shows that this cross-flow has no significant effect on the selection of the critical mode. However, interaction with the capillary transition zone enhances the instability of the boundary layer, such that the onset of instabilities occurs earlier, when the diffusive boundary layer is thinner. The onset time may be reduced by a factor of five, which corresponds to the thickness of the diffusive boundary layer at onset being reduced by a factor of two. This reduced thickness of the boundary layer at onset can be interpreted in terms of a reduced portion of the critical mode that must ’fit’ inside the boundary layer when the other portion of the mode is confined within the capillary transition zone. Direct numerical simulations for the non-linear regime show that the mass transfer rate can be enhanced up to four times when the cross-flow is accounted for. This increase is related to advective inflow of CO2-saturated water across the interface. Therefore, the contribution from dissolution to the safety of geological storage of CO2 begins earlier and can be considerably larger than showed by estimates that neglect the capillary transition zone.

[1]  Karsten Pruess,et al.  Laboratory Flow Experiments for Visualizing Carbon Dioxide-Induced, Density-Driven Brine Convection , 2009, Transport in Porous Media.

[2]  Theodore D. Foster,et al.  Effect of Boundary Conditions on the Onset of Convection , 1968 .

[3]  Erik Lindeberg,et al.  Vertical convection in an aquifer column under a gas cap of CO2 , 1997 .

[4]  M. Elenius,et al.  Convective mixing in geological carbon storage , 2011 .

[5]  Hamdi A. Tchelepi,et al.  Convective dissolution of carbon dioxide in saline aquifers , 2010 .

[6]  B. Metz.  IPCC special report on carbon dioxide capture and storage , 2005 .

[7]  Karsten Pruess,et al.  Numerical Modeling Studies of The Dissolution-Diffusion-Convection ProcessDuring CO2 Storage in Saline Aquifers , 2008 .

[8]  J. L. Robinson,et al.  Theoretical analysis of convective instability of a growing horizontal thermal boundary layer , 1976 .

[9]  George Shu Heng Pau,et al.  High-resolution simulation and characterization of density-driven flow in CO2 storage in saline aquifers , 2009 .

[10]  Jesús Carrera,et al.  Effect of dispersion on the onset of convection during CO2 sequestration , 2009, Journal of Fluid Mechanics.

[11]  David Roberts,et al.  Satellite Imaging to Monitor CO 2 Movement at Krechba, Algeria , 2009 .

[12]  Anders Vretblad,et al.  Fourier Analysis and Its Applications , 2005 .

[13]  A. Slim,et al.  Onset and cessation of time-dependent, dissolution-driven convection in porous media , 2010 .

[14]  Marc Andre Hesse.  Mathematical modeling and multiscale simulation of CO2 storage in saline aquifers , 2008 .

[15]  Yongan Gu,et al.  Accelerated mass transfer of CO2 in reservoir brine due to density-driven natural convection at high pressures and elevated temperatures , 2006 .

[16]  A. Bejan,et al.  Convection in Porous Media , 1992 .

[17]  Rouhollah Farajzadeh,et al.  The effect of heterogeneity on the character of density-driven natural convection of CO2 overlying a brine layer , 2011 .

[18]  H. Tchelepi,et al.  Onset of convection in a gravitationally unstable diffusive boundary layer in porous media , 2005, Journal of Fluid Mechanics.

[19]  Dongxiao Zhang,et al.  Convective stability analysis of the long-term storage of carbon dioxide in deep saline aquifers , 2006 .

[20]  Andy Chadwick,et al.  Layer spreading and dimming within the CO2 plume at the sleipner field in the north sea , 2011 .

[21]  Philip Ringrose,et al.  Simulation of CO2 distribution at the In Salah storage site using high-resolution field-scale models , 2011 .

[22]  Lincoln Paterson,et al.  Role of Convective Mixing in the Long-Term Storage of Carbon Dioxide in Deep Saline Formations , 2005 .

[23]  Lincoln Paterson,et al.  Onset of convection in anisotropic porous media subject to a rapid change in boundary conditions , 2005 .

[24]  Andy Chadwick,et al.  Modelling carbon-dioxide accumulation at Sleipner: implications for underground carbon storage , 2007 .

[25]  G. Folland.  Fourier analysis and its applications , 1992 .