HR: 1340h
AN: NG33C-0188    [Abstracts]
TI: Onset of convection in a gravitationally unstable, diffusive boundary layer in porous media.
AU: * Riaz, A
EM: ariaz@stanford.edu
AF: Stanford University, Department of Petroleum Engineering 065 Green Earth Sciences Bldg. 367 Panama Street, Stanford, CA 94305 United States
AU: Tchelepi, H
EM: tchelepi@pangea.Stanford.EDU
AF: Stanford University, Department of Petroleum Engineering 065 Green Earth Sciences Bldg. 367 Panama Street, Stanford, CA 94305 United States
AB: We present a linear stability analysis of density driven, miscible flow in porous media in the context of CO2 sequestration in saline aquifers. CO2 dissolution into the underlying brine leads to a local density increase that results in a gravitational instability. The physical phenomenon is analogous to the thermal convective instability in a semi-infinite domain, due to step change in temperature at the boundary. The critical time for the onset of convection in such problems has not been determined accurately by previous studies. We present a solution, based on the dominant mode of the self-similar diffusion operator, which can accurately predict the critical time and the associated unstable wavenumber. This approach is used to explain the instability mechanisms of the critical time and the longwave cutoff in a semi-infinite domain. The dominant mode solution however, is valid only for a small parameter range. We extend the analysis by employing the quasi steady state approximation (QSSA) which provides accurate solutions in the self-similar coordinate system. For large times, both the maximum growth rate and the most dangerous mode decay as t^1/4.
DE: 1832 Groundwater transport
DE: 3215 Instability analysis
DE: 3255 Spectral analysis (3205, 3280)
DE: 4255 Numerical modeling (0545, 0560)
DE: 4901 Abrupt/rapid climate change (1605)
SC: Nonlinear Geophysics [NG]
MN: Fall Meeting 2005