Onset of Convection in a Gravitationally Unstable,
Diffusive Boundary Layer in Porous Media
with Amir Riaz, Hamdi Tchelepi, and Franklin Orr, Jr.
We carry out a linear stability analysis of the density driven, miscible flow in porous
media in the context of CO2 sequestration. The physical phenomenon is analogous to
the thermal convective instability in a fluid cooled uniformly from above or heated from
below, in a semi-infinite half-space. CO2 dissolution into the underlying brine leads to a
local density increase that results in a gravitational instability. The problem is cast into
the self-similar form to benefit from localized eigenfunctions of the streamwise diffusion
operator. In contrast to the flow in an unbounded domain, the current problem in the
semi-infinite domain yields a critical time for instability as well as a longwave cutoff. In
order to avoid the quasi-steady-state approximation (QSSA), a dominant mode approach
is used to highlight the early time instability mechanism. Comparison with the initial-
value-problem shows that this method gives exact results for both the critical time and
the longwave cutoff. We also show by comparing with the initial-value-problem that the
QSSA in the self-similar setting provides reasonably accurate solutions for all times.
The linear stability theory is extended to the nonlinear regime by very high accuracy
direct numerical simulations. The nonlinear simulations show good agreement with the
linear stability predictions for small times. Macroscopic fingers display intense nonlinear
interactions at inception. This gravitational instability significantly increases the rate of
CO2 dissolution into the brine in high permeability reservoirs.
for more details please see:
- A Riaz, M Hesse, H Tchelepi, F. M. Orr Jr.(2006) Onset of Convection in a Gravitationally Unstable, Diffusive Boundary Layer in Porous Media J. Fluid Mechanics, 548, 87 - 111 [pdf]
- 2005 APS Division of Fluid Dynamics 58th Annual Meeting [pdf]
- Fundamentals of Fluid Flow 2004/Fall AGU 2005 [pdf]
Convective Fluxes
We are currently investigating the long term behavior of the convecting system. In particular we are interested in the statistical time averaged flux in a semi infinite convecting system. Some preliminary results have been presented at the Supri-C Affiliate meeting 2005 [talk]
Other recent papers on convection in the brine
I hope to provide some links to other interesting research on density driven convection in CO2 storage in saline aquifers:
- C. Yang and Y. Gu (2006) Accelerated Mass Transfer of CO2 in Reservoir Brine Due to
Density-Driven Natural Convection at High Pressures and Elevated
Temperatures, Ind. Eng. Chem. Res., 45, 2430-2436 [pdf]
- J. Ennis-King, I. Preston, and L. Paterson (2005) Onset of convection in anisotropic porous media subject to a rapid change in boundary conditions, Physics of Fluids., 17 (084107), [pdf]
- X. Xu, S. Chen, D. Zhang (2006) Convective stability analysis of the long term storage of carbon dioxide in deep saline aquifers, Advances in Water Resources., 29, pp. 397-407, [pdf]
- Hassan Hassanzadeh, Mehran Pooladi-Darvish and David W. Keith (in press). Stability of a Fluid in a Horizontal Saturated Porous Layer: Effect of Non linear Concentration Profile, Initial, and Boundary Conditions. Transport in Porous Media
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