We present a linear stability analysis of density-driven miscible flow in porous media in the context of carbon dioxide sequestration in saline aquifers. Carbon dioxide 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, owing to a 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 long-wave 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 $t^{1/4}$. The long-wave and the short-wave cutoff modes scale as $t^{1/5}$ and $t^{4/5}$, respectively. The instability problem is also analysed in the nonlinear regime by high-accuracy direct numerical simulations. The nonlinear simulations at short times show good agreement with the linear stability predictions. At later times, macroscopic fingers display intense nonlinear interactions that significantly influence both the front propagation speed and the overall mixing rate. A dimensional analysis for typical aquifers shows that for a permeability variation of 1—3000 mD, the critical time can vary from 2000 yrs to about 10 days while the critical wavelength can be between 200 m and 0.3 m.

The Laplace–Young equation is solved for axisymmetric menisci, analytically in terms of elliptic integrals for all possible types of pendular rings and liquid bridges when the effect of gravity is negligible, numerically for selected other cases in order to assess gravity's effect. Meniscus shapes, mean curvatures, areas and enclosed volumes are reported, as are capillary forces. It is shown that capillary attraction may become capillary repulsion when wetting is imperfect. The special configurations of vanishing capillary force and of zero mean curvature are treated. The range of utility of the convenient ‘circle approximation’ is evaluated.

[1] Relative permeabilities are the key descriptors in classical formulations of multiphase flow in porous media. Experimental evidence and an analysis of pore-scale physics demonstrate conclusively that relative permeabilities are not single functions of fluid saturations and that they display strong hysteresis effects. In this paper, we evaluate the relevance of relative permeability hysteresis when modeling geological CO 2 sequestration processes. Here we concentrate on CO 2 injection in saline aquifers. In this setting the CO 2 is the nonwetting phase, and capillary trapping of the CO 2 is an essential mechanism after the injection phase during the lateral and upward migration of the CO 2 plume. We demonstrate the importance of accounting for CO 2 trapping in the relative permeability model for predicting the distribution and mobility of CO 2 in the formation. We conclude that modeling of relative permeability hysteresis is required to assess accurately the amount of CO 2 that is immobilized by capillary trapping and therefore is not available to leak. We also demonstrate how the mechanism of capillary trapping can be exploited (e.g., by controlling the injection rate or alternating water and CO 2 injection) to improve the overall effectiveness of the injection project.

No abstract

Field experiments were conducted to test ideas for fossil fuel carbon dioxide ocean disposal as a solid hydrate at depths ranging from 349 to 3627 meters and from 8 degrees to 1.6 degrees C. Hydrate formed instantly from the gas phase at 349 meters but then decomposed rapidly in ambient seawater. At 3627 meters, the seawater-carbon dioxide interface rose rapidly because of massive hydrate formation, forcing spillover of the liquid carbon dioxide from the container. A strong barrier between the liquid carbon dioxide and interaction with the sediments was observed. A pool of liquid carbon dioxide on the sea floor would expand in volume more than four times, forming hydrate, which will dissolve.

Motivated by geological carbon dioxide (CO2) storage, we present a vertical-equilibrium sharp-interface model for the migration of immiscible gravity currents with constant residual trapping in a two-dimensional confined aquifer. The residual acts as a loss term that reduces the current volume continuously. In the limit of a horizontal aquifer, the interface shape is self-similar at early and at late times. The spreading of the current and the decay of its volume are governed by power-laws. At early times the exponent of the scaling law is independent of the residual, but at late times it decreases with increasing loss. Owing to the self-similar nature of the current the volume does not become zero, and the current continues to spread. In the hyperbolic limit, the leading edge of the current is given by a rarefaction and the trailing edge by a shock. In the presence of residual trapping, the current volume is reduced to zero in finite time. Expressions for the up-dip migration distance and the final migration time are obtained. Comparison with numerical results shows that the hyperbolic limit is a good approximation for currents with large mobility ratios even far from the hyperbolic limit. In gently sloping aquifers, the current evolution is divided into an initial near-parabolic stage, with power-law decrease of volume, and a later near-hyperbolic stage, characterized by a rapid decay of the plume volume. Our results suggest that the efficient residual trapping in dipping aquifers may allow CO2 storage in aquifers lacking structural closure, if CO2 is injected far enough from the outcrop of the aquifer.

No abstract

The possibility that substantial quantities of CO2 can be injected into subsurface porous rock formations has been investigated sufficiently to show that pore space available to contain the CO2 is abundant. Multiple rock types and physical mechanisms can be used to trap the CO2 indefinitely. With careful site selection and operations, leakage to the near-surface region can be avoided. The next step is to test these injection processes at the scale of a large power plant.