The results of experiments involving instability, known as fingering, in a circular Hele Shaw cell with inward and outward flow are presented. The width of fingers in this situation is examined, and an approximate equation for the growth of fingers is proposed. The equation rα = cos (nθ) is shown to fit the shape of long fingers.

Previous studies of fluid convection in porous media have considered the onset of convection in isotropic systems and the steady convection in anisotropic systems. This paper bridges between these and develops new results for the onset of convection in anisotropic porous media subject to a rapid change in boundary conditions. These results are relevant to sedimentary formations where the average vertical permeability is some fraction γ of the average horizontal permeability. Linear and global stability analyses are used to define the critical time tc at which the instability occurs as a function of γ and the dimensionless Rayleigh-Darcy number Ra* for both thermal and solute-driven convection in an infinite horizontal slab. Numerical results and approximate analytical solutions are obtained for both a slab of finite thickness and the limit of large slab thickness. For a thick slab, the increase in tc as γ decreases is approximately given by (1+γ)4∕(16γ2). One important application is to the geological storage of carbon dioxide where it is shown that the use of an effective vertical permeability in estimating the critical time is only valid for low permeabilities. The time scale for the onset of convection in geological storage can range from less than a year (for high-permeability formations) to decades or centuries (for low-permeability ones).

Summary Storage of carbon dioxide in deep formations is being actively considered for the reduction of greenhouse gas emissions. Relevant experience in the petroleum industry comes from natural gas storage and enhanced recovery using carbon dioxide, but this experience is over a time scale less than the hundreds or thousands of years required for carbon dioxide storage. On these long timescales, different mechanisms need to be considered. In the long term, the dominant mechanism for dissolution of carbon dioxide in formation water is convective mixing rather than pure diffusion. This arises because the density of formation water increases upon dissolution of carbon dioxide, creating a density instability. Linear stability analysis has been used to estimate the time required for this instability to occur in anisotropic systems. For sufficiently thick formations with moderate vertical permeability, this time ranges from less than a year up to a few hundred years. Further approximate analysis shows that the time needed for the injected gas to dissolve completely is typically much longer, on the order of hundreds of years to tens of thousands of years, depending on the vertical permeability. This theoretical analysis is compared with the results of numerical simulations. Introduction If the emissions of carbon dioxide from the use of fossil fuels continue on the current scale, then it has been predicted that significant changes in the global climate will occur in the next 100 years.1 Deep cuts in emissions will be needed in the next few decades in order to stabilize atmospheric carbon dioxide at reasonable levels so that the extent of the climatic changes can be limited.2 Such cuts can ultimately only be achieved by a broad strategy that encompasses both alternative energy sources and the "cleaner" use of existing reserves of fossil fuels. In the latter category, one possible technical solution is to store carbon dioxide emissions in a form where they will not reach the atmosphere for decades to centuries. Because current emissions from fossil-fuel usage are around 6 to 7 Gt of carbon per year (equivalent to 22 to 5 Gt of carbon dioxide), any form of storage must have considerable capacity if it is to make a significant contribution to reducing emissions. Two leading options are storage deep in the ocean or underground.3 In the absence of carbon credits or taxes, the most economically attractive forms of underground storage in the short term are enhanced recovery schemes, whereby carbon dioxide is injected both to increase production and to provide storage. However, the potential storage capacity forCO2 in enhanced recovery operations is not large compared to the scale of emissions, nor are such opportunities always present close to sources of CO2.An alternative form of underground storage is injection in deep saline formations, because these are widely available and have a large total storage capacity.

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