Determination of CO₂ convective mixing flux in saline aquifers based on the optimality

When carbon dioxide is sequestrated in a saline aquifer, the dissolution of carbon dioxide plume results in density difference between the brine with dissolved carbon dioxide and the ambient brine. This causes fingering flow and transport, or convective mixing, that is the dominant mechanism for the carbon dioxide solubility trapping. This work presents the first theoretical relationship for the carbon dioxide convective mixing flux from the plume that is critical for evaluating the long-term safety of carbon dioxide storage in a saline aquifer. This new development is based on the optimality: the density-difference driven fingering flow and transport are self-organized in such a way that the downward mass transport rate of dissolved carbon dioxide is maximized. The optimality has a root in non-equilibrium thermodynamics and been successfully applied to modeling the gravitational fingering flow for soil water in the vadose zone. Our theoretical relationship is shown to be able to accurately predict the experimental results of the convective mixing flux in three-dimensional porous media that were reported by the two different research groups. The average relative error between the theoretical flux values and experimental observations is about 10% or less, while uncertainties exist in the test observations. The flux for Sleipner carbon dioxide injection site (22 kg/m²/yr), estimated using our new relationship, is also consistent with the previous estimates in the literature, in a range between 0 and 30 kg/m²/yr with the most likely value of 15 kg/m²/yr, that were obtained using a complex model to analyze the field data. These comparisons support the usefulness and validity of our relationship that does not need the knowledge of individual fingers associated with the convective mixing and is easy to use in practice.