Quantifying the effects of the Korteweg stress tensor on the CO2-brine interface mass transport in permeable media

For the climate change solution of CO₂ capture in deep geological formations, supercritical CO₂ is injected in confines brine aquifers where is self allocated between the impermeable cap rock and the brine. Once it reaches this configuration, CO₂ begins partially to diffuse into the brine layer. However, the mixture solution obeys a nonlinear equation of state such that the CO₂-brine mixing layer becomes heavier than the brine beneath causing a cabbeling-like process that triggers fingers. The gravitational instabilities fosters the vertical transport and the dissolution of CO₂ into the brine. When the diffusion rate is slow, a density gradient between CO₂ and brine gives rise to a weak transient interface tension. Two miscible fluids are studied using the Hele-Shaw equations for Boussinesq fluid with the additional density dependent tensor known as the Korteweg stress. Here, we report direct numerical simulations to quantity the impact of the interface tension on the nondimensional mass flux and a novel scaling law that integrates Korteweg stress effects. The results show that the interface tensor affects the development of protoplumes by inhibiting diffusion and their coalescence the key mechanism for their grow in time.