Onset of nonlinear convection during CO2 sequestration

When supercritical CO2 is injected in a saline aquifer, the CO2 dissolves into underlying brine and diffuses downwards. Eventually, a gravitational instability causes flow perturbations to grow and trigger nonlinear convection. This convection mixes the brine and increases the rate of CO2 dissolution. To date, the initial linear instability of perturbations has been studied extensively; however, the subsequent onset of nonlinear convection remains understudied. We demonstrate that the onset time of nonlinear convection can be accurately determined from an asymptotic expansion that is two orders-of-magnitude faster than a direct numerical simulation. Using the expansion, we explore the sensitivity of the onset time to the initial perturbation magnitude and wavelength, as well as the initial time at which a perturbation is initiated. We find there is an optimal combination of initial perturbation time and wavelength that minimizes the onset time, and we obtain analytical relationships for these optimal parameters in terms of aquifer properties and initial perturbation magnitude. These results show the importance of the initial perturbation time and magnitude, which are often overlooked in previous studies.