The effect of chemical reaction on the onset of gravitational instabilities in a fluid saturated within a vertical Hele-Shaw cell: Theoretical and numerical studies

In relation with the carbon dioxide sequestration into a saline aquifer, the effect of first order chemical reaction on the onset of buoyancy-driven convection in a Hele-Shaw cell is analyzed theoretically and numerically. For the steady state base concentration field, new stability equations are derived under the linear stability theory and the Brinkman equation, and solved in the global domain. However, for the transient base field, these stability equations are transformed into a similar domain. By expanding the disturbance quantities using orthonormal functions, linear stability equations for the transient base field are solved analytically. Through the present linear analysis, we identified the governing parameters for the onset of chemo-convection in a Hele-Shaw cell. The present stability criteria for the steady-state and transient cases suggested that the fast geochemical reaction suppresses the onset of buoyancy-driven instability motion, however, enhances the diffusion flux. Using the linear stability analysis result as an initial condition for the nonlinear analysis, direct numerical simulations are also conducted. The present linear stability analysis and the nonlinear numerical simulation support each other.