Modeling the \(\mathrm{CO}_2\) sequestration convection problem using the lattice Boltzmann method (Q474211)

Summary: This paper presents an investigation of the density-driven problem that rises during the \(CO_{2}\) sequestration into saline aquifer. The lattice Boltzmann method (LBM) is implemented in a way to solve this mixing problem (the brine problem along with the solute transport). The \(CO_{2}\)-brine interface was located at the top of the considered domain. Different Rayleigh numbers were used in order to investigate this problem. When Rayleigh number is low, we got steady-state concentration contours describing a Rayleigh-Bénard type of convection. Moreover, when the Rayleigh number was selected to be big enough, we observe that the system is less stable and a convective fingering is initiated. This instability is caused by a higher density difference between the brine and the sequestrated \(CO_{2}\). Note here that the turbulence is not taken into account in the study. After the onset this convective instability, the brine with a high \(CO_{2}\) concentration migrates down into the porous medium. This study is based on a statistical LBM theory without assuming periodicity in any directions and without considering any type of disturbances in order to turnon the instability behavior.