Onset of density-driven convection in porous media

(Work done in collaboration with Rajesh Pawar(LANL), Philip Stauffer (LANL), Prof. Shiyi Chen(JHU) and Prof. Dongxiao Zhang(USC))

Geological storage of carbon dioxide (CO₂) has gained popularity as one of the promising ways of reducing greenhouse gas emissions in the near future. When carbon dioxide is buried in saline aquifers at depths of more than 1km, it exists in a supercritical state due to the local pressure and temperature. The density of supercritical carbondioxide is significantly lower than that of the surrounding brine and it rises upwards due to buoyancy. The supercritical CO₂ slowly dissolves in the underlying brine. Since the density of brine saturated with CO₂ is slightly (by about 1%) larger than that of unsaturated brine, this system is gravitationally unstable and under suitable conditions, leads to convection in the form of "fingers" of CO₂-rich brine penetrating downwards.

We have used Non-modal Stability Theory to obtain rigorous estimates of the length and timescales associated with this convective process. The results from these calculations were compared with three-dimensional pseudospectral simulations of the governing equations. The typical fingering patterns obtained from these simulations is shown below:

The results from the stability analysis were found to be in excellent agreement with the pseudospectral simulations and taken together, they give a good understanding of the dynamics of the instability.

Flow in fractal porous media

(Work done in association with Prof. Charles Meneveau and Prof. Shiyi Chen)

Traditional upscaling techniques look at the process of obtained grid-scale effective permeabilities as a bottom-up approach, where the effective permeabilities are computed by successively coarse graining the fine scale permeability field. We have developed a new approach called Renormalized Numerical Simulations where we use the approach of downscaling as opposed to upscaling. More details will be added soon.

Applications of the Lattice-Boltzmann method

(Work done in collaboration with Zhenhua Xia (main contributor), Kevin Connington, Prof. Shiyi Chen, Pengtao Yue and Prof. James Feng)

We have used the Lattice-Boltzmann method coupled to a Newtonian dynamics solver to simulate the sedimentation of a two-dimensional elliptical particle in a channel with Newtonian fluid. We identified all the nondimensional parameters that govern the dynamics of sedimentation and performed a detailed investigation of the effect of each parameter. In particular, we focused on the mode of sedimentation when the channel becomes extremely narrow and the boundary effects dominate the flow.