Miscible gravitational instability of initially stable horizontal interface in a porous medium: Non-monotonic density profiles

To simulate a CO2 sequestration process, some researchers employed a water/propylene glycol (PPG) system which shows a non-monotonic density profile. Motivated by this fact, the stability of the diffusion layer of two miscible fluids saturated in a porous medium is analyzed. For a non-monotonic density profile system, linear stability equations are derived in a global domain, and then transformed into a system of ordinary differential equations in an infinite domain. Initial growth rate analysis is conducted without the quasi-steady state approximation (QSSA) and shows that initially the system is unconditionally stable for the least stable disturbance. For the time evolving case, the ordinary differential equations are solved applying the eigen-analysis and numerical shooting scheme with and without the QSSA. To support these theoretical results, direct numerical simulations are conducted using the Fourier spectral method. The results of theoretical linear stability analyses and numerical simulations validate one another. The present linear and nonlinear analyses show that the water/PPG system is more unstable than the CO2/brine one, and the flow characteristics of these two systems are quite different from each other. (C) 2014 AIP Publishing LLC.