Non-modal growth of perturbations in density-driven convection in porous media

Abstract

In the context of geologic sequestration of carbon dioxide in saline aquifers, much interest has been focused on the process of density-driven convection resulting from dissolution of CO2 in brine in the underlying medium. Recent investigations have studied the time and length scales characteristic of the onset of convection based on the framework of linear stability theory. It is well known that the non-autonomous nature of the resulting matrix does not allow a normal mode analysis and previous researchers have either used a quasi-static approximation or solved the initial-value problem with arbitrary initial conditions. In this manuscript, we describe and use the recently developed non-modal stability theory to compute maximum amplifications possible, optimized over all possible initial perturbations. Non-modal stability theory also provides us with the structure of the most-amplified (or optimal) perturbations. We also present the details of three-dimensional spectral calculations of the governing equations. The results of the amplifications predicted by non-modal theory compare well to those obtained from the spectral calculations.

The effect of interface movement and viscosity variation on the stability of a diffusive interface between aqueous and gaseous CO2

“…Another approach is called amplification theory (AT). 9,14,15 The idea is to expand the perturbed quantities in the streamwise direction in the eigenfunctions c 0 f , i.e., u 1 ∼ a n (t) sin(nπ z).…”

Plume dynamics in Hele-Shaw porous media convection

“…The hydrodynamic instability of two-phase porous media convection is similar to the thickening and instability of thermal layers in thermal convection [2], although in that case the flow rapidly becomes fully nonlinear whereas the porous media allow for a simpler formulation. Analytic calculations and numerical simulations have been performed [3][4][5][6][7][8][9][10] to evaluate the time to instability and the resulting mass transport efficiency. Laboratory experiments, however, have not been able to capture the main features of instability and mass transfer in realistic highpressure supercritical CO 2 brine systems.…”

Convective Instability and Mass Transport of Diffusion Layers in a Hele-Shaw Geometry

“…However, similar to thermal layers [3], the diffusion layer must thicken enough to become unstable. Analytical and numerical calculations have been performed [4][5][6][7][8][9] to predict the instability incubation time and subsequent mass transport in CO 2 -brine systems. However, the difficulties in realizing a laboratory experiment for the purposes of testing the scenario are considerable, e.g.…”

“…Non-dimensional scalings and solution techniques for the conservation of momentum, mass, and concentration are described in detail elsewhere [4][5][6][7][8][9]. Here, we discuss the di- mensionless parameters and a few details relevant to our experiment.…”

“…Near the finger tips and the finger cores the Pelect number can approach 50, and the advection-diffusion equation may be modified by Taylor dispersion [17] with the effective diffusion coefficient 15 times larger than molecular diffusion. Neglecting the impact of P e within the finger cores, the Rayleigh number Ra = ∆ρgKH/ρνD governs the flow [4][5][6][7][8][9]. Here, g is the acceleration due to gravity and all fluid properties are evaluated at c w = 0.3.…”