Prediction of the Minimum Onset Time for Convection in a Gravitationally Unstable Diffusive Boundary Layer Using a Finite Difference Pressure Solver

Abstract

CO 2 dissolution as one of the most promising mechanisms for trapping of CO 2 free phase into brine causes increased density of the brine and initiation of gravitational instability that eventually leads to densitydriven natural convection in brine aquifers. The gravitational instability of a diffusive boundary layer in porous media has been studied in several papers in recent years and there are several methods in the literature for prediction of the onset time for convection and the related unstable wavelength.In this study we present a numerical solution for prediction of the critical time for the onset of convection and the critical unstable wavelength in semi-infinite anisotropic homogeneous brine aquifer models. A finite difference pressure solver is used for solving this numerical problem. The numerical model is initialized by the recent developed approach and the gravitational instability is triggered by a weak wavy perturbation with dimensionless wavenumber of K. The minimum of the calculated time for onset of instability as a function of wavenumber is called the critical time and the associated wavenumber to this critical time is the critical unstable wavenumber. The results of this analysis shows acceptable agreement with previously published ones derived from other methods. By applying this prediction approach in more complex numerical models, their related critical time for the onset of convection and the critical unstable wavelength can be calculated.

Effect of Convective Mixing Process on Storage of CO2 in Saline Aquifers with Layered Permeability

“…The qualitative average value of the critical wavelength of convection fingers, observed after the onset of convection, is computed by selecting a centered horizontal segment (to remove the edge effect) of the CO2-water interface and dividing this distance by the number of convection fingers in this segment. The onset time of convection and the critical wavelength of convection fingers (calculated from the experiments conducted in the homogeneous cell) are transferred to dimensionless forms using a length scale and a time scale as given in Equations 4 and 5, and the values can be compared with the numerically predicted values [14,15,18,19,21,22,[44][45][46][47]…”

“…Numerical studies for describing the convective mixing process and its effectiveness in storing CO2 into the homogeneous saline aquifers are reported several years ago [2][3][4][5][6][7][8][9][10][11][12]. Furthermore, the gravitational instability of a diffusive boundary layer has been described using theoretical methodologies in recent years to predict the onset time of convection and the related unstable wavelength in the homogeneous models [13][14][15][16][17][18][19][20][21][22].…”