Improving the worthiness of the Elder problem as a benchmark for buoyancy driven convection models

Abstract

AbstractAn important trapping mechanism associated with the geosequestration of CO~2~ is that of dissolution into the formation water. Although supercritical CO~2~ is significantly less dense than water, experimental data reported in the literature show that the density of an aqueous solution of CO~2~ could be slightly greater. Under normal situations, the transfer of gas to solution is largely controlled by the relatively slow process of molecular diffusion. However, the presence of variable densities can trigger off gravity instabilities leading to much larger-scale convection processes. Such processes can potentially enhance rates of dissolution by an order of magnitude. Consequently there is a need for future performance assessment models to incorporate buoyancy driven convection (BDC). A major issue associated with BDC models is that of grid convergence when benchmarking to the Elder problem. The Elder problem originates from a heat convection experiment whereby a rectangular Hele-Shaw cell was heated over the central half of its base. A quarter of the way through the experiment, Elder (1967) observed six plumes, with four narrow plumes in the center and two larger plumes at the edges. As the experiment progressed, only four plumes remained. The issue is that depending on the grid resolution used when seeking to model this problem, modelers have found that different schemes yield steady states with either one, two or three plumes. The aim of this paper is to clarify and circumvent the issue of multiple steady state solutions in the Elder problem using a pseudospectral method.