Convection in Porous Media with Thermal and Chemical Buoyancy: A Comparison of Two Models for Solute Dispersion

Abstract

Results of a study of the role of solute dispersion model on convection in porous media heated and salted from below are given. In the first model, use is made of an effective dispersion coefficient that is taken as a constant scalar. In the second, a velocity-dependent dispersivity term that explicitly considers both molecular and mechanical dispersion is used. The results show that for the particular cases studied (Ra = 600φ/σ = 1, aspect ratio = 1, Rρ = 0 and Rρ = 0.5), although the choice of dispersion model does not affect the basic character of the fluid dynamics of the system, the details of the solute fields are somewhat different. In the case of the passive tracer (Rρ = 0), the solute fields for both models evolve to a steady-state which is very similar. The main difference between the evolution of the solute fields for Rρ = 0 is that in the case of the simple model, the solute field mixes more quickly. For Rρ = 0.5, chaotic flow characterizes convection for both dispersion models and regions of sharp solute gradients are highly mobile in time and space. The main difference between the two solute dispersion models for Rρ = 0.5 is that the interior of the solute field is less homogeneous and more saline in the case of the simple dispersion model.