Vigorous convection in a layered, heterogeneous porous medium

Abstract:

Convective flow in a porous medium plays an important role in numerous geophysical and industrial processes, and has recently been investigated in the context of geological CO₂ sequestration. Previous studies of vigorous porous convection at high Rayleigh number Ra have focused on homogeneous porous media, whereas natural porous media are often highly heterogeneous. In particular, many geological porous formations are interspersed with thin, roughly horizontal, low-permeability layers. In order to gain understanding of the interaction of low-permeability layering with convective flow, and to develop simple parameterized models of the underlying physical processes, we have performed a numerical study of high-Ra convection in a two-dimensional porous medium that contains a thin, horizontal, low-permeability interior layer. The medium is heated at the lower boundary and cooled at the upper, which sets up statistically steady convective flow throughout the domain. This archetypal system is readily applicable to compositional convection, owing to an assumption of thermal equilibrium between solid and liquid phase in the medium. We show that, in the limit that both the dimensionless thickness h and permeability Π of the low-permeability layer are small, the flow is described solely by the impedance of the layer Ω= h/Π and by Ra. As Ω → 0 (i.e. h → 0), the system reduces to a homogeneous medium. We observe two notable features as Ω is increased: the dominant horizontal lengthscale of the flow increases; and, surprisingly, the heat flux through the cell, as measured by the Nusselt number Nu, can increase. For larger values of Ω, Nu always decreases. We explore the dependence of the flow on Ra, and develop simple theoretical models to describe some of the observed features of the relationship Nu(Ω). The theoretical models have implications for the simulation of convective dissolution of CO₂ at reservoir scales, as heterogeneities can be much smaller than the grid scale and therefore must be parameterized.