Evaluation of flow and transport in variable-density fluids in heterogeneous porous media presents major scientific challenges. Where density inversions occur, free (or natural) convection can take place because of buoyancy and lead to transport of solutes or heat over larger spatial scales and over significantly shorter times than by diffusion or conduction. Porous medium heterogeneities are critical in the onset, growth, and dissipation of free convection and the heterogeneity structure (i.e., the order of the disorder) is a key factor. Heterogeneity exists at different scales in geological media and traditional Rayleigh Numbers are inadequate for predicting thermohaline convection. Pilot studies show that dense plumes take preferential pathways and, in particular, the connectedness of higher permeability zones is important in initiating, controlling, and dissipating instabilities. Horizontal low permeability units, such as shales, are often assumed to limit free convection. However, shale permeability can vary by as much as thirteen orders of magnitude and is controlled by pore/grain size, facies architecture and bedding type, and micro-/macro-fractures. Permeability may also vary with time. Hydraulic equivalents of the heterogeneity will underestimate free convection because the process is sensitive to local conditions in high permeability zones. Instability conditions are evaluated by examining critical solute fluxes and time constants in the fracture-matrix system. Results show that fracture spacing, fracture apertures, shale thickness, and the density gradient across the shale unit play key roles in governing fluid flow and solute transport. Episodes of density-driven flow are inferred even in the thick shale sequences, such as in the Gulf of Mexico Basin. Given the sensitivity of these phenomena to heterogeneity, quantitative methods are needed to characterize the order of permeability heterogeneity and for use in flow and transport models for variable-density fluids and free convection. New methods are needed to: 1) characterize permeability fields at the appropriate scales; 2) find key characteristics of the heterogeneity that can predict transport by buoyancy-driven flow; and 3) observe and measure field-scale free convection processes and not just infer them by the process of elimination.