Convection in a porous medium plays an important role in many geophysical and industrial processes, and is of particular current interest due to its implications for the long-term security of geologically sequestered CO_2. I will discuss two different convective systems in porous media, with the aid of 2D direct numerical simulations: first, a Rayleigh-Benard cell at high Rayleigh number, which gives an accurate characterization both of the convective flux and of the remarkable dynamical structure of the flow; and second, the evolution and eventual `shut-down' of convection in a sealed porous domain with a source of buoyancy along only one boundary. The latter case is also studied using simple box models and laboratory experiments, and can be extended to consider convection across an interface that can move and deform, rather than across a rigid boundary. The relevance of these results in the context of CO_2 sequestration will be discussed.
