Natural convection in porous media has been researched for a long time. In this study, the focus is on natural convection in two processes in porous media: CO2-sequestration in deep saline aquifers and CO2-Vapex processes. For the natural convection in saline aquifers, the onset of convection and pattern of instabilities are analyzed for an inclined layer and are compared with a horizontal layer. Then, the effect of thermal instability is added to the problem and a double-diffusion (thermohaline) convection is studied. In the second part the effect of instabilities, if present, is studied in the CO2-Vapex process. The analysis is based on a model for the boundary layer in the interface of CO2 chamber/heavy oil. The effect of dispersion and variation of viscosity in the boundary layer are considered in the analysis.