A numerical study, using a finite element formulation, is conducted in order to study double diffusive phenomena in porous media. The Brinkman model is used as the momentum balance equation and is solved simultaneously with mass and energy balance equations in a two-dimensional domain. Special emphasis is given to the study of double diffusive phenomena in a layered porous bed with contrasting permeabilities. The extent of cross flow and its role in determining the shape. as well as the propagation, of the intruding plume are studied for a range of both thermal and solutal parameters. The study is completed for a wide range of permeability contrasts.