This paper numerically investigates the interaction between thermodiffuion and buoyancy driven convection in a laterally heated vertical porous cavity for different permeability. The Firoozabadi model is applied to binary hydrocarbon mixtures: (i) the mixture of 1,2,3,4 tetrahydronaphtalene (THN) and dodecane (C12) with mass fraction of 50% for each component, (ii) 1,2,3,4 tetrahydronaphtalene and isobutylbenzene (IBB) with mass fraction of 50% for each component, and (iii) isobutylbenzene and dodecane with mass fraction of 50% for each component. The thermal and molecular diffusion coefficients, which are functions of the temperature and other properties of mixture, are calculated at each point of the grid. Numerical results revealed that when permeability is low the thermodiffusion effect is dominant in the composition separation process. As the permeability increases the thermodiffusion effect and buoyancy-driven convection combine their actions to enhance the composition separation process. As the permeability increases further the buoyancy-driven convection becomes dominant in the cavity and becomes detrimental to separation in the cavity.