A cavity of 10 mm in width, 10 mm in height, and 32.1 mm in horizontal length filled with Al2O3 porous medium designed in Pau project to investigate thermal diffusion phenomena, or Ludwig-Soret effect. A lateral heating condition was applied with 10 °C at the left wall and 50 °C at the right wall. The thermosolutal convection of a binary mixture of water-ethanol at 75.0 MPa pressure, a ternary mixture with methane, n-butane, and n-dodecan at 35.0 MPa pressure, and a ternary mixture of n-dodecane, isobutylbenzene, and tetrahydonaphthalene at atmosphere pressure inside the Al2O3 porous medium cavity were numerically investigated. The thermal conductivity and the permeability of Al2O3 porous medium on the Ludwig-Soret effect were analyzed, the former had little influence, but the later had strong impact on the compositional separation at the steady state of thermosolutal convection, which were analyzed globally with separation ratio. The distributions of component mole fraction(s) on the horizontal and vertical lines in the center of the porous cavity were also shown to study the details of the compositional separation at the steady state of thermosolutal convection. Recommendations are made for the experimental design based on the results of numerical analysis