Experiments were performed in the purpose of studying the isotopic consequences of the diffusional transport of hydrocarbon gases through sediment rocks. Linked to a numerical model, these gas diffusion experiments through a shale porous plug allowed us to correlate porosity and diffusivity of the migration medium. Significant isotopic fractionations (carbon and hydrogen) of methane, and ethane at a lesser degree were observed. This is in contradiction with the actual dogma of isotope geochemistry of natural gases which claims that no fractionation occurs during gas migration. The genetic characterization of natural gases by using the isotopic signature of methane appears as an ambiguous method.