Radon emanation which is the fraction of radon-222 atoms released in the connected pore space of a porous material, increases when the water content increases because of the low recoil range of this atom in water compared with air. This complex phenomenon is studied using reconstructed porous media and random packings where the phase distribution is obtained by a lattice Boltzmann technique incorporating interfacial tension and wetting. The influence of the pore structure, of the recoil range and of saturation, is systematically studied. The numerical results are in good agreement with data from uranium mine tailings.